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b/.idea/inspectionProfiles/profiles_settings.xml @@ -0,0 +1,7 @@ + + + + \ No newline at end of file diff --git a/.idea/misc.xml b/.idea/misc.xml new file mode 100644 index 0000000..12f37ed --- /dev/null +++ b/.idea/misc.xml @@ -0,0 +1,4 @@ + + + + \ No newline at end of file diff --git a/.idea/modules.xml b/.idea/modules.xml new file mode 100644 index 0000000..dff51e4 --- /dev/null +++ b/.idea/modules.xml @@ -0,0 +1,8 @@ + + + + + + + + \ No newline at end of file diff --git a/.idea/workspace.xml b/.idea/workspace.xml new file mode 100644 index 0000000..58fe99d --- /dev/null +++ b/.idea/workspace.xml @@ -0,0 +1,1042 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + true + DEFINITION_ORDER + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + project + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 1501598665662 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/Code_It_Out_Questions/1_Simple_Prime_Numbers.py b/Code_It_Out_Questions/1_Simple_Prime_Numbers.py new file mode 100644 index 0000000..a400ff0 --- /dev/null +++ b/Code_It_Out_Questions/1_Simple_Prime_Numbers.py @@ -0,0 +1,62 @@ +''' +Question +Today Motu learned a new concept in maths called least prime factor, +(ie It is the smallest prime divisor of a number), The teacher gave Motu an assignment +to find all numbers with the same smallest prime factor as a number X upto a limit L +Motu is really lazy and is asking you to solve it for him. Can you take up the challenge ? + +Input +The first line takes into account N and L +N is the number of questions Teacher asked and L is the limit upto which we have to check the numbers +After that N lines follow Each with one input X + +Output +Output the number of numbers upto L (Inclusive) with the same least prime factor as the number X (Inclusive) + + +0 and 1 are not considered as least prime factors and hence excluded from all calculations + +Sample Cases + +Sample input | Sample Output +4 16 | +3 | 3 +2 | 8 +5 | 1 +10 | 0 + +Explanation + +For 3 the numbers 3 , 9 , 15 has their least prime divisor as 3 +For 2 the numbers 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 has their least prime divisor as 2 +For 5 There is no other number other than 5 +For 10 , 10 itself is not the least prime divisor , hence the answer is 0 + +Constraints + +N <= 100000 +L <= 10^7 + +''' + +#Answer in Python 2 + + +X,M = map(int , raw_input().split(" ")) + + +P = [1 for _ in xrange(M+1)] +P[0] , P[1] = 0,0 +i = 2 +while i*i <= M : + if P[i] == 1 : + for j in xrange(i*i,M+1,i) : + if P[j] == 1: + P[j] = 0 + P[i] += 1 + i += 1 + +for i in range(X): + num = input() + print P[num] + diff --git a/Code_It_Out_Questions/2_Free_Chocolates.py b/Code_It_Out_Questions/2_Free_Chocolates.py new file mode 100644 index 0000000..90667fe --- /dev/null +++ b/Code_It_Out_Questions/2_Free_Chocolates.py @@ -0,0 +1,75 @@ +''' +Motu visits a new chocolate shop in the town called BioChocolates . Its run by a Biology professor called Damu +Damu makes chocolates using uses special type of organic cells. + +Damu agress to give Motu Free chocolates if he solves his problem. + +Damu has two types of Cells A and B +The cells are highly active so in one step either Every cell from A regenerates and moves to B. Or Every cell from B regenerates and moves to A + +For Example if you had 3 Cells of Type A and 2 Cells of Type B +Either you get 5 Cells of type A and 2 Cells of Type B +or You get 3 Cells of Type A and 5 Cells of Type B +Motu has to find the least number of steps it takes for one cell of type A and B to reach a given number of Cells + +Example + +if we have to reach 4,7 +Initially we have A = 1 and B = 1 +After step 1 we have A = 1 and B = 2 ( A goes to B ) +After step 2 we have A = 1 and B = 3 ( A goes to B ) +After step 3 we have A = 4 and B = 3 ( B goes to A ) +After step 4 we have A = 4 and B = 7 ( A goes to B ) +So in 4 steps we reach required cell count + +Input +The first line contains the number of test cases +The next line consists of the required cell counts of Cell A followed by required cell counts of Cell B + +Output +Output one line containing the number of steps required to reach the required cell count from initial condition ( Initially Both Cell Counts are 1) +If a particular cell count cannot be achived Print "impossible" + +Constraints +The number of cells can be upto 10^19 + +Sample input | Sample Output +4 | +2 1 | 1 +4 7 | 4 +2 4 | impossible +4 2 | impossible + +Constraints + +N < 100000 +M,F > 0 +M,F < 10^50 + +*You might wanna consider using large variable datatypes to avoid overflow errors and other issues* + +''' + +#Python 2 + +def recsol(a,b,lev): + if (a <= 0 or b <= 0): return + if (a == 1 and b == 1): return lev + if(a > b and (( a / b ) -1) > 0 ): + time = (a / b) -1 + a = a - b * ((a / b) - 1) + return recsol(a, b, time + lev) + elif(b> a and (( b / a ) -1) > 0 ): + time = (( b / a ) ) -1 + b = b - a * (( b / a ) - 1) + return recsol(a, b,time + lev) + return recsol(a-b,b,lev+1) or recsol(a,b-a,lev+1) + +inp = input() +for i in range(inp): + M , F = map(int , raw_input("").split(" ")) + if(M > 10 ** 50 or F > 10 ** 50 or M < 0 or F < 0):print "-1" + val = recsol(M,F,0) + if(val == None):print "impossible" + else: print val + diff --git a/Code_It_Out_Questions/3_Turn_Game.py b/Code_It_Out_Questions/3_Turn_Game.py new file mode 100644 index 0000000..6f969f4 --- /dev/null +++ b/Code_It_Out_Questions/3_Turn_Game.py @@ -0,0 +1,52 @@ +''' + +Motu wants to play a game with his friends. +All of his play a new game where every player is named numbers from 1 and are made to stand in a circle, +And from player 1 they would shout numbers from 1 .. if its a multiple of 2 they are removed from the game. the game continues the cyle (last one left --> first one left) +The last player standing wins the game + +Motu wants to know where he has to stand to win. You are asked to find the position he has to stand given the number of players + +Input Format +The first line indicates N the number of test cases. +N test cases follow the first Line Each with the Number of Players (P) + +Constraints +1 ≤ P ≤ 100000 + +1 ≤ N < 10000 + +Output Format +The position That will win has to be outputted for each test case + +Sample input | Sample Output +4 | +2 | 1 +3 | 3 +4 | 1 +6 | 5 + + +Explanation +There are four test cases in the input. + +With 6 Players, First Player Yells 1 , Second Player Yells 2 and he is removed , Third Player Yells 3 , Fourth Player Yells 4 and he is removed , +5th Player yells 5 , 6th Player Yells 6 and is removed , 1st player yells 7 , 3rd player yells 8 and is removed , 5th player yells 9 , +1st player yells 10 and is removed +Only 5th player Remains + +With 5 Players, First Player Yells 1 , Second Player Yells 2 and he is removed , Third Player Yells 3 , Fourth Player Yells 4 and he is removed , +5th Player yells 5, First Player Yells 6 and is removed, Third player yells 7 , 5th Player yells 8 anb is removed , +Only Third Player remains and he wins the game + +''' + + +#Solution for python 3 Py3 + +for _ in range(int(input())): + num = int(input()) + last_roll = 2 ** (num.bit_length() - 1) + n = (num - (last_roll - 1)) * 2 - 1 + print(n) + diff --git a/Code_It_Out_Questions/4_Destroy_Bacteria.py b/Code_It_Out_Questions/4_Destroy_Bacteria.py new file mode 100644 index 0000000..c34dca0 --- /dev/null +++ b/Code_It_Out_Questions/4_Destroy_Bacteria.py @@ -0,0 +1,66 @@ +''' + +Motu was called in for an emergency at the hospital. +A Disease is spereading and only Motu can solve it + +He is given with a bacteria count of a person and he has to reuce the bacteria count to zero in the most minimun no of steps + +The hospital has 3 methods to control the count of the bacteria + +1) They can use their advanced machines to remove one Bacteria +2) They can use their bacteria Inserter to insert one Bacteria +3) They have a speical prototype machine which can exactly divide the number of bacteria into two . (since its a prototype machine only even number of bacteria can be divided using this method) + +Motu cannot handle all the cases at the hospial so he is asking for your help ! Can you help Him ? + +You will be given a Bacteria count as input , You have to find the least no of steps to reduce the number of bacteria to 0 with the provided 3 methods in the hospital + +For example: + +Given Input 4 :> +4 --> 2 --> 1 --> 0 +In 3 steps we can reduce to 0 hence the answer is 0 + +Given Input 15 :> +15 --> 16 --> 8 --> 4 --> 2 --> 1 --> 0 +We can reduce to 0 in 6 steps hence 6 is the answer + +Since the bacteria is spreading quickly you can expect bacteria count upto 10^19 . So Use Large datatypes to input data and handle it. + +Input +The first line takes into account N +N is the number of Test Cases that follow +After that N lines contain the bacteria count for each test case + +Output +Output the number of steps required to reduce the bacteria count to 0 with the methods given in the questions + +Sample Cases + +Sample input | Sample Output +4 | +4 | 3 +5 | 4 +15 | 6 +20 | 6 + + +''' + +def answer(n): + counter = 0 + num = long(n) + while(num > 1): + if num % 2 == 0: + num = num / 2 + elif num == 3 or num % 4 == 1: + num -= 1 + elif num % 4 == 3 : + num += 1 + else: + break + counter += 1 + return counter + 1 + +for i in range(input()): + print answer(input()) \ No newline at end of file diff --git a/Code_It_Out_Questions/5_Motu's_Plants.py b/Code_It_Out_Questions/5_Motu's_Plants.py new file mode 100644 index 0000000..a3ee5b8 --- /dev/null +++ b/Code_It_Out_Questions/5_Motu's_Plants.py @@ -0,0 +1,120 @@ +''' + +Motu Has got a special formula fertilizer for growing plants, +one applying one unit of the fertilizer the plant grows one unit + +Motu wants to know how many ways he can plant his plants in such a way that he has atleast two plants and +-> Two plants should not have same height +-> Each plant must have increasing heights +-> every unit of the fertilizer has to be used + +Given the amount of fertilizer. Find how many ways motu can plant his plants. + +Assuming he has an unlimited supply of plant seeds + +Explanation + +Given that he has 5 units of fertilizer + +he can plant the plants in the following fasion + +| +| | +| | | +| | or | | +4 1 3 2 + +Constraint +He can have a maximum of 500 units of fertilizers + +Input +It has an input of F , The amount of fertilizer he has + +Output +The different number of ways he can plant his plants + +Sample Cases + +Sample input | Sample Output + | +6 | 3 +7 | 4 +10 | 9 + +''' + +''' +def answer(n): + combinations = [[0 for rows in range(n)] for cols in range(n + 1)] + + # If n < 3, there are no possibilities for building the stairwell. + for first_three in range(3): + for num in range(first_three, n): + combinations[first_three][num] = 1 + + # For the rest of them, the formula is incremental. + for num in range(3, n + 1): + for bot in range(2, n): + combinations[num][bot] = combinations[num][bot - 1] + if bot <= num: + combinations[num][bot] += combinations[num - bot][bot - 1] + + # This index on the matrix should contain our solution to the number of distinct combinations. + return combinations[n][n - 1] + +if __name__ == '__main__': + # This prints out the results of this function on any value between (including) 3 and 200. + # It's just for debugging. + print("Format:\n Number of Bricks --> Distinct Partitions") + for bricks in range(3, 200): + print(' ', bricks, " --> ", str(answer(bricks))) + +''' + + +# Alternate solutions + + +steps = 0 + +#Grandest Staircase + +def memoize(f): + + class memodict(dict): + def __init__(self, f): + self.f = f + def __call__(self, *args): + return self[args] + def __missing__(self, key): + ret = self[key] = self.f(*key) + return ret + return memodict(f) + +@memoize +def step(num): + ss=0 + if(num <= 2):return 0 + if(num < 5):return 1 + for i in range(num-1,0,-1): + if ((num - i) > i ):ss = ss + smallsteps(i,num-i);continue + elif(i == (num - i)):pass + else:ss += 1 + temp = step(num - i) + ss = ss + temp + return ss + +def natsum(n):return ((n*(n+1))/2) + +@memoize +def smallsteps(num,lim): + sum = 0 + if(natsum(num-1) < lim):return 0 + for i in range(num - 1 , 0 , -1): + if(i > lim):continue + nlim = lim - i + if(nlim == 0):sum = sum + 1 + else:sum = sum + smallsteps(i,nlim) + return sum + +print(step(int(input()))) diff --git a/Code_It_Out_Questions/6_Demonetisation.py b/Code_It_Out_Questions/6_Demonetisation.py new file mode 100644 index 0000000..a5a29bf --- /dev/null +++ b/Code_It_Out_Questions/6_Demonetisation.py @@ -0,0 +1,68 @@ +''' + +Motu Has Just recieved some amount of money from the bank and as he reaches home he hears news of demonetisation ! +Given the type of Money Denominations in Existence Show how many different ways he can make change for his money, +Motu is Really desparate for your help ! + +Assume we have infinite amount of Each Denominations + +Explanation + +If there are 5 avaliable notes now [7,6,3,1,2] if Motu took 3 Rs from Bank he can +Change it into ( (1,1,1),(2,1),(3) ) So there are 3 ways to change his notes + + +Input Format +First Line contains the Money he has With him Followed by the number of denominations of Notes avaliable +Second line contatins all the various denominations that are avaliable + +Output Format +Output one number containing the number of possible ways to get change + +Constraints + +Each Denomination <= 50 +Number of Denominations <= 50 +Money He Has <= 250 + +Sample Cases + +Sample input | Sample Output +4 4 | +8 1 2 3 | 4 + +''' +// Solution In C++ + +#include + +using namespace std; + +int c[52]; +int numCoins; +long long table[52][252]; +bool calculated[52][252]; +long long solve(int i, int make) +{ + if(make<0) return 0; + if(make==0)return 1; + if(i > numCoins) return 0; + if(calculated[i][make] == false){ //eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make); + calculated[i][make] = true; + } + return table[i][make]; +} +int main(){ + + int make; + cin>>make>>numCoins; + for(int i=1;i<=numCoins;i++){ + cin>>c[i]; + } + cout< + +int main() +{ + int X,M,i,num; + scanf("%d",&X); + scanf("%d",&M); + X = 1; + M = 200; + //P = [1 for _ in xrange(M+1)] + int P[M+1]; + for(int x=0; x < M+1; x++) + P[x] = 1; + + P[0] = 0, P[1] = 0; + i = 2; + while(i*i <= M) + { + if(P[i] == 1) + { + //for j in xrange(i*i,M+1,i) + for(int j=i*i; j < M+1; j+=i) + { + if (P[j] == 1) + { + P[j] = 0; + P[i] += 1; + } + } + } + i += 1; + } + + for(i=0; i + + +unsigned long long int recsol(unsigned long long int a,unsigned long long int b,unsigned long long int lev) { + unsigned long long int time; + while (a >= 1 && b >= 1) { + if (a > b && ((a / b) - 1) > 0 ) + { + time = (a / b) - 1; + a = (a) - b * ((a / b) - 1); + lev = time + lev; + } + else if(b > a && ((b / a) - 1) > 0 ){ + time = ((b / a)) - 1; + b = (b) - a * ((b / a) - 1); + lev =time + lev; + } + else{ + if (b > a){ + b = b - a; + lev = lev + 1;} + else if (a > b){ + a = a-b; + lev = lev + 1;} + else + return 0; + } + if (a == 1 && b == 1) + return lev; + if(a <= 0 || b <= 0 ) + return -1; + } +} + +int main(){ + int inp ; + unsigned long long int data1 , data2 , ans ; + scanf("%d",&inp) ; + for(int i=0 ; i < inp ; i++){ + scanf("%llu %llu",&data1,&data2); + ans = recsol(data1,data2,0); + if(ans == 0){ + printf("impossible\n"); + continue; + } + + printf("%llu\n" , ans); + + } + return 0; + +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/C/3.C b/Code_It_Out_Questions/Other_Solutions_Untested/C/3.C new file mode 100644 index 0000000..e8bcdd5 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/C/3.C @@ -0,0 +1,20 @@ + +#include +#include + +int main() +{ + int y,n; + //for _ in range(int(input())) + scanf("%d",&y); + for(int x=0;x + +int main() +{ + int counter,num; + scanf("%d",&num); + counter = 0; + while(num > 1){ + if (num % 2 == 0) + num = num / 2; + else if (num == 3 || num % 4 == 1) + num -= 1; + else if (num % 4 == 3) + num += 1; + else + break; + counter += 1; + } + printf("%d",&counter); + +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/C/5.C b/Code_It_Out_Questions/Other_Solutions_Untested/C/5.C new file mode 100644 index 0000000..737e2d5 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/C/5.C @@ -0,0 +1,56 @@ + +#include + +unsigned long long int array[501], list[501][501]; + +unsigned long long int natsum(unsigned long long int n){ + return ((n*(n+1))/2); +} + +unsigned long long int smallsteps(unsigned long long int num,unsigned long long int lim){ + if(list[num][lim] != 0)return list[num][lim]; + unsigned long long int sum = 0, nlim,i; + if(natsum(num-1) < lim) return 0; + for (i=num-1; i>0; i--){ + if(i > lim){ continue;} + nlim = lim - i; + if(nlim == 0){ sum = sum + 1;} + else sum = sum + smallsteps(i,nlim); + } + list[num][lim] = sum; + return sum; +} + +unsigned long long int step(unsigned long long int num) { + + if(array[num] != 0)return array[num]; + unsigned long long int ss=0,i,temp; + if(num <= 2) return 0; + if(num < 5) return 1; + for (i=num-1;i>0;i--){ + + if ((num - i) > i ){ + ss = ss + smallsteps(i,num-i);continue; + } + else if(i == (num - i)) + {} + else{ + ss += 1;} + temp = step(num - i); + ss = ss + temp; + } + array[num] = ss; + return ss; +} + +int main() +{ + for(int i =0; i<501; i++) + {array[i] = 0; + for(int j =0; j<501; j++) { + list[i][j] = 0; + } + } + printf("%llu",step(500)); + return 0; +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/C/6.C b/Code_It_Out_Questions/Other_Solutions_Untested/C/6.C new file mode 100644 index 0000000..be38399 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/C/6.C @@ -0,0 +1,30 @@ +#include + +int c[52]; +int numCoins; +long long table[52][252]; +int calculated[52][252]; +long long solve(int i, int make) +{ + if(make<0) return 0; + if(make==0)return 1; + if(i > numCoins) return 0; + if(calculated[i][make] == 0){ //eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make); + calculated[i][make] = 1; + } + return table[i][make]; +} +int main(){ + + int make,i,j; + scanf("%d%d",&make,&numCoins); + for(i = 0; i< 52; i++) + for(j = 0; j< 252; j++) + calculated[i][j] = 0; + for(i=0;i<=numCoins;i++){ + scanf("%d",&c[i]); + } + printf("%d",solve(1, make)); + return 0; +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/C/7.C b/Code_It_Out_Questions/Other_Solutions_Untested/C/7.C new file mode 100644 index 0000000..9c30dd9 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/C/7.C @@ -0,0 +1,24 @@ +#include +// #include +void main(){ + int ar[100],size,i,largest,count=0; + // clrscr(); + scanf("%d",&size); + for(i=0;ilargest){ + largest=ar[i]; + } + } + for(i=0;i +using namespace std; + +int main() +{ + int X,M,i,num; + cin>>X; + cin>>M; + + //P = [1 for _ in xrange(M+1)] + int P[M+1]; + for(int x=0; x < M+1; x++) + P[x] = 1; + + P[0] = 0, P[1] = 0; + i = 2; + while(i*i <= M) + { + if(P[i] == 1) + { + //for j in xrange(i*i,M+1,i) + for(int j=i*i; j < M+1; j+=i) + { + if (P[j] == 1) + { + P[j] = 0; + P[i] += 1; + } + } + } + i += 1; + } + + for(i=0; i>num; + cout< +#include + +using namespace std; + +unsigned long long int recsol(unsigned long long int a,unsigned long long int b,unsigned long long int lev) { + unsigned long long int time; + while (a >= 1 && b >= 1) { + if (a > b && ((a / b) - 1) > 0 ) + { + time = (a / b) - 1; + a = (a) - b * ((a / b) - 1); + lev = time + lev; + } + else if(b > a && ((b / a) - 1) > 0 ){ + time = ((b / a)) - 1; + b = (b) - a * ((b / a) - 1); + lev =time + lev; + } + else{ + if (b > a){ + b = b - a; + lev = lev + 1;} + else if (a > b){ + a = a-b; + lev = lev + 1;} + else + return 0; + } + if (a == 1 && b == 1) + return lev; + if(a <= 0 || b <= 0 ) + return -1; + } +} + +int main(){ + printf("%llu" , recsol(1,456789,0)); + return 0; + +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/CPP/3.cpp b/Code_It_Out_Questions/Other_Solutions_Untested/CPP/3.cpp new file mode 100644 index 0000000..a37df8b --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/CPP/3.cpp @@ -0,0 +1,22 @@ + +#include +#include +using namespace std; + +int main() +{ + int y,n; + //for _ in range(int(input())) + cin>>y; + for(int x=0;x>num; + last_roll = pow(2,(floor(log2(num)))); + n = (num - (last_roll - 1)) * 2 - 1; + cout< +using namespace std; + +int main() +{ + string n; + int counter=0,num; + cin>>num; + while(num > 1) + { + if(num % 2 == 0) + num = num / 2; + else if(num == 3 || num % 4 == 1) + num -= 1; + else if(num % 4 == 3) + num += 1; + else + break; + counter += 1; + } + cout< + +using namespace std; + +unsigned long long int array[501], list[501][501]; + +unsigned long long int natsum(unsigned long long int n){ + return ((n*(n+1))/2); +} + +unsigned long long int smallsteps(unsigned long long int num,unsigned long long int lim){ + if(list[num][lim] != 0)return list[num][lim]; + unsigned long long int sum = 0, nlim,i; + if(natsum(num-1) < lim) return 0; + for (i=num-1; i>0; i--){ + if(i > lim){ continue;} + nlim = lim - i; + if(nlim == 0){ sum = sum + 1;} + else sum = sum + smallsteps(i,nlim); + } + list[num][lim] = sum; + return sum; +} + +unsigned long long int step(unsigned long long int num) { + + if(array[num] != 0)return array[num]; + unsigned long long int ss=0,i,temp; + if(num <= 2) return 0; + if(num < 5) return 1; + for (i=num-1;i>0;i--){ + + if ((num - i) > i ){ + ss = ss + smallsteps(i,num-i);continue; + } + else if(i == (num - i)) + {} + else{ + ss += 1;} + temp = step(num - i); + ss = ss + temp; + } + array[num] = ss; + return ss; +} + +int main() +{ + for(int i =0; i<501; i++) + {array[i] = 0; + for(int j =0; j<501; j++) { + list[i][j] = 0; + } + } + cout< + +using namespace std; + +long getWays(long n, vector < long > c){ + // Complete this function + vector table(n+1); + table[0]=1; + for(long i=0;i> n >> m; + vector c(m); + for(int c_i = 0; c_i < m; c_i++){ + cin >> c[c_i]; + } + // Print the number of ways of making change for 'n' units using coins having the values given by 'c' + long ways = getWays(n, c); + cout< +// #include +void main(){ + int ar[100],size,i,largest,count=0; + // clrscr(); + cin>>size; + for(i=0;i>ar[i]; + } + largest=ar[0]; + for(i=0;ilargest){ + largest=ar[i]; + } + } + for(i=0;i +// #include +void main(){ + int ar[100],size,i,largest,count=0; + // clrscr(); + scanf("%d",&size); + for(i=0;ilargest){ + largest=ar[i]; + } + } + for(i=0;i +// #include +void main(){ + int ar[100],size,i,largest,count=0; + // clrscr(); + cin>>size; + for(i=0;i>ar[i]; + } + largest=ar[0]; + for(i=0;ilargest){ + largest=ar[i]; + } + } + for(i=0;i 0 +M,F < 10^50 + +*You might wanna consider using large variable datatypes to avoid overflow errors and other issues* + +''' + +#Python 2 + +def recsol(a,b,lev): + if (a <= 0 or b <= 0): return + if (a == 1 and b == 1): return lev + if(a > b and (( a / b ) -1) > 0 ): + time = (a / b) -1 + a = a - b * ((a / b) - 1) + return recsol(a, b, time + lev) + elif(b> a and (( b / a ) -1) > 0 ): + time = (( b / a ) ) -1 + b = b - a * (( b / a ) - 1) + return recsol(a, b,time + lev) + return recsol(a-b,b,lev+1) or recsol(a,b-a,lev+1) + +inp = input() +for i in range(inp): + M , F = map(int , raw_input("").split(" ")) + if(M > 10 ** 50 or F > 10 ** 50 or M < 0 or F < 0):print "-1" + val = recsol(M,F,0) + if(val == None):print "impossible" + else: print val \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/3_Turn_Game.py b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/3_Turn_Game.py new file mode 100644 index 0000000..4247676 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/3_Turn_Game.py @@ -0,0 +1,55 @@ +''' + +Motu wants to play a game with his friends. +All of his play a new game where every player is named numbers from 1 and are made to stand in a circle, +And from player 1 they would shout numbers from 1 .. if its a multiple of 2 they are removed from the game. the game continues the cyle (last one left --> first one left) +The last player standing wins the game + +Motu wants to know where he has to stand to win. You are asked to find the position he has to stand given the number of players + +Input Format +The first line indicates N the number of test cases. +N test cases follow the first Line Each with the Number of Players (P) + +Constraints +1 ≤ P ≤ 100000 + +1 ≤ N < 263 + +Output Format +The position That will win has to be outputted for each test case + +Sample Input +4 +2 +3 +4 +6 +Sample Output +1 +3 +1 +5 +Explanation +There are four test cases in the input. + +With 2 petals, one would skip 1, tear 2, and then only 1 is left. + +With 3 petals, one would skip 1, tear 2, skip 3, tear 1, and then only 3 is left. + +With 4 petals, one would skip 1, tear 2, skip 3, tear 4, skip 1, tear 3, and then only 1 is left. + +With 6 petals, First Player Yells 1 , Second Player Yells 2 and he is removed , Third Player Yells 3 , Fourth Player Yells 4 and he is removed , 5th Player yells 5 , 6th Player Yells 6 and is removed , 1st player yells 7 , 3rd player yells 8 and is removed , 5th player yells 9 , 1st player yells 10 and is removed +Only 5 Remains + +''' + + +#Solution for python 3 Py3 + +for _ in range(int(input())): + num = int(input()) + last_roll = 2 ** (num.bit_length() - 1) + n = (num - (last_roll - 1)) * 2 - 1 + print(n) + diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/4_Destroy_Bacteria.py b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/4_Destroy_Bacteria.py new file mode 100644 index 0000000..12b869b --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/4_Destroy_Bacteria.py @@ -0,0 +1,63 @@ +''' + +Motu was called in for an emergency at the hospital. +A Disease is spereading and only Motu can solve it + +He is given with a bacteria count of a person and he has to reuce the bacteria count to zero in the most minimun no of steps + +The hospital has 3 methods to control the count of the bacteria + +1) They can use their advanced machines to remove one Bacteria +2) They can use their bacteria Inserter to insert one Bacteria +3) They have a speical prototype machine which can exactly divide the number of bacteria into two . (since its a prototype machine only even number of bacteria can be divided using this method) + +Motu cannot handle all the cases at the hospial so he is asking for your help ! Can you help Him ? + +You will be given a Bacteria count as input , You have to find the least no of steps to reduce the number of bacteria to 0 with the provided 3 methods in the hospital + +For example: + +Given Input 4 :> +4 --> 2 --> 1 --> 0 +In 3 steps we can reduce to 0 hence the answer is 0 + +Given Input 15 :> +15 --> 16 --> 8 --> 4 --> 2 --> 1 --> 0 +We can reduce to 0 in 6 steps hence 6 is the answer + +Since the bacteria is spreading quickly you can expect bacteria count with atmost 300 digits . So Use Large datatypes to input data and handle it. + +Input +The first line takes into account N +N is the number of Test Cases that follow +After that N lines contain the bacteria count for each test case + +Output +Output the number of steps required to reduce the bacteria count to 0 with the methods given in the questions + +Sample Cases + +Sample input | Sample Output +4 16 | +3 | 3 +2 | 8 +5 | 1 +10 | 0 + + +''' + +def answer(n): + counter = 0 + num = long(n) + while(num > 1): + if num % 2 == 0: + num = num / 2 + elif num == 3 or num % 4 == 1: + num -= 1 + elif num % 4 == 3 : + num += 1 + else: + break + counter += 1 + return counter + 1 diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/5_Motu's_Plants.py b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/5_Motu's_Plants.py new file mode 100644 index 0000000..a3ee5b8 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/5_Motu's_Plants.py @@ -0,0 +1,120 @@ +''' + +Motu Has got a special formula fertilizer for growing plants, +one applying one unit of the fertilizer the plant grows one unit + +Motu wants to know how many ways he can plant his plants in such a way that he has atleast two plants and +-> Two plants should not have same height +-> Each plant must have increasing heights +-> every unit of the fertilizer has to be used + +Given the amount of fertilizer. Find how many ways motu can plant his plants. + +Assuming he has an unlimited supply of plant seeds + +Explanation + +Given that he has 5 units of fertilizer + +he can plant the plants in the following fasion + +| +| | +| | | +| | or | | +4 1 3 2 + +Constraint +He can have a maximum of 500 units of fertilizers + +Input +It has an input of F , The amount of fertilizer he has + +Output +The different number of ways he can plant his plants + +Sample Cases + +Sample input | Sample Output + | +6 | 3 +7 | 4 +10 | 9 + +''' + +''' +def answer(n): + combinations = [[0 for rows in range(n)] for cols in range(n + 1)] + + # If n < 3, there are no possibilities for building the stairwell. + for first_three in range(3): + for num in range(first_three, n): + combinations[first_three][num] = 1 + + # For the rest of them, the formula is incremental. + for num in range(3, n + 1): + for bot in range(2, n): + combinations[num][bot] = combinations[num][bot - 1] + if bot <= num: + combinations[num][bot] += combinations[num - bot][bot - 1] + + # This index on the matrix should contain our solution to the number of distinct combinations. + return combinations[n][n - 1] + +if __name__ == '__main__': + # This prints out the results of this function on any value between (including) 3 and 200. + # It's just for debugging. + print("Format:\n Number of Bricks --> Distinct Partitions") + for bricks in range(3, 200): + print(' ', bricks, " --> ", str(answer(bricks))) + +''' + + +# Alternate solutions + + +steps = 0 + +#Grandest Staircase + +def memoize(f): + + class memodict(dict): + def __init__(self, f): + self.f = f + def __call__(self, *args): + return self[args] + def __missing__(self, key): + ret = self[key] = self.f(*key) + return ret + return memodict(f) + +@memoize +def step(num): + ss=0 + if(num <= 2):return 0 + if(num < 5):return 1 + for i in range(num-1,0,-1): + if ((num - i) > i ):ss = ss + smallsteps(i,num-i);continue + elif(i == (num - i)):pass + else:ss += 1 + temp = step(num - i) + ss = ss + temp + return ss + +def natsum(n):return ((n*(n+1))/2) + +@memoize +def smallsteps(num,lim): + sum = 0 + if(natsum(num-1) < lim):return 0 + for i in range(num - 1 , 0 , -1): + if(i > lim):continue + nlim = lim - i + if(nlim == 0):sum = sum + 1 + else:sum = sum + smallsteps(i,nlim) + return sum + +print(step(int(input()))) diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/6_Demonetisation.py b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/6_Demonetisation.py new file mode 100644 index 0000000..73ecdf7 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/6_Demonetisation.py @@ -0,0 +1,65 @@ +''' + +Motu Has Just recieved some amount of money from the bank and as he reaches home he hears news of demonetisation ! +Given the type of Money Denominations in Existence Show how many different ways he can make change for his money, +Motu is Really desparate for your help ! + +Assume we have infinite amount of Each Denominations + +Explanation + +If there are 5 avaliable notes now [7,6,3,1,2] if Motu took 3 Rs from Bank he can +Change it into ( (1,1,1),(2,1),(3) ) So there are 3 ways to change his notes + + +Input Format +First Line contains the Money he has With him Followed by the number of denominations of Notes avaliable +Second line contatins all the various denominations that are avaliable + +Output Format +Output one number containing the number of possible ways to get change + +Constraints + +Each Denomination <= 50 +Number of Denominations <= 50 +Money He Has <= 250 + +Sample Cases + +Sample input | Sample Output +4 4 | +8 1 2 3 | 4 + +''' +// Solution In C++ + +#include + +using namespace std; + +int c[52]; +int numCoins; +long long table[52][252]; +bool calculated[52][252]; +long long solve(int i, int make) +{ + if(make<0) return 0; + if(make==0)return 1; + if(i > numCoins) return 0; + if(calculated[i][make] == false){ //eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make); + calculated[i][make] = true; + } + return table[i][make]; +} +int main(){ + + int make; + cin>>make>>numCoins; + for(int i=1;i<=numCoins;i++){ + cin>>c[i]; + } + cout< +#include +void main() +{ + int X,M,*P, i,j,num; + cin>>X>>M; + + P = new int[M+1]; + P[0]= P[1]= 0; + for(int _=2; _<=M; _++) + P[_]= 1; + i=2; + while(i*i <=M) + { + if(P[i] ==1) + for(j= i*i; j>num; + cout< +#include + +unsigned long long int recsol(unsigned long long int a,unsigned long long int b,unsigned long long int lev) { + unsigned long long int time; + while (a >= 1 && b >= 1) { + cout< b && ((a / b) - 1) > 0 ) + { + time = (a / b) - 1; + a = a - b * ((a / b) - 1); + lev = time + lev; + } + else if(b > a && ((b / a) - 1) > 0 ){ + time = ((b / a)) - 1; + b = b - a * ((b / a) - 1); + lev =time + lev; + } + else{ + if (b-a > 0) + b = b - a; + else if (a-b > 0) + a = a-b; + } + if (a == 1 && b == 1) + return lev; + if(a <0 || b < 0 ) + + return -1; + } +} + +int main(){ + clrscr(); + cout< + +unsigned long long int recsol(unsigned long long int a,unsigned long long int b,unsigned long long int lev) { + unsigned long long int time; + while (a >= 1 && b >= 1) { + printf("%d %d \n" , a,b); + if (a > b && ((a / b) - 1) > 0 ) + { + time = (a / b) - 1; + a = a - b * ((a / b) - 1); + lev = time + lev; + } + else if(b > a && ((b / a) - 1) > 0 ){ + time = ((b / a)) - 1; + b = b - a * ((b / a) - 1); + lev =time + lev; + } + else{ + if (b-a > 0) + b = b - a; + else if (a-b > 0) + a = a-b; + } + if (a == 1 && b == 1) + return lev; + if(a <0 || b < 0 ) + return -1; + } +} + +int main(){ + printf("%llu" , recsol(1,12345678912345678999,0)); + +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.C-issues.txt b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.C-issues.txt new file mode 100644 index 0000000..606c460 --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.C-issues.txt @@ -0,0 +1 @@ +printf("%llu" , recsol(1,4294967295,0)); // max number with 1 is 4294967295 (10 digits) \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.CPP b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.CPP new file mode 100644 index 0000000..9cb0a3f --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q2.CPP @@ -0,0 +1,36 @@ +#include + +using namespace std; + +unsigned long long int recsol(unsigned long long int a,unsigned long long int b,unsigned long long int lev) { + unsigned long long int time; + while (a >= 1 && b >= 1) { + cout< b && ((a / b) - 1) > 0 ) + { + time = (a / b) - 1; + a = a - b * ((a / b) - 1); + lev = time + lev; + } + else if(b > a && ((b / a) - 1) > 0 ){ + time = ((b / a)) - 1; + b = b - a * ((b / a) - 1); + lev =time + lev; + } + else{ + if (b-a > 0) + b = b - a; + else if (a-b > 0) + a = a-b; + } + if (a == 1 && b == 1) + return lev; + if(a <0 || b < 0 ) + + return -1; + } +} + +int main(){ + cout< +#include +#include + +void main() +{ +clrscr(); +int t,num,last_roll,n; +cin>>t; +for(int i=0;i>num; + last_roll = pow(2,floor(log(num)/log(2)+1)); + n = (num - (last_roll - 1)) * 2 - 1; + cout<<"BL:"< +#include + +void main() +{ +int t,num,last_roll,n; +cin>>t; +for(int i=0;i>num; + last_roll = pow(2,floor(log(num)/log(2))); + n = (num - (last_roll - 1)) * 2 - 1; + cout<<"Ans:"< +#include + +void main() +{ + clrscr(); + int n=1,counter,num; + while(n) + { + cin>>n; + counter = 0; + num = long(n); + while(num > 1){ + if (num % 2 == 0) + num = num / 2; + else if (num == 3 || num % 4 == 1) + num -= 1; + else if (num % 4 == 3) + num += 1; + else + break; + counter += 1; + } + cout<<"Ans:"< +#include + +void main() +{ + clrscr(); + int n=1,counter,num; + while(n) + { + cin>>n; + counter = 0; + num = long(n); + while(num > 1){ + if (num % 2 == 0) + num = num / 2; + else if (num == 3 || num % 4 == 1) + num -= 1; + else if (num % 4 == 3) + num += 1; + else + break; + counter += 1; + } + cout<<"Ans:"< + +unsigned long long int array[501], list[501][501]; + +unsigned long long int natsum(unsigned long long int n){ + return ((n*(n+1))/2); +} + +unsigned long long int smallsteps(unsigned long long int num,unsigned long long int lim){ + if(list[num][lim] != 0)return list[num][lim]; + unsigned long long int sum = 0, nlim,i; + if(natsum(num-1) < lim) return 0; + for (i=num-1; i>0; i--){ + if(i > lim){ continue;} + nlim = lim - i; + if(nlim == 0){ sum = sum + 1;} + else sum = sum + smallsteps(i,nlim); + } + list[num][lim] = sum; + return sum; +} + +unsigned long long int step(unsigned long long int num) { + + if(array[num] != 0)return array[num]; + unsigned long long int ss=0,i,temp; + if(num <= 2) return 0; + if(num < 5) return 1; + for (i=num-1;i>0;i--){ + + if ((num - i) > i ){ + ss = ss + smallsteps(i,num-i);continue; + } + else if(i == (num - i)) + {} + else{ + ss += 1;} + temp = step(num - i); + ss = ss + temp; + } + array[num] = ss; + return ss; +} + +int main() +{ + for(int i =0; i<501; i++) + {array[i] = 0; + for(int j =0; j<501; j++) { + list[i][j] = 0; + } + } + printf("%llu",step(500)); + return 0; +} \ No newline at end of file diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q5.CPP b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q5.CPP new file mode 100644 index 0000000..48a2c4e --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/Mathew/Q5.CPP @@ -0,0 +1,60 @@ + +#include + +using namespace std; + +unsigned long long int array[501], list[501][501]; + +unsigned long long int natsum(unsigned long long int n){ + return ((n*(n+1))/2); +} + +unsigned long long int smallsteps(unsigned long long int num,unsigned long long int lim){ + if(list[num][lim] != 0)return list[num][lim]; + unsigned long long int sum = 0, nlim,i; + if(natsum(num-1) < lim) return 0; + for (i=num-1; i>0; i--){ + if(i > lim){ continue;} + nlim = lim - i; + if(nlim == 0){ sum = sum + 1;} + else sum = sum + smallsteps(i,nlim); + } + list[num][lim] = sum; + return sum; +} + +unsigned long long int step(unsigned long long int num) { + + if(array[num] != 0)return array[num]; + unsigned long long int ss=0,i,temp; + if(num <= 2) return 0; + if(num < 5) return 1; + for (i=num-1;i>0;i--){ + + if ((num - i) > i ){ + ss = ss + smallsteps(i,num-i);continue; + } + else if(i == (num - i)) + {} + else{ + ss += 1;} + temp = step(num - i); + ss = ss + temp; + } + array[num] = ss; + return ss; +} + +int main() +{ + unsigned long long int i = 0; + for(int i =0; i<501; i++) + {array[i] = 0; + for(int j =0; j<501; j++) { + list[i][j] = 0; + } + } + cin>>i; + cout< + +using namespace std; + + +int c[52]; +int numCoins; +long long table[52][252]; +int calculated[52][252]; +long long solve(int i, int make) +{ + if(make<0) return 0; + if(make==0)return 1; + if(i > numCoins) return 0; + if(calculated[i][make] == 0){ //eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make); + calculated[i][make] = 1; + } + return table[i][make]; +} +int main(){ + + int make,i,j; + cin>>make>>numCoins; + for(i = 0; i< 52; i++) + for(j = 0; j< 252; j++) + calculated[i][j] = 0; + for(i=0;i<=numCoins;i++){ + cin>>c[i]; + } + cout< + +using namespace std; + + +int c[52]; +int numCoins; +long long table[52][252]; +int calculated[52][252]; +long long solve(int i, int make) +{ + if(make<0) return 0; + if(make==0)return 1; + if(i > numCoins) return 0; + if(calculated[i][make] == 0){ //eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make); + calculated[i][make] = 1; + } + return table[i][make]; +} +int main(){ + + int make,i,j; + cin>>make>>numCoins; + for(i = 0; i< 52; i++) + for(j = 0; j< 252; j++) + calculated[i][j] = 0; + for(i=0;i<=numCoins;i++){ + cin>>c[i]; + } + cout<numCoins): return 0 + if(calculated[i][make] == False): #eliminating overlap + table[i][make] = solve(i, make - c[i]) + solve(i+1, make) + calculated[i][make] = True + return table[i][make] +c = [] +make, numCoins = map(int, input().strip().split()) +for i in range(1,numCoins+1): + c.append(int(input())) +print(solve(1, make)) diff --git a/Code_It_Out_Questions/Other_Solutions_Untested/melbin/5.cpp b/Code_It_Out_Questions/Other_Solutions_Untested/melbin/5.cpp new file mode 100644 index 0000000..a156c4d --- /dev/null +++ b/Code_It_Out_Questions/Other_Solutions_Untested/melbin/5.cpp @@ -0,0 +1,47 @@ +#include +using namespace std; + +int answer(int n) +{ + int combinations[n][n+1]; + //combinations = [[0 for rows in range(n)] for cols in range(n + 1)] + for(int rows=0; rows < n; rows++) + { + for (int cols=0; cols < n+1; cols++) + { + combinations[rows][cols] = 0; + } + } + + // If n < 3, there are no possibilities for building the stairwell. + //for first_three in range(3) + for(int first_three=0; first_three < 3; first_three++) + { + for(int num=first_three; num < n; num++) + combinations[first_three][num] = 1; + } + + // For the rest of them, the formula is incremental. + //for num in range(3, n + 1): + for(int num=3; num < n+1; num++) + { + for(int bot=2; bot Distinct Partitions\n"; + //for bricks in range(3, 200): + cin>>bricks; + cout<<" "< "<= len(list) - 1): + break + sum += (list[index + j] - list[index]) ** 2 + i += 1 + print sum, \ No newline at end of file diff --git a/Extras/5.py b/Extras/5.py new file mode 100755 index 0000000..8dcb8a2 --- /dev/null +++ b/Extras/5.py @@ -0,0 +1,21 @@ +def check(lis): + for i in lis: + if i==0:return False + return True + +a = input() +for k in range(1,a+1): + mul = 1 + val = input() + fin = val + if(val == 0):print "Case #{}: INSOMNIA".format(k);continue + chk = [0,0,0,0,0,0,0,0,0,0] + while True: + for i in str(val): + chk[int(i)] = chk[int(i)] + 1 + if(check(chk)): + print "Case #{}: {}".format(k,val) + break + mul+=1 + val = fin * mul + #Case #1: INSOMNIA \ No newline at end of file diff --git a/Extras/test.py b/Extras/test.py new file mode 100755 index 0000000..8c3b78b --- /dev/null +++ b/Extras/test.py @@ -0,0 +1,24 @@ +def fin(num,lis): + lens = lis.__len__() + for i in range(1,lens+1): + if(lis[lens-i] <= num):return lens-i + print lis , " " , min(lis) + return lis.index(min(lis)) +input() +lis = raw_input().split(" ") +len = len(lis) +for i in range(0,len): + lis[i] = int(lis[i]) +lis = sorted(lis) +ans = 0 +for k in range(1,len+1): + num = k ** 2 + ret = fin(num,lis) + print num - int(lis[ret]) + if(num - int(lis[ret]) > 0): + ans = ans + num - int(lis[ret]) + '''else: + ans = ans + (num - int(lis[ret])) * -1 + ''' + del lis[ret] +print ans diff --git a/Hacker_Earth_Learning/find_coprime.py b/Hacker_Earth_Learning/find_coprime.py new file mode 100644 index 0000000..7e8b73f --- /dev/null +++ b/Hacker_Earth_Learning/find_coprime.py @@ -0,0 +1,15 @@ + +def finder(a,b): + if(a > b):return 0 + for i in range(2,b): + if(b % i == 0 ):return 0 + return 1 + +cases = input() +for case in range(cases): + inp = input() + out = 0 + for i in range(1,inp+1): + for k in range(1,inp+1): + if(finder(i,k)):out+=1 + print out \ No newline at end of file diff --git a/Hacker_Earth_Learning/football_test_stack.py b/Hacker_Earth_Learning/football_test_stack.py new file mode 100644 index 0000000..2e92b73 --- /dev/null +++ b/Hacker_Earth_Learning/football_test_stack.py @@ -0,0 +1,17 @@ +times = input() +while times: + num,top = raw_input().split(" ") + num = int(num) + stack = [top] + while num: + current = raw_input() + if(current[0] == "P"): + stack.append(current[2:]) + before = top + top = current[2:] + else: + stack.append(stack[-2]) + num-=1 + print "Player" , stack.pop() + times-=1 + diff --git a/Hacker_Earth_Learning/prime_string.py b/Hacker_Earth_Learning/prime_string.py new file mode 100644 index 0000000..2eb5d69 --- /dev/null +++ b/Hacker_Earth_Learning/prime_string.py @@ -0,0 +1,84 @@ +''' +Alice has just learnt about primeStrings. A string is a primeString if the number of distinct alphabets used in the string is a prime and also the number of occurrences of each alphabet in the string is also a prime. +Given a String you need to tell if it is a primeString or not. + +Input: + +First line contains +T +T which is the number of test cases. +T +T lines follow each containing a string of characters ' +a +a' to ' +z +z'. + +Output: + +For each input, output "YES" if the number is a primeString or "NO" if not. + +SAMPLE INPUT +3 +ababb +abcab +aabbccdd +SAMPLE OUTPUT +YES +NO +NO +Explanation +Case 1: +2 +2 different alphabets each occurring +2 +2 and +3 +3 times respectively so string "ababb" is a PrimeString. + +Case 2: In second string char ' +a +a' occurs +2 +2 times, char ' +b +b' occurs +2 +2 times but char ' +c +c' occur only +1 +1 time which is not a prime number that's why string "abcab" is not a PrimeString. + +Case 3: String contains +4 +4 distinct alphabets and +4 +4 is not a prime Number so the string "aabbccdd" is not a PrimeString. + + +''' + +def normal_prime(num): + if(num == 1):return 0 + if(num < 3 ):return 1 + if(num % 2 == 0 ):return 0 + for i in xrange(3,int(num ** 0.5)+1,2): + if(num % i == 0):return 0 + return 1 + +cases = input() + +for case in range(cases): + no_of_occur = {} + for i in raw_input(): + no_of_occur[i] = no_of_occur.get(i,0) + 1 + done = 1 + if(normal_prime(len(no_of_occur.keys())) == 1): + done = 0 + for k in no_of_occur.keys(): + if(normal_prime(no_of_occur[k]) == 0): + done = 1 + break + if(done == 0):print "YES" + else: print "NO" \ No newline at end of file diff --git a/Hacker_Earth_Learning/save_girlfriend.py b/Hacker_Earth_Learning/save_girlfriend.py new file mode 100644 index 0000000..c0664c7 --- /dev/null +++ b/Hacker_Earth_Learning/save_girlfriend.py @@ -0,0 +1,25 @@ +# Failed Miserably + +val = {} + +def find(num): + init = 0; + if(num in val.keys()):return val[num] + for i in range(1,num/2): + if(num % i == 0):init += 1 + val[num] = init + return init + +cases = input() +for case in range(cases): + a,b = map(int , raw_input().split(" ")) + max_floor = [] + for i in range(a,b+1): + max_floor.append(find(i)) + max_floor.sort() + temp = max_floor[0] + life = 1 + for i in max_floor: + if(i != temp):break + life += 1 + print life \ No newline at end of file diff --git a/Hacker_Earth_Learning/signal_range_stack.py b/Hacker_Earth_Learning/signal_range_stack.py new file mode 100644 index 0000000..fdc2047 --- /dev/null +++ b/Hacker_Earth_Learning/signal_range_stack.py @@ -0,0 +1,15 @@ +times = input() +while times: + val = input() + towers = map(int , raw_input().strip().split(" ")) + temp = 0 + while temp != val: + current = towers[temp] + loopval = 0 ; + for i in range(0,temp+1): + if(current > towers[i]): + loopval+=1 + temp+=1 + print loopval+1, + print + times-=1 \ No newline at end of file diff --git a/Hacker_Earth_Study/Graph_Theory/check_tree.py b/Hacker_Earth_Study/Graph_Theory/check_tree.py new file mode 100644 index 0000000..ba72334 --- /dev/null +++ b/Hacker_Earth_Study/Graph_Theory/check_tree.py @@ -0,0 +1,40 @@ +''' +Our Code Monk recently learnt about Graphs and is very excited! + +He went over to the Graph-making factory to watch some freshly prepared graphs. Incidentally, one of the workers at the factory was ill today, so Monk decided to step in and do her job. + +The Monk's Job is to Identify whether the incoming graph is a tree or not. He is given N, the number of vertices in the graph and the degree of each vertex. + +Find if the graph is a tree or not. + +Input: +First line contains an integer N, the number of vertices. +Second line contains N space-separated integers, the degrees of the N vertices. + +Output: +Print "Yes" (without the quotes) if the graph is a tree or "No" (without the quotes) otherwise. + +Constraints: +1 <= N <= 100 +1 <= Degreei <= 1000 + +References: +Graphs and Trees + +SAMPLE INPUT +3 +1 2 1 +SAMPLE OUTPUT +Yes +Time Limit: + +''' + + +n = int(raw_input()) +l = map(int, raw_input().split()) +ans = sum(l) +if ans == 2*(n-1): + print "Yes" +else: + print "No" \ No newline at end of file diff --git a/Hacker_Earth_Study/Graph_Theory/learning_graph.py b/Hacker_Earth_Study/Graph_Theory/learning_graph.py new file mode 100644 index 0000000..ac17985 --- /dev/null +++ b/Hacker_Earth_Study/Graph_Theory/learning_graph.py @@ -0,0 +1,53 @@ +N,M,K = map(int , raw_input().split(" ")) +K= K-1 +val = map(int , raw_input().split(" ")) + +temp = 1 + +node_val_dict = {} +node_reverse_dict = {} + +for i in val : + node_val_dict[temp] = i + if(i in node_reverse_dict.keys()):node_reverse_dict[i].append(temp) + else: node_reverse_dict[i] = [temp] + temp += 1 +nodes = {} + +for i in range(1,N+1): + nodes[i] = [] + +for i in range(M): + temp = map(int , raw_input().split(" ")) + nodes[temp[0]].append(temp[1]) + nodes[temp[1]].append(temp[0]) + +nodes_changed = {} + +for i in nodes.keys(): + nodes_changed[i] = [node_val_dict[x] for x in nodes[i]] + +ans = [] + +for i in nodes.keys(): + temp = sorted(nodes_changed[i] , reverse=True) + if(len(temp) > K): + ans.append(temp[K]) + else:ans.append(-1) + +tester = 0 + +for i in ans: + tester += 1 + if(i == -1):print "-1" + else: + if len(node_reverse_dict[i]) > 1: + temp = sorted(node_reverse_dict[i]) + for x,y in enumerate(temp): + if(y not in nodes[tester] ):del temp[x] + print temp + for j in temp: + if(j in nodes[tester]):print j;break + else: + print node_reverse_dict[i][0] + diff --git a/Iem_delete.py b/Iem_delete.py new file mode 100755 index 0000000..72e4c33 --- /dev/null +++ b/Iem_delete.py @@ -0,0 +1,8 @@ +for i in range(0,input()): + data = raw_input().split("IEM") + while("".join(data) != "".join("".join(data).split("IEM"))): + data = "".join(data).split("IEM") + if("".join(data).strip() == ""): + print "Yes" + else: + print "No" diff --git a/LLTN_iem_16.py b/LLTN_iem_16.py new file mode 100755 index 0000000..d36012c --- /dev/null +++ b/LLTN_iem_16.py @@ -0,0 +1,30 @@ +temp = [] +check = ["I","E","M"] +current = -1 +ongoing = 0 +score = 0 +i = 0 +data = raw_input() +while i < len(data): + pos = check.index(data[i]) + print score + if(ongoing == 0): + if(data[i] != "I"):i=i+1;continue + else: + current = 0 + score+=1 + ongoing = 1 + else: + if(pos == (current + 1) or pos == current): + score = score + 1 + current = pos + else: + if(current == 2): + temp.append(score) + score = 0 + ongoing = 0 + continue + i=i+1; +if(current ==2): + temp.append(score) +print temp \ No newline at end of file diff --git a/Level1_1_1_Foobar.py b/Level1_1_1_Foobar.py new file mode 100644 index 0000000..6b118fa --- /dev/null +++ b/Level1_1_1_Foobar.py @@ -0,0 +1,7 @@ +def answer(area): + lis = [] + while area>0: + val = int(area ** 0.5) ** 2 + lis.append(val) + area -=val + return lis diff --git a/Level1_1_Foo.py b/Level1_1_Foo.py new file mode 100644 index 0000000..1474de8 --- /dev/null +++ b/Level1_1_Foo.py @@ -0,0 +1,18 @@ +# Braille Translation 2 + +sent = "the quick brown fox jumped over the lazy dog" +temp = "011110110010100010000000111110101001010100100100101000000000110000111010101010010111101110000000110100101010101101000000010110101001101100111100100010100110000000101010111001100010111010000000011110110010100010000000111000100000101011101111000000100110101010110110" +val = {'s' : '011100'} +for i in sent: + val[i] = temp[0:6] + temp = temp[6:] + +def answer(plaintext): + if(len(plaintext) > 50 ):return -1 + out = "" + for i in plaintext: + if(i.isupper()):out = out + "000001";i = i.lower() + out = out + val[i] + return out + +print answer("code") \ No newline at end of file diff --git a/Level2_2_Foo.py b/Level2_2_Foo.py new file mode 100644 index 0000000..383c227 --- /dev/null +++ b/Level2_2_Foo.py @@ -0,0 +1,63 @@ +#dont_get_volunteered (Least Knight Moves) + +def move(x, y, fx,fy): + smallest = [] + stack = [] + limit = range(0, 8) + stack.append((x,y,0)) + movesl = [] + for i in range(0, 8): movesl.append([0] * 8) + movesl[x][y] = 1 + while len(stack)!= 0: + new = stack[0] + x = new[0] + y = new[1] + moves = new[2] + if(x == fx and y == fy):smallest.append(moves) + moves = moves + 1 + if(x+1 in limit and y+2 in limit and movesl[x+1][y+2] == 0 ): + stack.append((x+1,y+2,moves)) + movesl[x+1][y+2] = 1 + if(x-1 in limit and y+2 in limit and movesl[x-1][y+2] == 0 ): + stack.append((x -1, y + 2, moves)) + movesl[x - 1][y + 2] = 1 + if(x+1 in limit and y-2 in limit and movesl[x+1][y-2] == 0 ): + stack.append((x + 1, y - 2, moves)) + movesl[x + 1][y - 2] = 1 + if(x-1 in limit and y-2 in limit and movesl[x-1][y-2] == 0 ): + stack.append((x - 1, y - 2, moves)) + movesl[x - 1][y - 2] = 1 + if(x+2 in limit and y+1 in limit and movesl[x+2][y+1] == 0 ): + stack.append((x + 2, y + 1, moves)) + movesl[x + 2][y + 1] = 1 + if(x+2 in limit and y-1 in limit and movesl[x+2][y-1] == 0 ): + stack.append((x + 2, y -1, moves)) + movesl[x + 2][y - 1] = 1 + if(x-2 in limit and y+1 in limit and movesl[x-2][y+1] == 0 ): + stack.append((x -2 , y + 1, moves)) + movesl[x - 2][y + 1] = 1 + if(x-2 in limit and y-1 in limit and movesl[x-2][y-1] == 0 ): + stack.append((x -2, y -1, moves)) + movesl[x - 2][y - 1] = 1 + del stack[0] + return min(smallest) + + + + + +def answer(src, dest): + if (src == dest): return 0; + if (src < 0 or dest < 0 or src > 63 or dest > 63): return -1 + x = int(src % 8) + y = int((src - x) / 8) + dx = int(dest % 8) + dy = int((dest - dx) / 8) + return move(x, y, dx,dy) + + +for i in range(0,64): + for k in range(0,64): + print "For " , i , " " , k , " " ,answer(i,k) + + diff --git a/Level2_3_Foo.py b/Level2_3_Foo.py new file mode 100644 index 0000000..31970b5 --- /dev/null +++ b/Level2_3_Foo.py @@ -0,0 +1,18 @@ +def prod(n): + out = 1 + for i in n:out *= i + return out + +def answer(list): + if(len(list) > 50):return "-1" + if(len(list) == 1):return str(list[0]) + list.sort() + neg = [];pos=[] + for i in list: + if i < 0 : neg.append(i) + elif(i>0):pos.append(i) + if(len(neg) % 2 != 0):del neg[-1] + if(len(pos) == 0):return 0 + return str(prod(pos) * prod(neg)) + +print answer( [-2,-3,-4,-5]) \ No newline at end of file diff --git a/Level3_1_Foo.py b/Level3_1_Foo.py new file mode 100644 index 0000000..0846e66 --- /dev/null +++ b/Level3_1_Foo.py @@ -0,0 +1,23 @@ + + + +def recsol(a,b,lev): + if (a <= 0 or b <= 0): return + if (a == 1 and b == 1): return lev + if(a > b and (( a / b ) -1) > 0 ): + time = (a / b) -1 + a = a - b * ((a / b) - 1) + return recsol(a, b, time + lev) + elif(b> a and (( b / a ) -1) > 0 ): + time = (( b / a ) ) -1 + b = b - a * (( b / a ) - 1) + return recsol(a, b,time + lev) + return recsol(a-b,b,lev+1) or recsol(a,b-a,lev+1) + +def answer(M, F): + M = int(M) + F = int(F) + if(M > 10 ** 50 or F > 10 ** 50 or M < 0 or F < 0):return "-1" + val = recsol(M,F,0) + if(val == None):return "impossible" + else: return str(val) diff --git a/Level3_2_Foo.py b/Level3_2_Foo.py new file mode 100644 index 0000000..58fb3ee --- /dev/null +++ b/Level3_2_Foo.py @@ -0,0 +1,13 @@ +def f(n): + if(n%4 == 0):return n + elif(n%4==1):return 1 + elif(n%4==2):return n+1 + elif(n%4==3):return 0 + +def answer(start,length): + result = 0 + for i in xrange(length): + result = result ^ f((start + i*length ) -1) ^ f(start + (i+1)*length -(i+1)) + return result + +print answer(17,4000000) \ No newline at end of file diff --git a/Level3_3_Foo.py b/Level3_3_Foo.py new file mode 100644 index 0000000..07e876a --- /dev/null +++ b/Level3_3_Foo.py @@ -0,0 +1,44 @@ + +steps = 0 + +#Grandest Staircase + +def memoize(f): + + class memodict(dict): + def __init__(self, f): + self.f = f + def __call__(self, *args): + return self[args] + def __missing__(self, key): + ret = self[key] = self.f(*key) + return ret + return memodict(f) + +@memoize +def step(num): + ss=0 + if(num <= 2):return 0 + if(num < 5):return 1 + for i in range(num-1,0,-1): + if ((num - i) > i ):ss = ss + smallsteps(i,num-i);continue + elif(i == (num - i)):pass + else:ss += 1 + temp = step(num - i) + ss = ss + temp + return ss + +def natsum(n):return ((n*(n+1))/2) + +@memoize +def smallsteps(num,lim): + sum = 0 + if(natsum(num-1) < lim):return 0 + for i in range(num - 1 , 0 , -1): + if(i > lim):continue + nlim = lim - i + if(nlim == 0):sum = sum + 1 + else:sum = sum + smallsteps(i,nlim) + return sum + +print step() diff --git a/Level4_1_Foo.py b/Level4_1_Foo.py new file mode 100644 index 0000000..225d91e --- /dev/null +++ b/Level4_1_Foo.py @@ -0,0 +1,76 @@ +from fractions import gcd + + +def is_power_of_two(x): + return (x & (x - 1)) == 0 and x != 0 + +def has_exit(i, j): + return is_power_of_two((i+j) / gcd(i,j)) + +class Guard: + def __init__(self, bananas): + self.bananas = bananas + self.exit = [] + self.loop = [] + +def dn(list_nodes, node): + for n in node.exit: + n.exit.remove(node) + for n in node.loop: + n.loop.remove(node) + list_nodes.remove(node) + +def disconnect_pair(list_nodes, node1, node2): + dn(list_nodes, node1) + dn(list_nodes, node2) + + +def answer(banana_list): + nb_guard = len(banana_list) + g = [Guard(banana_list[i]) for i in xrange(nb_guard)] + for i in xrange(0, nb_guard-1): + for j in xrange(i+1, nb_guard): + if has_exit(banana_list[i], banana_list[j]): + g[i].exit.append(g[j]) + g[j].exit.append(g[i]) + else: + g[i].loop.append(g[j]) + g[j].loop.append(g[i]) + + counter = 0 + pairs = [] + + """" + if nb_guard % 2 == 1: + singleton_guard = Guard(-1) + for guard in g: + singleton_guard.exit.append(guard) + guard.exit.append(singleton_guard) + g.append(singleton_guard) + counter -= 1 + """ + + while len(g) > 0: + g.sort(key=lambda x: len(x.exit), reverse=True) + + current_guard = g[0] # + found_good = False + for candidate_pair in g[1:]: + if candidate_pair in current_guard.loop: + pairs.append((current_guard, candidate_pair)) + disconnect_pair(g, current_guard, candidate_pair) + found_good = True + break + if not found_good: + counter += 2 + pairs.append((current_guard, g[1])) + disconnect_pair(g, current_guard, g[1]) + + return counter + + +if __name__ == "__main__": + print answer([1, 1]) + print answer([1, 7, 3, 21, 13, 19]) + print answer([3, 3, 2, 6, 6]) + print answer([1, 7, 21]) \ No newline at end of file diff --git a/Level4_2.py b/Level4_2.py new file mode 100644 index 0000000..514f076 --- /dev/null +++ b/Level4_2.py @@ -0,0 +1,65 @@ +import decimal +inf = decimal.Decimal("Infinity") + +def answer(entrances, exits, path): + transform(entrances, exits, path) + flow = 0 + length = len(path) + flows = [[0 for i in range(length)] for j in range(length)] + start = 0 + end = length - 1 + while True: + ap_flow, parents = bfs(start, end, path, flows) + if ap_flow == 0: + break + flow += ap_flow + v = end + while v != start: + u = parents[v] + flows[u][v] += ap_flow + flows[v][u] -= ap_flow + v = u + return flow + +def bfs(start, end, path, flows): + global inf + length = len(path) + parents = [-1] * length + parents[start] = -2 + queue = [] + queue.append(start) + while queue and parents[end] == -1: + u = queue.pop(0) + for v in range(length): + cf = path[u][v] - flows[u][v] + if cf > 0 and parents[v] == -1: + queue.append(v) + parents[v] = u + if parents[end] == -1: + return 0, parents + v = end + delta = inf + while v != start: + u = parents[v] + cf = path[u][v] - flows[u][v] + delta = min(delta, cf) + v = u + return delta, parents + +def transform(entrances, exits, path): + global inf + length = len(path) + entrances = [i + 1 for i in entrances] + exits = [i + 1 for i in exits] + for row in path: + row.insert(0, 0) + row.append(0) + start_row = [0] * (length + 2) + for i in entrances: + start_row[i] = inf + path.insert(0, start_row) + end_row = [0] * (length + 2) + for i in exits: + path[i][-1] = inf + path.append(end_row) + return entrances, exits, path \ No newline at end of file diff --git a/November_easy_hackerearth/divisible_trio.py b/November_easy_hackerearth/divisible_trio.py new file mode 100644 index 0000000..53587a1 --- /dev/null +++ b/November_easy_hackerearth/divisible_trio.py @@ -0,0 +1,13 @@ +n , m = map(int , raw_input().split(" ")) +lis = map(int , raw_input().split(" ")) +mapper = {} +print lis +for i in lis: + mod = i % m + print mapper + if(mod in mapper.keys()):getval = mapper[mod] + else:getval = [] + if i not in getval: + getval.append(i) + mapper[mod] = getval +print mapper \ No newline at end of file diff --git a/November_easy_hackerearth/funny_sub_array.py b/November_easy_hackerearth/funny_sub_array.py new file mode 100644 index 0000000..a9998b7 --- /dev/null +++ b/November_easy_hackerearth/funny_sub_array.py @@ -0,0 +1,21 @@ + +def max_funny(inp , pos ): + stack = [] + cur = inp[pos] + length = 1 + for i in range(pos+1 , len(inp)): + length += 1 + if(inp[i] == cur):print inp[pos:i+1] ; stack.append(length) + print stack + return max(stack) + +input() +inp = raw_input().split(" ") +looked= [] +large = 0 +for j,i in enumerate(inp): + if i not in looked: + new = max_funny(inp[:] , j ) + looked.append(i) + if(new > large):large = new +print new \ No newline at end of file diff --git a/November_easy_hackerearth/max_inser.py b/November_easy_hackerearth/max_inser.py new file mode 100644 index 0000000..c01f5d3 --- /dev/null +++ b/November_easy_hackerearth/max_inser.py @@ -0,0 +1,16 @@ + +val = input() +uniq = [] +current = [] +series = [0] +for temp in range(val): + i , j , k = map(int , raw_input().split(" ")) + if(i in current):series.append(series[0]);series[0] = 0 + current.append(i) + series[0] += 1 + out = 0 + print series + for lim in range(j,k+1): + for t in series: + if(t >= lim ):out = out + (t//lim) + print out \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..521875d --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +# Competitive_solutions +All my competitive programming Solutions diff --git a/Select_city.py b/Select_city.py new file mode 100644 index 0000000..b50ace9 --- /dev/null +++ b/Select_city.py @@ -0,0 +1,40 @@ +''' +James has decided to take a break from his work. He makes a plan to visit India for a few days with his family. He knows a lot about India, and also about the various cities he could visit. He decides to write down all the cities on a paper. Let the number of cities be n. Now, he shows the list to his wife and asks her, the city/cities she wants to visit. He tells her that she can select any city/cities and any number of cities. The wife says, she needs a day to decide. + +After this, James calls his son and tells him all about the trip, and the list of cities. He gives him a task and asks him, the number of ways the city/cities can be chosen from the list, if the total number of cities written on the list is n. The cities are numbered from 1 to n. At least 1 city has to be selected. + +He now asks your help to find the answer for the question that was asked to him. +The problem consists of a number of test cases. + +INPUT: +The first line of input contains the number of test cases t. +Then t lines follow, each contains a number n, the number of cities. + +OUTPUT: +Output contains t lines; each line contains the answer for that test case. As the answer can be large, print the answer modulo 10^9+7 + +CONSTRAINTS +1<=t<=100000 +1<=n<=1012 + +Tester: +SAMPLE INPUT +2 +2 +1 +SAMPLE OUTPUT +3 +1 +Explanation +For test case 1: The only ways to select the cities is 1 2 1 2 Therefore the answer is 3. + +For test case 2: The only way to select a city is 1 Therefore the answer is 1. + +Source : Hacker Earth + +''' + +def find(num): + return (2 ** num - 1) % 10**9+7 +for loop in range(input()): + print find(input()) diff --git a/Sieve_prime_Check.py b/Sieve_prime_Check.py new file mode 100644 index 0000000..964f133 --- /dev/null +++ b/Sieve_prime_Check.py @@ -0,0 +1,30 @@ +''' + +The Sieve Method to Find if a number is prime or not + +''' + +all_num = {} #This dict will store all final results i.e which all numbers are prime or not + +def sieve_check(num): + for i in xrange(2,int(num ** 0.5)): + if(all_num.get(i,0) == 0): + for k in xrange(2,num): + if(i*k > num):break + all_num[i*k] = 1 + if(num % k == 0):return + + +def normal_prime(num): + if(num < 3 ):return 1 + if(num % 2 == 0 ):return 0 + for i in xrange(3,int(num ** 0.5)+1,2): + if(num % i == 0):return 0 + return 1 + +for i in range(input()): + if(normal_prime(input()) == 1): + print "prime" + else: + print "composite" +#print sieve_check(3659707955798852) \ No newline at end of file diff --git a/Tcs_CodeVita_2017_Round2/.aesthetic_building.py.swp b/Tcs_CodeVita_2017_Round2/.aesthetic_building.py.swp new file mode 100644 index 0000000000000000000000000000000000000000..da96d0432116a76db11866ef8e8394d7ab474d20 GIT binary patch literal 12288 zcmeI2&x+JQ5XO5w=xJTqJqzV5LT6?&`J=Efkb|rj55gikAi50MNzY7U(rMD2S!H2; z0$)H81aF>v1|LH30X+Eum>0z0PiL~i74x@wVqq0_69Hhe7C1%W~C$-Eo^p5naO)sTqM1Tl%1h(0oI11fn zzjq7vcApR#B0vO)01+SpM1Tko0U|&I{v!fbZ?V@n@0D)m-R{2i+r8V;jR+6{B0vO) z01+SpM1Tko0U|&IhyW4z2MMGZV;{E}yLKI$$KU@izW=}PF!l}g33Z0bQ7=%>QAeno zs2`Z~74;USPzkD!0@NPL)x3(LAOb{y2oM1xKm>>Y5g-CYfCvzQzlH!{SXl@^iI`iv z(5W%ZEktg_xLLWKuB5VHMWNS6ZZk@?7AoUasuqI7D$QZ&uD+^^AcmnIdEPGxkU;C@ zYnL~O+N42r>2;M7DAJew;ve7USyS^Ey_ZM4IrG4ej@w*0cSmqLh9rT|YX?~So06Kl zQHI#Z=~OCRTkegF&ZXr&=ymP78u*^nh(Ag>UCLZED96kJ#iXt>eivg@!q$}nQx|I( zxJH+|4uD5t7(ySon>QLt5BhzGJ@BBh&&vuV7VOA1U3Ja*Fwe`fGT1DlZl`T4hb$9w Rm`jz-N@ICz8@gPy{RFq^$x#3R literal 0 HcmV?d00001 diff --git a/Tcs_CodeVita_2017_Round2/aesthetic_building.py b/Tcs_CodeVita_2017_Round2/aesthetic_building.py new file mode 100644 index 0000000..217e7b1 --- /dev/null +++ b/Tcs_CodeVita_2017_Round2/aesthetic_building.py @@ -0,0 +1,23 @@ +def findcost(floors,base): + sum = 0 + for i in range(base , base - floors , -1): + sum = sum + (1000 * (max(1,i) ** 2) ) + return sum + +time = input() +while time: + num , base = map(int , raw_input().strip().split(" ")) + buildings = map(int , raw_input().strip().split(" ")) + if(num %2 == 0): + val = max(buildings[num/2] , buildings[(num/2) -1]) + temp = range((val-num/2)+1 , val+1) + temp.extend(range( val , val-num/2 ,-1)) + else: + val = buildings[num/2] + temp = range((val-num/2) , val) + temp.extend(range( val , val-num/2 -1 ,-1)) + out = 0 + for i in range(0,num): + out = out + findcost((temp[i] - buildings[i]) , base) + time-=1 + print out \ No newline at end of file diff --git a/Tcs_CodeVita_2017_Round2/antidote.py b/Tcs_CodeVita_2017_Round2/antidote.py new file mode 100644 index 0000000..2772273 --- /dev/null +++ b/Tcs_CodeVita_2017_Round2/antidote.py @@ -0,0 +1,174 @@ +size = input() +temp = size +grid = [] +while temp: + grid.append(map(int,raw_input().strip().split(" "))) + temp-=1 +posinf = map(int,raw_input().strip().split(" ")) +poscur = map(int,raw_input().strip().split(" ")) +posinf[0] = posinf[0]- 1 +posinf[1] = posinf[1] -1 + +poscur[0] = poscur[0]- 1 +poscur[1] = poscur[1] -1 + +infected = [[posinf[0] , posinf[1]]] + +infque = [] + +def infect(posx,posy,level): + if(level == 2 ):return + if(posx + 1 < size ): + if(grid[posx+1][posy] == 1 ): + if( [posx+1,posy] not in infected ): + grid[posx+1][posy] = level - 1 + infected.append([posx+1,posy]) + infque.append([posx+1,posy,level-1]) + if(posy + 1 < size): + if(grid[posx][posy+1] == 1 ): + if([posx,posy+1] not in infected): + grid[posx][posy+1] = level - 1 + infected.append([posx,posy+1]) + infque.append([posx,posy +1 ,level-1]) + if(posx + 1 < size and posy + 1 < size): + if(grid[posx+1][posy+1] == 1 ): + if([posx+1,posy+1] not in infected): + grid[posx+1][posy+1] = level - 1 + infected.append([posx+1 , posy+1]) + infque.append([posx+1,posy+1,level-1]) + if(posx + 1 < size and posy - 1 >= 0): + if(grid[posx+1][posy-1] == 1 ): + if([posx+1 , posy-1] not in infected): + grid[posx+1][posy-1] = level - 1 + infected.append([posx+1,posy-1]) + infque.append([posx+1,posy -1,level-1]) + if(posx - 1 >= 0 ): + if(grid[posx-1][posy] == 1 ): + if( [posx-1,posy] not in infected ): + grid[posx-1][posy] = level - 1 + infected.append([posx-1,posy]) + infque.append([posx-1,posy,level-1]) + + if(posy - 1 >= 0): + if(grid[posx][posy-1] == 1 ): + if([posx,posy-1] not in infected): + grid[posx][posy-1] = level - 1 + infected.append([posx,posy-1]) + infque.append([posx,posy - 1,level-1]) + if(posx - 1 >= 0 and posy - 1 >= 0): + if(grid[posx-1][posy-1] == 1 ): + if([posx-1,posy-1] not in infected): + grid[posx-1][posy-1] = level - 1 + infected.append([posx-1 , posy-1]) + infque.append([posx-1,posy -1,level-1]) + if(posx - 1 >= 0 and posy + 1 < size): + if(grid[posx-1][posy+1] == 1 ): + if([posx-1 , posy+1] not in infected): + grid[posx-1][posy+1] = level - 1 + infected.append([posx-1,posy+1]) + infque.append([posx-1,posy+1,level-1]) + if(len(infque) > 0): + a = infque[0][0] + b = infque[0][1] + c = infque[0][2] + del infque[0] + infect(a,b,c) + return + +cured = [[poscur[0] , poscur[1]]] +curque = [] + +def cure(posx,posy,level): + if(posx + 1 < size ): + if(grid[posx+1][posy] > 1 ): + if( [posx+1,posy] not in cured ): + if(level == 1 ): + grid[posx+1][posy] = 1 + else: + grid[posx+1][posy] = grid[posx+1][posy] - 1 + cured.append([posx+1,posy]) + curque.append([posx+1,posy,level+1]) + if(posy + 1 < size): + if(grid[posx][posy+1] > 1 ): + if([posx,posy+1] not in cured): + if(level == 1 ): + grid[posx][posy+1] = 1 + else: + grid[posx][posy+1] = grid[posx][posy+1] - 1 + cured.append([posx,posy+1]) + curque.append([posx,posy +1 ,level+1]) + if(posx + 1 < size and posy + 1 < size): + if(grid[posx+1][posy+1] > 1 ): + if([posx+1,posy+1] not in cured): + if(level == 1 ): + grid[posx+1][posy+1] = 1 + else: + grid[posx+1][posy+1] = grid[posx+1][posy+1] - 1 + cured.append([posx+1 , posy+1]) + curque.append([posx+1,posy+1,level+1]) + if(posx + 1 < size and posy - 1 >= 0): + if(grid[posx+1][posy-1] > 1 ): + if([posx+1 , posy-1] not in cured): + if(level == 1 ): + grid[posx+1][posy-1] = 1 + else: + grid[posx+1][posy-1] = grid[posx+1][posy-1] - 1 + cured.append([posx+1,posy-1]) + curque.append([posx+1,posy -1,level+1]) + if(posx - 1 >= 0 ): + if(grid[posx-1][posy] > 1 ): + if( [posx-1,posy] not in cured ): + if(level == 1 ): + grid[posx-1][posy] = 1 + else: + grid[posx-1][posy] = grid[posx-1][posy] - 1 + cured.append([posx-1,posy]) + curque.append([posx-1,posy,level+1]) + + if(posy - 1 >= 0): + if(grid[posx][posy-1] > 1 ): + if([posx,posy-1] not in cured): + if(level == 1 ): + grid[posx][posy-1] = 1 + else: + grid[posx][posy-1] = grid[posx][posy-1] - 1 + cured.append([posx,posy-1]) + curque.append([posx,posy - 1,level+1]) + if(posx - 1 >= 0 and posy - 1 >= 0): + if(grid[posx-1][posy-1] > 1 ): + if([posx-1,posy-1] not in cured): + if(level == 1 ): + grid[posx-1][posy-1] = 1 + else: + grid[posx-1][posy-1] = grid[posx-1][posy-1] - 1 + cured.append([posx-1 , posy-1]) + curque.append([posx-1,posy -1,level+1]) + if(posx - 1 >= 0 and posy + 1 < size): + if(grid[posx-1][posy+1] > 1 ): + if([posx-1 , posy+1] not in cured): + if(level == 1 ): + grid[posx-1][posy+1] = 1 + else: + grid[posx-1][posy+1] = grid[posx-1][posy+1] - 1 + cured.append([posx-1,posy+1]) + curque.append([posx-1,posy+1,level+1]) + if(len(curque) > 0): + a = curque[0][0] + b = curque[0][1] + c = curque[0][2] + del curque[0] + cure(a,b,c) + return + +def prgrid(): + for i in grid: + for k in i: + print k, + print + +grid[posinf[0]][posinf[1]] = 5 +infect(posinf[0],posinf[1],6) +grid[poscur[0]][poscur[1]] = 1 +cure(poscur[0] , poscur[1] , 1) +prgrid() + diff --git a/Tcs_CodeVita_2017_Round2/enclosing_items.py b/Tcs_CodeVita_2017_Round2/enclosing_items.py new file mode 100644 index 0000000..b40969e --- /dev/null +++ b/Tcs_CodeVita_2017_Round2/enclosing_items.py @@ -0,0 +1,30 @@ +symb = ["(", ")", "{", "}" ,"[" ,"]" ,"<" ,">", "/","\\"] +open_tag = ["(", "{" ,"[" ,"<" , "/"] +close_tag = [ ")", "}" ,"]" ,">" ,"\\"] + +dic_sym = { ")" : "(" , "}" : "{" , "]" : "[" , ">" : "<" , "\\" : "/" } + +times = input() +while times: + data = raw_input() + string = "" + inside = 0 + for i in range(0,len(data)): + try: + if(data[i] == "@" and data[i+1] == "*"):inside+=1 + if(data[i] == "*" and data[i+1] == "@"):inside-=1 + except: + pass + if inside == 0 and data[i] in symb : string = string + data[i] + out = "True" + tags = [""] + for i in string: + if i in open_tag: + tags.append(i) + elif i in close_tag: + rev = dic_sym.get(i) + if(rev == tags[-1] and len(tags) > 0):del tags[-1] + else: out = "False" + if len(tags) > 1: out = "False" + print out + times-=1 \ No newline at end of file diff --git a/Tcs_CodeVita_2017_Round2/photograph.py b/Tcs_CodeVita_2017_Round2/photograph.py new file mode 100644 index 0000000..3097172 --- /dev/null +++ b/Tcs_CodeVita_2017_Round2/photograph.py @@ -0,0 +1,33 @@ + +def varience(results): + # calculate mean + m = sum(results) / len(results) + + # calculate variance using a list comprehension + return (sum([(xi - m)**2 for xi in results]) / len(results)) + + +inputs = raw_input().split(",") +data = list(map(int , raw_input().split(","))) +"""data_sort = list(data) +data_sort.sort() +print(data_sort) + +print("Printing Varience") +print(data) +print("\n" + str(statistics.stdev(data) ) ) + +sd = statistics.stdev(data) +var = {} +for i in data: + val = 0 + for k in data: + if( ((i -k) **2 )< (sd ** 2) ):continue + val = val + ((i - k) ** 2) + var[i] = val +print(var)""" + +import itertools +dictout = {} +temp = list(itertools.combinations(data,int(inputs[1]),3)) +print temp diff --git a/Xtreme/Jarawi and The Interview.py b/Xtreme/Jarawi and The Interview.py new file mode 100644 index 0000000..3ba16af --- /dev/null +++ b/Xtreme/Jarawi and The Interview.py @@ -0,0 +1,22 @@ + +import re + + +def sequence_in(s1, s2): + """Does `s1` appear in sequence in `s2`?""" + temp = re.findall( + "*".join(s1) , s2) + if(len(temp) >= 1):return True + return False + +maindict = raw_input() +no = input() +for i in range(no): + ans = 0 + sub = "" + temp = raw_input() + for k in range(temp.__len__() - 1 , -1 , -1): + sub = temp[k] + sub + if(sequence_in(sub , maindict )):ans +=1 + else:break + print ans diff --git a/Xtreme/batbear.py b/Xtreme/batbear.py new file mode 100644 index 0000000..099cdf1 --- /dev/null +++ b/Xtreme/batbear.py @@ -0,0 +1,45 @@ +from collections import defaultdict + +class Graph: + def __init__(self, vertices): + self.V = vertices + self.graph = defaultdict(list) + def addEdge(self, v, w): + self.graph[v].append(w) + self.graph[w].append(v) + + + def isCyclicUtil(self, v, visited, parent): + + visited[v] = True + + for i in self.graph[v]: + if visited[i] == False: + if (self.isCyclicUtil(i, visited, v)): + return True + + elif parent != i: + return True + + return False + + def isCyclic(self): + visited = [False] * (self.V) + for i in range(self.V): + if visited[i] == False: + if (self.isCyclicUtil(i, visited, -1)) == True: + return True + + return False + + +inp = input() +for i in range(inp): + lim , gnodes = map(int , raw_input().split(" ")) + g = Graph(lim) + nodes = map(int , raw_input().split(" ")) + while nodes != []: + g.addEdge(nodes[0],nodes[1]) + del nodes[0:2] + if(g.isCyclic()):print"1" + else:print "0" \ No newline at end of file diff --git a/Xtreme/beetlebag.py b/Xtreme/beetlebag.py new file mode 100644 index 0000000..c892e29 --- /dev/null +++ b/Xtreme/beetlebag.py @@ -0,0 +1,40 @@ +def finder(lis , pos,value): + for i,j in enumerate(lis): + if(j[pos] == value): + return i + return -1 + +def finder2(lis , pos,value,pos2,value2): + for i,j in enumerate(lis): + if(j[pos] == value and j[pos2] == value2): + return i + return -1 + +for i in range(input()): + tweight ,no = map(int , raw_input().split(" ")) + lis = [] + for k in range(no): + a,b = map(int , raw_input().split(" ")) + lis.append((b/(a*1.0) , a , b)) + tp = 0 + ans = 0 + while tweight > 0 : + if(no == 0):break + try: + pos = finder(lis , 0 ,(max(map(lambda x: x[0], lis)))) + val = lis[pos][0] + except: + break + + if len([x for x in lis if x[0] == val ]) > 1: + test = [x[2] for x in lis if x[0] == val ] + maxval = max(test) + pos = finder2(lis , 0 , val , 2 , maxval) + val = lis[pos] + if(lis[pos][1] <= tweight ): + tweight = tweight - lis[pos][1] + ans += lis[pos][2] + no -= 1 + del lis[pos] + + print ans \ No newline at end of file diff --git a/Xtreme/cheering_up_bob.py b/Xtreme/cheering_up_bob.py new file mode 100644 index 0000000..c7db700 --- /dev/null +++ b/Xtreme/cheering_up_bob.py @@ -0,0 +1,36 @@ +moves = {} +for i in range(1,10): + moves[i] = map(int , raw_input().split(" ")) + +board = ['-'] * 10 + +def CheckWin(): + if(board[0] == board[1] and board[1] == board[2] and board[0] == 'X'): + return [0,1,2] + elif(board[3] == board[4] and board[4] == board[5] and board[3] == 'X'): + return [3, 4, 5] + elif(board[6] == board[7] and board[7] == board[8] and board[6] == 'X'): + return [6, 7, 8] + elif(board[0] == board[3] and board[3] == board[6] and board[0] == 'X'): + return [0, 3, 6] + elif(board[1] == board[4] and board[4] == board[7] and board[1] == 'X'): + return [1, 4, 7] + elif(board[2] == board[5] and board[5] == board[8] and board[2] == 'X'): + return [2, 5, 8] + elif(board[0] == board[4] and board[4] == board[8] and board[4] == 'X'): + return [0, 4, 8] + elif(board[2] == board[4] and board[4] == board[6] and board[4] == 'X'): + return [2, 4, 6] + return False + +def dicttonum(lis): + return ((lis[0] - 1) * 3) + (lis[1] -1) + +for i in range(1,10): + print dicttonum(moves[i]) + board[dicttonum(moves[i])] = "X" + winningpos = CheckWin() + print board + if CheckWin() != False:print i ; break + +print winningpos \ No newline at end of file diff --git a/Xtreme/circular_disk.py b/Xtreme/circular_disk.py new file mode 100644 index 0000000..3c718d8 --- /dev/null +++ b/Xtreme/circular_disk.py @@ -0,0 +1,21 @@ +import string +import math + +rad = input() +dict = {} +for i in range(26): + char , val = raw_input().split(" ") + dict[char.lower()] = float(val) +inp = raw_input().strip() +prev = '' +out = 0 +for i in inp: + i = i.lower() + if(i not in string.lowercase):continue + if(i == prev):continue + if(prev == ''):prev = i ; out += rad ;continue + temp = abs(( 2 * rad * math.sin(math.radians(abs(dict[prev] - dict[i]) / 2)))) + out = out + temp + prev = i + +print int(math.ceil(out)) \ No newline at end of file diff --git a/Xtreme/dr.fibonacci.py b/Xtreme/dr.fibonacci.py new file mode 100644 index 0000000..ef57e29 --- /dev/null +++ b/Xtreme/dr.fibonacci.py @@ -0,0 +1,9 @@ + +def fib(n): + a,b,c = 0,1,0 + while c < n: + a, b , c = b, a + b , c+1 + return b + +inp = input() +for i in range(inp):print (fib(input() % 60) % 10) diff --git a/Xtreme/factorial.py b/Xtreme/factorial.py new file mode 100644 index 0000000..d000785 --- /dev/null +++ b/Xtreme/factorial.py @@ -0,0 +1,6 @@ +import math + +for i in range(0,20): + print math.factorial(i) + + #371842544 \ No newline at end of file diff --git a/Xtreme/fast_and_curious.py b/Xtreme/fast_and_curious.py new file mode 100644 index 0000000..a8fd2f4 --- /dev/null +++ b/Xtreme/fast_and_curious.py @@ -0,0 +1,73 @@ +looped = [] + +class graph: + def __init__(self): + self.neighbors = {} + + def add_vertex(self, v): + if v not in self.neighbors: + self.neighbors[v] = [] + + def add_edge(self, u, v): + self.neighbors[u].append(v) + # if u == v, do not connect u to itself twice + if u != v: + self.neighbors[v].append(u) + + def vertices(self): + return list(self.neighbors.keys()) + + def vertex_neighbors(self, v): + return self.neighbors[v] + +def is_cyclic_graph(G): + Q = [] + V = G.vertices() + + layer = {v: -1 for v in V} + + for v in V: + layer = {v: -1 for v in V} + # v has already been explored; move on + if layer[v] != -1: + continue + + # take v as a starting vertex + layer[v] = 0 + Q.append(v) + + # as long as Q is not empty + while len(Q) > 0: + + # get the next vertex u of Q that must be looked at + u = Q.pop(0) + + C = G.vertex_neighbors(u) + for z in C: + # if z is being found for the first time + if layer[z] == -1: + layer[z] = layer[u] + 1 + Q.append(z) + elif layer[z] >= layer[u]: + looped.append(z) + + + + + +maxval , no = map(int , raw_input().split(" ")) + +g = graph() + +for i in range(1,no+1): + g.add_vertex(i) + +for i in range(no): + a,b = map(int , raw_input().split(" ")) + g.add_edge(a,b) + +is_cyclic_graph(g) + +val = set(range(1,no)) - set(looped) + +for i in val :print i diff --git a/Xtreme/odd_paths.py b/Xtreme/odd_paths.py new file mode 100644 index 0000000..e5a1fe5 --- /dev/null +++ b/Xtreme/odd_paths.py @@ -0,0 +1,40 @@ +from collections import defaultdict + +looped = [] + +class Graph: + def __init__(self, vertices): + self.V = vertices + self.graph = defaultdict(list) + + def addEdge(self, v, w): + self.graph[v].append(w) + self.graph[w].append(v) + + + + def Checker(self , listvertex ,visited, pvertex,level): + for i in listvertex: + if(i == pvertex ):looped.append(level);return + if(i in visited): continue + visited.append(i) + self.Checker(self.graph[i],visited[:],pvertex,level + 1) + return False + + def CheckCycle(self,vertex): + return self.Checker(self.graph[vertex] , [vertex] , vertex,1) + + +maxval , no = map(int , raw_input().split(" ")) + +g = Graph(no) + +for i in range(no): + a,b = map(int , raw_input().split(" ")) + g.addEdge(a, b) + +for i in range(1,maxval+1): + g.CheckCycle(i) + + +out = set(range(1,maxval+1)) - set(looped) \ No newline at end of file diff --git a/Xtreme/pre1.py b/Xtreme/pre1.py new file mode 100644 index 0000000..b4d2a09 --- /dev/null +++ b/Xtreme/pre1.py @@ -0,0 +1,37 @@ +from collections import defaultdict + +class Graph: + def __init__(self, vertices): + self.V = vertices + self.graph = defaultdict(list) + + def addEdge(self, v, w): + self.graph[v].append(w) + self.graph[w].append(v) + + def Checker(self , listvertex ,visited, pvertex,level): + for i in listvertex: + if(i == pvertex and level > 2):return True + if(i in visited): continue + visited.append(i) + return self.Checker(self.graph[i],visited,pvertex,level + 1) + return False + + def CheckCycle(self,vertex): + return self.Checker(self.graph[vertex] , [] , vertex,1) + + +maxval , no = map(int , raw_input().split(" ")) + +g = Graph(no) + +for i in range(no): + a,b = map(int , raw_input().split(" ")) + g.addEdge(a, b) + +out = [] + +for i in range(1,maxval+1): + if(g.CheckCycle(i) == False):out.append(i) + +for i in out:print i \ No newline at end of file diff --git a/Xtreme/quipu func.py b/Xtreme/quipu func.py new file mode 100644 index 0000000..4b287ba --- /dev/null +++ b/Xtreme/quipu func.py @@ -0,0 +1,15 @@ +def count(n,div): + out = 0 + for i in range(1,n+1): + if(i % div == 0):continue + if(n% i == 0):out += 1 + return out + +no , a , b = map(int,raw_input().split()) + +for i in range(no): + pd = input() + final = 0 + for k in range(a,b+1): + final += count(k,pd) + print final diff --git a/Xtreme/rexor.py b/Xtreme/rexor.py new file mode 100644 index 0000000..e3c7e75 --- /dev/null +++ b/Xtreme/rexor.py @@ -0,0 +1,48 @@ + +def moduleu0(num,length,offset): + while num > length + offset: + + num = num - length + return num + +def minsize(d1,d2,l): + temp = 0 + while d2 > d1: + temp = d2 + d2 -= l + return temp - d1 + +no = input() + + +def f(n): + if (n % 4 == 0): + return n + elif (n % 4 == 1): + return 1 + elif (n % 4 == 2): + return n + 1 + elif (n % 4 == 3): + return 0 + + +for i in range(no): + l,h,n,d1,d2 = map(int , raw_input().split(" ")) + #testing the pos of diagonals + if(moduleu0(d1,l,n) > (l + n)/2 ): + newd1 , newd2 = d1,d2 + while d2 > d1 : d2 = d2 - l + while newd1 < newd2 : newd1 = newd1 + l + d1,d2 = d2,newd1 + remove = [] + minisize = minsize(d1,d2,l) + while d1 b): + a = a//2 + else: + b = b//2 + + + +inp = input() +for i in range(inp): + a,b = map(int ,raw_input().split(" ")) + lca = findlca(a,b) + print int(math.log(a,2)) + int(math.log(b,2)) - (2 * int(math.log(max(lca,1),2) )) + diff --git a/Xtreme/xor.py b/Xtreme/xor.py new file mode 100644 index 0000000..58fb3ee --- /dev/null +++ b/Xtreme/xor.py @@ -0,0 +1,13 @@ +def f(n): + if(n%4 == 0):return n + elif(n%4==1):return 1 + elif(n%4==2):return n+1 + elif(n%4==3):return 0 + +def answer(start,length): + result = 0 + for i in xrange(length): + result = result ^ f((start + i*length ) -1) ^ f(start + (i+1)*length -(i+1)) + return result + +print answer(17,4000000) \ No newline at end of file diff --git a/Xtreme/xtreme_study.py b/Xtreme/xtreme_study.py new file mode 100644 index 0000000..0a7e2cf --- /dev/null +++ b/Xtreme/xtreme_study.py @@ -0,0 +1,30 @@ +dictionary = {} + +temp = [] + +while True: + val = raw_input() + if(val == ""):break + splitted = val.split(" ") + temp.append((int(splitted[0]) , splitted[1:])) + +temper = [] + +for i in temp: + for k in i[1]: + if(k not in temper):temper.append(k) + if(len(i[1]) not in dictionary.keys() ):dictionary[len(i[1])] = [] + dictionary[len(i[1])].append(i) + +for i in dictionary.keys(): + dictionary[i] = sorted(dictionary[i], key=lambda t: t[0]) + +low = [] + +need = temper.__len__() + +def lowest(n,have,time): + if(len(have) == need):return + for i in dictionary[n]: + if(list(set(temper) - set(have)) in i[1]):return + for i in range(len(have),need): diff --git a/abel.py b/abel.py new file mode 100644 index 0000000..b128a2b --- /dev/null +++ b/abel.py @@ -0,0 +1,31 @@ +MAX_SIZE = 20232; +isPrime = [] +SPF = [] +prime = [] + +def mani_sieve(N): + isPrime[0] = False + isPrime[1] = False + for i in range(2,N): + if( isPrime[i] ): + prime.append(i) + SPF[i] = i + j = 0 + while j< len(prime) and i*prime[j] = len(st)):return -1 + return st[pos] + +posi = 0 +for i in range(0,max(len(str1),len(str2))): + if(getter(str1,i) != getter(str2,i)):break + posi +=1 +moves = ((len(str1) - posi) + len(str2) - posi) + +check = 0 + +if(moves <= times): + if(moves != times): + if(len(str1) + len(str2) < times): + print "Yes" + check = 1 + elif((moves - times) %2 != 0):print "No";check = 1 + if(check == 0):print "Yes" + else: + print "Yes" +else:print "No" diff --git a/brick_count.py b/brick_count.py new file mode 100644 index 0000000..02846c0 --- /dev/null +++ b/brick_count.py @@ -0,0 +1,42 @@ + +import math + + +def memoize(f): + + class memodict(dict): + def __init__(self, f): + self.f = f + def __call__(self, *args): + return self[args] + def __missing__(self, key): + ret = self[key] = self.f(*key) + return ret + return memodict(f) + + +@memoize +def build_stair(reserve, previous_step): + if reserve == 0: + return 1 + + + min_brick = (-1+math.sqrt(1+8*reserve)) / 2 + min_brick = int(math.ceil(min_brick)) + + if previous_step == -1: + max_bricks = reserve + else: + max_bricks = previous_step + max_bricks = min(max_bricks, reserve+1) + + nb_stairs = 0 + for i in range(min_brick, max_bricks): + nb_stairs += build_stair(reserve-i, i) + return nb_stairs + + +def answer(n): + return build_stair(n, -1) + +print answer(200) \ No newline at end of file diff --git a/choco_hr.py b/choco_hr.py new file mode 100755 index 0000000..726d69f --- /dev/null +++ b/choco_hr.py @@ -0,0 +1,5 @@ +for i in range(0,input()): + s = sum([int(x) for x in raw_input().split("")]) + if(s % 2 == 0 ): + + else:print "Not Possible" \ No newline at end of file diff --git a/comp1.py b/comp1.py new file mode 100644 index 0000000..e69de29 diff --git a/consecletter.py b/consecletter.py new file mode 100755 index 0000000..cf22ca7 --- /dev/null +++ b/consecletter.py @@ -0,0 +1,12 @@ +#for code monk .. P1 Q2pytho + + +for i in range(0,input()): + dat = raw_input() + temp,chk = dat[0],dat[0] + for i in dat[1:]: + if chk != i: + temp = temp + i + chk = i + print temp + diff --git a/die_iem_16.py b/die_iem_16.py new file mode 100755 index 0000000..6f73520 --- /dev/null +++ b/die_iem_16.py @@ -0,0 +1,3 @@ +lis = ["-","Manish","Manish","Deep","Deep","Utsav","Utsav"] +for i in range(0,input()): + print lis[input()] \ No newline at end of file diff --git a/distict.py b/distict.py new file mode 100644 index 0000000..5426130 --- /dev/null +++ b/distict.py @@ -0,0 +1,15 @@ +import base64 + +MESSAGE = ''' +DU4QHRYLBAEaFhAKVk4EGhAJFVVFERdTGQUPDRQPFBdOEQoQUQwQHBANDBcNFhwQUQwFDhoaFQFO +EQoQUQANCwcNBRsLXVUXWklECRYACBcfVF1VGB1ESE9IRgcHXV9THQwHT1lIRgAIU1JZAhpESE9I +RgEIV1UXWklEDhoHRlJTERdHHwdCTwg= +''' + +KEY = 'vichuhari100' + +result = [] +for i, c in enumerate(base64.b64decode(MESSAGE)): + result.append(chr(ord(c) ^ ord(KEY[i % len(KEY)]))) + +print ''.join(result) \ No newline at end of file diff --git a/foobar2.py b/foobar2.py new file mode 100644 index 0000000..c7b455e --- /dev/null +++ b/foobar2.py @@ -0,0 +1,87 @@ +def get_coord(num): + """ + This will serve as a helper function in our algorithm. + We're solving the knight's shortest path problem, so I'm + breaking the input into a grid-like fashion. + """ + x = int(num%8) + y = int((num-x)/8) + return x, y + + +def answer(src, dest): + """ + I'll tackle this problem using recursion and depth-first search. + :param src: The location we begin at. + :param dest: The destination, an integer. + :return: The shortest number of steps required to reach the destination. + """ + class board: + grid = grid = [[0 for col in range(8)] for row in range(8)] + bunks = board() + + def dfs(srcx, srcy, level): + """ + On each iteration of this algorithm, we will check all eight squares + that our knight can reach from our source tile. If they have not + yet been traversed to, we will mark them with our current + recursion level, and then run this algorithm from those tiles. + We use the created grid mapping to determine how many moves are required + to reach dest from src. + :param srcx: x co-ordinate of this recursive iteration + :param srcy: y co-ordinate of this recursive iteration + :param level: how many times we've called this function + :return: nothing + """ + def mark(x, y, level): + if x not in range(8) or y not in range(8): + return + # A helper function mostly to keep our code readable. + # We change the mark on the tile either if we find a larger level, + if bunks.grid[x][y] > level or bunks.grid[x][y] == 0: + bunks.grid[x][y] = level + return True + # This also isn't java, so we're not protected from out-of-bounds accesses. + if srcx not in range(8) or srcy not in range(8): + return + # If the tile's level is not 0 and less than ours, our traversal to this point + # is pointless. We return. + if bunks.grid[srcx][srcy] != 0 and bunks.grid[srcx][srcy] < level-1: + return + # So first, the 8 possibilities. + # We mark up... + mark(srcx-1, srcy+2, level) + mark(srcx+1, srcy+2, level) + # Right... + mark(srcx+2, srcy-1, level) + mark(srcx+2, srcy+1, level) + # Down... + mark(srcx-1, srcy-2, level) + mark(srcx+1, srcy-2, level) + # Then left. + mark(srcx-2, srcy-1, level) + mark(srcx-2, srcy+1, level) + # Then we traverse to these tiles and repeat the algorithm on each one. + dfs(srcx-1, srcy+2, level+1) + dfs(srcx+1, srcy+2, level+1) + dfs(srcx+2, srcy-1, level+1) + dfs(srcx+2, srcy+1, level+1) + dfs(srcx-1, srcy-2, level+1) + dfs(srcx+1, srcy-2, level+1) + dfs(srcx-2, srcy-1, level+1) + dfs(srcx-2, srcy+1, level+1) + + if src == dest: + # If the coordinates are the same, we have no calculations to do. + return 0 + else: + srcx, srcy = get_coord(src) + destx, desty = get_coord(dest) + dfs(srcx, srcy, 1) + print("End grid:") + for num in range(8): + print(bunks.grid[num]) + print("Moves to dest: " + str(bunks.grid[destx][desty])) + return bunks.grid[destx][desty] + +answer(1,57) \ No newline at end of file diff --git a/formula.py b/formula.py new file mode 100755 index 0000000..e69de29 diff --git a/gift_friends.py b/gift_friends.py new file mode 100755 index 0000000..9cf2776 --- /dev/null +++ b/gift_friends.py @@ -0,0 +1,18 @@ +#for code monk .. P1 Q2 + +for i in range(0,input()): + friends,gift = map(int ,raw_input().split(" ")) + friend_gift = [] + for friend in xrange(0,friends): + friend_gift.append(input()) + print "START" + for val in range(0,friends): + tot_val = 0; + for gifts in friend_gift[val:]: + tot_val = tot_val + int(gifts) + if(tot_val == gift):print "YES" + if(tot_val >= gift):break + if(tot_val == gift):break + if(tot_val != gift ):print "NO" + + diff --git a/google/lead.py b/google/lead.py new file mode 100755 index 0000000..c9541e6 --- /dev/null +++ b/google/lead.py @@ -0,0 +1,22 @@ +val = input() +for k in range(0,val): + dat = [] + lav = input() + for i in range(0,lav): + dat.append(raw_input()) + max_len = 0 + max = "" + new = [] + for i in dat: + p = [] + for l in i: + if(l not in p):p.append(l) + new.append("".join(p)) + for i in new: + if(i.__len__() > max_len): + max_len = i.__len__() + max = i + elif(i.__len__() == max.__len__() and i < max): + max_len = i.__len__() + max = i + print "Case #" +str(k+1) + ": ", dat[new.index(max)] diff --git a/google/rain.py b/google/rain.py new file mode 100755 index 0000000..23e1cb9 --- /dev/null +++ b/google/rain.py @@ -0,0 +1,23 @@ +import copy + +val = input() +for m in range(0,val): + dat = raw_input().split(" ") + wat = [] + for i in range(0,int(dat[0])): + wat.append(raw_input().split(" ")) + small = 1001 + for i in range(1,int(dat[1]) -1): + if(int(wat[0][i]) < small ):small = int(wat[0][i]) + for i in range(1,int(dat[1]) -1): + if(int(wat[-1][i]) < small ):small = int(wat[-1][i]) + for i in range(1,int(dat[0]) -1): + if(int(wat[i][0]) < small):small = int(wat[i][0]) + if(int(wat[i][-1]) < small):small = int(wat[i][-1]) + water = 0 + + for i in range(1,int(dat[0]) - 1): + for k in range(1,int(dat[1]) - 1): + if int(wat[i][k]) < small: + water = water + small - int(wat[i][k]) + print "Case #" +str(m+1) + ": ", water,small \ No newline at end of file diff --git a/ict1.py b/ict1.py new file mode 100755 index 0000000..6b3b14e --- /dev/null +++ b/ict1.py @@ -0,0 +1,9 @@ +dat = raw_input() + " :" +val = raw_input() +sum = len(val) * -1 +ans = dat.split(val) +if(len(ans) == 1 ):print "-1" +else: + for i in ans[:-1]: + sum = sum + len(i) + len(val) + print sum \ No newline at end of file diff --git a/ict2.py b/ict2.py new file mode 100755 index 0000000..566f3a4 --- /dev/null +++ b/ict2.py @@ -0,0 +1,12 @@ +import string +low = string.lowercase * 2 +up = string.uppercase * 2 +out = "" +for i in raw_input(): + if(i in low): + out = out + low[low.find(i) + 2] + elif(i in up ): + out = out + up[up.find(i) + 2] + else: + out = out + i +print out \ No newline at end of file diff --git a/ieee_dog_walk.py b/ieee_dog_walk.py new file mode 100755 index 0000000..671a5ca --- /dev/null +++ b/ieee_dog_walk.py @@ -0,0 +1,19 @@ +__author__ = 'vignesh' + +for i in range(0,input()): + dogs,walkers = [int(x) for x in raw_input().split()] + dog_size = [] + for t in range(dogs): + dog_size.append(input()) + dog_size.sort() + grp = dogs/walkers + ans = 0 + for w in range(walkers-1): + val = 0 + + size = dog_size[:grp] + ans = ans + max(size) - min(size) + del dog_size[:grp] + print dog_size + ans = max(dog_size) - min(dog_size) + print ans diff --git a/ieee_food_truck.py b/ieee_food_truck.py new file mode 100755 index 0000000..79d97cc --- /dev/null +++ b/ieee_food_truck.py @@ -0,0 +1,29 @@ +import sys +from math import radians, cos, sin, asin, sqrt + + +def distance(lon1, lat1, lon2, lat2): + lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2]) + diflon = lon2 - lon1 + diflat = lat2 - lat1 + temp1 = sin(diflat/2)**2 + cos(lat1) * cos(lat2) * sin(diflon/2)**2 + temp2 = 2 * asin(sqrt(temp1)) + dist = 6378.137 * temp2 + return dist +''' +18.9778972,72.8321983 +1.0 +Date&Time,Latitude,Longitude,PhoneNumber +10/21/2016 13:34,18.912875,72.822318,9020320100 +10/21/2016 10:35,18.9582233,72.8275845,9020320024 +10/21/2016 15:20,18.95169982,72.83525604,9020320047 +10/21/2016 15:23,18.9513048,72.8343388,9020357980 + +''' + +print distance(18.9778972,72.8321983, 18.97523003,72.83494865) +orglat , orglong = [float(x) for x in raw_input().split(" ")] +dis = float(raw_input()) +raw_input() + + diff --git a/ieee_full_adder.py b/ieee_full_adder.py new file mode 100755 index 0000000..c94772e --- /dev/null +++ b/ieee_full_adder.py @@ -0,0 +1,49 @@ +__author__ = 'vignesh' + +str1 = raw_input() +str2 = raw_input() +str3 = raw_input() +str4 = raw_input() +no,lis = (str1.split(" ")) +no = int(no) +lis = list(lis) * 3 +sum1,sum2 = [],[] +for i in str2.strip(): + sum1.append(i) +for i in str3[1:].strip(): + sum2.append(i) +print sum1,sum2 +if(len(sum1) > len(sum2)):sum1,sum2 = sum2,sum1 +length = len(sum2) +dat = [0] * length +ans = [] +index = 0 +while len(sum2) != 0: + dat1 = 0 + val1,val2 = "","" + if(len(sum1) != 0 ): + val1 = sum1[-1] + dat1 = lis.index(str(val1)) + if(len(sum1) == 1): sum1 = [] + else:del sum1[-1] + val2 = sum2[-1] + del sum2[-1] + dat2 = lis.index(str(val2)) + dat[index] + sum = dat1 + dat2 + if(sum >= no ): + diff = (sum) / no + fsum = sum - (no * diff) + value = fsum + if(index +1 != length): + dat[index+1] =dat[index+1] + diff + else: + dat.append(no) + ans.append(lis[sum]) + index = index + 1 +ans.reverse() +print str1 +print str2 +print str3 +print str4 +ansprint = " " + ''.join(ans) +print ansprint \ No newline at end of file diff --git a/ieee_password.py b/ieee_password.py new file mode 100755 index 0000000..55def00 --- /dev/null +++ b/ieee_password.py @@ -0,0 +1,17 @@ +import copy +import string +lower = string.lowercase * 2 +password = list(raw_input()) +current = copy.deepcopy(password) +for i in xrange(input()): + values = raw_input().split(" ") + values = [int(x)-1 for x in values] + if(values[0] == 0): + if(current[values[1]:values[2]+1] == current[values[3]:values[3]+(values[2] - values[1] + 1) ]): + print "Y" + else: + print "N" + if(values[0] == 1): + current[values[1]:values[2] +1] = current[values[3]:values[3]+(values[2] - values[1] + 1) ] + if(values[0] == 2): + current[values[1]:values[2] +1] = [lower[lower.index(x) + 1] for x in current[values[1]:values[2] +1]] diff --git a/ieee_petals.py b/ieee_petals.py new file mode 100755 index 0000000..be9a38a --- /dev/null +++ b/ieee_petals.py @@ -0,0 +1,10 @@ +import math +for i in range(input()): + val = int(raw_input()) + root = long(math.log(val,2)) + num = long(val) - ((2 ** root)) + if(num < 0 ):num = long(val) - ((2 ** (root-1))) + print (2*num)+1 + + + diff --git a/ieee_prime.py b/ieee_prime.py new file mode 100755 index 0000000..7a7a287 --- /dev/null +++ b/ieee_prime.py @@ -0,0 +1,17 @@ +def p(n): # will print out primes between 0 and n + s=[True]*(n/2) + for i in xrange(int((n/2-1)/2) >> 1): + for j in xrange((i*(i+3)<<1)+3,n/2,(i<<1)+3): s[j]=False + return [2] + [((i<<1)+3) for i in xrange(n/2) if (s[i])] + +def primechk(val,prime): + for i in prime: + for k in prime: + temp = val -i-k + if( temp in prime and temp != i and temp != k and i !=k ): + print i , k , (temp) + return 0 + return 0 +val = input() +prime = p(val)[2:] +primechk(val,prime) \ No newline at end of file diff --git a/ieee_stone.py b/ieee_stone.py new file mode 100755 index 0000000..77c354c --- /dev/null +++ b/ieee_stone.py @@ -0,0 +1,14 @@ +t = input() +for i in range(0,t): + no = input() + turns = 0 + for j in range(0,no): + pile = input() + pile_stone = [int(x) for x in raw_input().split()] + for k in range(0,pile): + if pile_stone[k]>1: + turns += (pile_stone[k]-1)/2 + if turns % 2 == 0: + print 'Bob' + else: + print 'Alice' \ No newline at end of file diff --git a/lambs.py b/lambs.py new file mode 100644 index 0000000..9ac6d56 --- /dev/null +++ b/lambs.py @@ -0,0 +1,36 @@ +def fib(limit): + if (limit < 2): + return 1; + n_1 = 1 + n_2 = 1; + times = 2 + sum = 2 + while True : + n_new = n_1 + n_2; + n_1 = n_2; + n_2 = n_new; + sum += n_new + if(sum > limit ):break + times += 1 + return times; + +def power(limit): + mul = 0 + sum = 0 + while True: + sum = sum + 2 ** mul + if(sum > limit):break + mul += 1 + sum = sum - 2 ** mul + if(limit - sum >= (2** (mul-1) + 2** (mul -2) )): mul+=1 + return mul + +def answer(total_lambs): + if total_lambs >= 10 and total_lambs <= 10 ** 9: + return fib(total_lambs) - power(total_lambs) + return 0 + +print answer(13) + +print "max " , fib(13) +print "min " , power(13) \ No newline at end of file diff --git a/luggage.py b/luggage.py new file mode 100755 index 0000000..f07b73f --- /dev/null +++ b/luggage.py @@ -0,0 +1,15 @@ +#for code monk .. P2 Q2 + +for i in range(0,input()): + friends = input() + friend_weight = [] + for friend in xrange(0,friends): + friend_weight.append(input()) + out = [] + for k in range(0,friends): + temp = 0 + for day in friend_weight[k:]: + if(day < friend_weight[k]): + temp = temp +1 + out.append(temp) + print ' '.join([str(x) for x in out]) \ No newline at end of file diff --git a/max_val.py b/max_val.py new file mode 100755 index 0000000..7f68810 --- /dev/null +++ b/max_val.py @@ -0,0 +1,33 @@ +data = raw_input().split(" ") +wl = int(data[0]) +ar = int(data[1]) +print type(wl),type(ar) +def suf_area(l,b,h): + return (2*l*b) + (2*b*h) + (2*l*h) +def vol(n): + return n[0]*n[1]*n[2] +def approxans(val,wl): + if(val <= wl and val + .1 >= wl):return True + return False +max_val = [0] * 3 +lc = 0.01 +h,l,b=0,0,0 +loop = 0 +while True: + loop+=1 + print "CH " ,loop + l = l + 0.1 + if(4*(b+l+h) > wl):break + while True: + h = h + 0.1 + if(4*(b+l+h) > wl):h=0;break + while True: + b = b+0.1 + if((4*(b+l+h)) != float(wl)): + if((4*(b+l+h)) > wl):print "brocken at" , l , " " , h , " " , b;b=0;break + print l ," ",h," ",b + if(vol(max_val) < vol([l,b,h]) and approxans(suf_area(l,b,h),ar) and approxans(4*(l+b+h),wl)): + print l,b,h + max_val = [l,b,h] +print vol(max_val) +print max_val \ No newline at end of file diff --git a/merger.py b/merger.py new file mode 100755 index 0000000..8952e78 --- /dev/null +++ b/merger.py @@ -0,0 +1,18 @@ +#for code monk .. P2 Q3 + +for i in range(0,input()): + raw_input() + arr1 = [int(x) for x in raw_input().split(" ")] + arr2 = [int(x) for x in raw_input().split(" ")] + arr1.append(-1) + arr2.append(-1) + a1,a2 = 0,0 + while True: + if(arr1[a1] == -1 and arr2[a2] == -1):break + if(arr1[a1] > arr2[a2]): + print arr1[a1], + a1 = a1+1 + else: + print arr2[a2], + a2 = a2+1 + print "" diff --git a/misc.py b/misc.py new file mode 100755 index 0000000..38f3999 --- /dev/null +++ b/misc.py @@ -0,0 +1,21 @@ +b = 28 +s = 22 +n=int(input()) +lis = ['6', str(b)] +a=[] +for i in range(103): + s += 16 + b += s + lis.append(b) +for i in range(len(lis)): + a.append(('0' * (5 - len(str(lis[i]))))+str(lis[i])) +k=0 + + + +for i in range(0,n+1): + if (i!=0):print(' ' * (n - i), end="") + for j in range(0,i): + print( a[k], end=" ") + k+=1 + if(i != 0):print('') diff --git a/monk_in_grass.py b/monk_in_grass.py new file mode 100755 index 0000000..1b3bb98 --- /dev/null +++ b/monk_in_grass.py @@ -0,0 +1,43 @@ +#for code monk .. P2 Q4 + + +def sum_row_col(arr,time): + row,col = [],[] + for x in range(0,time): + r,c=0,0 + for y in range(0,time): + r = r + data[x][y] + c = c + data[y][x] + row.append(r) + col.append(c) + return [row,col] + +for i in range(0,input()): + time,lim = (int(x) for x in raw_input().split(" ")) + data = [] + ans = 0 + for tim in range(0,time): + data.append([int(x) for x in raw_input().split(" ")]) + row,col = sum_row_col(data,time) + while lim != 0: + lim-=1 + mc = min(col) + mr = min(row) + if(mc == mr): + if(sum(col) < sum(row)): + ans += mc + col[col.index(mc)] += time + for tim in range(0,time):row[tim] +=1 + else: + ans += mr + for tim in range(0,time):col[tim] +=1 + row[row.index(mr)] += time + elif(mc < mr): + ans += mc + col[col.index(mc)] += time + for tim in range(0,time):row[tim] +=1 + else: + ans += mr + for tim in range(0,time):col[tim] +=1 + row[row.index(mr)] += time + print ans diff --git a/monk_palindrome.py b/monk_palindrome.py new file mode 100644 index 0000000..99154d8 --- /dev/null +++ b/monk_palindrome.py @@ -0,0 +1,15 @@ +n = input() +while n: + val = raw_input() + leng = len(val) - 1 + temp = "".join([ val[leng-x] for x,y in enumerate(val) ]) + # to reverse temp = val[::-1] + if( val == temp): + if(leng % 2 == 0): + print "YES ODD" + else: + print "YES EVEN" + else: + print "NO" + n-=1 + diff --git a/monk_welcome_problem.py b/monk_welcome_problem.py new file mode 100644 index 0000000..242f118 --- /dev/null +++ b/monk_welcome_problem.py @@ -0,0 +1,4 @@ +input() +arr1 = map(int , raw_input().split(" ")) +arr2 = map(int , raw_input().split(" ")) +print " ".join(map(str ,[x + y for x , y in zip(arr1 , arr2) ])) diff --git a/myst_maze.py b/myst_maze.py new file mode 100755 index 0000000..eaa0448 --- /dev/null +++ b/myst_maze.py @@ -0,0 +1,49 @@ +__author__ = 'vignesh' +import copy + +rc = input() +maze = [] +for i in range(rc-1): + maze.append( ["X"] * (rc)) +maze.append(["-"] * rc) + +def mazer(x,y): + if(x == rc- 1): + maze[x][y] = "O" + else: + maze[x][y] = "-" + try: + if(maze[x][y+1] == "X" and maze[x][y-1] == "X" and maze[x-1][y] == "X" and maze[x+1][y] == "X"):return False + except: + pass + for i in range(0,rc): + if(maze[0][i] == "-" ): + if(search(copy.deepcopy(maze),0,i)): + return True + return False + +def search(mazed,x, y): + if mazed[x][y] == "O": + return True + elif mazed[x][y] == "X" or mazed[x][y] == "V": + return False + mazed[x][y] = "V" + + if ((x < len(mazed)-1 and search(mazed,x+1, y)) + or (y > 0 and search(mazed,x, y-1)) + or (x > 0 and search(mazed,x-1, y)) + or (y < len(mazed)-1 and search(mazed,x, y+1))): + return True + return False + +looper = 0 +check = True +while True: + looper+=1 + temp = raw_input() + if(temp == "-1"):break + xv,yv = (int(x) for x in temp.split(" ")) + if(mazer(xv - 1,yv -1)): + print looper;check=False;break +if(check):print -1 + diff --git a/navendu.py b/navendu.py new file mode 100644 index 0000000..f0b3b85 --- /dev/null +++ b/navendu.py @@ -0,0 +1,7 @@ +def answer(x,y): + if(len(y) > len(x)):x,y = y,x + for i in x: + if i not in y:return i + return -1 + +print answer([13,5,6,2,5],[5,2,5,13]) \ No newline at end of file diff --git a/pretty_print.py b/pretty_print.py new file mode 100644 index 0000000..cb51a94 --- /dev/null +++ b/pretty_print.py @@ -0,0 +1,34 @@ +def space1(i,j): + out = "" + for i in range(j-i): + out += " " + return out + +def space2(i): + out = "" + for i in range(0,i*2): + out += " " + return out + +inp = list(raw_input()) +inp.reverse() +output = """""" + +for i,j in enumerate(inp): + l = len(inp) + current = l - i + if(i == 0): + output += space1(i,l) + output += j + "\n" + else: + output += space1(i,l) + output += j + output += space2(i) + output += j + "\n" + +output = output.rstrip() +print output +reverse_style = output.split("\n") +reverse_style.reverse() +for line in reverse_style: + print line \ No newline at end of file diff --git a/primer.py b/primer.py new file mode 100644 index 0000000..a61255e --- /dev/null +++ b/primer.py @@ -0,0 +1,16 @@ +def answer(n): + string = "2357" + num = 10 + while True: + if (prime(num)): string += str(num) + if (len(string) >= 10005): break + num += 1 + ans = 3 + return string[n:n + 5] +import math +def prime(n): + for i in range(2, int(math.sqrt(n)) + 1 ): + if (n % i == 0): return False + return True + +print answer(10000) \ No newline at end of file diff --git a/pytudes/LICENSE b/pytudes/LICENSE new file mode 100644 index 0000000..1e68790 --- /dev/null +++ b/pytudes/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2010-2017 Peter Norvig + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/pytudes/README.md b/pytudes/README.md new file mode 100644 index 0000000..9c1edc8 --- /dev/null +++ b/pytudes/README.md @@ -0,0 +1,75 @@ +# pytudes + +"An *étude* (a French word meaning *study*) is an instrumental musical composition, usually short, of considerable difficulty, and designed to provide practice material for perfecting a particular musical skill." — [Wikipedia](https://en.wikipedia.org/wiki/%C3%89tude) + +This project contains **pytudes**—Python programs for perfecting programming skills. + +Some are in Jupyter (IPython) notebooks, some in `.py` files. You can view the files here, or clone the project, or run the notebooks online by clicking this button: [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/norvig/pytudes/master) + +# Index of Jupyter (IPython) Notebooks + +|Logic and Number Puzzles| +|---| +|[Advent of Code 2017](https://github.com/norvig/pytudes/blob/master/ipynb/Advent%202017.ipynb)
*Puzzle site with a coding puzzle each day for Advent 2017; currently ongoing.*| +|[Advent of Code 2016](https://github.com/norvig/pytudes/blob/master/ipynb/Advent%20of%20Code.ipynb)
*Puzzle site with a coding puzzle each day for Advent 2016*.| +|[Translating English Sentences into Propositional Logic Statements](https://github.com/norvig/pytudes/blob/master/ipynb/PropositionalLogic.ipynb)
*Automatically converting informal English sentences into formal Propositional Logic.*| +|[The Puzzle of the Misanthropic Neighbors](https://github.com/norvig/pytudes/blob/master/ipynb/Mean%20Misanthrope%20Density.ipynb)
*How crowded will this neighborhood be, if nobody wants to live next door to anyone else?*| +|[Countdown to 2016](https://github.com/norvig/pytudes/blob/master/ipynb/Countdown.ipynb)
*Solving the equation 10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016. From an Alex Bellos puzzle.*| +|[Sicherman Dice](https://github.com/norvig/pytudes/blob/master/ipynb/Sicherman%20Dice.ipynb)
*Find a pair of dice that is like a regular pair of dice, only different.*| +|[Beal's Conjecture Revisited](https://github.com/norvig/pytudes/blob/master/ipynb/Beal.ipynb)
*A search for counterexamples to Beal's Conjecture*| +|[When is Cheryl's Birthday?](https://github.com/norvig/pytudes/blob/master/ipynb/Cheryl.ipynb)
*Solving the "Cheryl's Birthday" logic puzzle.*| +|[When Cheryl Met Eve: A Birthday Story](https://github.com/norvig/pytudes/blob/master/ipynb/Cheryl-and-Eve.ipynb)
*Inventing new puzzles in the Style of Cheryl's Birthday.*| +|[Sol Golomb's Rectangle Puzzle](https://github.com/norvig/pytudes/blob/master/ipynb/Golomb-Puzzle.ipynb)
*A Puzzle involving placing rectangles of different sizes inside a square. Bonus: cryptarithmetic.*| +|[WWW: Will Warriors Win?](https://github.com/norvig/pytudes/blob/master/ipynb/WWW.ipynb)
*Golden State Warriors probability of winning the 2016 NBA title.*| + +|Word Games| +|---| +|[Ghost](https://github.com/norvig/pytudes/blob/master/ipynb/Ghost.ipynb)
*The word game Ghost (add letters, try to avoid making a word).*| +|[World's Longest Palindrome](https://github.com/norvig/pytudes/blob/master/ipynb/pal3.ipynb)
*Searching for a long Panama-style palindrome, this time letter-by-letter.*| +|[Refactoring a Crossword Game Program](https://github.com/norvig/pytudes/blob/master/ipynb/Scrabble.ipynb)
*Refactoring the Scrabble / Word with Friends game from Udacity 212.*| +|[xkcd 1313: Regex Golf](https://github.com/norvig/pytudes/blob/master/ipynb/xkcd1313.ipynb)
*Find the smallest regular expression; inspired by Randall Monroe.*| +|[xkcd 1313: Regex Golf (Part 2: Infinite Problems)](https://github.com/norvig/pytudes/blob/master/ipynb/xkcd1313-part2.ipynb)
*Regex Golf: better, faster, funner. With Stefan Pochmann.*| +|[Let's Code About Bike Locks](https://github.com/norvig/pytudes/blob/master/ipynb/Fred%20Buns.ipynb)
*A tale of a bicycle combination lock that uses letters instead of digits. Inspired by Bike Snob NYC.*| +|[Gesture Typing](https://github.com/norvig/pytudes/blob/master/ipynb/Gesture%20Typing.ipynb)
*What word has the longest path on a gesture-typing smartphone keyboard? Inspired by Nicolas Schank and Shumin Zhai.*| +|[How to Do Things with Words, or Statistical Natural Language Processing in Python](https://github.com/norvig/pytudes/blob/master/ipynb/How%20to%20Do%20Things%20with%20Words.ipynb)
*Spelling Correction, Secret Codes, Word Segmentation, and more: grab your bag of words.*| + +|Computer Science Algorithms, Concepts, and Problems| +|---| +|[A Chaos Game with Triangles](https://github.com/norvig/pytudes/blob/master/ipynb/Sierpinski.ipynb)
*A surprising appearance of the Sierpinski triangle in a random walk between vertexes.*| +|[BASIC Interpreter](https://github.com/norvig/pytudes/blob/master/ipynb/BASIC.ipynb)
*How to write an interpreter for the BASIC programming language.*| +|[Bad Grade, Good Experience](https://github.com/norvig/pytudes/blob/master/ipynb/Snobol.ipynb)
*As a student, did you ever get a bad grade on a programming assignment? (Snobol, Concordance)*| +|[Conway's Game of Life](https://github.com/norvig/pytudes/blob/master/ipynb/Life.ipynb)
*The cellular automata zero-player game.*| +|[A Concrete Introduction to Probability](https://github.com/norvig/pytudes/blob/master/ipynb/Probability.ipynb)
*Code and examples of the basic principles of Probability Theory.*| +|[Probability, Paradox, and the Reasonable Person Principle](https://github.com/norvig/pytudes/blob/master/ipynb/ProbabilityParadox.ipynb)
*Some classic paradoxes in Probability Theory, and how to think about disagreements.*| +|[The Convex Hull Problem](https://github.com/norvig/pytudes/blob/master/ipynb/Convex%20Hull.ipynb)
*A classic Computer Science Algorithm.*| +|[The Traveling Salesperson Problem](https://github.com/norvig/pytudes/blob/master/ipynb/TSP.ipynb)
*Another of the classics.*| +|[Economics Simulation](https://github.com/norvig/pytudes/blob/master/ipynb/Economics.ipynb)
*A simulation of a simple economic game.*| +|[Project Euler Utilities](https://github.com/norvig/pytudes/blob/master/ipynb/Project%20Euler%20Utils.ipynb)
*My utility functions for the Project Euler problems, including `Primes` and `Factors`.*| + +# Index of Python Files + +| **File** | **Description** | **Documentation**| +|:--------|:-------------------|----| +|[SET.py](https://github.com/norvig/pytudes/blob/master/py/SET.py)|Analyze the card game [SET](http://www.setgame.com/set).|[SET.html](http://norvig.com/SET.html)| +|[beal.py](https://github.com/norvig/pytudes/blob/master/py/beal.py)|Search for counterexamples to Beal's Conjecture|[beal.html](http://norvig.com/beal.html) +|[docex.py](https://github.com/norvig/pytudes/blob/master/py/docex.py)|A framework for running unit tests, similar to `doctest`.| +|[ibol.py](https://github.com/norvig/pytudes/blob/master/py/ibol.py)|An Exercise in Species Barcoding|[ibol.html](http://norvig.com/ibol.html) +|[lettercount.py](https://github.com/norvig/pytudes/blob/master/py/lettercount.py)|Convert Google Ngram Counts to Letter Counts|[mayzner.html](http://norvig.com/mayzner.html) +|[lis.py](https://github.com/norvig/pytudes/blob/master/py/lis.py)|Lisp Interpreter written in Python|[lispy.html](http://norvig.com/lispy.html) +|[lispy.py](https://github.com/norvig/pytudes/blob/master/py/lispy.py)|Even Better Lisp Interpreter written in Python|[lispy2.html](http://norvig.com/lispy2.html) +|[lispytest.py](https://github.com/norvig/pytudes/blob/master/py/lispytest.py)|Tests for Lisp Interpreters| +|[pal.py](https://github.com/norvig/pytudes/blob/master/py/pal.py)|Find long palindromes|[palindrome.html](http://norvig.com/palindrome.html) +|[pal2.py](https://github.com/norvig/pytudes/blob/master/py/pal2.py)|Find longer palindromes|[palindrome.html](http://norvig.com/palindrome.html) +|[pal3.py](https://github.com/norvig/pytudes/blob/master/py/pal3.py)|Find even longer palindromes|[palindrome.html](http://norvig.com/palindrome.html) +|[py2html.py](https://github.com/norvig/pytudes/blob/master/py/py2html.py)|Pretty-printer to format Python files as html| +|[spell.py](https://github.com/norvig/pytudes/blob/master/py/spell.py)|Spelling corrector|[spell-correct.html](http://norvig.com/spell-correct.html) +|[sudoku.py](https://github.com/norvig/pytudes/blob/master/py/sudoku.py)|Program to solve sudoku puzzles|[sudoku.html](http://norvig.com/sudoku.html) +|[testaccum.py](https://github.com/norvig/pytudes/blob/master/py/testaccum.py)|Tests for my failed Python `accumulation display` proposal|[pyacc.html](http://norvig.com/pyacc.html) +|[yaptu.py](https://github.com/norvig/pytudes/blob/master/py/yaptu.py)|Yet Another Python Templating Utility| + +# Etudes for Programmers + +I got the idea for the "etudes" part of the name from this [1978 book by Charles Wetherell](https://books.google.com/books/about/Etudes_for_programmers.html?id=u89WAAAAMAAJ) +that was very influential to me when I was learning to program. + +![](https://images-na.ssl-images-amazon.com/images/I/51ZnZH29dvL._SX394_BO1,204,203,200_.jpg) diff --git a/pytudes/data/advent2016/input1.txt b/pytudes/data/advent2016/input1.txt new file mode 100644 index 0000000..456904d --- /dev/null +++ b/pytudes/data/advent2016/input1.txt @@ -0,0 +1 @@ +R4, R5, L5, L5, L3, R2, R1, R1, L5, R5, R2, L1, L3, L4, R3, L1, L1, R2, R3, R3, R1, L3, L5, R3, R1, L1, R1, R2, L1, L4, L5, R4, R2, L192, R5, L2, R53, R1, L5, R73, R5, L5, R186, L3, L2, R1, R3, L3, L3, R1, L4, L2, R3, L5, R4, R3, R1, L1, R5, R2, R1, R1, R1, R3, R2, L1, R5, R1, L5, R2, L2, L4, R3, L1, R4, L5, R4, R3, L5, L3, R4, R2, L5, L5, R2, R3, R5, R4, R2, R1, L1, L5, L2, L3, L4, L5, L4, L5, L1, R3, R4, R5, R3, L5, L4, L3, L1, L4, R2, R5, R5, R4, L2, L4, R3, R1, L2, R5, L5, R1, R1, L1, L5, L5, L2, L1, R5, R2, L4, L1, R4, R3, L3, R1, R5, L1, L4, R2, L3, R5, R3, R1, L3 diff --git a/pytudes/data/advent2016/input10.txt b/pytudes/data/advent2016/input10.txt new file mode 100644 index 0000000..b3db0ac --- /dev/null +++ b/pytudes/data/advent2016/input10.txt @@ -0,0 +1,231 @@ +value 23 goes to bot 208 +bot 125 gives low to bot 58 and high to bot 57 +value 13 goes to bot 161 +bot 178 gives low to bot 88 and high to bot 172 +value 59 goes to bot 128 +bot 173 gives low to bot 83 and high to bot 202 +bot 189 gives low to bot 35 and high to bot 55 +bot 123 gives low to bot 90 and high to bot 169 +bot 148 gives low to bot 101 and high to bot 134 +bot 36 gives low to bot 78 and high to bot 105 +bot 196 gives low to bot 171 and high to bot 45 +bot 157 gives low to bot 179 and high to bot 87 +bot 124 gives low to bot 25 and high to bot 80 +bot 55 gives low to bot 99 and high to bot 201 +value 17 goes to bot 4 +bot 127 gives low to bot 118 and high to bot 142 +bot 9 gives low to bot 61 and high to bot 198 +bot 71 gives low to bot 86 and high to bot 96 +bot 86 gives low to bot 98 and high to bot 149 +bot 176 gives low to bot 89 and high to bot 171 +bot 38 gives low to bot 107 and high to bot 63 +bot 67 gives low to bot 77 and high to bot 7 +bot 131 gives low to output 6 and high to bot 151 +bot 97 gives low to bot 33 and high to bot 16 +bot 89 gives low to bot 27 and high to bot 36 +bot 29 gives low to bot 185 and high to bot 11 +bot 92 gives low to bot 189 and high to bot 122 +bot 77 gives low to output 7 and high to bot 191 +bot 14 gives low to bot 152 and high to bot 179 +bot 49 gives low to bot 76 and high to bot 64 +value 2 goes to bot 155 +bot 159 gives low to bot 182 and high to bot 49 +bot 129 gives low to bot 141 and high to bot 40 +bot 50 gives low to output 1 and high to bot 47 +bot 93 gives low to output 5 and high to bot 167 +bot 112 gives low to output 13 and high to bot 51 +bot 165 gives low to bot 163 and high to bot 123 +bot 13 gives low to bot 75 and high to bot 74 +bot 141 gives low to bot 178 and high to bot 207 +bot 37 gives low to bot 42 and high to bot 139 +value 31 goes to bot 92 +bot 44 gives low to bot 16 and high to bot 91 +bot 172 gives low to bot 84 and high to bot 27 +bot 39 gives low to bot 44 and high to bot 154 +bot 170 gives low to bot 95 and high to bot 146 +bot 98 gives low to bot 193 and high to bot 17 +bot 4 gives low to bot 26 and high to bot 109 +bot 197 gives low to bot 71 and high to bot 106 +bot 132 gives low to bot 161 and high to bot 181 +bot 54 gives low to bot 156 and high to bot 148 +bot 140 gives low to bot 0 and high to bot 25 +bot 59 gives low to output 10 and high to bot 93 +bot 206 gives low to bot 2 and high to bot 200 +bot 5 gives low to bot 201 and high to bot 173 +bot 81 gives low to bot 24 and high to bot 30 +bot 33 gives low to bot 100 and high to bot 113 +bot 73 gives low to bot 60 and high to bot 129 +bot 43 gives low to output 14 and high to bot 204 +bot 143 gives low to bot 176 and high to bot 196 +bot 182 gives low to bot 70 and high to bot 76 +bot 139 gives low to bot 117 and high to bot 180 +bot 31 gives low to bot 131 and high to bot 137 +bot 179 gives low to bot 31 and high to bot 28 +bot 74 gives low to bot 29 and high to bot 160 +bot 7 gives low to bot 191 and high to bot 21 +bot 83 gives low to bot 165 and high to bot 116 +bot 142 gives low to bot 144 and high to bot 107 +bot 187 gives low to bot 129 and high to bot 68 +value 61 goes to bot 32 +bot 32 gives low to bot 72 and high to bot 53 +bot 53 gives low to bot 121 and high to bot 199 +bot 79 gives low to bot 143 and high to bot 196 +bot 0 gives low to bot 92 and high to bot 194 +bot 8 gives low to bot 56 and high to bot 209 +value 43 goes to bot 72 +bot 95 gives low to output 18 and high to bot 112 +bot 104 gives low to bot 41 and high to bot 185 +bot 198 gives low to bot 103 and high to bot 48 +bot 17 gives low to bot 69 and high to bot 156 +bot 138 gives low to output 0 and high to bot 77 +bot 76 gives low to bot 127 and high to bot 164 +bot 110 gives low to bot 206 and high to bot 60 +bot 60 gives low to bot 200 and high to bot 141 +bot 134 gives low to bot 67 and high to bot 7 +bot 90 gives low to bot 12 and high to bot 192 +bot 208 gives low to bot 155 and high to bot 182 +bot 87 gives low to bot 28 and high to bot 195 +bot 108 gives low to bot 53 and high to bot 186 +bot 150 gives low to bot 154 and high to bot 56 +bot 204 gives low to output 17 and high to bot 58 +bot 174 gives low to bot 138 and high to bot 67 +bot 195 gives low to bot 147 and high to bot 81 +bot 24 gives low to bot 146 and high to bot 3 +bot 12 gives low to bot 119 and high to bot 9 +value 37 goes to bot 35 +bot 137 gives low to bot 151 and high to bot 170 +bot 1 gives low to output 2 and high to bot 22 +bot 63 gives low to bot 150 and high to bot 8 +bot 133 gives low to bot 140 and high to bot 124 +bot 154 gives low to bot 91 and high to bot 110 +bot 145 gives low to bot 47 and high to bot 18 +bot 109 gives low to bot 159 and high to bot 82 +bot 202 gives low to bot 116 and high to bot 37 +bot 168 gives low to bot 133 and high to bot 177 +bot 193 gives low to bot 93 and high to bot 69 +bot 191 gives low to output 16 and high to bot 21 +bot 135 gives low to bot 82 and high to bot 163 +bot 130 gives low to bot 102 and high to bot 114 +bot 26 gives low to bot 208 and high to bot 159 +bot 152 gives low to bot 22 and high to bot 31 +bot 118 gives low to bot 136 and high to bot 144 +bot 149 gives low to bot 17 and high to bot 54 +bot 64 gives low to bot 164 and high to bot 119 +bot 120 gives low to bot 64 and high to bot 12 +bot 180 gives low to bot 188 and high to bot 130 +bot 203 gives low to bot 204 and high to bot 125 +bot 3 gives low to bot 46 and high to bot 104 +bot 114 gives low to bot 205 and high to bot 79 +bot 25 gives low to bot 194 and high to bot 20 +bot 65 gives low to bot 181 and high to bot 118 +bot 169 gives low to bot 192 and high to bot 117 +bot 51 gives low to output 8 and high to bot 50 +bot 41 gives low to bot 50 and high to bot 145 +bot 20 gives low to bot 23 and high to bot 10 +bot 106 gives low to bot 96 and high to bot 126 +bot 23 gives low to bot 5 and high to bot 6 +value 11 goes to bot 43 +value 47 goes to bot 189 +value 5 goes to bot 115 +bot 46 gives low to bot 51 and high to bot 41 +bot 115 gives low to bot 43 and high to bot 203 +bot 209 gives low to bot 73 and high to bot 187 +bot 16 gives low to bot 113 and high to bot 62 +bot 101 gives low to bot 174 and high to bot 134 +bot 167 gives low to output 20 and high to bot 158 +value 3 goes to bot 133 +bot 184 gives low to bot 125 and high to bot 100 +bot 155 gives low to bot 166 and high to bot 70 +bot 88 gives low to bot 81 and high to bot 84 +value 19 goes to bot 0 +bot 171 gives low to bot 36 and high to bot 45 +bot 186 gives low to bot 199 and high to bot 97 +bot 111 gives low to bot 209 and high to bot 85 +bot 22 gives low to output 4 and high to bot 131 +bot 166 gives low to bot 132 and high to bot 65 +bot 6 gives low to bot 173 and high to bot 52 +bot 75 gives low to bot 104 and high to bot 29 +bot 91 gives low to bot 62 and high to bot 206 +bot 164 gives low to bot 142 and high to bot 38 +bot 15 gives low to bot 160 and high to bot 197 +bot 66 gives low to bot 198 and high to bot 188 +bot 199 gives low to bot 184 and high to bot 33 +bot 122 gives low to bot 55 and high to bot 5 +bot 68 gives low to bot 40 and high to bot 143 +bot 128 gives low to bot 4 and high to bot 94 +bot 27 gives low to bot 13 and high to bot 78 +bot 34 gives low to bot 195 and high to bot 88 +bot 94 gives low to bot 109 and high to bot 135 +bot 158 gives low to output 3 and high to bot 138 +bot 47 gives low to output 15 and high to bot 59 +bot 163 gives low to bot 120 and high to bot 90 +bot 48 gives low to bot 111 and high to bot 102 +bot 40 gives low to bot 207 and high to bot 176 +bot 144 gives low to bot 153 and high to bot 39 +bot 201 gives low to bot 162 and high to bot 83 +bot 72 gives low to bot 115 and high to bot 121 +bot 156 gives low to bot 19 and high to bot 101 +bot 185 gives low to bot 145 and high to bot 183 +bot 103 gives low to bot 8 and high to bot 111 +bot 192 gives low to bot 9 and high to bot 66 +value 71 goes to bot 140 +bot 205 gives low to bot 68 and high to bot 79 +bot 151 gives low to output 11 and high to bot 95 +bot 153 gives low to bot 97 and high to bot 44 +bot 105 gives low to bot 15 and high to bot 175 +bot 11 gives low to bot 183 and high to bot 86 +bot 160 gives low to bot 11 and high to bot 71 +bot 56 gives low to bot 110 and high to bot 73 +bot 207 gives low to bot 172 and high to bot 89 +bot 181 gives low to bot 108 and high to bot 136 +bot 175 gives low to bot 197 and high to bot 106 +bot 69 gives low to bot 167 and high to bot 19 +bot 58 gives low to output 9 and high to bot 1 +bot 78 gives low to bot 74 and high to bot 15 +bot 21 gives low to output 12 and high to output 19 +bot 190 gives low to bot 168 and high to bot 177 +value 29 goes to bot 190 +bot 107 gives low to bot 39 and high to bot 150 +bot 61 gives low to bot 63 and high to bot 103 +bot 52 gives low to bot 202 and high to bot 37 +value 53 goes to bot 168 +bot 30 gives low to bot 3 and high to bot 75 +bot 116 gives low to bot 123 and high to bot 42 +bot 85 gives low to bot 187 and high to bot 205 +bot 99 gives low to bot 94 and high to bot 162 +bot 126 gives low to bot 54 and high to bot 148 +bot 19 gives low to bot 158 and high to bot 174 +bot 82 gives low to bot 49 and high to bot 120 +bot 42 gives low to bot 169 and high to bot 139 +value 41 goes to bot 190 +bot 188 gives low to bot 48 and high to bot 130 +bot 113 gives low to bot 14 and high to bot 157 +bot 177 gives low to bot 124 and high to bot 80 +bot 18 gives low to bot 59 and high to bot 193 +bot 96 gives low to bot 149 and high to bot 126 +bot 62 gives low to bot 157 and high to bot 2 +bot 45 gives low to bot 105 and high to bot 175 +bot 2 gives low to bot 87 and high to bot 34 +bot 147 gives low to bot 170 and high to bot 24 +bot 70 gives low to bot 65 and high to bot 127 +bot 162 gives low to bot 135 and high to bot 165 +bot 117 gives low to bot 66 and high to bot 180 +bot 100 gives low to bot 57 and high to bot 14 +bot 57 gives low to bot 1 and high to bot 152 +bot 121 gives low to bot 203 and high to bot 184 +bot 10 gives low to bot 6 and high to bot 52 +bot 84 gives low to bot 30 and high to bot 13 +value 7 goes to bot 166 +bot 136 gives low to bot 186 and high to bot 153 +bot 161 gives low to bot 32 and high to bot 108 +bot 102 gives low to bot 85 and high to bot 114 +bot 80 gives low to bot 20 and high to bot 10 +bot 200 gives low to bot 34 and high to bot 178 +bot 119 gives low to bot 38 and high to bot 61 +bot 28 gives low to bot 137 and high to bot 147 +bot 35 gives low to bot 128 and high to bot 99 +value 67 goes to bot 132 +bot 146 gives low to bot 112 and high to bot 46 +bot 194 gives low to bot 122 and high to bot 23 +value 73 goes to bot 26 +bot 183 gives low to bot 18 and high to bot 98 diff --git a/pytudes/data/advent2016/input12.txt b/pytudes/data/advent2016/input12.txt new file mode 100644 index 0000000..0eeb395 --- /dev/null +++ b/pytudes/data/advent2016/input12.txt @@ -0,0 +1,23 @@ +cpy 1 a +cpy 1 b +cpy 26 d +jnz c 2 +jnz 1 5 +cpy 7 c +inc d +dec c +jnz c -2 +cpy a c +inc a +dec b +jnz b -2 +cpy c b +dec d +jnz d -6 +cpy 14 c +cpy 14 d +inc a +dec d +jnz d -2 +dec c +jnz c -5 diff --git a/pytudes/data/advent2016/input2.txt b/pytudes/data/advent2016/input2.txt new file mode 100644 index 0000000..118bf27 --- /dev/null +++ b/pytudes/data/advent2016/input2.txt @@ -0,0 +1,5 @@ +LURLDDLDULRURDUDLRULRDLLRURDUDRLLRLRURDRULDLRLRRDDULUDULURULLURLURRRLLDURURLLUURDLLDUUDRRDLDLLRUUDURURRULURUURLDLLLUDDUUDRULLRUDURRLRLLDRRUDULLDUUUDLDLRLLRLULDLRLUDLRRULDDDURLUULRDLRULRDURDURUUUDDRRDRRUDULDUUULLLLURRDDUULDRDRLULRRRUUDUURDULDDRLDRDLLDDLRDLDULUDDLULUDRLULRRRRUUUDULULDLUDUUUUDURLUDRDLLDDRULUURDRRRDRLDLLURLULDULRUDRDDUDDLRLRRDUDDRULRULULRDDDDRDLLLRURDDDDRDRUDUDUUDRUDLDULRUULLRRLURRRRUUDRDLDUDDLUDRRURLRDDLUUDUDUUDRLUURURRURDRRRURULUUDUUDURUUURDDDURUDLRLLULRULRDURLLDDULLDULULDDDRUDDDUUDDUDDRRRURRUURRRRURUDRRDLRDUUULLRRRUDD 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+LDUURLLULRUURRDLDRUULRDRDDDRULDLURDDRURULLRUURRLRRLDRURRDRLUDRUUUULLDRLURDRLRUDDRDDDUURRDRRURULLLDRDRDLDUURLDRUULLDRDDRRDRDUUDLURUDDLLUUDDULDDULRDDUUDDDLRLLLULLDLUDRRLDUUDRUUDUDUURULDRRLRRDLRLURDRURURRDURDURRUDLRURURUUDURURUDRURULLLLLUDRUDUDULRLLLRDRLLRLRLRRDULRUUULURLRRLDRRRDRULRUDUURRRRULDDLRULDRRRDLDRLUDLLUDDRURLURURRLRUDLRLLRDLLDRDDLDUDRDLDDRULDDULUDDLLDURDULLDURRURRULLDRLUURURLLUDDRLRRUUDULRRLLRUDRDUURLDDLLURRDLRUURLLDRDLRUULUDURRDULUULDDLUUUDDLRRDRDUDLRUULDDDLDDRUDDD +DRRDRRURURUDDDRULRUDLDLDULRLDURURUUURURLURURDDDDRULUDLDDRDDUDULRUUULRDUDULURLRULRDDLDUDLDLULRULDRRLUDLLLLURUDUDLLDLDRLRUUULRDDLUURDRRDLUDUDRULRRDDRRLDUDLLDLURLRDLRUUDLDULURDDUUDDLRDLUURLDLRLRDLLRUDRDUURDDLDDLURRDDRDRURULURRLRLDURLRRUUUDDUUDRDRULRDLURLDDDRURUDRULDURUUUUDULURUDDDDUURULULDRURRDRDURUUURURLLDRDLDLRDDULDRLLDUDUDDLRLLRLRUUDLUDDULRLDLLRLUUDLLLUUDULRDULDLRRLDDDDUDDRRRDDRDDUDRLLLDLLDLLRDLDRDLUDRRRLDDRLUDLRLDRUURUDURDLRDDULRLDUUUDRLLDRLDLLDLDRRRLLULLUDDDLRUDULDDDLDRRLLRDDLDUULRDLRRLRLLRUUULLRDUDLRURRRUULLULLLRRURLRDULLLRLDUUUDDRLRLUURRLUUUDURLRDURRDUDDUDDRDDRUD diff --git a/pytudes/data/advent2016/input20.txt b/pytudes/data/advent2016/input20.txt new file mode 100644 index 0000000..e408924 --- /dev/null +++ b/pytudes/data/advent2016/input20.txt @@ -0,0 +1,1176 @@ +2365712272-2390766206 +2569947483-2579668543 +1348241901-1362475328 +2431265968-2450509895 +2146385-2259474 +2935960035-2940597034 +448888033-460770571 +1993433098-1995841061 +1479295247-1481053053 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position 5 to position 3 +swap letter e with letter f +swap position 6 with position 3 +swap letter a with letter e +reverse positions 0 through 1 +reverse positions 0 through 4 +swap letter c with letter e +reverse positions 1 through 7 +rotate right 1 step +reverse positions 6 through 7 +move position 7 to position 1 +move position 4 to position 0 +move position 4 to position 6 +move position 6 to position 3 +swap position 1 with position 6 +swap position 5 with position 7 +swap position 2 with position 5 +swap position 6 with position 5 +swap position 2 with position 4 +reverse positions 2 through 6 +reverse positions 3 through 5 +move position 3 to position 5 +reverse positions 1 through 5 +rotate left 1 step +move position 4 to position 5 +swap letter c with letter b +swap position 2 with position 1 +reverse positions 3 through 4 +swap position 3 with position 4 +reverse positions 5 through 7 +swap letter b with letter d +reverse positions 3 through 4 +swap letter c with letter h +rotate based on position of letter b +rotate based on position of letter e +rotate right 3 steps +rotate right 7 steps +rotate left 2 steps +move position 6 to position 1 +reverse positions 1 through 3 +rotate based on position of letter b +reverse positions 0 through 4 +swap letter g with letter c +move position 1 to position 5 +rotate right 4 steps +rotate left 2 steps +move position 7 to position 2 +rotate based on position of letter c +move position 6 to position 1 +swap letter f with letter g +rotate right 6 steps +swap position 6 with position 2 +reverse positions 2 through 6 +swap position 3 with position 1 +rotate based on position of letter h +reverse positions 2 through 5 +move position 1 to position 3 +rotate right 1 step +rotate right 7 steps +move position 6 to position 3 +rotate based on position of letter h +swap letter d with letter h +rotate left 0 steps +move position 1 to position 2 +swap letter a with letter g +swap letter a with letter g +swap position 4 with position 2 +rotate right 1 step +rotate based on position of letter b +swap position 7 with position 1 +rotate based on position of letter e +move position 1 to position 4 +move position 6 to position 3 +rotate left 3 steps +swap letter f with letter g +swap position 3 with position 1 +swap position 4 with position 3 +swap letter f with letter c +rotate left 3 steps +rotate left 0 steps +rotate right 3 steps +swap letter d with letter e +swap position 2 with position 7 +move position 3 to position 6 +swap position 7 with position 1 +swap position 3 with position 6 +rotate left 5 steps +swap position 2 with position 6 diff --git a/pytudes/data/advent2016/input22.txt b/pytudes/data/advent2016/input22.txt new file mode 100644 index 0000000..31b7ee6 --- /dev/null +++ b/pytudes/data/advent2016/input22.txt @@ -0,0 +1,914 @@ +root@ebhq-gridcenter# df -h +Filesystem Size Used Avail Use% +/dev/grid/node-x0-y0 92T 70T 22T 76% +/dev/grid/node-x0-y1 86T 65T 21T 75% +/dev/grid/node-x0-y2 88T 73T 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column x=6 by 1 +rotate column x=5 by 1 +rotate column x=3 by 1 +rotate column x=2 by 1 +rotate column x=1 by 1 +rotate column x=0 by 1 +rect 9x1 +rotate row y=0 by 40 +rotate column x=44 by 1 +rotate column x=35 by 5 +rotate column x=18 by 5 +rotate column x=15 by 3 +rotate column x=10 by 5 +rotate row y=5 by 15 +rotate row y=4 by 10 +rotate row y=3 by 40 +rotate row y=2 by 20 +rotate row y=1 by 45 +rotate row y=0 by 35 +rotate column x=48 by 1 +rotate column x=47 by 5 +rotate column x=46 by 5 +rotate column x=45 by 1 +rotate column x=43 by 1 +rotate column x=40 by 1 +rotate column x=38 by 2 +rotate column x=37 by 3 +rotate column x=36 by 2 +rotate column x=32 by 2 +rotate column x=31 by 2 +rotate column x=28 by 1 +rotate column x=23 by 3 +rotate column x=22 by 3 +rotate column x=21 by 5 +rotate column x=20 by 1 +rotate column x=18 by 1 +rotate column x=17 by 3 +rotate column x=13 by 1 +rotate column x=10 by 1 +rotate column x=8 by 1 +rotate column x=7 by 5 +rotate column x=6 by 5 +rotate column x=5 by 1 +rotate column x=3 by 5 +rotate column x=2 by 5 +rotate column x=1 by 5 diff --git a/pytudes/data/advent2016/input9.txt b/pytudes/data/advent2016/input9.txt new file mode 100644 index 0000000..800446b --- /dev/null +++ b/pytudes/data/advent2016/input9.txt @@ -0,0 +1 @@ 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diff --git a/pytudes/data/advent2017/input1.txt b/pytudes/data/advent2017/input1.txt new file mode 100644 index 0000000..b7e8ce6 --- /dev/null +++ b/pytudes/data/advent2017/input1.txt @@ -0,0 +1 @@ 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diff --git a/pytudes/data/advent2017/input12.txt b/pytudes/data/advent2017/input12.txt new file mode 100644 index 0000000..990a764 --- /dev/null +++ b/pytudes/data/advent2017/input12.txt @@ -0,0 +1,2000 @@ +0 <-> 659, 737 +1 <-> 1, 1433 +2 <-> 982, 1869 +3 <-> 306, 380, 1462, 1827 +4 <-> 1076 +5 <-> 794, 1451 +6 <-> 146, 1055 +7 <-> 834, 1557 +8 <-> 1333 +9 <-> 849, 906, 1863 +10 <-> 362, 505 +11 <-> 33, 938, 1896 +12 <-> 490, 913 +13 <-> 189, 690 +14 <-> 796 +15 <-> 56, 280, 1288, 1721 +16 <-> 16 +17 <-> 904 +18 <-> 150, 1394, 1458 +19 <-> 1773 +20 <-> 70 +21 <-> 993 +22 <-> 22 +23 <-> 285, 1004 +24 <-> 209, 727 +25 <-> 614, 1590 +26 <-> 113 +27 <-> 1321, 1341 +28 <-> 351, 730, 1037 +29 <-> 29, 1828 +30 <-> 1378, 1983 +31 <-> 705, 1035 +32 <-> 1042, 1519 +33 <-> 11, 886 +34 <-> 360, 1101, 1531, 1877 +35 <-> 971, 1652 +36 <-> 188 +37 <-> 1935 +38 <-> 38 +39 <-> 39, 1472 +40 <-> 84, 1110 +41 <-> 483, 895, 1035, 1864, 1919 +42 <-> 624, 813, 1484, 1517 +43 <-> 492 +44 <-> 947, 1572 +45 <-> 45, 1589, 1748, 1836 +46 <-> 1821 +47 <-> 123, 206, 239 +48 <-> 146 +49 <-> 235, 871 +50 <-> 172, 1672 +51 <-> 504 +52 <-> 585, 678, 878 +53 <-> 484, 543, 1282 +54 <-> 374, 723 +55 <-> 1956 +56 <-> 15 +57 <-> 583, 1159, 1596 +58 <-> 313, 580, 1101 +59 <-> 1529, 1788 +60 <-> 60 +61 <-> 1033, 1857 +62 <-> 874 +63 <-> 63, 1007, 1316, 1673 +64 <-> 1140 +65 <-> 1136 +66 <-> 1337, 1546 +67 <-> 67, 1468 +68 <-> 298, 951 +69 <-> 906 +70 <-> 20, 1977 +71 <-> 1956 +72 <-> 146, 1465 +73 <-> 911 +74 <-> 1345 +75 <-> 711 +76 <-> 732, 789, 1499, 1637 +77 <-> 1897 +78 <-> 78, 379 +79 <-> 96, 462, 847 +80 <-> 886, 907 +81 <-> 1564 +82 <-> 1362, 1680 +83 <-> 225, 916 +84 <-> 40, 1460 +85 <-> 330 +86 <-> 1370 +87 <-> 87, 640 +88 <-> 806, 1411 +89 <-> 1732 +90 <-> 603 +91 <-> 547, 904 +92 <-> 1106 +93 <-> 782 +94 <-> 401, 1039, 1148, 1356 +95 <-> 95, 344, 1092 +96 <-> 79 +97 <-> 1555, 1649 +98 <-> 133 +99 <-> 866 +100 <-> 116, 1183, 1450 +101 <-> 964 +102 <-> 521, 843 +103 <-> 1002 +104 <-> 675, 1752, 1760 +105 <-> 447 +106 <-> 625 +107 <-> 200, 923, 1573 +108 <-> 108, 1535 +109 <-> 1938, 1984 +110 <-> 992 +111 <-> 410, 436, 1789, 1985 +112 <-> 730, 1742 +113 <-> 26, 774, 1620 +114 <-> 891 +115 <-> 556, 980, 1502 +116 <-> 100, 405, 438 +117 <-> 1220, 1747 +118 <-> 417 +119 <-> 1671 +120 <-> 225 +121 <-> 215, 1414 +122 <-> 1421 +123 <-> 47, 488, 1390 +124 <-> 1750 +125 <-> 1020, 1456, 1645, 1811 +126 <-> 945, 988, 1558 +127 <-> 1562 +128 <-> 246, 419, 878, 1057 +129 <-> 198, 214, 526 +130 <-> 1572 +131 <-> 624 +132 <-> 1086 +133 <-> 98, 430, 1950 +134 <-> 1179 +135 <-> 1603 +136 <-> 136 +137 <-> 137, 248 +138 <-> 604 +139 <-> 1080, 1744, 1829 +140 <-> 786, 890, 1336 +141 <-> 819, 835 +142 <-> 142, 1657 +143 <-> 590, 670 +144 <-> 622 +145 <-> 182, 930, 1164, 1741 +146 <-> 6, 48, 72, 152 +147 <-> 1880 +148 <-> 1486 +149 <-> 1595 +150 <-> 18, 653 +151 <-> 1834 +152 <-> 146, 289, 1949 +153 <-> 1379 +154 <-> 694, 1025 +155 <-> 1143, 1469 +156 <-> 437, 1492, 1616 +157 <-> 1044 +158 <-> 410, 1391 +159 <-> 1327 +160 <-> 387, 892, 963, 1287 +161 <-> 964, 1017 +162 <-> 786, 1098, 1351, 1445, 1508 +163 <-> 415 +164 <-> 255, 790, 1410 +165 <-> 252, 425, 1186, 1662, 1838 +166 <-> 791, 1012 +167 <-> 167, 836, 1922 +168 <-> 1586, 1998 +169 <-> 679, 914 +170 <-> 1975 +171 <-> 672 +172 <-> 50 +173 <-> 614 +174 <-> 723 +175 <-> 246, 747 +176 <-> 400, 1338 +177 <-> 573, 1617, 1724 +178 <-> 473, 1572 +179 <-> 183 +180 <-> 200, 1380 +181 <-> 1394, 1657 +182 <-> 145, 1825 +183 <-> 179, 399, 955, 1236, 1295, 1840 +184 <-> 712 +185 <-> 185 +186 <-> 551, 1627 +187 <-> 1195 +188 <-> 36, 440, 1277, 1362 +189 <-> 13 +190 <-> 1111 +191 <-> 985, 1372 +192 <-> 496, 1137, 1283 +193 <-> 827, 1053 +194 <-> 610 +195 <-> 1231, 1497 +196 <-> 1960 +197 <-> 584, 1359 +198 <-> 129, 651, 714, 1663 +199 <-> 1047, 1805 +200 <-> 107, 180, 658, 1397 +201 <-> 1590 +202 <-> 1268, 1768 +203 <-> 1683 +204 <-> 567, 1848 +205 <-> 276 +206 <-> 47, 461, 1794 +207 <-> 207 +208 <-> 1248 +209 <-> 24, 1589 +210 <-> 1063, 1504 +211 <-> 907, 1815 +212 <-> 1948 +213 <-> 388 +214 <-> 129, 561, 793, 1569 +215 <-> 121, 252 +216 <-> 216, 1728 +217 <-> 761 +218 <-> 631, 816 +219 <-> 459, 807, 1008 +220 <-> 1231, 1447 +221 <-> 713, 1541 +222 <-> 856, 924, 1924 +223 <-> 1103 +224 <-> 1426, 1761 +225 <-> 83, 120, 242, 784 +226 <-> 311, 560 +227 <-> 587, 667, 984, 1091 +228 <-> 1852 +229 <-> 229, 1198, 1204 +230 <-> 1505, 1944 +231 <-> 1158, 1594, 1925 +232 <-> 232, 345, 1417 +233 <-> 828, 1677 +234 <-> 982 +235 <-> 49, 1012, 1254, 1956 +236 <-> 489, 893, 1545 +237 <-> 988, 1450 +238 <-> 1719, 1791 +239 <-> 47, 736, 1027 +240 <-> 1167, 1457 +241 <-> 270 +242 <-> 225, 814, 1873 +243 <-> 243, 282, 914 +244 <-> 302, 328, 559 +245 <-> 1753 +246 <-> 128, 175 +247 <-> 1230, 1660, 1824 +248 <-> 137, 537, 1423 +249 <-> 1209, 1391, 1749 +250 <-> 298 +251 <-> 799 +252 <-> 165, 215 +253 <-> 1437, 1741 +254 <-> 1356 +255 <-> 164 +256 <-> 310 +257 <-> 1267, 1821 +258 <-> 1177, 1876 +259 <-> 1257, 1432 +260 <-> 311, 1115 +261 <-> 1504 +262 <-> 1268 +263 <-> 565, 1023 +264 <-> 408, 1806 +265 <-> 1009, 1144 +266 <-> 599, 616 +267 <-> 1182 +268 <-> 1026, 1456, 1470, 1854 +269 <-> 269, 686 +270 <-> 241, 1445 +271 <-> 1232 +272 <-> 487, 863, 1286 +273 <-> 1614, 1748 +274 <-> 1332 +275 <-> 1010, 1334 +276 <-> 205, 478, 888, 1049 +277 <-> 277, 1330 +278 <-> 734, 1561 +279 <-> 535, 1190, 1913 +280 <-> 15 +281 <-> 1206 +282 <-> 243, 475, 1571 +283 <-> 283, 1936 +284 <-> 324, 702, 844, 1601 +285 <-> 23 +286 <-> 286, 1080, 1127 +287 <-> 295 +288 <-> 805 +289 <-> 152, 656, 691, 993 +290 <-> 595, 616, 1199 +291 <-> 1028, 1218, 1844 +292 <-> 1447 +293 <-> 378, 1771 +294 <-> 811, 1790 +295 <-> 287, 367, 693 +296 <-> 861, 1948, 1950 +297 <-> 1631 +298 <-> 68, 250, 641, 745 +299 <-> 299, 898, 1152, 1574 +300 <-> 353 +301 <-> 990, 1340, 1960 +302 <-> 244 +303 <-> 1645 +304 <-> 445, 448, 557, 1611 +305 <-> 1350, 1442 +306 <-> 3, 445 +307 <-> 567 +308 <-> 1799 +309 <-> 864 +310 <-> 256, 853, 1911 +311 <-> 226, 260, 970 +312 <-> 1308 +313 <-> 58 +314 <-> 1795 +315 <-> 1225, 1627, 1903 +316 <-> 1065, 1991 +317 <-> 317 +318 <-> 546, 1415 +319 <-> 1883 +320 <-> 417, 1040 +321 <-> 1927 +322 <-> 686 +323 <-> 1018, 1619 +324 <-> 284 +325 <-> 1114 +326 <-> 474, 872 +327 <-> 439 +328 <-> 244 +329 <-> 329 +330 <-> 85, 1868 +331 <-> 331, 680, 1224, 1243, 1291 +332 <-> 1748 +333 <-> 1673 +334 <-> 676, 1306 +335 <-> 809 +336 <-> 797, 1559, 1858 +337 <-> 978, 1874 +338 <-> 538, 1077 +339 <-> 432, 1033 +340 <-> 340 +341 <-> 1267, 1683 +342 <-> 587, 726 +343 <-> 1560, 1705 +344 <-> 95 +345 <-> 232, 1032 +346 <-> 581, 1992 +347 <-> 530 +348 <-> 667, 1479 +349 <-> 1620 +350 <-> 861, 998, 1069 +351 <-> 28 +352 <-> 352 +353 <-> 300, 1513 +354 <-> 1109, 1747 +355 <-> 950, 965, 1394, 1616 +356 <-> 1136 +357 <-> 1443, 1698 +358 <-> 973, 1814 +359 <-> 1662 +360 <-> 34, 921 +361 <-> 1418 +362 <-> 10, 668, 1656 +363 <-> 450, 766 +364 <-> 615, 1941 +365 <-> 1071 +366 <-> 749, 1375 +367 <-> 295, 1708, 1925 +368 <-> 383, 928 +369 <-> 369 +370 <-> 651, 1048 +371 <-> 665, 1460, 1686 +372 <-> 390, 958, 1682 +373 <-> 1559 +374 <-> 54, 1395, 1847 +375 <-> 799, 1061, 1383, 1773 +376 <-> 376 +377 <-> 1463 +378 <-> 293, 872, 917 +379 <-> 78, 449 +380 <-> 3, 1117 +381 <-> 1995 +382 <-> 846, 896, 1506, 1918 +383 <-> 368, 477 +384 <-> 1009, 1788 +385 <-> 1926 +386 <-> 1602 +387 <-> 160, 667 +388 <-> 213, 713 +389 <-> 586 +390 <-> 372, 1140 +391 <-> 863 +392 <-> 590, 1259, 1384 +393 <-> 645 +394 <-> 423, 1537 +395 <-> 782, 1496, 1893 +396 <-> 1497 +397 <-> 397 +398 <-> 847, 1265 +399 <-> 183, 743, 1564 +400 <-> 176 +401 <-> 94 +402 <-> 402 +403 <-> 558 +404 <-> 572 +405 <-> 116 +406 <-> 769, 1563 +407 <-> 1790 +408 <-> 264 +409 <-> 847 +410 <-> 111, 158, 1467, 1880, 1902 +411 <-> 1221 +412 <-> 858, 1088, 1848 +413 <-> 1589 +414 <-> 468, 637 +415 <-> 163, 415 +416 <-> 416, 817 +417 <-> 118, 320, 1671 +418 <-> 1029, 1987 +419 <-> 128, 765 +420 <-> 420, 1180 +421 <-> 1170, 1766 +422 <-> 563, 1400, 1904, 1926 +423 <-> 394 +424 <-> 730 +425 <-> 165, 478, 957 +426 <-> 1505 +427 <-> 1478, 1780 +428 <-> 1658 +429 <-> 650 +430 <-> 133 +431 <-> 469, 1491 +432 <-> 339 +433 <-> 667, 1549 +434 <-> 852 +435 <-> 435 +436 <-> 111 +437 <-> 156 +438 <-> 116, 874 +439 <-> 327, 1387 +440 <-> 188, 540 +441 <-> 441 +442 <-> 692 +443 <-> 1037, 1153 +444 <-> 758, 1064 +445 <-> 304, 306 +446 <-> 1072, 1495, 1890 +447 <-> 105, 1665 +448 <-> 304, 591 +449 <-> 379 +450 <-> 363, 450, 466 +451 <-> 1135 +452 <-> 990, 1344, 1604 +453 <-> 1390, 1755 +454 <-> 1853 +455 <-> 1199, 1735, 1852 +456 <-> 484 +457 <-> 457, 1973 +458 <-> 786 +459 <-> 219 +460 <-> 1655, 1777 +461 <-> 206, 753 +462 <-> 79, 668 +463 <-> 699 +464 <-> 1843 +465 <-> 829, 978, 1820 +466 <-> 450 +467 <-> 770, 1475 +468 <-> 414, 613, 1230 +469 <-> 431, 1470 +470 <-> 1292, 1659 +471 <-> 603 +472 <-> 719, 1398 +473 <-> 178, 1419 +474 <-> 326, 866 +475 <-> 282 +476 <-> 1512, 1669 +477 <-> 383 +478 <-> 276, 425 +479 <-> 1029 +480 <-> 603 +481 <-> 991, 1878 +482 <-> 1726, 1783 +483 <-> 41, 855 +484 <-> 53, 456 +485 <-> 1814 +486 <-> 1470 +487 <-> 272, 1693 +488 <-> 123 +489 <-> 236, 1155, 1793 +490 <-> 12, 1349, 1498 +491 <-> 913 +492 <-> 43, 1121, 1822 +493 <-> 1148 +494 <-> 619, 1528 +495 <-> 1960 +496 <-> 192 +497 <-> 497 +498 <-> 1185 +499 <-> 1933 +500 <-> 1948 +501 <-> 1364, 1433, 1826 +502 <-> 893, 933 +503 <-> 514 +504 <-> 51, 821, 1116 +505 <-> 10, 905 +506 <-> 506 +507 <-> 892 +508 <-> 508 +509 <-> 1078 +510 <-> 1716 +511 <-> 1197, 1900 +512 <-> 568, 1284, 1422 +513 <-> 1604, 1817, 1927 +514 <-> 503, 773, 1725, 1883 +515 <-> 1396 +516 <-> 542 +517 <-> 1299 +518 <-> 1562 +519 <-> 1622 +520 <-> 1254, 1868, 1881 +521 <-> 102, 1765 +522 <-> 1438, 1980 +523 <-> 1779 +524 <-> 1235, 1968 +525 <-> 1267, 1484 +526 <-> 129 +527 <-> 1211 +528 <-> 597, 1017 +529 <-> 529, 609 +530 <-> 347, 1737, 1890 +531 <-> 851, 1320 +532 <-> 709 +533 <-> 819, 1091 +534 <-> 856 +535 <-> 279, 535 +536 <-> 536 +537 <-> 248, 1317, 1763 +538 <-> 338, 1793 +539 <-> 539, 1485 +540 <-> 440, 1216 +541 <-> 541 +542 <-> 516, 1232, 1831 +543 <-> 53, 1234 +544 <-> 639, 1090 +545 <-> 1898 +546 <-> 318, 1208 +547 <-> 91 +548 <-> 569, 750, 1090 +549 <-> 1720 +550 <-> 660 +551 <-> 186 +552 <-> 642, 672, 723 +553 <-> 1927 +554 <-> 717, 1841, 1997 +555 <-> 1938 +556 <-> 115, 1453 +557 <-> 304, 904 +558 <-> 403, 1438 +559 <-> 244, 1046 +560 <-> 226 +561 <-> 214, 793, 1570 +562 <-> 1992 +563 <-> 422 +564 <-> 860 +565 <-> 263, 804 +566 <-> 566 +567 <-> 204, 307 +568 <-> 512, 1084 +569 <-> 548, 985, 1910 +570 <-> 665, 1844 +571 <-> 735 +572 <-> 404, 1026, 1111 +573 <-> 177, 1994 +574 <-> 846 +575 <-> 723, 738, 795, 802, 926, 1215 +576 <-> 1650, 1962, 1996 +577 <-> 1501, 1670 +578 <-> 1504 +579 <-> 1016, 1729 +580 <-> 58 +581 <-> 346, 581 +582 <-> 749 +583 <-> 57, 613, 1219, 1941 +584 <-> 197, 1366 +585 <-> 52, 1518 +586 <-> 389, 1597 +587 <-> 227, 342 +588 <-> 1408 +589 <-> 1229 +590 <-> 143, 392, 1044, 1078 +591 <-> 448, 1289 +592 <-> 592 +593 <-> 711 +594 <-> 770 +595 <-> 290, 1169 +596 <-> 1854 +597 <-> 528, 755, 1241, 1982 +598 <-> 663, 806 +599 <-> 266 +600 <-> 1065, 1694 +601 <-> 746 +602 <-> 827 +603 <-> 90, 471, 480, 1083 +604 <-> 138, 1003 +605 <-> 1703 +606 <-> 1289 +607 <-> 1309 +608 <-> 808, 1100 +609 <-> 529, 1621, 1943 +610 <-> 194, 610 +611 <-> 1337, 1609 +612 <-> 980, 1350 +613 <-> 468, 583 +614 <-> 25, 173, 1623, 1914 +615 <-> 364, 775 +616 <-> 266, 290 +617 <-> 1514 +618 <-> 1031 +619 <-> 494, 1761 +620 <-> 1126, 1150, 1221, 1513, 1712 +621 <-> 1770 +622 <-> 144, 1761 +623 <-> 1367 +624 <-> 42, 131 +625 <-> 106, 914 +626 <-> 1849 +627 <-> 1477 +628 <-> 1379 +629 <-> 969 +630 <-> 1114 +631 <-> 218, 1935, 1979 +632 <-> 1015, 1665, 1816, 1819 +633 <-> 1326, 1628 +634 <-> 1347, 1720 +635 <-> 816 +636 <-> 636 +637 <-> 414, 1566 +638 <-> 1668 +639 <-> 544, 824, 1542 +640 <-> 87 +641 <-> 298, 1196 +642 <-> 552, 1619 +643 <-> 972 +644 <-> 814 +645 <-> 393, 1148, 1205, 1302 +646 <-> 969 +647 <-> 935, 1575 +648 <-> 648, 1424 +649 <-> 1794 +650 <-> 429, 854, 1586, 1711 +651 <-> 198, 370 +652 <-> 996, 1996 +653 <-> 150, 1919 +654 <-> 654 +655 <-> 658 +656 <-> 289 +657 <-> 978, 1954 +658 <-> 200, 655 +659 <-> 0, 825, 1258, 1792 +660 <-> 550, 1232 +661 <-> 661, 1405 +662 <-> 662 +663 <-> 598 +664 <-> 1014 +665 <-> 371, 570, 1247 +666 <-> 989, 1778 +667 <-> 227, 348, 387, 433 +668 <-> 362, 462, 703, 1091 +669 <-> 1184 +670 <-> 143 +671 <-> 671, 901 +672 <-> 171, 552 +673 <-> 1865 +674 <-> 972, 1961 +675 <-> 104, 1581, 1800 +676 <-> 334, 1995 +677 <-> 1836 +678 <-> 52 +679 <-> 169 +680 <-> 331 +681 <-> 823 +682 <-> 921 +683 <-> 1800 +684 <-> 750, 1505 +685 <-> 722, 1338, 1993 +686 <-> 269, 322 +687 <-> 989, 1178 +688 <-> 1338 +689 <-> 1535 +690 <-> 13, 690 +691 <-> 289, 721 +692 <-> 442, 1014 +693 <-> 295 +694 <-> 154, 862 +695 <-> 1552, 1735 +696 <-> 1044 +697 <-> 993, 1793, 1801 +698 <-> 698 +699 <-> 463, 1022, 1399 +700 <-> 897, 1085 +701 <-> 1782, 1987 +702 <-> 284 +703 <-> 668, 1031 +704 <-> 704, 849 +705 <-> 31 +706 <-> 1909 +707 <-> 1276 +708 <-> 1301 +709 <-> 532, 1607 +710 <-> 1094 +711 <-> 75, 593, 1251, 1297 +712 <-> 184, 712 +713 <-> 221, 388, 713 +714 <-> 198 +715 <-> 1607 +716 <-> 1110 +717 <-> 554, 1819 +718 <-> 1755 +719 <-> 472, 1942 +720 <-> 1043, 1984 +721 <-> 691, 1641 +722 <-> 685, 1360, 1679 +723 <-> 54, 174, 552, 575 +724 <-> 1466 +725 <-> 1231 +726 <-> 342, 1023 +727 <-> 24 +728 <-> 1928 +729 <-> 975, 1759 +730 <-> 28, 112, 424, 1324 +731 <-> 731 +732 <-> 76, 1698 +733 <-> 1895 +734 <-> 278 +735 <-> 571, 1440 +736 <-> 239 +737 <-> 0, 1214, 1949 +738 <-> 575, 985 +739 <-> 1467 +740 <-> 740, 1449, 1885 +741 <-> 1243 +742 <-> 845, 1588, 1676, 1956, 1980 +743 <-> 399 +744 <-> 744, 1990 +745 <-> 298, 1966 +746 <-> 601, 1294, 1601 +747 <-> 175, 1106 +748 <-> 1433, 1565, 1795 +749 <-> 366, 582 +750 <-> 548, 684, 1210 +751 <-> 751, 1967 +752 <-> 765, 1297 +753 <-> 461 +754 <-> 754 +755 <-> 597, 1089 +756 <-> 756 +757 <-> 1350, 1936 +758 <-> 444, 1044, 1279 +759 <-> 996, 1310 +760 <-> 1943 +761 <-> 217, 1333 +762 <-> 1671 +763 <-> 1761 +764 <-> 1881 +765 <-> 419, 752 +766 <-> 363, 928, 1100 +767 <-> 1220, 1986 +768 <-> 1337 +769 <-> 406, 1307 +770 <-> 467, 594, 1707 +771 <-> 1624, 1782 +772 <-> 1230 +773 <-> 514, 1266, 1305 +774 <-> 113, 1198 +775 <-> 615, 1753 +776 <-> 1307 +777 <-> 1785 +778 <-> 778, 1776 +779 <-> 992 +780 <-> 1406 +781 <-> 781, 1272 +782 <-> 93, 395, 1207 +783 <-> 1544, 1729 +784 <-> 225, 1168, 1587 +785 <-> 1050 +786 <-> 140, 162, 458, 786, 1060 +787 <-> 1210 +788 <-> 1431 +789 <-> 76 +790 <-> 164, 882 +791 <-> 166, 1688 +792 <-> 792, 946 +793 <-> 214, 561 +794 <-> 5, 1561 +795 <-> 575, 1208, 1875 +796 <-> 14, 1205, 1427 +797 <-> 336, 1006, 1352 +798 <-> 1176, 1754 +799 <-> 251, 375 +800 <-> 840, 1471 +801 <-> 801, 1246, 1897 +802 <-> 575 +803 <-> 1692 +804 <-> 565, 859, 1978 +805 <-> 288, 1447 +806 <-> 88, 598 +807 <-> 219, 1579 +808 <-> 608 +809 <-> 335, 867, 1734, 1843 +810 <-> 1279 +811 <-> 294, 1043, 1560, 1583, 1600 +812 <-> 1487, 1527 +813 <-> 42, 1405 +814 <-> 242, 644, 1175, 1638 +815 <-> 1050, 1177 +816 <-> 218, 635, 1427 +817 <-> 416 +818 <-> 1765, 1999 +819 <-> 141, 533 +820 <-> 1238, 1393 +821 <-> 504, 1755 +822 <-> 1320, 1397 +823 <-> 681, 1120, 1798 +824 <-> 639 +825 <-> 659 +826 <-> 1722, 1834 +827 <-> 193, 602, 968 +828 <-> 233, 1835 +829 <-> 465 +830 <-> 951 +831 <-> 1606 +832 <-> 1619, 1964 +833 <-> 1109 +834 <-> 7, 962, 1869 +835 <-> 141 +836 <-> 167, 875, 1145 +837 <-> 1752 +838 <-> 838, 1146 +839 <-> 1247 +840 <-> 800 +841 <-> 1337 +842 <-> 1438, 1466 +843 <-> 102 +844 <-> 284 +845 <-> 742 +846 <-> 382, 574 +847 <-> 79, 398, 409 +848 <-> 959 +849 <-> 9, 704 +850 <-> 915, 1455, 1911, 1987 +851 <-> 531, 1001 +852 <-> 434, 1172 +853 <-> 310, 1533 +854 <-> 650 +855 <-> 483, 868, 1598 +856 <-> 222, 534, 1133 +857 <-> 857, 1249, 1923 +858 <-> 412, 1540, 1575, 1607 +859 <-> 804, 1655 +860 <-> 564, 1243 +861 <-> 296, 350, 1130, 1521 +862 <-> 694 +863 <-> 272, 391, 1558 +864 <-> 309, 1071, 1227 +865 <-> 1537, 1669, 1825 +866 <-> 99, 474 +867 <-> 809, 867, 1004 +868 <-> 855, 1539 +869 <-> 1550 +870 <-> 1885 +871 <-> 49 +872 <-> 326, 378, 1552 +873 <-> 1307 +874 <-> 62, 438 +875 <-> 836, 1056, 1326 +876 <-> 876 +877 <-> 1933 +878 <-> 52, 128, 1527 +879 <-> 879 +880 <-> 1292, 1561, 1770 +881 <-> 881, 981 +882 <-> 790, 882, 932 +883 <-> 1322, 1963 +884 <-> 1842 +885 <-> 885 +886 <-> 33, 80, 1765, 1959 +887 <-> 1012 +888 <-> 276 +889 <-> 1391 +890 <-> 140 +891 <-> 114, 891 +892 <-> 160, 507 +893 <-> 236, 502, 1602 +894 <-> 1525 +895 <-> 41 +896 <-> 382 +897 <-> 700 +898 <-> 299 +899 <-> 1797 +900 <-> 1736 +901 <-> 671, 944, 1147 +902 <-> 1597, 1940 +903 <-> 1283 +904 <-> 17, 91, 557, 1169, 1764 +905 <-> 505 +906 <-> 9, 69, 942 +907 <-> 80, 211, 1348 +908 <-> 1398 +909 <-> 909 +910 <-> 1683 +911 <-> 73, 911 +912 <-> 1929 +913 <-> 12, 491, 1591 +914 <-> 169, 243, 625, 1867 +915 <-> 850, 1538 +916 <-> 83 +917 <-> 378 +918 <-> 1438 +919 <-> 1951 +920 <-> 1814 +921 <-> 360, 682, 1952 +922 <-> 922 +923 <-> 107, 1161, 1254 +924 <-> 222 +925 <-> 1691 +926 <-> 575 +927 <-> 1165, 1270 +928 <-> 368, 766 +929 <-> 1707, 1914 +930 <-> 145, 1096, 1434, 1791 +931 <-> 931, 1983 +932 <-> 882 +933 <-> 502, 1921 +934 <-> 1297 +935 <-> 647, 1319 +936 <-> 1255 +937 <-> 1210 +938 <-> 11 +939 <-> 1348, 1666 +940 <-> 1408 +941 <-> 1440 +942 <-> 906 +943 <-> 1977 +944 <-> 901 +945 <-> 126 +946 <-> 792 +947 <-> 44, 1400 +948 <-> 948, 1045 +949 <-> 967 +950 <-> 355 +951 <-> 68, 830, 969 +952 <-> 1225, 1757, 1929 +953 <-> 1534, 1726 +954 <-> 1511, 1888 +955 <-> 183, 1418 +956 <-> 1702 +957 <-> 425 +958 <-> 372 +959 <-> 848, 1512 +960 <-> 1868 +961 <-> 1509 +962 <-> 834, 1678 +963 <-> 160 +964 <-> 101, 161 +965 <-> 355 +966 <-> 1740, 1866 +967 <-> 949, 1802 +968 <-> 827, 1534 +969 <-> 629, 646, 951 +970 <-> 311 +971 <-> 35, 1670 +972 <-> 643, 674, 1449 +973 <-> 358 +974 <-> 974 +975 <-> 729, 1955 +976 <-> 1495 +977 <-> 1603, 1889 +978 <-> 337, 465, 657, 1615, 1953 +979 <-> 1801 +980 <-> 115, 612, 1239 +981 <-> 881 +982 <-> 2, 234, 1411, 1511 +983 <-> 1970 +984 <-> 227, 984 +985 <-> 191, 569, 738 +986 <-> 1926 +987 <-> 987 +988 <-> 126, 237, 1894 +989 <-> 666, 687, 1079 +990 <-> 301, 452, 1903 +991 <-> 481, 1435 +992 <-> 110, 779, 1637 +993 <-> 21, 289, 697, 1675 +994 <-> 1151, 1639 +995 <-> 1090, 1798 +996 <-> 652, 759, 1229 +997 <-> 1253, 1380, 1553 +998 <-> 350, 1812 +999 <-> 1128 +1000 <-> 1566 +1001 <-> 851 +1002 <-> 103, 1229 +1003 <-> 604, 1156, 1232, 1420 +1004 <-> 23, 867 +1005 <-> 1085, 1174, 1899 +1006 <-> 797 +1007 <-> 63, 1282 +1008 <-> 219, 1008, 1977 +1009 <-> 265, 384, 1731 +1010 <-> 275, 1438, 1474 +1011 <-> 1289 +1012 <-> 166, 235, 887, 1342, 1471 +1013 <-> 1013, 1886 +1014 <-> 664, 692, 1229 +1015 <-> 632, 1015 +1016 <-> 579 +1017 <-> 161, 528 +1018 <-> 323 +1019 <-> 1684 +1020 <-> 125 +1021 <-> 1036, 1450 +1022 <-> 699, 1600, 1962 +1023 <-> 263, 726 +1024 <-> 1295 +1025 <-> 154, 1025 +1026 <-> 268, 572, 1610 +1027 <-> 239, 1269 +1028 <-> 291, 1275 +1029 <-> 418, 479, 1957 +1030 <-> 1184 +1031 <-> 618, 703 +1032 <-> 345 +1033 <-> 61, 339, 1033 +1034 <-> 1166, 1291 +1035 <-> 31, 41 +1036 <-> 1021, 1228 +1037 <-> 28, 443, 1227 +1038 <-> 1178 +1039 <-> 94, 1578 +1040 <-> 320, 1992 +1041 <-> 1041 +1042 <-> 32, 1486 +1043 <-> 720, 811 +1044 <-> 157, 590, 696, 758, 1433, 1739 +1045 <-> 948 +1046 <-> 559, 1241 +1047 <-> 199, 1962 +1048 <-> 370 +1049 <-> 276, 1885 +1050 <-> 785, 815 +1051 <-> 1051, 1290 +1052 <-> 1165 +1053 <-> 193, 1446, 1488 +1054 <-> 1081 +1055 <-> 6 +1056 <-> 875 +1057 <-> 128, 1137 +1058 <-> 1112, 1173 +1059 <-> 1226, 1538 +1060 <-> 786 +1061 <-> 375, 1639, 1988 +1062 <-> 1748 +1063 <-> 210, 1692 +1064 <-> 444 +1065 <-> 316, 600, 1689 +1066 <-> 1709 +1067 <-> 1067 +1068 <-> 1068 +1069 <-> 350 +1070 <-> 1196 +1071 <-> 365, 864, 1827 +1072 <-> 446, 1142 +1073 <-> 1931 +1074 <-> 1529 +1075 <-> 1075 +1076 <-> 4, 1717, 1879, 1969 +1077 <-> 338 +1078 <-> 509, 590 +1079 <-> 989, 1282 +1080 <-> 139, 286 +1081 <-> 1054, 1992 +1082 <-> 1115, 1451, 1704 +1083 <-> 603, 1271 +1084 <-> 568, 1233 +1085 <-> 700, 1005, 1939 +1086 <-> 132, 1745, 1901 +1087 <-> 1519 +1088 <-> 412 +1089 <-> 755 +1090 <-> 544, 548, 995, 1768 +1091 <-> 227, 533, 668, 1141 +1092 <-> 95 +1093 <-> 1271, 1946 +1094 <-> 710, 1102 +1095 <-> 1546 +1096 <-> 930 +1097 <-> 1288 +1098 <-> 162, 1933 +1099 <-> 1456 +1100 <-> 608, 766 +1101 <-> 34, 58, 1108 +1102 <-> 1094, 1938 +1103 <-> 223, 1117 +1104 <-> 1457, 1605, 1654 +1105 <-> 1105 +1106 <-> 92, 747 +1107 <-> 1699 +1108 <-> 1101, 1201 +1109 <-> 354, 833, 1285, 1874 +1110 <-> 40, 716 +1111 <-> 190, 572, 1440 +1112 <-> 1058, 1193 +1113 <-> 1113 +1114 <-> 325, 630, 1853 +1115 <-> 260, 1082 +1116 <-> 504 +1117 <-> 380, 1103 +1118 <-> 1118 +1119 <-> 1353, 1871 +1120 <-> 823 +1121 <-> 492, 1196 +1122 <-> 1122 +1123 <-> 1725 +1124 <-> 1892 +1125 <-> 1344 +1126 <-> 620 +1127 <-> 286, 1138 +1128 <-> 999, 1268 +1129 <-> 1129 +1130 <-> 861 +1131 <-> 1874 +1132 <-> 1913 +1133 <-> 856 +1134 <-> 1185, 1767 +1135 <-> 451, 1975 +1136 <-> 65, 356, 1487 +1137 <-> 192, 1057 +1138 <-> 1127, 1782 +1139 <-> 1240 +1140 <-> 64, 390, 1385 +1141 <-> 1091 +1142 <-> 1072, 1587 +1143 <-> 155, 1143 +1144 <-> 265 +1145 <-> 836, 1401 +1146 <-> 838 +1147 <-> 901, 1483 +1148 <-> 94, 493, 645, 1167 +1149 <-> 1818 +1150 <-> 620, 1237, 1264 +1151 <-> 994, 1844 +1152 <-> 299, 1167 +1153 <-> 443, 1947 +1154 <-> 1803 +1155 <-> 489, 1163 +1156 <-> 1003, 1635, 1668 +1157 <-> 1340, 1809 +1158 <-> 231 +1159 <-> 57 +1160 <-> 1558 +1161 <-> 923 +1162 <-> 1590 +1163 <-> 1155 +1164 <-> 145, 1164, 1283 +1165 <-> 927, 1052, 1678, 1934 +1166 <-> 1034 +1167 <-> 240, 1148, 1152, 1462 +1168 <-> 784 +1169 <-> 595, 904 +1170 <-> 421 +1171 <-> 1667 +1172 <-> 852, 1195, 1323, 1444 +1173 <-> 1058, 1389 +1174 <-> 1005 +1175 <-> 814 +1176 <-> 798 +1177 <-> 258, 815, 1401 +1178 <-> 687, 1038, 1331 +1179 <-> 134, 1179 +1180 <-> 420 +1181 <-> 1181 +1182 <-> 267, 1677 +1183 <-> 100 +1184 <-> 669, 1030, 1969 +1185 <-> 498, 1134, 1673, 1750 +1186 <-> 165 +1187 <-> 1893 +1188 <-> 1236, 1365 +1189 <-> 1334, 1732 +1190 <-> 279 +1191 <-> 1620 +1192 <-> 1257 +1193 <-> 1112 +1194 <-> 1770 +1195 <-> 187, 1172, 1964 +1196 <-> 641, 1070, 1121, 1729 +1197 <-> 511, 1273, 1607 +1198 <-> 229, 774 +1199 <-> 290, 455, 1860 +1200 <-> 1901 +1201 <-> 1108 +1202 <-> 1378 +1203 <-> 1591 +1204 <-> 229 +1205 <-> 645, 796, 1250 +1206 <-> 281, 1824 +1207 <-> 782 +1208 <-> 546, 795, 1700 +1209 <-> 249 +1210 <-> 750, 787, 937 +1211 <-> 527, 1981 +1212 <-> 1212, 1369 +1213 <-> 1512 +1214 <-> 737 +1215 <-> 575 +1216 <-> 540, 1216 +1217 <-> 1312, 1340 +1218 <-> 291, 1586 +1219 <-> 583, 1554 +1220 <-> 117, 767 +1221 <-> 411, 620, 1221 +1222 <-> 1612, 1710 +1223 <-> 1223, 1374 +1224 <-> 331 +1225 <-> 315, 952, 1263 +1226 <-> 1059, 1928 +1227 <-> 864, 1037, 1823 +1228 <-> 1036, 1613 +1229 <-> 589, 996, 1002, 1014, 1906 +1230 <-> 247, 468, 772, 1821, 1837 +1231 <-> 195, 220, 725 +1232 <-> 271, 542, 660, 1003, 1232, 1606 +1233 <-> 1084, 1366, 1738 +1234 <-> 543, 1408 +1235 <-> 524 +1236 <-> 183, 1188 +1237 <-> 1150 +1238 <-> 820, 1521 +1239 <-> 980 +1240 <-> 1139, 1240 +1241 <-> 597, 1046 +1242 <-> 1646 +1243 <-> 331, 741, 860 +1244 <-> 1522, 1870 +1245 <-> 1245 +1246 <-> 801 +1247 <-> 665, 839 +1248 <-> 208, 1932 +1249 <-> 857 +1250 <-> 1205 +1251 <-> 711 +1252 <-> 1888 +1253 <-> 997, 1593 +1254 <-> 235, 520, 923, 1382 +1255 <-> 936 +1256 <-> 1718 +1257 <-> 259, 1192 +1258 <-> 659, 1917 +1259 <-> 392 +1260 <-> 1260 +1261 <-> 1261, 1376 +1262 <-> 1936 +1263 <-> 1225 +1264 <-> 1150, 1567 +1265 <-> 398 +1266 <-> 773, 1373 +1267 <-> 257, 341, 525 +1268 <-> 202, 262, 1128 +1269 <-> 1027 +1270 <-> 927 +1271 <-> 1083, 1093 +1272 <-> 781 +1273 <-> 1197 +1274 <-> 1760 +1275 <-> 1028, 1827 +1276 <-> 707, 1900 +1277 <-> 188 +1278 <-> 1463 +1279 <-> 758, 810 +1280 <-> 1920 +1281 <-> 1942 +1282 <-> 53, 1007, 1079 +1283 <-> 192, 903, 1164, 1690 +1284 <-> 512, 1584 +1285 <-> 1109, 1285 +1286 <-> 272 +1287 <-> 160 +1288 <-> 15, 1097, 1905 +1289 <-> 591, 606, 1011 +1290 <-> 1051 +1291 <-> 331, 1034 +1292 <-> 470, 880 +1293 <-> 1501, 1899 +1294 <-> 746, 1294 +1295 <-> 183, 1024 +1296 <-> 1580 +1297 <-> 711, 752, 934 +1298 <-> 1298 +1299 <-> 517, 1299 +1300 <-> 1300 +1301 <-> 708, 1301 +1302 <-> 645 +1303 <-> 1355, 1492 +1304 <-> 1361, 1746 +1305 <-> 773 +1306 <-> 334, 1325 +1307 <-> 769, 776, 873, 1333 +1308 <-> 312, 1851, 1966 +1309 <-> 607, 1459, 1496 +1310 <-> 759 +1311 <-> 1381, 1520 +1312 <-> 1217 +1313 <-> 1983 +1314 <-> 1314 +1315 <-> 1315, 1647 +1316 <-> 63 +1317 <-> 537 +1318 <-> 1973 +1319 <-> 935, 1517 +1320 <-> 531, 822 +1321 <-> 27, 1837 +1322 <-> 883, 1664 +1323 <-> 1172 +1324 <-> 730 +1325 <-> 1306 +1326 <-> 633, 875 +1327 <-> 159, 1553 +1328 <-> 1974 +1329 <-> 1939 +1330 <-> 277, 1515 +1331 <-> 1178, 1590 +1332 <-> 274, 1332 +1333 <-> 8, 761, 1307, 1333 +1334 <-> 275, 1189, 1482 +1335 <-> 1478 +1336 <-> 140 +1337 <-> 66, 611, 768, 841 +1338 <-> 176, 685, 688, 1449 +1339 <-> 1339 +1340 <-> 301, 1157, 1217, 1630 +1341 <-> 27 +1342 <-> 1012 +1343 <-> 1408 +1344 <-> 452, 1125, 1622 +1345 <-> 74, 1835 +1346 <-> 1860 +1347 <-> 634, 1428 +1348 <-> 907, 939 +1349 <-> 490, 1349 +1350 <-> 305, 612, 757 +1351 <-> 162 +1352 <-> 797, 1818 +1353 <-> 1119, 1353 +1354 <-> 1436 +1355 <-> 1303 +1356 <-> 94, 254 +1357 <-> 1419, 1664, 1680 +1358 <-> 1358 +1359 <-> 197 +1360 <-> 722, 1909 +1361 <-> 1304 +1362 <-> 82, 188, 1448 +1363 <-> 1752 +1364 <-> 501 +1365 <-> 1188, 1661 +1366 <-> 584, 1233 +1367 <-> 623, 1394, 1781 +1368 <-> 1886 +1369 <-> 1212 +1370 <-> 86, 1370 +1371 <-> 1772 +1372 <-> 191, 1473 +1373 <-> 1266 +1374 <-> 1223, 1981 +1375 <-> 366, 1375 +1376 <-> 1261, 1599 +1377 <-> 1675 +1378 <-> 30, 1202, 1406, 1845 +1379 <-> 153, 628, 1557 +1380 <-> 180, 997 +1381 <-> 1311, 1407, 1666 +1382 <-> 1254 +1383 <-> 375, 1714 +1384 <-> 392 +1385 <-> 1140, 1933 +1386 <-> 1949 +1387 <-> 439, 1387 +1388 <-> 1770 +1389 <-> 1173, 1679 +1390 <-> 123, 453, 1733 +1391 <-> 158, 249, 889, 1945 +1392 <-> 1881 +1393 <-> 820 +1394 <-> 18, 181, 355, 1367 +1395 <-> 374, 1404 +1396 <-> 515, 1860 +1397 <-> 200, 822 +1398 <-> 472, 908, 1622, 1701 +1399 <-> 699 +1400 <-> 422, 947, 1551 +1401 <-> 1145, 1177 +1402 <-> 1764 +1403 <-> 1875 +1404 <-> 1395 +1405 <-> 661, 813 +1406 <-> 780, 1378 +1407 <-> 1381 +1408 <-> 588, 940, 1234, 1343, 1603, 1865 +1409 <-> 1427 +1410 <-> 164 +1411 <-> 88, 982 +1412 <-> 1452 +1413 <-> 1707, 1766 +1414 <-> 121 +1415 <-> 318, 1415, 1612 +1416 <-> 1416 +1417 <-> 232 +1418 <-> 361, 955, 1418, 1737 +1419 <-> 473, 1357 +1420 <-> 1003 +1421 <-> 122, 1973 +1422 <-> 512, 1870 +1423 <-> 248 +1424 <-> 648 +1425 <-> 1425 +1426 <-> 224, 1946 +1427 <-> 796, 816, 1409 +1428 <-> 1347 +1429 <-> 1810, 1862 +1430 <-> 1430 +1431 <-> 788, 1488 +1432 <-> 259, 1432 +1433 <-> 1, 501, 748, 1044 +1434 <-> 930 +1435 <-> 991 +1436 <-> 1354, 1436 +1437 <-> 253 +1438 <-> 522, 558, 842, 918, 1010 +1439 <-> 1649 +1440 <-> 735, 941, 1111 +1441 <-> 1707 +1442 <-> 305, 1930 +1443 <-> 357 +1444 <-> 1172 +1445 <-> 162, 270, 1636 +1446 <-> 1053 +1447 <-> 220, 292, 805 +1448 <-> 1362 +1449 <-> 740, 972, 1338 +1450 <-> 100, 237, 1021 +1451 <-> 5, 1082 +1452 <-> 1412, 1572 +1453 <-> 556 +1454 <-> 1454 +1455 <-> 850 +1456 <-> 125, 268, 1099 +1457 <-> 240, 1104 +1458 <-> 18, 1576 +1459 <-> 1309, 1503 +1460 <-> 84, 371 +1461 <-> 1747, 1879 +1462 <-> 3, 1167, 1807 +1463 <-> 377, 1278, 1499, 1971 +1464 <-> 1908 +1465 <-> 72 +1466 <-> 724, 842 +1467 <-> 410, 739 +1468 <-> 67 +1469 <-> 155, 1652 +1470 <-> 268, 469, 486 +1471 <-> 800, 1012, 1471, 1510 +1472 <-> 39 +1473 <-> 1372 +1474 <-> 1010, 1915 +1475 <-> 467, 1658 +1476 <-> 1476 +1477 <-> 627, 1477 +1478 <-> 427, 1335, 1907 +1479 <-> 348 +1480 <-> 1480 +1481 <-> 1802 +1482 <-> 1334 +1483 <-> 1147, 1524 +1484 <-> 42, 525 +1485 <-> 539 +1486 <-> 148, 1042, 1549 +1487 <-> 812, 1136 +1488 <-> 1053, 1431 +1489 <-> 1708, 1931 +1490 <-> 1807 +1491 <-> 431 +1492 <-> 156, 1303 +1493 <-> 1493 +1494 <-> 1853 +1495 <-> 446, 976 +1496 <-> 395, 1309 +1497 <-> 195, 396, 1974 +1498 <-> 490, 1626 +1499 <-> 76, 1463 +1500 <-> 1722 +1501 <-> 577, 1293 +1502 <-> 115 +1503 <-> 1459, 1507 +1504 <-> 210, 261, 578, 1521, 1718 +1505 <-> 230, 426, 684, 1634 +1506 <-> 382, 1921 +1507 <-> 1503 +1508 <-> 162, 1667 +1509 <-> 961, 1509 +1510 <-> 1471 +1511 <-> 954, 982, 1582 +1512 <-> 476, 959, 1213, 1703 +1513 <-> 353, 620 +1514 <-> 617, 1546 +1515 <-> 1330, 1595 +1516 <-> 1946 +1517 <-> 42, 1319 +1518 <-> 585 +1519 <-> 32, 1087 +1520 <-> 1311 +1521 <-> 861, 1238, 1504 +1522 <-> 1244, 1653 +1523 <-> 1523 +1524 <-> 1483 +1525 <-> 894, 1525 +1526 <-> 1924 +1527 <-> 812, 878 +1528 <-> 494 +1529 <-> 59, 1074 +1530 <-> 1530 +1531 <-> 34, 1531 +1532 <-> 1638 +1533 <-> 853 +1534 <-> 953, 968 +1535 <-> 108, 689 +1536 <-> 1589 +1537 <-> 394, 865 +1538 <-> 915, 1059 +1539 <-> 868 +1540 <-> 858, 1745 +1541 <-> 221 +1542 <-> 639 +1543 <-> 1746 +1544 <-> 783, 1544 +1545 <-> 236 +1546 <-> 66, 1095, 1514 +1547 <-> 1628 +1548 <-> 1548 +1549 <-> 433, 1486 +1550 <-> 869, 1550 +1551 <-> 1400, 1787 +1552 <-> 695, 872 +1553 <-> 997, 1327 +1554 <-> 1219 +1555 <-> 97 +1556 <-> 1840 +1557 <-> 7, 1379 +1558 <-> 126, 863, 1160 +1559 <-> 336, 373 +1560 <-> 343, 811 +1561 <-> 278, 794, 880, 1561 +1562 <-> 127, 518, 1562 +1563 <-> 406 +1564 <-> 81, 399 +1565 <-> 748 +1566 <-> 637, 1000 +1567 <-> 1264 +1568 <-> 1568 +1569 <-> 214 +1570 <-> 561, 1849 +1571 <-> 282 +1572 <-> 44, 130, 178, 1452 +1573 <-> 107 +1574 <-> 299 +1575 <-> 647, 858 +1576 <-> 1458, 1633 +1577 <-> 1833, 1939 +1578 <-> 1039, 1802 +1579 <-> 807, 1853 +1580 <-> 1296, 1580, 1907 +1581 <-> 675 +1582 <-> 1511, 1605, 1756 +1583 <-> 811 +1584 <-> 1284 +1585 <-> 1817 +1586 <-> 168, 650, 1218 +1587 <-> 784, 1142 +1588 <-> 742 +1589 <-> 45, 209, 413, 1536 +1590 <-> 25, 201, 1162, 1331 +1591 <-> 913, 1203 +1592 <-> 1820 +1593 <-> 1253 +1594 <-> 231 +1595 <-> 149, 1515 +1596 <-> 57, 1976 +1597 <-> 586, 902 +1598 <-> 855 +1599 <-> 1376 +1600 <-> 811, 1022 +1601 <-> 284, 746 +1602 <-> 386, 893 +1603 <-> 135, 977, 1408 +1604 <-> 452, 513 +1605 <-> 1104, 1582 +1606 <-> 831, 1232 +1607 <-> 709, 715, 858, 1197 +1608 <-> 1793 +1609 <-> 611, 1808 +1610 <-> 1026, 1964 +1611 <-> 304 +1612 <-> 1222, 1415, 1769 +1613 <-> 1228, 1847 +1614 <-> 273 +1615 <-> 978 +1616 <-> 156, 355 +1617 <-> 177 +1618 <-> 1618 +1619 <-> 323, 642, 832 +1620 <-> 113, 349, 1191, 1746 +1621 <-> 609 +1622 <-> 519, 1344, 1398 +1623 <-> 614 +1624 <-> 771, 1989 +1625 <-> 1625 +1626 <-> 1498 +1627 <-> 186, 315 +1628 <-> 633, 1547 +1629 <-> 1706 +1630 <-> 1340 +1631 <-> 297, 1800 +1632 <-> 1806 +1633 <-> 1576 +1634 <-> 1505 +1635 <-> 1156 +1636 <-> 1445 +1637 <-> 76, 992, 1920, 1995 +1638 <-> 814, 1532 +1639 <-> 994, 1061 +1640 <-> 1640 +1641 <-> 721 +1642 <-> 1739, 1945 +1643 <-> 1643 +1644 <-> 1644, 1908 +1645 <-> 125, 303 +1646 <-> 1242, 1646 +1647 <-> 1315 +1648 <-> 1957 +1649 <-> 97, 1439, 1783 +1650 <-> 576 +1651 <-> 1651 +1652 <-> 35, 1469 +1653 <-> 1522 +1654 <-> 1104 +1655 <-> 460, 859 +1656 <-> 362 +1657 <-> 142, 181 +1658 <-> 428, 1475 +1659 <-> 470 +1660 <-> 247 +1661 <-> 1365 +1662 <-> 165, 359 +1663 <-> 198 +1664 <-> 1322, 1357 +1665 <-> 447, 632 +1666 <-> 939, 1381 +1667 <-> 1171, 1508 +1668 <-> 638, 1156 +1669 <-> 476, 865, 1699 +1670 <-> 577, 971 +1671 <-> 119, 417, 762, 1804 +1672 <-> 50, 1672, 1687 +1673 <-> 63, 333, 1185 +1674 <-> 1674 +1675 <-> 993, 1377 +1676 <-> 742, 1813 +1677 <-> 233, 1182, 1846 +1678 <-> 962, 1165 +1679 <-> 722, 1389 +1680 <-> 82, 1357 +1681 <-> 1681, 1702, 1895 +1682 <-> 372 +1683 <-> 203, 341, 910 +1684 <-> 1019, 1948 +1685 <-> 1982 +1686 <-> 371 +1687 <-> 1672 +1688 <-> 791 +1689 <-> 1065, 1689 +1690 <-> 1283 +1691 <-> 925, 1878 +1692 <-> 803, 1063, 1732 +1693 <-> 487 +1694 <-> 600 +1695 <-> 1695, 1794 +1696 <-> 1696 +1697 <-> 1802 +1698 <-> 357, 732 +1699 <-> 1107, 1669 +1700 <-> 1208 +1701 <-> 1398 +1702 <-> 956, 1681 +1703 <-> 605, 1512 +1704 <-> 1082 +1705 <-> 343 +1706 <-> 1629, 1775 +1707 <-> 770, 929, 1413, 1441 +1708 <-> 367, 1489 +1709 <-> 1066, 1862 +1710 <-> 1222 +1711 <-> 650 +1712 <-> 620 +1713 <-> 1713 +1714 <-> 1383 +1715 <-> 1911 +1716 <-> 510, 1716 +1717 <-> 1076 +1718 <-> 1256, 1504 +1719 <-> 238 +1720 <-> 549, 634, 1720 +1721 <-> 15 +1722 <-> 826, 1500 +1723 <-> 1880 +1724 <-> 177, 1724 +1725 <-> 514, 1123, 1797 +1726 <-> 482, 953 +1727 <-> 1914 +1728 <-> 216, 1982 +1729 <-> 579, 783, 1196, 1800 +1730 <-> 1730, 1972 +1731 <-> 1009 +1732 <-> 89, 1189, 1692 +1733 <-> 1390 +1734 <-> 809 +1735 <-> 455, 695 +1736 <-> 900, 1736 +1737 <-> 530, 1418 +1738 <-> 1233, 1888 +1739 <-> 1044, 1642, 1834 +1740 <-> 966 +1741 <-> 145, 253 +1742 <-> 112 +1743 <-> 1980 +1744 <-> 139 +1745 <-> 1086, 1540 +1746 <-> 1304, 1543, 1620 +1747 <-> 117, 354, 1461 +1748 <-> 45, 273, 332, 1062 +1749 <-> 249 +1750 <-> 124, 1185 +1751 <-> 1835 +1752 <-> 104, 837, 1363 +1753 <-> 245, 775 +1754 <-> 798, 1876 +1755 <-> 453, 718, 821 +1756 <-> 1582 +1757 <-> 952, 1772, 1841 +1758 <-> 1758, 1830, 1878 +1759 <-> 729 +1760 <-> 104, 1274 +1761 <-> 224, 619, 622, 763, 1868 +1762 <-> 1762 +1763 <-> 537 +1764 <-> 904, 1402 +1765 <-> 521, 818, 886, 1782 +1766 <-> 421, 1413 +1767 <-> 1134 +1768 <-> 202, 1090 +1769 <-> 1612 +1770 <-> 621, 880, 1194, 1388 +1771 <-> 293 +1772 <-> 1371, 1757 +1773 <-> 19, 375 +1774 <-> 1774 +1775 <-> 1706, 1915 +1776 <-> 778 +1777 <-> 460, 1918 +1778 <-> 666 +1779 <-> 523, 1846 +1780 <-> 427 +1781 <-> 1367 +1782 <-> 701, 771, 1138, 1765 +1783 <-> 482, 1649, 1783 +1784 <-> 1784, 1872 +1785 <-> 777, 1785 +1786 <-> 1858 +1787 <-> 1551 +1788 <-> 59, 384, 1865 +1789 <-> 111 +1790 <-> 294, 407, 1969 +1791 <-> 238, 930 +1792 <-> 659 +1793 <-> 489, 538, 697, 1608 +1794 <-> 206, 649, 1695 +1795 <-> 314, 748 +1796 <-> 1796 +1797 <-> 899, 1725, 1797 +1798 <-> 823, 995 +1799 <-> 308, 1799 +1800 <-> 675, 683, 1631, 1729 +1801 <-> 697, 979, 1858 +1802 <-> 967, 1481, 1578, 1697 +1803 <-> 1154, 1803 +1804 <-> 1671 +1805 <-> 199 +1806 <-> 264, 1632, 1806 +1807 <-> 1462, 1490 +1808 <-> 1609, 1808 +1809 <-> 1157 +1810 <-> 1429 +1811 <-> 125 +1812 <-> 998 +1813 <-> 1676 +1814 <-> 358, 485, 920, 1814 +1815 <-> 211 +1816 <-> 632 +1817 <-> 513, 1585 +1818 <-> 1149, 1352 +1819 <-> 632, 717 +1820 <-> 465, 1592 +1821 <-> 46, 257, 1230 +1822 <-> 492 +1823 <-> 1227, 1891 +1824 <-> 247, 1206 +1825 <-> 182, 865 +1826 <-> 501 +1827 <-> 3, 1071, 1275 +1828 <-> 29 +1829 <-> 139 +1830 <-> 1758 +1831 <-> 542 +1832 <-> 1862 +1833 <-> 1577 +1834 <-> 151, 826, 1739, 1882 +1835 <-> 828, 1345, 1751, 1835 +1836 <-> 45, 677 +1837 <-> 1230, 1321 +1838 <-> 165, 1856 +1839 <-> 1842, 1953 +1840 <-> 183, 1556 +1841 <-> 554, 1757 +1842 <-> 884, 1839 +1843 <-> 464, 809 +1844 <-> 291, 570, 1151 +1845 <-> 1378 +1846 <-> 1677, 1779 +1847 <-> 374, 1613 +1848 <-> 204, 412 +1849 <-> 626, 1570 +1850 <-> 1850 +1851 <-> 1308 +1852 <-> 228, 455 +1853 <-> 454, 1114, 1494, 1579 +1854 <-> 268, 596 +1855 <-> 1855 +1856 <-> 1838 +1857 <-> 61 +1858 <-> 336, 1786, 1801, 1937 +1859 <-> 1908 +1860 <-> 1199, 1346, 1396 +1861 <-> 1861 +1862 <-> 1429, 1709, 1832, 1900 +1863 <-> 9 +1864 <-> 41, 1975 +1865 <-> 673, 1408, 1788 +1866 <-> 966, 1873 +1867 <-> 914 +1868 <-> 330, 520, 960, 1761 +1869 <-> 2, 834 +1870 <-> 1244, 1422 +1871 <-> 1119 +1872 <-> 1784 +1873 <-> 242, 1866 +1874 <-> 337, 1109, 1131 +1875 <-> 795, 1403 +1876 <-> 258, 1754 +1877 <-> 34 +1878 <-> 481, 1691, 1758 +1879 <-> 1076, 1461 +1880 <-> 147, 410, 1723 +1881 <-> 520, 764, 1392, 1955 +1882 <-> 1834 +1883 <-> 319, 514 +1884 <-> 1969 +1885 <-> 740, 870, 1049 +1886 <-> 1013, 1368 +1887 <-> 1887 +1888 <-> 954, 1252, 1738 +1889 <-> 977 +1890 <-> 446, 530 +1891 <-> 1823 +1892 <-> 1124, 1892 +1893 <-> 395, 1187, 1893 +1894 <-> 988 +1895 <-> 733, 1681 +1896 <-> 11 +1897 <-> 77, 801 +1898 <-> 545, 1898 +1899 <-> 1005, 1293 +1900 <-> 511, 1276, 1862 +1901 <-> 1086, 1200 +1902 <-> 410 +1903 <-> 315, 990 +1904 <-> 422 +1905 <-> 1288, 1905 +1906 <-> 1229 +1907 <-> 1478, 1580 +1908 <-> 1464, 1644, 1859 +1909 <-> 706, 1360 +1910 <-> 569 +1911 <-> 310, 850, 1715 +1912 <-> 1912 +1913 <-> 279, 1132 +1914 <-> 614, 929, 1727 +1915 <-> 1474, 1775 +1916 <-> 1916 +1917 <-> 1258 +1918 <-> 382, 1777 +1919 <-> 41, 653 +1920 <-> 1280, 1637 +1921 <-> 933, 1506 +1922 <-> 167 +1923 <-> 857 +1924 <-> 222, 1526, 1924 +1925 <-> 231, 367, 1925 +1926 <-> 385, 422, 986 +1927 <-> 321, 513, 553 +1928 <-> 728, 1226 +1929 <-> 912, 952, 1965 +1930 <-> 1442 +1931 <-> 1073, 1489 +1932 <-> 1248, 1932 +1933 <-> 499, 877, 1098, 1385 +1934 <-> 1165 +1935 <-> 37, 631 +1936 <-> 283, 757, 1262 +1937 <-> 1858 +1938 <-> 109, 555, 1102 +1939 <-> 1085, 1329, 1577 +1940 <-> 902, 1940 +1941 <-> 364, 583 +1942 <-> 719, 1281 +1943 <-> 609, 760 +1944 <-> 230 +1945 <-> 1391, 1642 +1946 <-> 1093, 1426, 1516 +1947 <-> 1153 +1948 <-> 212, 296, 500, 1684 +1949 <-> 152, 737, 1386 +1950 <-> 133, 296 +1951 <-> 919, 1951 +1952 <-> 921 +1953 <-> 978, 1839 +1954 <-> 657 +1955 <-> 975, 1881 +1956 <-> 55, 71, 235, 742 +1957 <-> 1029, 1648 +1958 <-> 1958 +1959 <-> 886 +1960 <-> 196, 301, 495 +1961 <-> 674 +1962 <-> 576, 1022, 1047 +1963 <-> 883 +1964 <-> 832, 1195, 1610 +1965 <-> 1929 +1966 <-> 745, 1308 +1967 <-> 751 +1968 <-> 524, 1968 +1969 <-> 1076, 1184, 1790, 1884 +1970 <-> 983, 1970 +1971 <-> 1463 +1972 <-> 1730 +1973 <-> 457, 1318, 1421 +1974 <-> 1328, 1497, 1974 +1975 <-> 170, 1135, 1864 +1976 <-> 1596 +1977 <-> 70, 943, 1008 +1978 <-> 804 +1979 <-> 631 +1980 <-> 522, 742, 1743 +1981 <-> 1211, 1374 +1982 <-> 597, 1685, 1728 +1983 <-> 30, 931, 1313 +1984 <-> 109, 720 +1985 <-> 111 +1986 <-> 767 +1987 <-> 418, 701, 850 +1988 <-> 1061 +1989 <-> 1624 +1990 <-> 744 +1991 <-> 316 +1992 <-> 346, 562, 1040, 1081 +1993 <-> 685 +1994 <-> 573 +1995 <-> 381, 676, 1637, 1995 +1996 <-> 576, 652 +1997 <-> 554 +1998 <-> 168 +1999 <-> 818 diff --git a/pytudes/data/advent2017/input13.txt b/pytudes/data/advent2017/input13.txt new file mode 100644 index 0000000..e911a64 --- /dev/null +++ b/pytudes/data/advent2017/input13.txt @@ -0,0 +1,43 @@ +0: 3 +1: 2 +2: 4 +4: 6 +6: 4 +8: 6 +10: 5 +12: 6 +14: 9 +16: 6 +18: 8 +20: 8 +22: 8 +24: 8 +26: 8 +28: 8 +30: 12 +32: 14 +34: 10 +36: 12 +38: 12 +40: 10 +42: 12 +44: 12 +46: 12 +48: 12 +50: 12 +52: 14 +54: 14 +56: 12 +62: 12 +64: 14 +66: 14 +68: 14 +70: 17 +72: 14 +74: 14 +76: 14 +82: 14 +86: 18 +88: 14 +96: 14 +98: 44 diff --git a/pytudes/data/advent2017/input16.txt b/pytudes/data/advent2017/input16.txt new file mode 100644 index 0000000..5311dbb --- /dev/null +++ b/pytudes/data/advent2017/input16.txt @@ -0,0 +1 @@ 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diff --git a/pytudes/data/advent2017/input18.txt b/pytudes/data/advent2017/input18.txt new file mode 100644 index 0000000..ea1762c --- /dev/null +++ b/pytudes/data/advent2017/input18.txt @@ -0,0 +1,41 @@ +set i 31 +set a 1 +mul p 17 +jgz p p +mul a 2 +add i -1 +jgz i -2 +add a -1 +set i 127 +set p 826 +mul p 8505 +mod p a +mul p 129749 +add p 12345 +mod p a +set b p +mod b 10000 +snd b +add i -1 +jgz i -9 +jgz a 3 +rcv b +jgz b -1 +set f 0 +set i 126 +rcv a +rcv b +set p a +mul p -1 +add p b +jgz p 4 +snd a +set a b +jgz 1 3 +snd b +set f 1 +add i -1 +jgz i -11 +snd a +jgz f -16 +jgz a -19 diff --git a/pytudes/data/advent2017/input19.txt b/pytudes/data/advent2017/input19.txt new file mode 100644 index 0000000..f18900e --- /dev/null +++ b/pytudes/data/advent2017/input19.txt @@ -0,0 +1,201 @@ + | + +-+ +-----------------------------+ +---+ +-------+ +-+ +-+ +-+ +-------+ +-+ + | | | | | | | | | | | | | | | | | + +-------------+ | +-+ +-------------------------------|---|---|---------------------------------------------------------+ | | | | | | | | +-+ | | + | | | | | | | | | | | | | | | | | | | | | + | | | | | | +-+ +---+ | | | +-------------------------------------------------|-------------+ | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | + +-------|-------------------|-|-+ | | +---+ I +-|---|-|---+ | | +-------------------------------------------------------------------|-|-----|---+ +-------+ + | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | +---------|-------------|---------+ +-|---------|---------|-----------+ | | | +---------|-|-------------------------------|-----+ | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | +---|-------------|-------|---|-|-------------+ | | | +-------|-+ | | | +---------------------|-----|---+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | 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| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | +-|-------|---|---+ +---------|-------------|-|-|-|-----|---|---|-|---------+ +-----|-----------------------------------|-----------|---|---|---|-|-------|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | T | | | | | | | | | | | | | | + +---|-----|-|-------|-------|---------------------------------|---|---------|-|-----|---|-----------------------|---------------|-|-----|---+ | | | | | | | | | | | +-+ | | +-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | +-----|-|-|-----|---|---------|---|-----------------------|-------|-|-----------|-|-|----------E------|-------|---|---+ | | | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | +-------|-----------|---------------------------|-|-|---|---|-----------|---|-----+ | | | | | | | | | | | | | +---|-----------|---------|---+ | | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | +-|-|-------------------------------|-|-|-------|-|---|---------|---------------+ | +---------------|---|---------|---------------------|---+ | | | | +-+ | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | +---------------------------------|-|-|---|---|-|---|-|-------|-----------|-------|-----------|---|-------------|---|-----|---|---|-----|-|-------|---+ | +-+ | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-----+ +-----+ | | | | | | | | | | | | | | | | | | +---|-+ | | | | | | +-----|-------|---------|-----------|-----+ | +---|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +---------------------------|---+ | | | | | | | | | | +-------|-------|-----------|-------|---|-----------|-|---------------------|-----|-|---+ | +-------|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | | | +---|-----------|---|-|-----|-------|---|-|-----+ | | +-|---------|---|---------|-|---|-+ | | +-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-----------|-----|-------|---|---------------------------------|-------|---|-------|---------------|-----------|---+ | | | | | | | | | +-----|-+ | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +---------------|-|-|---------|-----------------------------|-----|-|-------|-|---|-|---|---|-------|---------------|-------|---|-|-|---------|---+ | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | +-|---|-+ +-------------------------------+ | | | | | +-----|---|-------|---------------|-------|-------|---+ | | | +-----|-|---|-----------|-|---------------|---+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-----------|-----|-|---|-|---|-|---+ | | | | | | | | | | | | | | +---|---|---|-|-|-+ | | | | | +---|---------|-|-----|-|---|---+ +-----|---+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | +---------------|---|-------|---|-|-----|---|-----------|---|-|---------|-------|-|-|---+ | | +---+ | | | | +-+ | +---|-------------+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | +-------+ +-------|-----------------------------|---+ +-|-----------|-------+ | | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +---+ | | +-----|---------|---------|---------------|-------|-----|-+ | | | | | +---------|-----|-------|-------------|---------|-|-----------|-----|---+ | +-|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +---|-----+ | | | | | | | | | | | | | | | +-|---|-----|---|-----------|-------+ +-----|---|-----------------|-----|-------|-|---------------|-------|---+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | +---|---|-|-----|---+ | | | | | +---------|---|-------------------------------------|-|-------------------------|-|---+ | | | | +-------|-|-------+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | | | +---------|---------------|-----------|---|-------------|---------------|-----|-----------|---------+ | +-+ | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-----|-----|---------+ | | | | +---+ | | | +-----------------------|-----------------+ | | | | | | | | | | | | | +---------|---+ +-----|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | +---|-------|---|-+ | | +-------|---------------|-----------------------|---|---|-------------|-|-----------+ | | | | +-------|---|-|-+ | | +---|-----|-----------|---|---+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | | | | | | | | | | | | | | | +-|-----------------------+ | +-----------|---------------+ | | | +-|-----|-|-------+ | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + +-----|-----------|-------|-------|---------------|-------|-------------+ | +---+ +-|-----|-------------------|-------------|-|-----|---+ +-+ | | | | | | | +---+ +-+ | | +---+ | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | | +---+ | | | | | | | +---------------|-----|-----------------------------------------|---------+ | | | +-------|-----------+ | | | | + | | | | | | | | | | | | | | | | | | | | | | | | | | | | + | +-----------|-------|---------------|-|-----|-------------------------------------|-------------------|-----------+ | +-----+ +-----------------------+ | | | | | | + | | | | | | | | | | | | | | | | | | | | | | | | + | +---------------------------|-----|-------------------------------|-------|-----------------|-------------+ +-------------|-------------+ +-------|---+ | | | + | | | | | | | | | | | | | | | | | | | | | | + +-------------------|-----------------------|-|-----|---------------------------------------------+ +---------|---------------------------+ | | | +---|-+ | | | | | + | | | | | | | | | | | | | | | | | | | | | | + +-------+ +-+ +---------+ +-------------+ +---------|---------------------------|-----|---------------|-----------+ +---|-+ + | | | | | | | | | | + +-------------------------------------+ +-----------------+ +-----|-------------------------------+ | | + | | | | | | | | + +-------------------------------------------------------------------------------------------+ +-+ +---------------+ +-+ + diff --git a/pytudes/data/advent2017/input20.txt b/pytudes/data/advent2017/input20.txt new file mode 100644 index 0000000..391fca8 --- /dev/null +++ b/pytudes/data/advent2017/input20.txt @@ -0,0 +1,1000 @@ +p=<1199,-2918,1457>, v=<-13,115,-8>, a=<-7,8,-10> +p=<2551,2418,-1471>, v=<-106,-108,39>, a=<-6,-5,6> +p=<-73,1626,1321>, v=<58,-118,-8>, a=<-6,2,-9> +p=<-3297,-894,-551>, v=<183,31,-61>, a=<3,3,11> +p=<-1425,4298,617>, v=<32,-166,-32>, a=<7,-12,-1> +p=<-3718,877,1043>, v=<114,7,-20>, a=<10,-6,-4> +p=<-2089,-239,1142>, v=<52,12,3>, a=<7,0,-7> +p=<782,994,3311>, v=<16,-28,-32>, a=<-6,-3,-16> +p=<-937,2596,-109>, v=<-12,-117,-13>, a=<7,-3,2> +p=<-865,-2930,-1387>, v=<60,76,-56>, a=<-1,9,14> +p=<1196,-3308,2564>, v=<-26,59,0>, a=<-4,13,-15> +p=<-271,1957,-2944>, v=<8,-15,40>, a=<1,-10,13> +p=<-964,1228,1583>, v=<18,16,-12>, a=<4,-9,-8> +p=<-1639,1174,1970>, v=<84,-114,-138>, a=<1,5,3> +p=<-1840,1679,-1764>, v=<44,-20,91>, a=<8,-10,2> +p=<1104,-233,140>, v=<-21,-11,-28>, a=<-6,3,2> +p=<1136,-361,-3100>, v=<-40,14,98>, a=<-4,1,11> +p=<1480,-265,-1412>, v=<-36,42,18>, a=<-7,-3,8> +p=<144,-1217,-660>, v=<39,25,56>, a=<-6,6,-2> +p=<360,295,276>, v=<-51,-95,-11>, a=<3,9,-1> +p=<-2656,487,1228>, v=<78,12,-11>, a=<10,-5,-8> +p=<-1400,2295,-204>, v=<-9,-67,53>, a=<11,-9,-5> +p=<-1016,-769,-52>, v=<1,14,120>, a=<7,4,-14> +p=<1536,4167,-940>, v=<-99,-201,82>, a=<0,-7,-3> +p=<2398,3917,2412>, v=<-69,-51,-81>, a=<-3,-10,-2> +p=<-3283,536,733>, v=<46,72,-32>, a=<8,-8,0> +p=<-247,1180,-2901>, v=<46,-52,-18>, a=<-3,0,12> +p=<-2984,-499,-1475>, v=<-3,57,-8>, a=<11,-3,6> +p=<-431,2008,-3890>, v=<54,-40,49>, a=<-3,-4,10> +p=<2904,-775,-3614>, v=<5,-3,97>, a=<-11,3,5> +p=<2697,-1074,3401>, v=<38,70,-28>, a=<-13,-2,-10> +p=<-1259,1456,595>, v=<42,8,34>, a=<1,-6,-5> +p=<-1293,5020,-2110>, v=<-12,-199,93>, a=<7,-5,1> +p=<-1753,-1520,-320>, v=<-10,44,14>, a=<9,3,0> +p=<-2143,1040,-2220>, v=<83,-42,109>, a=<2,-1,0> +p=<-203,3210,-530>, v=<-56,-98,35>, a=<6,-6,-1> +p=<3017,-3820,290>, v=<-154,96,-6>, a=<0,9,-1> +p=<-1195,-180,-289>, v=<93,-30,-2>, a=<1,6,4> +p=<371,1368,953>, v=<-18,-16,-125>, a=<-2,-16,7> +p=<-1777,-426,-523>, v=<187,-16,24>, a=<-6,7,3> +p=<-2635,690,-1177>, v=<148,-83,59>, a=<11,3,6> +p=<431,-366,-1333>, v=<-62,18,124>, a=<4,1,-2> +p=<-2311,-750,143>, v=<147,11,-51>, a=<7,7,6> +p=<-151,354,-85>, v=<97,-29,-84>, a=<-13,-1,14> +p=<-325,-1602,779>, v=<-25,56,-13>, a=<8,11,-8> +p=<-385,-204,467>, v=<-7,37,0>, a=<6,-4,-6> +p=<665,-1272,-1195>, v=<-10,35,80>, a=<-7,10,3> +p=<-2525,7592,-6216>, v=<43,-14,0>, a=<1,-9,8> +p=<-68,4433,8721>, v=<-120,-113,-63>, a=<6,0,-8> +p=<-6971,-91,-561>, v=<-43,3,15>, a=<11,0,0> +p=<-2876,806,-8478>, v=<72,-60,58>, a=<0,2,8> +p=<-7907,4004,258>, v=<61,-42,-46>, a=<7,-3,2> +p=<-4358,6773,5523>, v=<50,-73,39>, a=<3,-5,-9> +p=<1941,1823,224>, v=<-102,-73,-54>, a=<1,-1,4> +p=<-1440,-1768,224>, v=<70,87,67>, a=<0,0,-7> +p=<-1776,3125,2870>, v=<20,-58,-4>, a=<6,-8,-12> +p=<1437,-697,-5635>, v=<-12,25,115>, a=<-5,1,14> +p=<-3603,-151,2366>, v=<30,-89,31>, a=<13,9,-13> +p=<-264,4805,3857>, v=<3,-105,-40>, a=<1,-11,-13> +p=<-831,-823,140>, v=<52,-35,5>, a=<-1,7,-1> +p=<2970,-634,1085>, v=<-52,110,-18>, a=<-8,-7,-3> +p=<1755,-4503,-1198>, v=<-18,102,8>, a=<-4,6,3> +p=<-4945,572,1727>, v=<42,-101,-5>, a=<12,6,-5> +p=<-70,5047,-2023>, v=<3,45,54>, a=<0,-19,2> +p=<-2845,4372,-2598>, v=<75,-110,116>, a=<3,-5,-1> +p=<-345,-228,-1898>, v=<-38,61,88>, a=<4,-4,-1> +p=<-2720,3622,1727>, v=<109,-2,-83>, a=<0,-11,1> +p=<-4045,-3228,-2448>, v=<-7,116,-7>, a=<13,1,8> +p=<580,3347,802>, v=<-10,48,19>, a=<-1,-14,-4> +p=<-1910,2875,1236>, v=<71,-54,88>, a=<-1,-1,-6> +p=<-2963,-6485,2406>, v=<-102,86,-42>, a=<9,4,-1> +p=<-18875,7633,-7890>, v=<86,-76,82>, a=<20,-6,6> +p=<391,9505,4980>, v=<-8,76,-108>, a=<0,-16,-1> +p=<-935,5800,-1533>, v=<-114,-129,59>, a=<7,-1,-1> +p=<-272,-7733,12858>, v=<69,18,10>, a=<-3,9,-17> +p=<-7292,613,12741>, v=<49,-116,-47>, a=<7,5,-14> +p=<3550,-518,-15339>, v=<51,33,73>, a=<-7,-1,16> +p=<4213,-8123,-2157>, v=<14,88,55>, a=<-6,6,0> +p=<-7721,418,-17250>, v=<80,69,2>, a=<6,-4,22> +p=<1738,-2831,-158>, v=<40,35,8>, a=<-12,10,0> +p=<2598,399,782>, v=<-66,10,45>, a=<-6,-3,-8> +p=<3068,129,-1558>, v=<-58,13,57>, a=<-9,-2,2> +p=<-1782,4139,-3628>, v=<-99,-93,171>, a=<18,-11,1> +p=<-1082,-3161,-498>, v=<55,83,67>, a=<0,7,-4> +p=<-5302,-1291,772>, v=<98,42,-70>, a=<16,2,3> +p=<808,979,232>, v=<-50,2,-1>, a=<1,-5,-1> +p=<-152,1479,-8>, v=<-86,61,11>, a=<9,-13,-1> +p=<1292,1700,-858>, v=<-72,-94,96>, a=<-4,-5,-4> +p=<304,-640,-455>, v=<53,-12,72>, a=<-11,9,-5> +p=<486,1063,-689>, v=<-52,-66,27>, a=<2,-2,4> +p=<993,-1823,182>, v=<-84,30,-47>, a=<1,16,5> +p=<-1230,-1615,-312>, v=<52,182,96>, a=<6,-8,-10> +p=<-268,1297,728>, v=<20,-105,-40>, a=<0,1,-2> +p=<1476,1697,875>, v=<5,-87,-71>, a=<-15,-5,1> +p=<1476,1193,-1813>, v=<-85,-51,46>, a=<-3,-5,11> +p=<932,-6376,-4019>, v=<-47,24,-82>, a=<1,12,14> +p=<-12763,29,8401>, v=<177,-19,-62>, a=<16,1,-14> +p=<5087,6059,1936>, v=<-139,-65,76>, a=<-2,-9,-9> +p=<-853,-721,-4889>, v=<28,6,40>, a=<0,1,8> +p=<-1288,329,-11219>, v=<58,33,96>, a=<-1,-3,18> +p=<1352,-286,4051>, v=<-61,38,-10>, a=<1,-2,-8> +p=<2477,-271,-4649>, v=<41,-40,32>, a=<-8,3,8> +p=<-1783,-376,-6944>, v=<59,41,155>, a=<0,-2,5> +p=<-8728,2204,-1514>, v=<27,48,-26>, a=<17,-8,5> +p=<2987,-7276,-1829>, v=<-100,54,-31>, a=<0,12,6> +p=<-86,2277,1643>, v=<48,-108,-103>, a=<-4,0,2> +p=<-1640,-726,3722>, v=<45,24,-48>, a=<3,1,-12> +p=<334,-4947,761>, v=<-82,71,-28>, a=<6,15,-1> +p=<2686,1290,572>, v=<-106,16,-41>, a=<-2,-7,1> +p=<1153,3663,152>, v=<-110,35,45>, a=<5,-19,-5> +p=<-3257,-957,-2620>, v=<45,35,-32>, a=<10,1,14> +p=<-4958,4524,-2179>, v=<16,-127,13>, a=<20,-8,8> +p=<-1913,2844,-898>, v=<47,-135,40>, a=<4,0,0> +p=<-3826,-5200,5502>, v=<-27,-24,31>, a=<8,10,-11> +p=<50,-7529,4380>, v=<34,27,-6>, a=<-2,11,-7> +p=<-362,3,273>, v=<20,20,-5>, a=<3,-4,-4> +p=<-927,-577,-887>, v=<82,89,56>, a=<2,-6,6> +p=<-942,-727,1133>, v=<78,-6,-102>, a=<3,14,-2> +p=<-92,-817,-222>, v=<-73,80,17>, a=<15,0,1> +p=<-1062,-87,-642>, v=<68,7,59>, a=<7,0,1> +p=<-532,-1332,-537>, v=<4,27,65>, a=<9,19,-2> +p=<8,888,968>, v=<-17,-19,-58>, a=<3,-13,-7> +p=<-1188,-1222,249>, v=<-13,12,39>, a=<5,3,-4> +p=<-672,-814,1713>, v=<28,45,3>, a=<0,-1,-6> 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+-762 +-588 +-17 +-809 +-436 +-483 +-16 +-410 +-180 +-568 +-37 +-687 +-444 +-619 +-211 +-386 +-673 +-600 +-155 +-558 +-849 +-37 +-717 +-867 +-236 +-98 +-165 +-579 +-677 +-691 +-602 +-878 +-555 +-893 +-773 +-395 +-942 +-661 +-850 +-881 +-485 +-312 +-689 +-258 +-899 +-120 +-227 +-349 +-467 +-404 +-45 +-919 +-329 +-365 +-22 +-462 +-632 +-498 +-873 +-288 +-901 +-655 +-321 +-922 +-882 +-416 +-946 +-320 +-5 +-57 +-352 +-711 +-197 +-705 +-737 +-439 +-39 +-252 +-1002 +-617 +-373 +-605 +-887 +-451 +-824 +-455 +-66 +-619 +-18 +-404 +-64 +-736 +-44 +-381 +-447 +-567 +-877 +-411 +-216 +-635 +-598 +-419 +-577 +-142 +-189 +-917 +-692 +-153 +-2 +-116 +-172 +-423 +-886 +-454 +-492 +-491 +-656 +-832 +-1036 +-468 +-23 +-709 +-292 +-668 +-454 +-478 +-302 +-182 +-677 +-904 +-648 +-513 +-901 +-331 +-750 +-445 +-758 +-842 +-372 +-471 +-109 +-239 +-704 +-817 +-340 +-591 +-40 diff --git a/pytudes/data/advent2017/input7.txt b/pytudes/data/advent2017/input7.txt new file mode 100644 index 0000000..e43ac95 --- /dev/null +++ b/pytudes/data/advent2017/input7.txt @@ -0,0 +1,1337 @@ +ifyzcgi (14) +axjvvur (50) +tcmdaji (40) -> wjbdxln, amtqhf +yjzqr (73) +smascq (97) +hyehtm (7) +oylvq (136) -> witry, cvlod +csyiik (34) +zivjpfo (23) -> lcchgb, bhqlq +ggfmiv (94) +vpltn (41) +gzxnn (171) -> mqodhde, djvkd +bsfygp (75) +dnrjb (9) +ohdnhx (261) -> tgiou, lndczw +frcrd (56) +cldaag (31) -> orbcuzi, teyakvf +vphlxz (26) +nljmcv (47) +xcxqa (6759) -> znely, rtsbgwx, hilafgl +hywzja (81) +ytxcti (60) +igzvp (68) +uzvsml (34) +keusrg (27) +tlmfw (45) -> pehflc, lefxyzt +hjmtrw (6772) -> cblhmk, zzflc, xsztla, iitbuxz, tckyc +ahjlf (1474) -> ejvipa, xhzyzer, pzwtjfj +egszxz (14) +skmuo (1607) -> rxsihsa, vsslzfp +ifyja (32) -> rvixnmq, aumrixf, wbenaek, jkkwtd, ywnsmem, mmhtyd, xmzzrgs +dwnokzu (311) -> xinfpy, lwvfsu +txbgfm (33) +roqfxg (62) -> wrhnq, rskara +autjn (29) +hnedp (10) +owxawf (60) -> twoyl, sikmtaj, lvptmrf +jensj (281) +sglkjsh (66) +eeziziu (34) +qjuuu (83) +iebulx (297) -> mqcflzv, nafrmeo +lhfuku (159) -> syzcti, ynhvfvx, ckegba +mxnlv (61) +emtjcx (60) +jspui (58) -> chlpx, xjkquk, afyxhh +nmikggy (64) +vatflrk (6) -> uxbhu, gekygl, xdyrvy, wesoooi, esphpt +jfcoc (41) +gyepcnc (6) +atbiby (80) -> aqtog, qjsvs +ygnkwn (52) +piexct (65) +uitfx (39) +rdvciwk (55) +jkgnvbn (23) +xpewzk (45) +vlqyxe (337) -> rosfnb, vphlxz +bmdgthp (215) -> kyfuyaf, tzrqqk +czafdho (24) +emuwzd (102) -> ifyzcgi, edotax +fwabsk (14) +uftnfv (53) +ndkcn (39) -> mkjuq, ghcgz, cxpwfir, lxwvf, nsghrq, vyvrn +srzfd (77) +gqhnstx (870) -> xmedt, brzucfh, layqazp +bdnjn (57) +pbckxv (14) +fbpbs (74) +zwutlym (92) +lzeud (290) -> igkrktn, oixlcn +gjctf (27) +azmneyd (60) +wbenaek (253) -> gdunxee, vgiqvsi, bmlkhaf +orpjw (72) +dgyulo (9) +qklqozd (125) -> otikjx, wuvhyc, dwejsn +waiwj (47) +bnevesk (256) -> dmglcj, blnwcb +yqnjd (50) +vvkkkpb (39) +ciprksz (84) +hblux (91) +dfywz (60) +jeiqx (26) +zdissfg (7) +mriqcjy (66) +eydak (49) +qwxwd (49) +plhlj (64) +nqgbp (67) +ewwfzg (70) +djzjiwd (44600) -> zszzkl, hrnrjrt, hjmtrw +mtflvu (71) +shesfq (143) -> ohdnhx, uhnqr, zdglrh, ripilxo, gfszte +huzokb (298) -> mnqii, mieqti +ohuvsf (83) +wcdibhx (196) -> xvwvc, ncmad, jkgnvbn +fxlbc (184) -> mdqeh, kmvcmg, sonvcww, pcckqq +lnknp (91) +swugafb (504) -> ryazls, vmkeu, fewrzd +pmadd (97) +mprgtb (42) +lorxjw (62) +welidg (97) +zzbad (30) -> npccgnv, yqnjd +dwejsn (40) +fvivo (225) -> worqh, yjzqr +zuawuo (111) -> jktlfu, uhvtpfy, ivlus +ikaol (26) +mmhtyd (220) -> yekmflj, nmikggy, xepgx +hujjten (37) +htqps (36) +dlobfkw (44) +fxrijc (57) +xgfad (33) -> zivlnu, ipsst +pafiy (17) -> dhtxpbb, dgcecu +cblhmk (1108) -> ggmhxx, tysdkgl, rrvbwb +kioga (93) +ljhlxc (83) +qsvbb (56) +uaffk (61) +lvptmrf (58) +hebhue (11) +eefyyr (10) +wyylpt (184) -> oneoorw, cfbaj +vmboh (90) +ghcgz (195) -> tajfmq, yzufk +jjhrmi (190) -> qhubjd, uycop +teduvv (25) +xjadrfg (28) +ugcccv (67) -> wehdeq, gyepcnc +psdzpg (38) +hyhbu (593) -> sblfh, ekvdv, iicpkf, xidtz +satjdgz (60) +cjbdxts (34) +gdunxee (53) +fqswta (47) +iwouvid (81) +iqbdxb (67) +ozbjpiq (16) +ysafyj (97) +lcchgb (82) +wkamonm (19) +waqca (61) +bbeyl (9) +rkfspx (17) +nggtuh (64) +jmypc (20) +yfegso (122) -> yhsmjfq, jzmacb, autjn, werkz +zirysk (72) +rtsbgwx (251) -> cbmqx, hvmlb, rsstvn, jtyurkp, gmkvgf, qkawtfu, ggwtf +yxgwsj (14) +xmgqmv (84) +lncmhi (48) +orclyi (30) +bjwny (94) +zehkwy (69) +mzajj (92) -> nljmcv, waiwj +ffsehyc (17) +agelbfq (343) -> iuchai, qynrx +dgcecu (86) +wtqxei (61) -> afywb, dqbfloz +vlmihf (32) +lovox (77) +cmvofka (30) +ttbuzrh (96) +vsunxw (196) -> pdbykx, dnynny, pqjua, jhnujj +skfnp (97) +upuybrd (300) -> dnrjb, rfknc, bbeyl +cpmebw (60) +wkmtw (59) +rpvwtq (5) +jenfafh (58) +pubtxq (51) +xlkwyg (55) +iltoh (22) +ctaazgn (103) -> hywzja, pywmbis +zxhqlfy (26) +dklujy (76) +khgvmj (66) +yfnkp (33) +edsjbi (37) +brtomr (75) +siqcu (15) +kxdehcg (13) +vmkeu (315) +momda (90) +pocvrcs (6) +sonvcww (17) +nemrt (91) +ldbkyg (75) +jsrrt (22) +ifuvyo (180) -> zvszwl, utewfcr, dtmbf +kfzqw (80) +iyfyi (41) +tykwy (44) +twgjdmg (24) +qface (27) +ygkdmh (74) +sblfh (120) -> gglxj, fqswta +gbldz (49) -> xitcp, jpynea +hmjpa (122) -> elovaun, uijgiu, apxgf, nlacdac +wsixz (14) +vgegr (83) +fggyk (46) +kjoru (16) +ixqrl (22) +gklehu (84) -> sazbmjz, piexct +xxego (33) +jxfimbl (95) -> nvpdisw, kioga +vymmkdf (116) -> ofqbu, sboms, obbpd, czafdho +jpwtbds (1608) -> zwutlym, qntzr +xsztla (828) -> cmdizw, qxkhq, nfcbi, rtutzu +wtfliw (87) +lbxrh (94) +ybioco (29) +yvdhwyh (102) -> xpewzk, hdxrbzc, vsaejz, pudso +eauxeyl (53) +skuazsw (70) +jlcie (99) +ckmftuc (21) -> khixdho, ihzsljz, uvkxner +yuikqm (68) +dqbfloz (87) +zofjia (133) -> gshsx, ntkpthi +vyvrn (173) -> lrjbgd, vwojto +tszockk (729) -> ctaazgn, gqbwc, wcdibhx, cujimpt +ydqqgrw (15) +hcxwql (398) -> lpoejf, cmvofka +gjedup (5) +arelp (195) +aonfn (235) -> kzkfcn, eefyyr +lsgbe (99) +gunvu (99) +kasaf (34) +imohij (13) +khwbzl (1131) -> zlbnkdc, ljmrml, roqfxg +nwikfyc (80) +khtegw (91) +epggt (90) +yapaib (175) -> gunvu, ymdmn +saawhdk (12641) -> vwvowk, ilcsp, vatflrk, iajts +qoetrb (15) +ztmmr (147) -> ypkhqlq, uitfx +uqfbnlo (69) +sgrhs (249) -> zymggc, wnvrg +hqjinj (101) -> skuazsw, ewwfzg +vmpnccn (73) -> bidhw, qriyeb, xsyzhcf, ehjjbu +vqddcl (71) +yffeit (76) +xvzinl (99) +znzbkh (16) -> swnan, tbioyr +gnjit (23) -> dhfagjw, xxnpoe +qojhhod (1789) -> sjdanf, hmjpa, szglq +aluqao (313) -> lyhlx, ouhuptm +ipysrdj (222) +worqh (73) +tsxfibs (46) -> yfnkp, edjlm, txbgfm +pcumn (420) -> qwcyozf, dskuj, anoxh, dkmkdfd, fkapr +mejwrm (139) -> oxsewk, zsknxq +aynpyne (44) +sikmtaj (58) +sbfprua (70) +wwofru (53) +nmuxe (88) +uuvtlk (74) +rqisvrh (2703) -> bvmgt, gbxxpd, ffinat, ympbbx, uimoc, shesfq +ehjjbu (89) +cbmqx (163) -> bnlbs, psdzpg +naekrk (70) +cvnrr (17) +pwnqyt (133) -> zijzutq, yvdhwyh, vbmyyrh +sagyrje (49) +efuysje (97) +pzwtjfj (74) -> oyienb, ozbjpiq +ggmhxx (42) -> fhhgts, cepxc, zwzxy +bhfui (13) +chlpx (87) +hmlbrz (55) +oneoorw (90) +kyfuyaf (79) +kiylza (88) +fghxbc (99) -> fozagvz, wqgssb, kqqsq, oijwjli +qgxgzo (14) +cubqfzc (184) -> qwmqci, dmvcduz +lcqfe (61) +xypffi (11) +qntzr (92) +mkjuq (181) -> jdiczst, edsjbi +dhtii (62) -> kfzqw, lbozpy +amtqhf (99) +ixknk (37) +iuapj (162) -> gzfrn, wqtuhe, fndyvvn, zjveu, iebulx, agelbfq +khtooum (53) +aecsfp (72) +fcdcdh (88) +junfev (18) +pxfrz (91) +xratfed (6) +gwbfat (26) +cvcblhv (73) -> jbnns, glkjrrs +sdfvrod (114) -> lcqfe, uigcn +xkfkucf (951) -> skbrota, pwvahdb, odpqjr +okkvefs (820) -> fpuscxk, zhdioii, gzxnn, koxnez +dgosy (59) +yhvndwy (27) +pefzsea (86) +xaogy (131) -> ixknk, ykvss, hujjten +nvpdisw (93) +lmkwafp (56) +cwnvk (51) -> tvdsktm, pwzsq, plhlj, ayqbj +phbtrm (171) -> hmmjjct, xzvln +mrmbyj (53) +jibemf (87) +tysdkgl (20) -> mrwbv, llkaoeh +fpuscxk (147) -> ypdumo, lvdrrk +ejkumeu (235) -> xypffi, nvcafwu, cvdows +uijgiu (38) +cjjynt (264) -> rkwhbhr, axjvvur +nobfn (236) +svanha (62) +nuxxmd (53) -> lybaepp, eolqn +vsaejz (45) +hbbpuc (238) -> thrvlt, ziiqv +tbley (31) -> nvfca, nojly, nguafeb +bkkwe (70) +tywzxwb (24) -> lbhlxqa, dklujy, vzxktth +ezqeusd (71) +qwcyozf (115) -> igzvp, vtefqb +xpwxo (80) +layqazp (39) +hwdtvvc (40) +pwnxw (69) +jobwpao (181) -> pqgiox, uloppmh +wrhnq (87) +amsfvm (53) -> nqgbp, bcldmsg +dfxjjzr (190) -> udaitd, sdktm +cnwzxpy (65) +kpvbt (85) +ifbhg (62) +cpeonw (27) +rsizei (20) +gmkvgf (63) -> tykwy, dlobfkw, aynpyne, vaovit +bjiuus (56) +bwpeux (17) +szrkuzi (27) +ygvpk (33701) -> saawhdk, svthizp, abamn +mjtji (35) +rqvvv (50) -> pzbxpou, rxzfdg +pozua (128) -> vljjqbw, hmlbrz +hmjueiq (79) +hdxrbzc (45) +twway (181) -> orclyi, hmdxion +jocmdmv (72) +lacddy (68) +lsxjl (94) +edotax (14) +gmirjhi (62) +iwicpur (10) +uigcn (61) +ynhvfvx (32) +ugavy (91) +jbgxcj (48) +zdglrh (239) -> csrww, haqaohl, gskveo, qoetrb +lmlsog (62) +sazbmjz (65) +ymeoz (24) -> lbxrh, lsxjl +hhqmsd (34) +ykmfoah (245) +lfdefc (30) +qynrx (53) +znely (919) -> qcmnpm, yjutt, yqgesx +cauig (58) +gvamhux (71) +hqqingt (13) +fiynt (72) +tyysd (63) -> cjjynt, lzeud, wyylpt, pewxc, ibevwow, fvmeeas, uksnrfx +igkrktn (37) +pzbxpou (87) +dllzp (59) +iblvki (11) +vaovit (44) +tcpduh (212) +btpvxq (56) -> urktg, ifnkl, hbbpuc, casmwo, ylqvuk, dblmcye, zvpboy +xxnpoe (67) +sboms (24) +whvvemg (83) -> tafss, vnfigul +ljjyy (64) +qvdid (70) +koxnez (71) -> bolpsk, pefzsea +elgtk (40) +wesoooi (87) -> pmadd, welidg +tiikt (92) +eadvs (797) -> ofnewz, neywe, qklqozd, ykmfoah +sreke (34) +clqqyi (51) +kuufl (1074) -> aonfn, cgrima, lhfuku +qswoy (7) -> bklfmch, xpwxo, eoustfr +rakfg (91) -> fiynt, opdtk, qkhvu +zvgsa (59) +gskveo (15) +clbbi (27) +ilcsp (844) -> pafiy, phbtrm, nwupf +blnwcb (17) +udaitd (23) +aewmad (73) +tvdsktm (64) +zavcu (25) +gglxj (47) +jmrlaxf (48) +sppxnti (48) +zhdioii (243) +olepfo (98) +ezsnmw (14) +hsmjm (25) +xmuxsr (44) -> bjiuus, qqjly +kmvcmg (17) +zuoeh (7782) -> hbaxtai, pmefov, zfteizz +sqxrad (80) -> marord, jbgxcj, xsmyok +vrbcn (34) +ibevwow (308) -> cvnabd, pbckxv, xrunic, ezsnmw +rqilp (25) -> quwfos, vekxdqh +ojfzokk (99) +bjwvw (209) +sygjhzp (36) -> hsxhyf, knqxdq +pjvnmqn (43) -> azoutv, jwhcmc +qqjly (56) +iezyfwf (20) +wrlkfij (55) +wuvhyc (40) +aqgtml (51) -> wywxu, tiikt, uwnwp +fhjysp (164) -> czvyrzi, nbmnwsq +rmlru (71) +bdiiv (15) +tlxekcp (42) +lbozpy (80) +uksnrfx (224) -> bkkwe, sbfprua +gmuwpyi (90) +zsqzm (64) +evhhfo (5) +xdyrvy (189) -> wyois, cwkdlil +gbxxpd (82) -> rynmge, hngao, vlqyxe, jhyjqxq +nzhqepw (60) +zfteizz (59) -> ytvjxq, vhoasjq, fwwub, xglsp, cubqfzc, nfucnzx +ulragq (39) +jgrsa (269) -> ukfsn, kptjhtd +uisnk (2228) -> tbley, eqkot, tlmfw, gnjit +chyhykz (59) +zjveu (437) -> qhyfphs, bfwnv +syliku (78) +syzcti (32) +nnmayb (85) +zdqmuey (209) -> ibkfqok, lhmgw +myopc (16) +cifdyio (74) +nguafeb (42) +dbczwnr (15) +vxede (10) +ouhuptm (52) +sdyox (93) +slahk (43) +skbrota (217) -> toeyz, gjcibb +hbaxtai (851) -> zynpp, ylbaxtu, rfwaq +hvdfq (112) -> imohij, pwetqid +zgfqdv (15) +dpqxfp (209) +arskvgv (88) +bqywl (157) -> ooufod, clqqyi +ymataqq (22) +krwgy (109) -> dllzp, xqpfvwx +ohsyhln (53) +ofqbu (24) +ccpnopa (59) +bfkbp (156) +bolpsk (86) +tckyc (456) -> dzfclsm, sqxrad, qkrpzl, ppcsoo, rqvvv +qbftkij (204) -> rtcfcyn, vlmihf +bpcnzi (82) +rhacrz (27) +wzbqh (306) -> xratfed, fjcobs, enlctw, pklcmix +qqnmzb (1723) -> mzyqoc, soirl, dhtii, ahbcl +tuvehcz (17) +yzufk (30) +xsmyok (48) +tgiou (19) +izvtqsa (84) +ooufod (51) +rfwaq (80) -> nmuxe, ttofoep +lpoejf (30) +oykwsk (76) +wdipy (92) +jbnns (93) +qcxiehu (312) -> eeune, gbldz, ztmmr +vsslzfp (91) +uimoc (30) -> crhojk, ejkumeu, lovaf, fhjysp, uxbrs, qbftkij +phtghp (3945) -> rpjozji, swnafht, swugafb, guyrnpn, evbtz, hyhbu +svthizp (1149) -> saddwx, olhnx, uisnk, iuapj, btpvxq, iovxjv +xvwvc (23) +ovpzt (139) -> dfywz, emtjcx +uatlbrq (17) +hmpisyb (41) -> igdtz, lnmhw, ttpmzgm, dkxzsaq +pehflc (56) +iedfk (49) -> ydqqgrw, bdiiv +nomeb (112) -> mmfuve, lxudoaz +ffuqr (90) +gsgwqk (204) -> ddraicf, dgyulo +igqle (222) +jhcwkl (41) +yfusbw (76) +lpsafeq (51) +lklqxg (83) +lofayaa (22) +itqwz (113) -> rhacrz, keusrg +xbidr (74) -> pozua, gisiv, skpux, tcmdaji, gorpw, yfegso, waakcx +pnouux (9) +ryazls (221) -> zhpfgzv, rvpxob +bxwng (53) +xwkyrer (8691) -> srnnjbb, qcxiehu, gqhnstx, ghdbwu +nbmnwsq (52) +cxfsoh (53) +gdylf (74) -> jlcie, hewatw, sdpsl +vksyy (96) -> wfpzhfz, phsmt, zuwaw +qekxzsx (87) +qzglav (42) -> ubxvdq, aqvtgi +xsoqzbe (1068) -> llgbz, itqwz, yxzlpnj +lndczw (19) +perzy (46) +oigsk (38) +uytsra (106) -> hkgxpgh, gzxddd +zszzkl (72) -> ifyja, cdqdm, rwmdbn, exwzzr, leyikdx +wfvjnxf (93) +pklcmix (6) +cvpuwrb (82) +ileugiu (225) +defbun (57) +fbzvm (72) -> vgexqw, cejtpyf +aduikk (133) -> kmfel, paopwt, hdjzg, qckzqv +shlfz (3932) -> swcvn, obwkzhc, pcumn +yhjhgu (57) +vgiqvsi (53) +iajts (451) -> izzzyqd, fegaac, jagdwg, mblvpm +kxwbdvm (1104) -> mzajj, ubuge, ddguar, znzbkh +rynmge (25) -> ecwjaw, zdqsmv, aodoc, pxfrz +bqxnoid (31) -> aqgtml, qprenhy, upuybrd, sgrhs, flptbw, mxwbp, boszym +kqqsq (37) +xrunic (14) +vqnyvr (57) +lvdrrk (48) +bamxvq (86) -> zywvdda, ygnkwn, taxrkif +xkzvo (33) +vhoasjq (226) -> uogva, tuvehcz +hkgxpgh (46) +zocwx (35) +qhyfphs (6) +coselm (44) +ypbrxyq (206) -> siqcu, kqicqf +ffgzg (151) +ujuunj (64) +iuchai (53) +ykvss (37) +ovszp (64) +helyfoo (65) +pryhgj (81) +fxhqq (29) +eeshl (30) +qzftgbx (44) +ppcsoo (26) -> gwqgewp, lsgbe +xinfpy (53) +ddraicf (9) +xidtz (126) -> azuoza, coselm +ipsst (23) +wzvzgg (60) +fqqyipa (200) -> eeshl, cxqeyt, qkhqrq +jpyvpw (20) +xhzyzer (82) -> pawvr, dckbvlg +boszym (129) -> rqrhrnz, beewze, evqibrc +kabqu (38) +sdpsl (99) +bekguie (31) +klovr (30) -> kihqh, wafjqj +zklbfdg (47) +ccter (84) +wzqanwj (240) -> zavcu, hsmjm +uxbrs (94) -> qekxzsx, odqns +dzxpqj (22) +csrww (15) +wwxak (108) -> vbmqj, ugavy +etfbuu (22) +miwst (40) +iiugq (15) +cuprzhk (40) +waakcx (238) +faijmsh (35) -> rwakmo, nwikfyc +cvlod (76) +sjgvkg (1566) -> cldaag, bjwvw, dpqxfp, dgdtt, ujbzq +ixxww (61) +mipqe (91) +xitcp (88) +lxudoaz (51) +ibkfqok (19) +ulchkal (55) +qubli (60) +tsamaj (1171) -> axgndac, vbuvkx, uqeag, qyurm, lzypz +mmpnppi (60) +prlvn (63) +ddwursx (245) -> sdwrx, jtfylv +aljgr (62) +glkjrrs (93) +vwftcva (46) +ylbaxtu (144) -> frcrd, shjxje +jqpdpr (14) +yzhvrx (90) -> viqvtzw, twway, zwzzce, hqjinj, mejwrm, yyursb, gfigt +iqoxkhd (91) +locrtxl (2681) -> xsoqzbe, oxoocfp, ndkcn, vmeubf +fbmajm (58) +rylaxjf (90) -> ojfzokk, iksaub +wyois (46) +ecwjaw (91) +alhlvth (36) -> zirysk, orpjw, zdxscz +jlofqwz (13) +sdktm (23) +bjvuicy (217) -> xjyyfe, rahgf, qqllir +hepkop (7311) -> xkfkucf, xbidr, yvgkdi +gqbwc (25) -> ytxcti, qubli, cpmebw, wzvzgg +yojcz (201) -> rkjuz, rmlru +obwkzhc (86) -> vksnq, tijwlva, szcozjr, krwgy, pnhpv, ydiicdl, kskts +cdqdm (2502) -> wnfqsa, jbqmy, hvdfq +gjcibb (23) +igdtz (83) +phsmt (112) -> jqpdpr, bmnsmqz +hdjzg (77) +jukxlr (29) +oajdx (61) +ktayld (179) -> skfnp, xwjmsjr +dkxzsaq (83) +utewfcr (50) +jljjai (14) -> fhycptc, olepfo, armfpvt +gnughzp (5) +oyienb (16) +kqicqf (15) +ggvwlp (80) +vlbivgc (13370) -> xcxqa, aeatvub, pwmrau, rqisvrh, hepkop, ogmoqb +kczlit (64) +mblvpm (124) -> fbmajm, ofwbsgp +wehdeq (6) +fegaac (206) -> ffsehyc, sapwhr +qpsirr (15) +gisiv (80) -> hmjueiq, unqui +xjkquk (87) +rsdub (61) +gzxddd (46) +oxsewk (51) +ahfdt (234) +wafjqj (80) +mhjeza (93) +bljkg (12) -> yivjj, cxcyrd, lorxjw +fkapr (39) -> wwofru, weyfsg, khtooum, ohsyhln +dtfdn (71) +zxgrq (25) +rlfqf (63) +hvisx (68) +laopkn (40) +zvszwl (50) +gorpw (55) -> jnrnwos, rsdub, uaffk +skmbdhz (54) -> scqtkga, xdojlm +ecaiau (424) -> rakfg, ddwursx, nsbzfgy +bfwnv (6) +uhvtpfy (47) +zafggcz (17) +qkrpzl (170) -> kjonvut, clbbi +bvmgrs (75) +iicpkf (16) -> vhkydm, htecpc +rbuwrpw (17) +funnv (5679) -> cdlzi, fpfpv, bqxnoid +flkkr (74) +brzucfh (39) +lfavcfd (72) +dmvcduz (38) +izdhn (1183) -> uytsra, xxmtvr, bljkg +hrnrjrt (9135) -> kuufl, khwbzl, tocvooe +eiatt (291) -> gfhummb, jsmde +czvyrzi (52) +ypkhqlq (39) +egxzjn (81) +qzzlmw (319) -> szrkuzi, cpeonw +xepgx (64) +iftyxdd (79) -> xmaqelf, htqps +rskara (87) +uytsdd (292) -> hyehtm, zdissfg +mqodhde (36) +ylqvuk (48) -> shdgsk, fcdcdh, kiylza, arskvgv +gisrnfs (23) +vntsex (77) +rwmdbn (2136) -> xmuxsr, bfkbp, ibjdru, ttvfha, zhohes +fhhgts (38) +opdtk (72) +beewze (66) +leyikdx (1995) -> ewswf, gaashgh, cwnvk +kcbwrrr (631) -> wzbqh, sysdxvb, huzokb, ifuvyo, ghakp, rqqlzs +jwhcmc (72) +mqcflzv (76) +ofwbsgp (58) +hiyswbt (889) -> ileugiu, suuhqpd, yffhk, htstksc +armfpvt (98) +zsknxq (51) +pewxc (246) -> rmexd, wkmtw +lhmgw (19) +qwmqci (38) +hioofm (319) +cujimpt (137) -> ovszp, zsqzm +htstksc (169) -> wsixz, egszxz, gzjut, rutqzk +quwfos (85) +tcjqw (81) +orbcuzi (89) +sybpg (49) -> sdyox, dwrwuoq +qyhvc (16) +sadnqcp (62) +zihpcn (232) -> jukxlr, louebj +zxygs (208) -> njvkdrp, hqqingt +gyoqtcg (77) +emwblax (49) +hewatw (99) +qxkvfid (53) +kglsx (74) +yhfpq (56) -> cxyfam, mjumixz +zivlnu (23) +xsyzhcf (89) +howlyws (206) -> gwyljq, xhhwwso +uycop (59) +yhxlzc (91) +isqvoex (30) +bklfmch (80) +tvrxaw (106) -> qdqtw, qpsirr, dbczwnr +lkreb (72) +kxyfb (90) +jnrnwos (61) +mxbrva (72) +qkhqrq (30) +gfhummb (40) +zwzzce (221) -> ahqfu, gjedup, evhhfo, rpvwtq +rrvbwb (34) -> wcmyn, haclvfu +enlctw (6) +yeaic (61) +otipr (480) -> gdrxgji, fonrd, wqoae +qxkhq (143) -> ixqrl, jsrrt +wbqeo (22) +iugsida (64) +azuoza (44) +yxemuyq (19) +fyouz (18) +bnlbs (38) +hilafgl (59) -> hmpisyb, ktayld, yapaib, bmdgthp, qzzlmw +shdgsk (88) +rnqgy (34) +kmwxj (92) +hmmjjct (9) +mefmo (46) +lwvfsu (53) +fixwkec (84) +haclvfu (61) +werkz (29) +iovxjv (1204) -> uhwnr, ypbrxyq, dfxjjzr, pxkypf, nobfn, tkdvenx, sdfvrod +dmglcj (17) +qprenhy (221) -> cxfsoh, mrmbyj +qmwmbsk (804) -> tmoui, amtayi, wgqpt, xaycmtu, kztkif +zywvdda (52) +ntkpthi (6) +jkkqxfr (1135) -> nomeb, fbzvm, gklehu +muptknj (66) +uwnwp (92) +ggwtf (213) -> vkaay, kxdehcg +afywb (87) +xglsp (94) -> ljhlxc, htpblzv +elovaun (38) +qhubjd (59) +exwzzr (1542) -> bchixdc, fphmu, hcxwql +xhhwwso (43) +uevxbyn (170) -> ucaee, yuikqm +pqgiox (50) +edjlm (33) +ypdumo (48) +ehhbjt (26) +cxyfam (98) +bhqlq (82) +abamn (8) -> tsamaj, qojhhod, kcbwrrr, ttfyrk, qqnmzb, tyysd, sjgvkg +sjdanf (49) -> ldbkyg, brtomr, qwfvm +wcjnjpf (57) +xzvln (9) +citaywz (64) +aqtog (66) +khdbe (9) +vksnq (85) -> vqddcl, ezqeusd +fkwbo (91) +jefjzvl (73) +azoutv (72) +aqvtgi (90) +vlyof (97) +gwyljq (43) +xmedt (39) +rsstvn (75) -> bpcnzi, cvpuwrb +vekxdqh (85) +toeyz (23) +pvyvx (99) +pwmrau (9594) -> roogi, ajcbzv, pwnqyt +qahzrif (63) +gzjut (14) +mzyqoc (194) -> yxgwsj, fwabsk +tkdvenx (44) -> sppxnti, lncmhi, jmrlaxf, qmati +vtefqb (68) +yekmflj (64) +pdbykx (14) +fpgyyu (67) +qjbbyb (26) +izzzyqd (186) -> djvfa, qrrvi, junfev +lsire (61685) -> locrtxl, shlfz, ycpcv +vbuvkx (204) -> tlxekcp, pxdkes +ahqfu (5) +cjxyp (81) +aeatvub (10983) -> hghjsk, vksyy, otipr +jhnujj (14) +cxpwfir (63) -> mhpzrw, txwzysl +gcydgf (22) +zlbnkdc (92) -> lfavcfd, lkreb +lrjbgd (41) +casmwo (246) -> nsbnixe, vntsex +rqqlzs (270) -> lfdefc, isqvoex +xtqthxs (44) +kjonvut (27) +mptovq (19) +dwrwuoq (93) +ziiqv (81) +vnfigul (38) +jpynea (88) +rplcrt (90) +flptbw (159) -> xmgqmv, ciprksz +nojly (42) +jbqmy (86) -> zxhqlfy, ehhbjt +ozhydny (40) +zzflc (92) -> rnyndr, eiatt, fvivo, gdylf +jktlfu (47) +njvkdrp (13) +qyurm (76) -> eauxeyl, nrwmjk, qxkvfid, rjmuly +bjyraf (7) +zhpfgzv (47) +qfcetm (30) -> iqoxkhd, gptyqwd +dhfagjw (67) +qriyeb (89) +ucaee (68) +djvkd (36) +scqtkga (54) +yvgkdi (992) -> pjvnmqn, kgoyufq, zivjpfo, amsfvm +zsukqjo (90) +hfmaqp (94) +gxsxqwt (20) +marord (48) +uloppmh (50) +iktmpdq (34) +wnvrg (39) +cxiturs (95) -> ttoer, jpwtbds, yykkph, yffpvf, ahjlf, yoxetv, okkvefs +fewrzd (24) -> efuysje, olrgu, rtmiw +swnan (85) +xdojlm (54) +dhtxpbb (86) +roogi (100) -> cesnj, wsvfkr, hzhcl +yffhk (143) -> jfcoc, vpltn +ffinat (630) -> avyoy, tywzxwb, zuawuo, vsunxw +txrfl (81) +eoustfr (80) +bxmcg (249) -> epggt, gfjsie +kdeqm (99) -> qjbbyb, ikaol +lfsvtih (97) -> aylxc, bekguie +qkhvu (72) +zzfcq (7259) -> balknnd, iiqzvha, kzzfvt, ecaiau +kebhn (106) -> iktmpdq, sreke, cjbdxts, ehlnex +ljmrml (178) -> fxhqq, ybioco +asozcan (96) +ceeotg (53) +fonrd (12) +fvmeeas (88) -> wdipy, khnjt, kmwxj +cejtpyf (71) +wsvfkr (193) -> liznr, yytpewc +evdwf (31) +wqgssb (37) +uhnqr (247) -> oncexf, jeiqx +xzmdis (24) -> yhjhgu, vqnyvr, taacpu +tafhilv (11) +mhpzrw (96) +cgrima (79) -> xvayjwv, eyxccr, xtqthxs, qzftgbx +nrwmjk (53) +yjutt (47) -> jocmdmv, iaoyb, aecsfp, mxbrva +cxcyrd (62) +fwwub (146) -> defbun, wcjnjpf +sapwhr (17) +ihzsljz (46) +zmkwnv (66) +yytpewc (50) +xdctkbj (83) -> zuoeh, tnqram, funnv, zzfcq, xwkyrer, cxiturs, phtghp +kptjhtd (86) +pcecbrn (66) +sdwrx (31) +dfiyju (49) +gxddhu (133) -> itlwpm, bdnjn +zvpboy (76) -> txrfl, egxzjn, iwouvid, cjxyp +fndyvvn (85) -> khtegw, aocfuj, mipqe, lnknp +ozvtqp (53) +kxizh (74) -> yojcz, uafhv, wnpnfiv, kivyltn, jxaorvd +zwzxy (38) +rkjuz (71) +jagdwg (46) -> ytiljvt, smascq +rutqzk (14) +zymggc (39) +afbzsz (148) -> vzcklke, ggvwlp +ymdmn (99) +twoyl (58) +lqcutyt (74) +nlacdac (38) +otikjx (40) +rxzfdg (87) +huvihu (49) +cfbaj (90) +lqlyf (59) +apxgf (38) +nqicerc (62) +iksaub (99) +avyoy (252) +kzzfvt (94) -> aluqao, oherzyz, dwnokzu +uqeag (162) -> prlvn, xtaoisd +crhojk (40) -> yffeit, yfusbw, oykwsk +oxoocfp (237) -> igqle, eukgf, qzglav, ipysrdj, gsgwqk, kevlq +aylxc (31) +khnjt (92) +ytvjxq (260) +xkxqc (64) +ogmoqb (8) -> uqmgmst, hiyswbt, qmwmbsk, skmuo, tszockk, kxizh, thbwh +nvfca (42) +xaycmtu (67) -> cnwzxpy, helyfoo +kklbcs (74) +wqtuhe (341) -> myookpi, gqikhhw +unqui (79) +vhkydm (99) +zcomxf (40) +hsxhyf (63) +rwakmo (80) +uogva (17) +cesnj (57) -> hrokzl, rtgobsq, kmfsmp, chyhykz +rtcfcyn (32) +qckzqv (77) +oixlcn (37) +iaoyb (72) +idrror (34) +bcldmsg (67) +lbxdtms (281) +adbxp (35) +qsjqlp (74) +mjumixz (98) +rtmiw (97) +jzmacb (29) +umgch (64) +rpjozji (279) -> faijmsh, xzmdis, arelp, guvke, rqilp, eqpuuzs +xvayjwv (44) +vgemekb (53) +odpqjr (263) +hekibe (63) +xmaqelf (36) +ivlus (47) +rkwhbhr (50) +pawvr (12) +crcrimv (57) +ukfsn (86) +nfcbi (117) -> zocwx, mjtji +qwfvm (75) +jfieeor (96) +eolqn (91) +bgehlas (6) +ruozk (10) +gqikhhw (54) +pqjua (14) +jtyurkp (239) +wjbdxln (99) +paopwt (77) +fefuzon (126) -> jenfafh, cauig +ifualyn (93) +npccgnv (50) +nvcafwu (11) +htecpc (99) +uxbhu (175) -> bxwng, ozvtqp +gzfrn (365) -> mprgtb, qkicc +qlwhsix (71) -> bjwny, ghapm +uvkxner (46) +kmfel (77) +ytiljvt (97) +cxqeyt (30) +yyursb (93) -> lqcutyt, uuvtlk +mpijr (88) +rpqbv (23) +oginzo (24) +sydjg (10) +ehlnex (34) +ukqmhyc (25) +gshsx (6) +nafrmeo (76) +ifwmfdm (114) -> jibemf, wtfliw +rmexd (59) +ujbzq (41) -> izvtqsa, ssnhc +scxdo (56) +bvmgt (1203) -> xqncgyu, tsxfibs, zofjia +vkaay (13) +pxdkes (42) +witry (76) +ttpmzgm (83) +pxgkg (69) +vwojto (41) +jcise (35) +tbioyr (85) +wnpnfiv (55) -> tehat, ttbuzrh, jfieeor +ejxib (53) +htpblzv (83) +dgdtt (155) -> qface, yhvndwy +weyfsg (53) +aodoc (91) +vmeubf (759) -> sygjhzp, ilhib, ldgyqh, uewdyd, skmbdhz +pwetqid (13) +pudso (45) +ibjdru (136) -> dzqqgbm, qivxs +rtgobsq (59) +kqiuy (81) -> ffuqr, rplcrt, gmuwpyi, zsukqjo +gfszte (23) -> pxgkg, zehkwy, pwnxw, uqfbnlo +ngxtfhu (25) +fphmu (62) -> jpvxzcn, xvzinl, pvyvx, lxgvhy +yxzlpnj (85) -> iyfyi, jhcwkl +khixdho (46) +pjjmau (353) -> hktzoq, oigsk +ttofoep (88) +fhycptc (98) +nsghrq (105) -> bvmgrs, bsfygp +hmdxion (30) +nsbzfgy (167) -> mplhwo, qvdid +hngao (361) -> olhfbr, qgxgzo +iitbuxz (1186) -> eexmf, emuwzd, zzbad +ywnsmem (246) -> qjuuu, ohuvsf +qjsvs (66) +uuyfecv (9) +uafhv (223) -> azmneyd, mmpnppi +aocfuj (91) +kaghlc (34) +eionkb (1079) -> hxmcaoy, sybpg, jfhqrla +hzhcl (127) -> vgegr, lklqxg +ssnhc (84) +ttfyrk (2158) -> xnxsdq, ffgzg, tvrxaw +nvfqmkw (96) +qrrvi (18) +ajcbzv (55) -> jjhrmi, jljjai, afbzsz +ydiicdl (93) -> iqbdxb, fpgyyu +eyxccr (44) +gdkjoit (56) +urktg (196) -> pxgcbfi, lacddy, hvisx +wuclmu (64) +rosfnb (26) +osjsm (87) +kgoyufq (133) -> holen, gjctf +kihqh (80) +xjyyfe (25) +gyfbgkr (16) -> gyoqtcg, lovox, srzfd +bidhw (89) +wfpzhfz (78) -> zyfwjxs, evdwf +rnyndr (149) -> kklbcs, ygkdmh, cifdyio +xqncgyu (25) -> nzhqepw, satjdgz +hvmlb (141) -> qwxwd, huvihu +txwzysl (96) +suuhqpd (48) -> ccpnopa, lqlyf, fxpoal +djviima (31) -> qyhvc, kjoru, myopc +ddguar (116) -> adbxp, jcise +wptyd (87) +obbpd (24) +anoxh (63) -> hfmaqp, ggfmiv +llgbz (167) +mhxheb (167) -> rkfspx, uatlbrq, cvnrr, bwpeux +yybnbso (89) +lxgvhy (99) +yffpvf (1698) -> pwoyfeh, zklbfdg +ttvfha (156) +tocvooe (99) -> fqqyipa, zihpcn, wzqanwj, wajnseu, bnevesk, wwxak +taxrkif (52) +rvixnmq (376) -> fyouz, nsnqedk +uhwnr (60) -> zjzgs, mpijr +djvfa (18) +rjmuly (53) +pnhpv (227) +sjaax (190) +amtayi (29) -> qsvbb, scxdo, inlrm +vbmyyrh (142) -> uwjowb, naekrk +gomcbqb (203) -> lofayaa, iltoh +oijwjli (37) +wajnseu (20) -> kxyfb, vmboh, zguzlx +hghjsk (348) -> fixwkec, gcowt +dzqqgbm (10) +guvke (19) -> brjgwq, kejtzg +jpvxzcn (99) +mplhwo (70) +dblmcye (325) -> bffnszc, zxgrq, ngxtfhu +ahbcl (178) -> hebhue, edlved, tafhilv, iblvki +liznr (50) +pwoyfeh (47) +jdiczst (37) +ejvipa (38) -> kpayh, uzvsml +oherzyz (53) -> yhxlzc, fkwbo, ziyyc, dlfmj +kivyltn (303) -> vxede, pjazwiy, ruozk, sydjg +szcmb (176) -> bjyraf, bvypab +ofxzyhr (22) +xmzzrgs (266) -> aewmad, jefjzvl +gdrxgji (12) +ziyyc (91) +wgqpt (29) -> evcveie, ccter +yykkph (63) -> gyfbgkr, fghxbc, qswoy, gomcbqb, tubhp, zdqmuey, gxddhu +yoxetv (1724) -> eeziziu, kaghlc +xqpfvwx (59) +fxaglf (49) +shjxje (56) +cdlzi (1615) -> wtqxei, mhxheb, nuxxmd +zytau (43) +ghakp (232) -> sagyrje, fxaglf +lbhlxqa (76) +bchixdc (431) -> khdbe, uuyfecv, pnouux +olhnx (1796) -> vymmkdf, qfcetm, atbiby, tcpduh, ymeoz +bvypab (7) +hregcx (66) +aucjw (62) +bmqhvfv (40) +fpfpv (1564) -> fxlbc, alhlvth, yhfpq +lzypz (220) -> rnqgy, csyiik +ujjoydl (38) +rfcbs (197) -> oajdx, yeaic +cmdizw (31) -> ydzibri, syliku +iiqzvha (1325) -> hnedp, iwicpur +zdqsmv (91) +neywe (59) -> lmlsog, svanha, sadnqcp +teyakvf (89) +inlrm (56) +kpayh (34) +spwqxpy (79) +ofnewz (83) -> pryhgj, tcjqw +knqxdq (63) +jtfylv (31) +jhyjqxq (363) -> jlofqwz, bhfui +kmfsmp (59) +kskts (115) -> gdkjoit, lmkwafp +hktzoq (38) +tajfmq (30) +zdxscz (72) +pywmbis (81) +yhsmjfq (29) +kzkfcn (10) +mieqti (16) +mxwbp (235) -> fggyk, mefmo +thrvlt (81) +wqoae (12) +yivjj (62) +aumrixf (40) -> ifualyn, kgqzrt, mhjeza, wfvjnxf +gfigt (211) -> iiugq, zgfqdv +cepxc (38) +vzxktth (76) +locto (240) -> oginzo, twgjdmg +vopqzha (10) -> kglsx, qsjqlp, flkkr, fbpbs +lxwvf (72) -> ixxww, mxnlv, waqca +zuwaw (84) -> tbaads, xjadrfg +oothjv (71) +tubhp (141) -> uftnfv, vgemekb +wywxu (92) +uwjowb (70) +pwzsq (64) +eexmf (130) +ldgyqh (30) -> mriqcjy, khgvmj +ewswf (307) +tbaads (28) +rxsihsa (91) +dtmbf (50) +tzhwvzt (89) +qivxs (10) +nfucnzx (68) -> nvfqmkw, asozcan +znwmvr (63) -> ymataqq, etfbuu, wbqeo, gcydgf +kejtzg (88) +eukgf (112) -> rdvciwk, ulchkal +skpux (146) -> vwftcva, perzy +uewdyd (152) -> uamqx, gnughzp +dnynny (14) +guyrnpn (413) -> bqywl, cvcblhv, ovpzt, qlwhsix +lnmhw (83) +llkaoeh (68) +ydzibri (78) +gaashgh (307) +vbmqj (91) +uqmgmst (1336) -> kdeqm, znwmvr, iftyxdd +tijwlva (187) -> gxsxqwt, yjrfr +fozagvz (37) +tafss (38) +dckbvlg (12) +oncexf (26) +jkkwtd (142) -> jhwrcb, pbkplz, momda +evqibrc (66) +mrwbv (68) +hrokzl (59) +soirl (206) -> uqjfarv, myqre +ubuge (186) +rtutzu (73) -> crcrimv, fxrijc +pmefov (983) -> gibdxij, whvvemg, lfsvtih, ckmftuc +tnqram (7095) -> kxwbdvm, rhcxf, nihiexp +dzfclsm (186) -> yxemuyq, mptovq +pjazwiy (10) +mnqii (16) +uqjfarv (8) +xnxsdq (76) -> ukqmhyc, teduvv, lmhamlz +lnwcryv (62) +lovaf (94) -> osjsm, wptyd +rhcxf (84) -> jgrsa, egtruqh, kqiuy, aduikk +evcveie (84) +lyhlx (52) +zjzgs (88) +brjgwq (88) +wnfqsa (138) +balknnd (377) -> kebhn, bamxvq, xaogy, fefuzon +ayqbj (64) +zynpp (67) -> qahzrif, rlfqf, hekibe +szglq (194) -> iezyfwf, jmypc, rsizei, jpyvpw +ocppbp (26) +wuknah (36) -> kczlit, nggtuh, umgch, xkxqc +ifnkl (324) -> kabqu, ujjoydl +eqkot (33) -> aljgr, lnwcryv +yjrfr (20) +cvdows (11) +lybaepp (91) +jxaorvd (343) +zkpfzio (145) -> vrbcn, kasaf, hhqmsd, idrror +evbtz (297) -> ifwmfdm, rylaxjf, oylvq, locto +srnnjbb (51) -> zxygs, rkwquj, owxawf, ahfdt +viqvtzw (117) -> gmirjhi, aucjw +nsnqedk (18) +wiapj (55) -> djzjiwd, lsire, vlbivgc, xdctkbj, ygvpk +jhwrcb (90) +zdnypzo (66) +eqpuuzs (149) -> gisrnfs, rpqbv +kevlq (156) -> xkzvo, xxego +fxpoal (59) +dlfmj (91) +pbkplz (90) +qdqtw (15) +qkicc (42) +axgndac (156) -> zdnypzo, sglkjsh +gptyqwd (91) +cwkdlil (46) +tmoui (91) -> ceeotg, ejxib +xxmtvr (154) -> ofxzyhr, dzxpqj +zijzutq (90) -> wuclmu, citaywz, ljjyy +xtaoisd (63) +szcozjr (215) -> bgehlas, pocvrcs +jfhqrla (155) -> miwst, elgtk +nsbnixe (77) +haqaohl (15) +eeune (31) -> ysafyj, vlyof +vgexqw (71) +ghapm (94) +swcvn (1105) -> sjaax, szcmb, klovr +lmhamlz (25) +louebj (29) +fjcobs (6) +holen (27) +qryui (49) +olhfbr (14) +wcmyn (61) +dkmkdfd (173) -> vvkkkpb, ulragq +odqns (87) +xwjmsjr (97) +rqrhrnz (66) +uamqx (5) +rkwquj (92) -> gvamhux, dtfdn +ncmad (23) +lefxyzt (56) +qcmnpm (335) +kgqzrt (93) +ttoer (916) -> howlyws, wuknah, bjvuicy +rahgf (25) +mdqeh (17) +ghdbwu (863) -> ifbhg, nqicerc +thbwh (832) -> rfcbs, hioofm, jspui +gfjsie (90) +mmfuve (51) +vzcklke (80) +bffnszc (25) +saddwx (1569) -> bxmcg, vmpnccn, pjjmau +bmnsmqz (14) +qkawtfu (111) -> ujuunj, iugsida +edlved (11) +pxgcbfi (68) +gekygl (247) -> zafggcz, rbuwrpw +egtruqh (389) -> ocppbp, gwbfat +rvpxob (47) +ympbbx (1243) -> spwqxpy, iedfk, ugcccv, djviima, xgfad +pxkypf (54) -> hblux, nemrt +qqllir (25) +tehat (96) +gibdxij (121) -> ohsvn, wkamonm +itlwpm (57) +rfknc (9) +ekvdv (44) -> kpvbt, nnmayb +gwqgewp (99) +cvnabd (14) +dskuj (165) -> slahk, zytau +yqgesx (175) -> zcomxf, bmqhvfv, hwdtvvc, laopkn +vljjqbw (55) +qmati (48) +afyxhh (87) +ubxvdq (90) +ckegba (32) +sysdxvb (66) -> zmkwnv, pcecbrn, hregcx, muptknj +nihiexp (930) -> vopqzha, uytsdd, uevxbyn +myqre (8) +nwupf (109) -> cuprzhk, ozhydny +tzrqqk (79) +pwvahdb (85) -> yybnbso, tzhwvzt +gcowt (84) +ohsvn (19) +zhohes (46) -> wrlkfij, xlkwyg +ripilxo (299) +vwvowk (1293) -> dgosy, zvgsa +bmlkhaf (53) +kztkif (55) -> mtflvu, oothjv +ycpcv (72) -> izdhn, yzhvrx, eionkb, eadvs, jkkqxfr +zyfwjxs (31) +esphpt (85) -> emwblax, dfiyju, qryui, eydak +jsmde (40) +zguzlx (90) +pcckqq (17) +hxmcaoy (235) +taacpu (57) +ilhib (60) -> pubtxq, lpsafeq +myookpi (54) +olrgu (97) +swnafht (44) -> lbxdtms, jensj, zkpfzio, jobwpao, jxfimbl diff --git a/pytudes/data/advent2017/input8.txt b/pytudes/data/advent2017/input8.txt new file mode 100644 index 0000000..b41d8f3 --- /dev/null +++ b/pytudes/data/advent2017/input8.txt @@ -0,0 +1,1000 @@ +utc dec -736 if p > -7 +tn inc -876 if qlm == 4 +uz dec 294 if l < 10 +a inc -904 if me >= -7 +tn inc 622 if ppl <= 6 +fr dec 17 if ufk > -10 +hkt inc -511 if mdk == 0 +t inc -290 if xxh <= -1 +l dec 727 if ufk < 7 +tn inc -576 if l == -727 +z inc 464 if dea >= -2 +ufk inc 755 if utc >= 735 +utc dec -720 if qlm <= 5 +a dec -277 if ufk <= 755 +xxh dec -640 if u == 0 +hkt inc 875 if m != -6 +ny inc -351 if p >= -4 +l inc 674 if dea > -7 +ufk dec -826 if p == 0 +mdk inc 377 if utc == 1456 +ppl dec 793 if q <= 4 +z dec 114 if mdk > 368 +ny dec -412 if ny >= -353 +utc dec 176 if a != -620 +utc dec -610 if p <= 1 +l inc -541 if xxh <= 635 +l inc 102 if ny < 66 +qlm dec 700 if l >= 43 +dea dec -202 if tn <= 38 +a inc 785 if a <= -629 +ny inc 414 if fr <= -21 +l inc 250 if hw <= -10 +l inc -516 if l > 41 +utc dec 358 if mdk > 373 +p dec -38 if z == 350 +uz dec -71 if a == -627 +t inc -713 if fr > -13 +l inc 242 if tn <= 53 +dea dec 600 if hw <= 8 +hw dec -92 if fr != -19 +hkt dec 67 if l <= -232 +qlm dec 523 if hw == 92 +utc dec -608 if q != -8 +m dec 314 if me < 9 +xxh inc -937 if xxh >= 638 +qlm dec 494 if m <= -313 +fr dec -590 if m <= -306 +utc inc -539 if tn == 46 +hkt dec 831 if p >= 43 +dea inc 510 if a > -627 +p inc 319 if m > -305 +m inc 736 if xxh >= -302 +ppl inc -712 if mdk == 377 +ny inc 21 if p <= 41 +hw inc -569 if hw != 92 +ppl inc 150 if dea < -595 +xxh dec -953 if z != 356 +ppl inc 578 if qlm <= -1714 +uz dec -733 if p >= 35 +xxh inc 100 if xxh >= 660 +hw dec -491 if ppl < -767 +t dec -64 if z < 347 +me dec 802 if dea > -601 +hkt inc 431 if hkt > 359 +utc inc -600 if q != 0 +u inc -223 if tn < 48 +tn inc 443 if uz <= 513 +l inc -349 if ny == 82 +utc inc -499 if xxh <= 661 +a inc 600 if hw >= 578 +z dec -636 if utc > 1099 +tn inc 75 if z == 986 +hkt dec 364 if mdk < 377 +ufk inc 249 if fr == 573 +l inc -429 if uz > 507 +hw dec -621 if ppl == -778 +l inc -620 if z != 980 +l inc 319 if tn == 564 +q dec -478 if ny <= 82 +utc dec -169 if uz < 519 +fr inc 124 if dea >= -607 +m dec -674 if p != 28 +m dec 744 if p != 44 +l dec -620 if hw <= 582 +utc dec -950 if p >= 37 +uz dec -122 if xxh < 660 +l inc -563 if z < 996 +hkt inc -514 if m <= 361 +l dec 525 if mdk == 377 +xxh inc -666 if u != -228 +a inc 934 if a <= -23 +a inc 817 if xxh >= -11 +me inc 450 if tn < 563 +hw inc 475 if xxh < -1 +fr dec 493 if xxh < -8 +uz inc -985 if qlm > -1724 +ppl inc 856 if qlm >= -1720 +hw inc -368 if me > -804 +ny dec -219 if p != 38 +u inc 1000 if ny > 79 +q dec 551 if hkt == 281 +uz dec 317 if dea >= -600 +uz inc -916 if qlm <= -1726 +hkt dec 915 if mdk != 380 +mdk inc 484 if l == -2392 +xxh inc 326 if dea > -607 +u dec -803 if me > -811 +q dec 689 if tn != 565 +hw dec 908 if p == 38 +z inc -173 if ppl > 72 +z dec 371 if tn < 565 +p inc 185 if u > 1571 +a inc 490 if mdk != 864 +tn dec -27 if u == 1580 +qlm inc 77 if m > 345 +p dec 364 if ufk <= 1836 +dea dec 308 if me == -802 +a inc -345 if hw == -218 +ny inc 603 if p <= -138 +fr inc -4 if utc > 2217 +me inc 118 if hkt <= -626 +hw inc -590 if z < 443 +me dec 279 if q <= -756 +me inc -50 if dea == -908 +ppl inc 708 if u <= 1586 +t inc -429 if mdk >= 854 +m dec -372 if uz > -676 +fr dec -840 if ppl == 787 +qlm dec -442 if tn != 584 +u dec 227 if l == -2402 +m inc 279 if z <= 446 +xxh inc -951 if t > -421 +t dec 530 if xxh != 317 +fr inc -621 if mdk <= 869 +a dec 480 if fr < 424 +q inc 988 if l == -2384 +u inc 313 if q < -757 +hw dec 237 if hkt == -634 +mdk dec 945 if t > -969 +me inc 631 if ny >= 679 +ny dec -740 if uz == -670 +t inc -310 if utc > 2213 +p dec -453 if utc >= 2218 +mdk inc -266 if hw == -1045 +a inc -887 if qlm == -1198 +ppl dec 521 if t >= -1270 +dea dec -685 if xxh != 310 +l inc -472 if m < 1013 +ufk inc -920 if l <= -2860 +u dec -503 if me <= -373 +ufk inc 547 if m > 998 +l inc -287 if p <= 309 +qlm dec -173 if q <= -755 +u dec -928 if z > 437 +hw inc 43 if hkt < -626 +utc inc -694 if me == -382 +fr dec -938 if tn > 584 +q inc 9 if mdk == -350 +dea inc 119 if m < 1012 +ny dec 210 if ufk <= 1465 +xxh inc 352 if q > -758 +dea inc 483 if hkt >= -639 +tn inc -652 if t >= -1266 +ufk inc 674 if ny >= 1207 +ppl dec 311 if z >= 442 +qlm inc 655 if m < 1005 +z dec 580 if uz < -661 +utc inc -977 if ppl <= -36 +xxh inc -25 if l == -2864 +me dec 252 if uz > -674 +mdk dec -98 if z <= -129 +p inc -276 if utc < 541 +hw dec 796 if xxh <= 649 +q inc -726 if z != -137 +fr dec 433 if ufk <= 2140 +hw inc -701 if z < -131 +hw dec 587 if mdk <= -244 +ny dec -734 if mdk <= -249 +qlm dec -311 if utc != 546 +ufk dec -405 if q > -1481 +p dec 97 if t != -1275 +t dec 597 if qlm >= -49 +ufk dec 389 if uz < -660 +l inc 765 if a < 504 +fr dec -948 if tn >= 586 +qlm dec 79 if m > 997 +ny inc 764 if p < 225 +a dec 419 if m != 1003 +q dec -860 if q != -1475 +fr inc 426 if hw > -3080 +ufk inc 0 if ppl != -36 +utc inc 939 if p >= 206 +m inc 830 if xxh < 650 +m inc -511 if hw > -3091 +u inc -720 if qlm > -134 +dea inc -147 if a <= 503 +u inc -322 if tn != 591 +ny dec 900 if ny != 2713 +ny inc -737 if me == -634 +fr inc -494 if l != -2097 +mdk inc -363 if ny != 1976 +l inc 991 if hkt > -636 +l dec 179 if dea != 232 +q dec -264 if ny != 1977 +l dec -976 if uz > -667 +tn inc 791 if hkt > -637 +ppl dec 225 if utc < 1495 +uz dec -527 if m > 1317 +a inc -644 if me < -624 +uz inc 160 if q >= -361 +u inc 577 if xxh > 650 +q inc 124 if xxh < 653 +l inc 268 if dea > 222 +hw inc 795 if uz < 10 +uz dec 934 if uz < 26 +tn inc 966 if ufk == 2150 +me dec -71 if p <= 222 +me inc 186 if ppl > -270 +m dec -377 if xxh <= 649 +ny dec 275 if mdk > -248 +qlm dec -574 if fr != 1371 +utc dec 78 if xxh > 638 +l inc 494 if u > 3315 +tn dec -595 if qlm > 435 +tn dec 113 if a <= -140 +fr inc -610 if ufk < 2148 +uz inc -791 if u != 3334 +uz inc 356 if t < -1276 +l dec -463 if utc < 1414 +tn inc -266 if a < -137 +p inc 747 if utc >= 1402 +z inc -671 if hkt == -634 +tn inc -441 if u != 3324 +fr inc 172 if hkt > -638 +tn dec -558 if qlm < 439 +a dec -234 if tn <= 2155 +t inc -325 if l >= 126 +t dec -685 if l > 110 +ufk inc -912 if z < -805 +ufk dec 0 if fr < 941 +fr dec 276 if a == -142 +xxh inc -972 if p < 967 +ufk inc 188 if mdk >= -245 +me inc -255 if t > -583 +qlm inc 451 if uz > -1710 +fr inc -921 if z >= -814 +q inc 272 if uz < -1705 +u dec 216 if p <= 956 +a inc 30 if z > -812 +tn dec -202 if dea == 232 +m inc 792 if ny != 1976 +uz dec -867 if z == -809 +ppl inc -765 if qlm != 894 +hkt inc 301 if xxh < -322 +p dec -839 if dea == 232 +utc dec -920 if m > 1694 +a inc -206 if mdk == -252 +ny dec -545 if ppl <= -1029 +me dec -860 if q >= 39 +ufk inc 644 if tn <= 2359 +hw dec 959 if t == -584 +qlm dec 667 if xxh != -321 +ufk inc 598 if a > -323 +ppl dec -514 if hw <= -4039 +uz dec 708 if p == 1801 +hw inc -902 if hkt != -333 +qlm dec 249 if tn != 2366 +mdk inc -570 if z > -812 +fr inc -47 if tn > 2350 +me inc -62 if hw != -4037 +qlm dec 796 if dea > 239 +q dec -201 if ppl == -521 +z inc 265 if ufk != 2481 +hw dec 597 if q >= 239 +ny dec 417 if uz > -1540 +hkt dec -866 if m <= 1704 +m inc 103 if m == 1699 +ufk inc -733 if qlm <= -28 +mdk dec -416 if z > -546 +ufk dec 477 if z < -543 +l dec 224 if m < 1799 +q inc 646 if u < 3327 +hkt dec -501 if qlm != -29 +ppl inc 321 if p > 1797 +a dec 678 if ufk == 1268 +u inc -878 if fr > -302 +t dec 523 if uz != -1552 +mdk dec -490 if fr != -304 +p dec -603 if ufk >= 1264 +tn inc -234 if qlm > -33 +mdk dec -51 if q <= 881 +a inc 672 if me < 244 +z dec 473 if m != 1797 +mdk dec -727 if utc == 2331 +ppl inc -59 if me == 235 +a dec -937 if uz <= -1547 +uz dec -352 if m >= 1798 +fr inc 693 if utc < 2333 +t inc 493 if hkt != 526 +hw inc 86 if hkt >= 533 +t dec 49 if ny != 2512 +utc inc 273 if me != 235 +xxh inc -871 if dea == 232 +z dec -707 if dea != 234 +mdk dec 362 if ny > 2528 +tn inc -825 if t <= -658 +uz dec 655 if xxh < -1195 +dea dec 231 if me < 242 +mdk dec -260 if xxh != -1200 +ppl dec -842 if mdk != 321 +l inc -957 if qlm == -23 +m dec 393 if ny > 2515 +ufk inc -648 if me < 243 +dea inc -251 if fr < 399 +a inc 772 if mdk < 323 +hkt inc 997 if fr > 383 +l dec 13 if dea == -240 +hkt dec -935 if tn >= 1291 +uz dec 992 if u < 3324 +hw dec -970 if t <= -655 +m inc 132 if mdk == 321 +hw inc 908 if hkt > 2464 +me inc -975 if l != 119 +ny dec -76 if dea >= -251 +ppl dec -844 if u >= 3322 +qlm dec 286 if ny >= 2597 +xxh dec 903 if uz != -1843 +u dec 992 if hkt <= 2471 +tn dec -663 if me > -735 +ny dec -598 if ppl >= 583 +m inc 84 if mdk != 318 +ufk inc -260 if t <= -668 +u dec -443 if fr >= 388 +l dec -116 if hw <= -2670 +m inc 816 if dea < -240 +t inc 319 if mdk != 317 +me inc -681 if z < -301 +m inc 451 if uz != -1845 +t inc 472 if mdk <= 330 +qlm inc -125 if z == -310 +ufk inc -419 if p > 2401 +l dec -7 if xxh <= -2096 +m dec 325 if fr < 380 +mdk inc -391 if hkt <= 2465 +xxh inc 491 if z != -315 +p inc -832 if utc > 2324 +t dec 304 if a > 2056 +xxh dec 107 if dea < -243 +l inc 220 if hw < -2681 +p dec -316 if p > 1565 +mdk inc 333 if utc == 2332 +ppl dec 961 if a >= 2055 +fr inc 230 if z <= -310 +hkt dec -715 if fr >= 615 +l inc -466 if p <= 1888 +qlm inc 185 if xxh >= -1725 +u inc -710 if t == -168 +z inc 15 if ppl < -371 +utc inc 422 if hw < -2683 +fr dec 688 if t > -181 +mdk dec 606 if a < 2064 +me dec 323 if z <= -289 +ppl dec 150 if uz > -1844 +t inc 617 if q > 879 +hw inc -212 if qlm != -255 +a inc 338 if m <= 2901 +utc dec 545 if l < -228 +tn dec 407 if z > -303 +mdk dec 784 if ppl >= -378 +q inc -352 if z == -295 +uz inc -644 if ppl <= -372 +fr dec 209 if dea < -242 +tn dec -605 if p >= 1879 +hkt dec 77 if mdk != -1470 +hw dec -280 if hw < -2676 +ufk dec 375 if qlm >= -248 +p inc -958 if xxh <= -1710 +a inc 653 if z != -295 +utc inc 493 if qlm == -255 +xxh dec -649 if q > 530 +z inc -993 if me != -1749 +t inc 119 if mdk <= -1451 +ufk dec 883 if utc <= 2825 +m inc -545 if qlm == -255 +tn inc 626 if dea != -253 +tn dec -111 if p > 923 +tn inc -719 if u <= 2780 +u inc 976 if u != 2767 +z inc -495 if ppl != -368 +z dec 481 if dea != -246 +ppl dec 539 if ppl >= -381 +uz dec 213 if uz >= -2504 +a inc -9 if tn < 1509 +ny dec 719 if u < 3757 +uz inc 718 if hkt <= 3103 +ny dec 378 if u >= 3748 +me dec 163 if xxh >= -1076 +t dec -569 if hkt > 3105 +fr inc -280 if a <= 2407 +l dec -908 if q != 527 +a inc -13 if me < -1912 +dea dec 584 if mdk <= -1464 +hw inc -988 if l >= 692 +tn dec 847 if mdk < -1451 +hw inc 568 if utc > 2822 +t dec 133 if tn < 659 +z inc 271 if q <= 539 +mdk inc -33 if q <= 545 +l inc 185 if dea >= -259 +xxh inc 36 if xxh != -1064 +a dec 70 if xxh >= -1042 +z inc 956 if p > 931 +utc inc -778 if dea != -244 +dea inc -868 if z > -1985 +t dec -872 if u >= 3750 +ppl dec 420 if u < 3747 +dea inc 372 if xxh >= -1043 +hkt dec 32 if u != 3759 +t inc 23 if uz == -1985 +ny dec 106 if ufk == -683 +dea dec -794 if t == 1441 +hkt dec -233 if t < 1435 +q dec -186 if ufk == -683 +u dec 328 if a >= 2331 +xxh inc -179 if z <= -1991 +utc inc -614 if qlm > -254 +fr dec 136 if m != 2349 +uz inc -942 if uz >= -2000 +me inc 391 if m >= 2340 +l dec -448 if utc > 2054 +me dec -64 if fr > -696 +utc dec -621 if qlm > -256 +z dec -622 if dea == 132 +a dec -228 if ny == 1992 +qlm inc 957 if a <= 2563 +t dec 178 if hkt == 3304 +me dec -583 if uz >= -2940 +xxh dec 22 if ny >= 1988 +ufk dec 294 if fr <= -690 +l dec 666 if a != 2559 +tn dec 135 if qlm >= 704 +hkt inc 524 if q == 722 +uz inc 448 if dea > 118 +q inc 299 if hkt >= 3832 +u dec 502 if p <= 931 +qlm dec -530 if l > 863 +m dec -677 if m > 2344 +uz inc -254 if qlm < 1236 +p inc 164 if tn != 663 +ny inc -208 if me >= -874 +hw inc 688 if ny >= 1775 +q dec -90 if ny < 1787 +qlm inc 602 if l <= 874 +xxh inc 442 if uz == -2739 +mdk inc 235 if xxh == -793 +a dec -225 if u > 2911 +m dec -706 if hkt <= 3831 +a dec 229 if ufk <= -977 +ppl dec 256 if xxh == -788 +t inc 1000 if p < 1087 +hw inc -970 if a <= 2564 +hw dec 398 if ny >= 1779 +ppl inc 984 if ufk != -968 +utc inc -979 if ufk != -967 +hw dec -383 if utc > 1678 +p dec 283 if xxh == -793 +hw inc -434 if ny <= 1786 +u dec -226 if l == 868 +l dec 943 if tn > 675 +xxh inc -64 if p >= 807 +ppl inc 577 if fr == -694 +dea inc 629 if ppl > 636 +u dec 113 if ufk != -984 +a inc 482 if dea < 760 +dea dec -232 if xxh == -857 +ny inc -952 if ufk < -967 +hkt inc 159 if p < 811 +z inc 530 if mdk == -1258 +m dec -745 if dea <= 988 +m inc -554 if mdk >= -1258 +fr inc -798 if xxh >= -864 +q dec -139 if utc > 1690 +m dec 962 if p < 808 +a inc -409 if u <= 2809 +u dec -30 if ppl > 643 +uz dec 502 if u < 2834 +l dec -653 if qlm == 1834 +qlm inc 732 if me <= -869 +tn dec 200 if fr >= -1495 +ny inc -26 if a <= 2632 +hkt inc -601 if ppl < 656 +t inc -277 if l <= 1521 +a inc -86 if xxh < -847 +hkt dec -42 if qlm >= 2566 +dea dec 218 if p >= 807 +ufk dec 870 if q > 815 +z inc 141 if z == -1463 +l dec 873 if mdk > -1263 +u dec 897 if ppl <= 653 +dea inc -239 if p < 809 +xxh inc 525 if uz >= -2746 +dea inc 827 if mdk > -1266 +dea dec -988 if ppl != 636 +ny dec 330 if m < 3923 +q inc -413 if hw > -2554 +hw inc 983 if mdk < -1250 +mdk dec 932 if hw >= -1573 +fr inc -984 if u >= 1934 +xxh dec -344 if qlm > 2566 +p dec 189 if tn != 464 +hw inc -986 if ny < 473 +m dec 233 if z > -1323 +mdk inc -803 if a >= 2542 +u dec -858 if dea > 2570 +me dec 215 if dea >= 2590 +q inc 945 if dea >= 2589 +z inc 55 if ny >= 471 +xxh dec -63 if a <= 2544 +fr dec -864 if ufk != -969 +me dec -330 if me <= -861 +ufk inc -96 if dea <= 2586 +fr inc 348 if uz >= -2739 +qlm inc -249 if q <= 805 +qlm dec -752 if uz < -2736 +hkt dec -389 if q < 818 +dea inc -169 if ppl == 646 +xxh inc -689 if z <= -1268 +tn inc 911 if m <= 3697 +ppl inc -390 if a != 2551 +a inc 87 if ufk != -1074 +z inc 413 if ppl == 262 +p inc 476 if mdk < -2052 +p dec -570 if z != -1257 +uz inc 266 if hkt <= 3654 +ppl inc -29 if ny <= 474 +ny inc -154 if ppl <= 264 +ufk inc -614 if uz < -2741 +dea dec -627 if xxh == -269 +me inc 553 if p < 1670 +q inc -413 if a > 2636 +q dec 754 if utc == 1688 +p dec 857 if m == 3688 +dea dec 883 if ufk >= -1074 +uz inc -485 if l == 647 +dea dec -979 if me <= 15 +hkt dec 738 if l > 642 +xxh inc 298 if tn < 1372 +uz dec 235 if l != 651 +m dec -170 if tn > 1379 +hkt inc 902 if a > 2619 +hkt inc 354 if hw < -1573 +qlm dec 512 if uz != -3462 +u inc -676 if t != 984 +a inc 635 if z == -1267 +ppl inc -756 if q <= 60 +t inc 662 if mdk == -2061 +qlm dec -900 if p > 807 +z dec 877 if hkt == 4176 +a dec -841 if uz > -3466 +dea inc 141 if u != 2115 +q inc 917 if dea != 3270 +ppl inc -582 if tn >= 1375 +dea dec -309 if xxh < -271 +utc inc -353 if hw <= -1578 +mdk dec 643 if q != 979 +hw inc -595 if fr != -1254 +xxh inc 736 if ny != 325 +hkt inc -692 if z == -2144 +p dec 500 if hw < -2170 +uz dec -168 if ppl >= -1083 +u dec 419 if hw > -2181 +fr inc -653 if u != 1704 +m inc -677 if qlm < 3716 +qlm dec -341 if u >= 1704 +me dec -926 if utc >= 1329 +qlm dec -462 if hw != -2174 +fr dec 604 if hw != -2173 +p dec -826 if uz >= -3291 +hkt inc -855 if ny <= 315 +utc dec -647 if dea > 3269 +xxh inc 483 if z < -2143 +l dec 93 if utc >= 1979 +dea inc -680 if fr != -1264 +me inc -293 if ufk != -1063 +uz dec 279 if t == 1636 +xxh inc -145 if u <= 1705 +q inc 269 if a > 4097 +ufk dec 734 if l >= 552 +z dec -270 if utc > 1977 +tn inc -154 if t <= 1645 +mdk inc 455 if uz < -3283 +dea inc 350 if utc < 1992 +hw dec -300 if ppl <= -1085 +ufk inc 337 if u >= 1699 +ppl inc -634 if l != 558 +t dec -583 if xxh == 805 +t dec 384 if dea >= 3620 +p dec -873 if m == 3011 +ufk inc -710 if uz < -3287 +hw inc -808 if hkt <= 3490 +hw dec -464 if u > 1702 +m dec -102 if mdk > -2256 +fr dec 579 if t > 1829 +dea dec -839 if qlm < 4519 +ufk dec -741 if l <= 545 +me inc -520 if z <= -1865 +mdk dec 824 if hkt < 3493 +qlm inc -703 if q <= 1243 +t dec 284 if qlm < 4517 +fr dec -527 if ufk == -2183 +me dec -995 if xxh == 805 +utc inc 498 if hw < -2525 +hw dec -350 if ufk <= -2174 +dea inc 143 if mdk == -3073 +utc dec 812 if l < 552 +ufk dec 679 if hkt <= 3490 +a inc -464 if ny < 317 +ufk inc 116 if hkt > 3483 +hw inc 77 if mdk < -3063 +hkt dec 851 if ny < 329 +uz dec -37 if uz != -3287 +hkt dec 45 if xxh == 805 +uz dec -682 if fr <= -1850 +dea inc 695 if hkt > 2582 +p dec 857 if hkt <= 2592 +fr inc 114 if dea < 5309 +q dec -714 if p < 1158 +utc dec 896 if ufk != -2752 +uz dec -937 if ufk < -2741 +p inc -807 if tn <= 1232 +ufk inc 788 if fr >= -1730 +ufk dec 519 if l > 558 +ufk dec 142 if tn < 1227 +ppl dec -561 if ufk > -2103 +dea dec 463 if fr >= -1728 +m inc 139 if tn != 1218 +fr dec -606 if q >= 1951 +qlm inc 934 if fr >= -1122 +a dec -910 if xxh < 815 +hw dec -564 if a <= 5015 +u dec -648 if hw > -1532 +hkt dec 601 if hkt <= 2588 +q dec -480 if hkt < 1997 +uz dec 596 if hkt >= 1983 +p dec -971 if u > 2347 +z dec 790 if m == 3252 +fr inc 281 if hw <= -1517 +uz dec 636 if hw == -1516 +l dec -582 if ny > 315 +ny inc 202 if dea < 5306 +mdk inc -251 if ppl > -1147 +me dec 826 if p == 1317 +qlm dec -11 if p == 1317 +z inc -166 if a >= 5011 +ny inc 455 if l >= 1127 +utc dec -156 if qlm < 4525 +q dec -147 if l <= 1129 +ufk inc 36 if ny < 978 +ppl dec -871 if uz < -2907 +fr inc 776 if t >= 1548 +qlm inc -510 if u != 2352 +z inc 373 if dea >= 5294 +uz dec -975 if fr <= -59 +fr dec -670 if z < -2459 +utc dec 322 if q != 2428 +l dec 3 if ppl != -282 +uz dec 728 if ny > 971 +ny dec -396 if p > 1308 +a inc -502 if mdk <= -3067 +ny dec -492 if uz <= -2666 +ppl inc -720 if t >= 1554 +uz inc -323 if hw != -1533 +ppl inc 805 if m >= 3252 +p inc 310 if qlm != 4520 +m dec 743 if dea >= 5299 +ppl inc 847 if t <= 1546 +p dec 89 if u != 2352 +a inc 472 if z < -2455 +me dec 301 if utc > 914 +ppl inc 740 if q < 2434 +ufk inc -633 if l > 1138 +ppl inc -51 if hw > -1529 +u dec -714 if fr >= -56 +z dec 510 if me >= 0 +l inc 664 if mdk != -3073 +qlm dec -742 if l < 1142 +ny dec -473 if tn == 1225 +fr inc -805 if ufk > -2093 +xxh dec -151 if fr > -74 +hw inc -734 if hw <= -1528 +p dec 976 if uz >= -2990 +mdk inc 523 if m == 2509 +u dec -176 if utc < 923 +me inc 766 if hkt != 1987 +ppl dec -392 if mdk != -2557 +l inc -756 if u > 2527 +fr inc -990 if xxh > 955 +l inc 901 if ufk > -2100 +xxh dec -856 if ppl >= 137 +hkt dec -989 if t == 1561 +p dec 846 if p > 339 +hkt inc -429 if dea != 5302 +u dec 534 if hw <= -1517 +uz dec 178 if xxh > 1803 +z dec 655 if m <= 2516 +xxh inc -340 if ny < 2334 +u inc -545 if dea != 5295 +p inc -996 if uz > -3172 +dea dec -140 if hkt != 1984 +q inc -764 if a <= 4985 +z inc 263 if uz == -3167 +l dec -929 if a <= 4985 +p inc -214 if uz >= -3170 +uz inc 393 if hw >= -1533 +tn inc -624 if me == -5 +me inc -474 if ufk != -2106 +ppl dec 475 if l <= 2214 +qlm inc 417 if u != 1449 +p inc -490 if qlm > 5257 +a inc 526 if u <= 1452 +ny inc -347 if u <= 1454 +p dec 397 if uz < -2765 +t dec 548 if u <= 1448 +ufk dec 514 if ufk > -2102 +l dec 744 if uz != -2782 +fr dec 810 if ppl == -333 +ppl dec -338 if qlm > 5258 +qlm dec 272 if q > 1665 +m dec 521 if ufk >= -2614 +uz dec 558 if me < -477 +p inc -632 if m >= 1987 +dea inc -237 if fr != -1864 +mdk dec 3 if utc > 917 +l inc -406 if dea >= 5213 +dea inc -268 if z == -2849 +utc inc 675 if q > 1664 +me dec -905 if p < -3230 +ufk inc -799 if u != 1439 +xxh inc 718 if hkt != 1987 +tn inc 156 if qlm >= 4984 +p inc -680 if fr == -1866 +ppl inc 423 if hkt >= 1980 +p inc -759 if ufk != -3405 +me inc 496 if qlm <= 4995 +m dec 111 if mdk != -2545 +u dec 351 if z < -2843 +uz dec -405 if xxh != 1804 +ny dec -634 if utc == 1592 +qlm inc 294 if l == 1463 +xxh inc -994 if a <= 5511 +a inc 460 if uz == -2927 +t inc -313 if u != 1093 +l inc 254 if hkt > 1978 +dea dec -290 if ppl <= 429 +ny inc 190 if z <= -2844 +ppl inc -865 if dea == 5220 +z dec 372 if utc <= 1595 +l dec -563 if u < 1104 +z inc -283 if xxh < 821 +q inc 967 if utc == 1595 +q dec -621 if ppl > 433 +l dec -221 if tn > 757 +l dec -935 if a >= 5962 +l inc -62 if l != 3225 +hkt dec -654 if t > 1240 +dea inc 87 if p == -4673 +l dec -166 if u <= 1098 +dea dec 183 if hw != -1529 +q dec 70 if p == -4667 +a dec -673 if ny < 2188 +q dec 295 if mdk != -2563 +m dec -26 if a == 6644 +qlm inc 378 if xxh != 816 +a dec 174 if l <= 3320 +fr inc 117 if dea >= 5131 +hkt dec -732 if hkt >= 2634 +ufk inc -838 if mdk != -2547 +ny inc -964 if a >= 6461 +hw dec -264 if a == 6470 +z dec -834 if ufk >= -4251 +l inc -658 if m > 1897 +xxh inc 400 if fr >= -1753 +hw dec 380 if hw <= -1265 +t inc -608 if utc < 1597 +ppl dec 352 if a > 6467 +l dec -355 if utc > 1591 +l dec 846 if dea <= 5128 +ppl dec 756 if fr < -1746 +utc dec 259 if p == -4673 +tn dec 160 if hw < -1257 +t inc -625 if t != 640 +xxh dec 804 if dea > 5130 +ny dec 227 if z <= -2665 +ppl dec 306 if uz != -2922 +q dec -671 if hw < -1262 +tn dec 149 if ufk == -4248 +p dec -583 if mdk == -2553 +hw inc 312 if uz <= -2919 +hkt inc 111 if tn >= 456 +q dec -23 if uz > -2918 +hw inc -291 if l > 3008 +me inc -744 if utc > 1327 +uz dec 188 if utc >= 1336 +hw dec -575 if z < -2663 +ppl dec 977 if ny != 988 +l dec -84 if dea < 5135 +p inc 905 if uz == -3115 +m inc 636 if m == 1903 +hkt dec 95 if p < -3178 +u inc 249 if utc > 1331 +uz dec -196 if qlm == 5662 +hkt inc -621 if fr > -1750 +z inc -859 if l < 3093 +l inc -789 if ppl > -1957 +me inc 916 if tn >= 457 +uz dec -115 if xxh != 406 +z dec -353 if z <= -2669 +hw inc -965 if ppl != -1960 +t inc 333 if qlm == 5662 +t dec 860 if z == -2310 +p dec -841 if l > 3104 +qlm inc 225 if t == 341 +utc inc -937 if p <= -3185 +qlm inc -191 if xxh < 424 +m dec 607 if q != 2354 +uz inc 807 if p >= -3178 +fr dec -431 if uz == -2804 +ppl dec -312 if t <= 341 +a dec -764 if mdk >= -2557 +utc dec 505 if a >= 7228 +ufk dec -148 if tn != 449 +utc dec -371 if utc != -100 +dea dec -11 if utc < 272 +ufk inc 329 if utc != 261 +utc dec -484 if z <= -2312 +m dec 784 if ppl == -1651 +xxh dec 669 if m <= 1147 +xxh inc -798 if me == 178 +p dec -832 if ppl == -1651 +ufk inc 266 if fr > -1318 +a inc -993 if fr >= -1319 +xxh inc 25 if ppl != -1652 +u inc -353 if hw == -1631 +p inc -338 if q >= 2340 +p dec 517 if utc >= 741 +ppl dec -221 if dea > 5137 +hw dec 949 if mdk < -2544 +tn inc 201 if ufk != -3781 +mdk inc 855 if t > 334 +m dec 604 if q <= 2353 +me inc 268 if tn <= 644 +tn inc -372 if m > 540 +l dec 275 if qlm >= 5687 +mdk dec -13 if p == -3199 +z dec -725 if tn > 286 +dea inc -843 if dea == 5142 +hw inc -603 if a >= 6234 +ppl inc 850 if tn <= 279 +l inc -601 if uz == -2804 +m inc 10 if z >= -2319 +fr inc -412 if xxh != -351 +me dec 726 if tn >= 277 +ny dec -719 if me < -544 +hw dec 413 if q > 2349 +a dec -229 if hkt == 2651 +t inc 620 if t != 347 +uz inc -216 if t <= 963 +fr inc 614 if me != -549 +xxh inc 536 if z < -2309 +q inc 974 if me < -548 +q inc -131 if ny == 1711 +tn dec 110 if tn > 274 +l inc 47 if p == -3208 +xxh inc -872 if dea >= 4295 +tn inc -667 if tn <= 169 +q dec 562 if mdk >= -1700 +a inc -16 if xxh != -685 +hw dec 649 if xxh == -695 +ufk inc 239 if l != 2268 +t dec 935 if ppl <= -576 +m dec 1000 if fr > -1120 +hkt inc -167 if xxh == -695 +ny inc 926 if uz > -3027 +m inc -729 if xxh > -693 +m inc -677 if a > 6221 +p dec -412 if qlm >= 5691 +m dec -678 if ufk < -3526 +ppl inc 206 if z < -2308 +m inc -961 if m != -445 +t inc -989 if mdk > -1701 +ppl dec 43 if q <= 1654 +xxh inc -619 if ny == 2637 +ppl dec 168 if xxh < -1312 +t inc 191 if xxh > -1320 +me inc 387 if hw >= -3826 +p inc 517 if q <= 1648 +q dec 577 if ppl > -589 +u dec -841 if fr <= -1115 +dea dec -791 if p <= -2793 +hkt inc 216 if tn != -500 +uz dec -333 if hkt >= 2490 +dea inc 46 if a > 6217 +mdk inc -168 if fr > -1117 +t inc -606 if fr > -1122 +me inc 662 if hkt != 2491 +uz dec 384 if p > -2806 +uz inc -848 if xxh < -1308 +ny inc 617 if tn < -497 +fr dec -359 if utc != 750 +m dec -911 if ufk <= -3530 +ppl dec -190 if mdk != -1858 +u dec -400 if t > -1388 +me inc -381 if u == 2235 +hw inc -548 if m == 466 +qlm inc -940 if mdk <= -1860 +dea dec 180 if z <= -2316 +hw inc 17 if tn != -504 +fr dec -769 if me > -277 +ppl inc -630 if hkt == 2482 +hw inc 825 if xxh == -1314 +utc dec -38 if hw < -3529 +q dec 851 if uz <= -3918 +me dec -417 if me > -274 +q inc 505 if ny < 3248 +ny dec 299 if fr > 9 +utc dec 996 if z == -2317 +z inc 157 if ppl == -395 +mdk inc -11 if mdk == -1866 +t dec -222 if ny <= 2964 +q dec 1000 if u <= 2244 +tn dec -704 if ppl >= -399 +l inc 666 if utc > -212 +q inc 890 if dea >= 4951 +tn inc 255 if xxh > -1324 +me dec -317 if p == -2796 +utc dec 651 if m >= 460 +dea dec -945 if q > 110 +ny inc -755 if z > -2169 +a inc 1 if utc < -858 +uz dec 840 if utc >= -861 +l dec 131 if ufk != -3542 +hkt inc -442 if u > 2236 +mdk dec -156 if hw == -3531 +ufk dec 380 if uz != -4756 +xxh dec 198 if p == -2796 +fr inc -946 if z != -2165 +q dec -736 if dea < 5898 +qlm inc -284 if fr == -934 +z dec 895 if t < -1152 +me dec -370 if l != 2806 +a dec -949 if dea >= 5906 +l inc -913 if uz <= -4758 +uz inc 15 if t > -1158 +m inc 535 if xxh > -1516 +me inc -896 if u > 2228 +m inc -821 if fr == -934 +me dec 754 if m <= 189 +xxh inc 685 if p >= -2802 +utc inc 149 if uz == -4744 +ufk dec -486 if hw <= -3535 +tn dec 617 if u != 2228 +fr inc -971 if ny < 2191 +l dec 933 if z < -3053 +q dec 269 if qlm > 4467 +me inc 449 if l < 968 +utc inc -359 if l <= 965 +tn inc -465 if p <= -2798 +xxh dec -811 if t <= -1149 +fr dec -106 if m <= 182 +uz inc 603 if p < -2794 +uz inc 310 if z <= -3064 +ny inc -764 if hw >= -3538 +mdk dec -843 if ufk < -3416 +a inc 49 if tn != -158 +dea inc 129 if ufk >= -3433 +ny dec 515 if ny < 1438 +q inc -603 if ufk < -3419 +tn dec 470 if hkt < 2496 +m inc -669 if utc <= -1067 +dea inc 401 if ny >= 912 +p inc 129 if tn >= -631 +p dec -708 if hw != -3540 +dea inc 932 if mdk == -1024 +tn dec -244 if ufk == -3426 +ny dec 632 if utc >= -1075 +ny dec -958 if z > -3063 +me dec -67 if hkt == 2490 +fr inc 431 if mdk > -1038 +ny dec -435 if z < -3052 +ny inc 997 if ny != 1686 +dea inc 397 if hw < -3537 +hw dec 232 if xxh == -16 +q inc 826 if p > -1960 +q inc -807 if z < -3045 +uz dec -645 if a < 6227 +me inc -725 if qlm < 4477 +xxh dec -440 if z == -3055 +mdk inc 647 if m <= -489 +t dec -497 if dea != 6827 +hkt dec -874 if hkt == 2490 diff --git a/pytudes/data/advent2017/input9.txt b/pytudes/data/advent2017/input9.txt new file mode 100644 index 0000000..a29e6c6 --- /dev/null +++ b/pytudes/data/advent2017/input9.txt @@ -0,0 +1 @@ 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diff --git a/pytudes/ipynb/.ipynb_checkpoints/Advent 2017-checkpoint.ipynb b/pytudes/ipynb/.ipynb_checkpoints/Advent 2017-checkpoint.ipynb new file mode 100644 index 0000000..1b5e6de --- /dev/null +++ b/pytudes/ipynb/.ipynb_checkpoints/Advent 2017-checkpoint.ipynb @@ -0,0 +1,3667 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# December 2017: Advent of Code Solutions\n", + "\n", + "Peter Norvig\n", + "\n", + "I'm doing the [Advent of Code](https://adventofcode.com) puzzles, just like [last year](https://github.com/norvig/pytudes/blob/master/ipynb/Advent%20of%20Code.ipynb). This time, my terms of engagement are:\n", + "\n", + "* I won't write a summary of each day's puzzle description. Follow the links in the section headers (e.g. **[Day 1](https://adventofcode.com/2017/day/1)**) to understand what each puzzle is asking. \n", + "* What you see is mostly the algorithm I first came up with first, although sometimes I go back and refactor if I think the original is unclear.\n", + "* I do clean up the code a bit even after I solve the puzzle: adding docstrings, changing variable names, changing input boxes to `assert` statements.\n", + "* I will describe my errors that slowed me down.\n", + "* Some days I start on time and try to code very quickly (although I know that people at the top of the leader board will be much faster than me); other days I end up starting late and don't worry about going quickly.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# Day 0: Imports and Utility Functions\n", + "\n", + "I might need these:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Python 3.x Utility Functions\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import re\n", + "import numpy as np\n", + "import math\n", + "import random\n", + "\n", + "from collections import Counter, defaultdict, namedtuple, deque, abc, OrderedDict\n", + "from functools import lru_cache\n", + "from statistics import mean, median, mode, stdev, variance\n", + "from itertools import (permutations, combinations, chain, cycle, product, islice, \n", + " takewhile, zip_longest, count as count_from)\n", + "from heapq import heappop, heappush\n", + "from numba import jit\n", + "\n", + "identity = lambda x: x\n", + "letters = 'abcdefghijklmnopqrstuvwxyz'\n", + "\n", + "cache = lru_cache(None)\n", + "\n", + "cat = ''.join\n", + "\n", + "Ø = frozenset() # Empty set\n", + "inf = float('inf')\n", + "BIG = 10 ** 999\n", + "\n", + "################ Functions for Input, Parsing\n", + "\n", + "def Input(day, year=2017):\n", + " \"Open this day's input file.\"\n", + " return open('data/advent{}/input{}.txt'.format(year, day))\n", + "\n", + "def Inputstr(day, year=2017): \n", + " \"The contents of this day's input file as a str.\"\n", + " return Input(day, year).read().rstrip('\\n')\n", + " \n", + "def Array(lines):\n", + " \"Parse an iterable of str lines into a 2-D array. If `lines` is a str, splitlines.\"\n", + " if isinstance(lines, str): lines = lines.splitlines()\n", + " return mapt(Vector, lines)\n", + "\n", + "def Vector(line):\n", + " \"Parse a str into a tuple of atoms (numbers or str tokens).\"\n", + " return mapt(Atom, line.replace(',', ' ').split())\n", + "\n", + "def Integers(text): \n", + " \"Return a tuple of all integers in a string.\"\n", + " return mapt(int, re.findall(r'-?\\b\\d+\\b', text))\n", + "\n", + "def Atom(token):\n", + " \"Parse a str token into a number, or leave it as a str.\"\n", + " try:\n", + " return int(token)\n", + " except ValueError:\n", + " try:\n", + " return float(token)\n", + " except ValueError:\n", + " return token\n", + " \n", + "def error(err=RuntimeError, *args): raise err(*args)\n", + "\n", + "################ Functions on Iterables\n", + "\n", + "def first(iterable, default=None): \n", + " \"The first item in an iterable, or default if it is empty.\"\n", + " return next(iter(iterable), default)\n", + "\n", + "def first_true(iterable, pred=None, default=None):\n", + " \"\"\"Returns the first true value in the iterable.\n", + " If no true value is found, returns *default*\n", + " If *pred* is not None, returns the first item\n", + " for which pred(item) is true.\"\"\"\n", + " # first_true([a,b,c], default=x) --> a or b or c or x\n", + " # first_true([a,b], fn, x) --> a if fn(a) else b if fn(b) else x\n", + " return next(filter(pred, iterable), default)\n", + "\n", + "def nth(iterable, n, default=None):\n", + " \"Returns the nth item of iterable, or a default value\"\n", + " return next(islice(iterable, n, None), default)\n", + "\n", + "def upto(iterable, maxval):\n", + " \"From a monotonically increasing iterable, generate all the values <= maxval.\"\n", + " # Why <= maxval rather than < maxval? In part because that's how Ruby's upto does it.\n", + " return takewhile(lambda x: x <= maxval, iterable)\n", + "\n", + "def groupby(iterable, key=identity):\n", + " \"Return a dict of {key(item): [items...]} grouping all items in iterable by keys.\"\n", + " groups = defaultdict(list)\n", + " for item in iterable:\n", + " groups[key(item)].append(item)\n", + " return groups\n", + "\n", + "def grouper(iterable, n, fillvalue=None):\n", + " \"\"\"Collect data into fixed-length chunks:\n", + " grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx\"\"\"\n", + " args = [iter(iterable)] * n\n", + " return zip_longest(*args, fillvalue=fillvalue)\n", + "\n", + "def overlapping(iterable, n):\n", + " \"\"\"Generate all (overlapping) n-element subsequences of iterable.\n", + " overlapping('ABCDEFG', 3) --> ABC BCD CDE DEF EFG\"\"\"\n", + " if isinstance(iterable, abc.Sequence):\n", + " yield from (iterable[i:i+n] for i in range(len(iterable) + 1 - n))\n", + " else:\n", + " result = deque(maxlen=n)\n", + " for x in iterable:\n", + " result.append(x)\n", + " if len(result) == n:\n", + " yield tuple(result)\n", + " \n", + "def pairwise(iterable):\n", + " \"s -> (s0,s1), (s1,s2), (s2, s3), ...\"\n", + " return overlapping(iterable, 2)\n", + "\n", + "def sequence(iterable, type=tuple):\n", + " \"Coerce iterable to sequence: leave alone if already a sequence, else make it `type`.\"\n", + " return iterable if isinstance(iterable, abc.Sequence) else type(iterable)\n", + "\n", + "def join(iterable, sep=''):\n", + " \"Join the items in iterable, converting each to a string first.\"\n", + " return sep.join(map(str, iterable))\n", + " \n", + "def powerset(iterable):\n", + " \"Yield all subsets of items.\"\n", + " items = list(iterable)\n", + " for r in range(len(items)+1):\n", + " for c in combinations(items, r):\n", + " yield c\n", + " \n", + "def quantify(ite1rable, pred=bool):\n", + " \"Count how many times the predicate is true.\"\n", + " return sum(map(pred, iterable))\n", + "\n", + "def length(iterable):\n", + " \"Same as len(list(iterable)), but without consuming memory.\"\n", + " return sum(1 for _ in iterable)\n", + "\n", + "def shuffled(iterable):\n", + " \"Create a new list out of iterable, and shuffle it.\"\n", + " new = list(iterable)\n", + " random.shuffle(new)\n", + " return new\n", + " \n", + "flatten = chain.from_iterable\n", + "\n", + "def repeat(n, fn, arg):\n", + " \"Repeat arg=fn(arg) n times.\"\n", + " for i in range(n):\n", + " arg = fn(arg)\n", + " return arg\n", + "\n", + "################ Making immutable objects\n", + " \n", + "class Set(frozenset):\n", + " \"A frozenset, but with a prettier printer.\"\n", + " def __repr__(self): return '{' + join(sorted(self), ', ') + '}'\n", + " \n", + "def canon(items, typ=None):\n", + " \"Canonicalize these order-independent items into a hashable canonical form.\"\n", + " typ = typ or (cat if isinstance(items, str) else tuple)\n", + " return typ(sorted(items))\n", + "\n", + "def mapt(fn, *args): \n", + " \"Do a map, and make the results into a tuple.\"\n", + " return tuple(map(fn, *args))\n", + " \n", + "################ Math Functions\n", + " \n", + "def transpose(matrix): return tuple(zip(*matrix))\n", + "\n", + "def isqrt(n):\n", + " \"Integer square root (rounds down).\"\n", + " return int(n ** 0.5)\n", + "\n", + "def ints(start, end):\n", + " \"The integers from start to end, inclusive: range(start, end+1)\"\n", + " return range(start, end + 1)\n", + "\n", + "def floats(start, end, step=1.0):\n", + " \"Yield floats from start to end (inclusive), by increments of step.\"\n", + " m = (1.0 if step >= 0 else -1.0)\n", + " while start * m <= end * m:\n", + " yield start\n", + " start += step\n", + " \n", + "def multiply(numbers):\n", + " \"Multiply all the numbers together.\"\n", + " result = 1\n", + " for n in numbers:\n", + " result *= n\n", + " return result\n", + "\n", + "import operator as op\n", + "\n", + "operations = {'>': op.gt, '>=': op.ge, '==': op.eq,\n", + " '<': op.lt, '<=': op.le, '!=': op.ne,\n", + " '+': op.add, '-': op.sub, '*': op.mul, \n", + " '/': op.truediv, '**': op.pow}\n", + "\n", + "################ 2-D points implemented using (x, y) tuples\n", + "\n", + "def X(point): x, y = point; return x\n", + "def Y(point): x, y = point; return y\n", + "\n", + "origin = (0, 0)\n", + "UP, DOWN, LEFT, RIGHT = (0, 1), (0, -1), (-1, 0), (1, 0)\n", + "\n", + "def neighbors4(point): \n", + " \"The four neighboring squares.\"\n", + " x, y = point\n", + " return ( (x, y-1),\n", + " (x-1, y), (x+1, y), \n", + " (x, y+1))\n", + "\n", + "def neighbors8(point): \n", + " \"The eight neighboring squares.\"\n", + " x, y = point \n", + " return ((x-1, y-1), (x, y-1), (x+1, y-1),\n", + " (x-1, y), (x+1, y),\n", + " (x-1, y+1), (x, y+1), (x+1, y+1))\n", + "\n", + "def cityblock_distance(P, Q=origin): \n", + " \"Manhatten distance between two points.\"\n", + " return sum(abs(p - q) for p, q in zip(P, Q))\n", + "\n", + "def distance(P, Q=origin): \n", + " \"Hypotenuse distance between two points.\"\n", + " return sum((p - q) ** 2 for p, q in zip(P, Q)) ** 0.5\n", + "\n", + "################ Debugging \n", + "\n", + "def trace1(f):\n", + " \"Print a trace of the input and output of a function on one line.\"\n", + " def traced_f(*args):\n", + " result = f(*args)\n", + " print('{}({}) = {}'.format(f.__name__, ', '.join(map(str, args)), result))\n", + " return result\n", + " return traced_f\n", + "\n", + "def grep(pattern, iterable):\n", + " \"Print lines from iterable that match pattern.\"\n", + " for line in iterable:\n", + " if re.search(pattern, line):\n", + " print(line)\n", + " \n", + "class Struct:\n", + " \"A structure that can have any fields defined.\"\n", + " def __init__(self, **entries): self.__dict__.update(entries)\n", + " def __repr__(self): \n", + " fields = ['{}={}'.format(f, self.__dict__[f]) \n", + " for f in sorted(self.__dict__)]\n", + " return 'Struct({})'.format(', '.join(fields))\n", + "\n", + "################ A* and Breadth-First Search (tracking states, not actions)\n", + "\n", + "def always(value): return (lambda *args: value)\n", + "\n", + "def Astar(start, moves_func, h_func, cost_func=always(1)):\n", + " \"Find a shortest sequence of states from start to a goal state (where h_func(s) == 0).\"\n", + " frontier = [(h_func(start), start)] # A priority queue, ordered by path length, f = g + h\n", + " previous = {start: None} # start state has no previous state; other states will\n", + " path_cost = {start: 0} # The cost of the best path to a state.\n", + " Path = lambda s: ([] if (s is None) else Path(previous[s]) + [s])\n", + " while frontier:\n", + " (f, s) = heappop(frontier)\n", + " if h_func(s) == 0:\n", + " return Path(s)\n", + " for s2 in moves_func(s):\n", + " g = path_cost[s] + cost_func(s, s2)\n", + " if s2 not in path_cost or g < path_cost[s2]:\n", + " heappush(frontier, (g + h_func(s2), s2))\n", + " path_cost[s2] = g\n", + " previous[s2] = s\n", + "\n", + "def bfs(start, moves_func, goals):\n", + " \"Breadth-first search\"\n", + " goal_func = (goals if callable(goals) else lambda s: s in goals)\n", + " return Astar(start, moves_func, lambda s: (0 if goal_func(s) else 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " # Functions for Input, Parsing\n", + " assert Array('''1 2 3\n", + " 4 5 6''') == ((1, 2, 3), \n", + " (4, 5, 6))\n", + " assert Vector('testing 1 2 3.') == ('testing', 1, 2, 3.0)\n", + " \n", + " # Functions on Iterables\n", + " assert first('abc') == first(['a', 'b', 'c']) == 'a'\n", + " assert first_true([0, None, False, {}, 42, 43]) == 42\n", + " assert nth('abc', 1) == nth(iter('abc'), 1) == 'b'\n", + " assert cat(upto('abcdef', 'd')) == 'abcd'\n", + " assert cat(['do', 'g']) == 'dog'\n", + " assert groupby([-3, -2, -1, 1, 2], abs) == {1: [-1, 1], 2: [-2, 2], 3: [-3]}\n", + " assert list(grouper(range(8), 3)) == [(0, 1, 2), (3, 4, 5), (6, 7, None)]\n", + " assert list(overlapping((0, 1, 2, 3, 4), 3)) == [(0, 1, 2), (1, 2, 3), (2, 3, 4)]\n", + " assert list(overlapping('abcdefg', 4)) == ['abcd', 'bcde', 'cdef', 'defg'] \n", + " assert list(pairwise((0, 1, 2, 3, 4))) == [(0, 1), (1, 2), (2, 3), (3, 4)]\n", + " assert sequence('seq') == 'seq'\n", + " assert sequence((i**2 for i in range(5))) == (0, 1, 4, 9, 16)\n", + " assert join(range(5)) == '01234'\n", + " assert join(range(5), ', ') == '0, 1, 2, 3, 4'\n", + " assert multiply([1, 2, 3, 4]) == 24\n", + " assert transpose(((1, 2, 3), (4, 5, 6))) == ((1, 4), (2, 5), (3, 6))\n", + " assert isqrt(9) == 3 == isqrt(10)\n", + " assert ints(1, 100) == range(1, 101)\n", + " assert identity('anything') == 'anything'\n", + " assert set(powerset({1, 2, 3})) == {\n", + " (), (1,), (1, 2), (1, 2, 3), (1, 3), (2,), (2, 3), (3,)}\n", + " assert quantify(['testing', 1, 2, 3, int, len], callable) == 2 # int and len are callable\n", + " assert quantify([0, False, None, '', [], (), {}, 42]) == 1 # Only 42 is truish\n", + " assert set(shuffled('abc')) == set('abc')\n", + " assert canon('abecedarian') == 'aaabcdeeinr'\n", + " assert canon([9, 1, 4]) == canon({1, 4, 9}) == (1, 4, 9)\n", + " assert mapt(math.sqrt, [1, 9, 4]) == (1, 3, 2)\n", + " \n", + " # Math\n", + " assert transpose([(1, 2, 3), (4, 5, 6)]) == ((1, 4), (2, 5), (3, 6))\n", + " assert isqrt(10) == isqrt(9) == 3\n", + " assert ints(1, 5) == range(1, 6)\n", + " assert list(floats(1, 5)) == [1., 2., 3., 4., 5.]\n", + " assert multiply(ints(1, 10)) == math.factorial(10) == 3628800\n", + " \n", + " # 2-D points\n", + " P = (3, 4)\n", + " assert X(P) == 3 and Y(P) == 4\n", + " assert cityblock_distance(P) == cityblock_distance(P, origin) == 7\n", + " assert distance(P) == distance(P, origin) == 5\n", + " \n", + " # Search\n", + " assert Astar((4, 4), neighbors8, distance) == [(4, 4), (3, 3), (2, 2), (1, 1), (0, 0)]\n", + " assert bfs((4, 4), neighbors8, {origin}) == [(4, 4), (3, 3), (2, 2), (1, 1), (0, 0)]\n", + " forty2 = always(42)\n", + " assert forty2() == forty2('?') == forty2(4, 2) == 42\n", + "\n", + " return 'pass'\n", + "\n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 1](https://adventofcode.com/2017/day/1): Inverse Captcha\n", + "\n", + "This was easier than I remember last year's puzzles being:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2014, (3, 2, 9, 4, 1, 9, 9, 4, 7, 1))" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "digits = mapt(int, Inputstr(1))\n", + "N = len(digits)\n", + "\n", + "N, digits[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1158" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(digits[i] \n", + " for i in range(N) \n", + " if digits[i] == digits[i - 1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1132" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(digits[i] \n", + " for i in range(N) \n", + " if digits[i] == digits[i - N // 2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 2](https://adventofcode.com/2017/day/2): Corruption Checksum\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "rows2 = Array('''790\t99\t345\t1080\t32\t143\t1085\t984\t553\t98\t123\t97\t197\t886\t125\t947\n", + "302\t463\t59\t58\t55\t87\t508\t54\t472\t63\t469\t419\t424\t331\t337\t72\n", + "899\t962\t77\t1127\t62\t530\t78\t880\t129\t1014\t93\t148\t239\t288\t357\t424\n", + "2417\t2755\t254\t3886\t5336\t3655\t5798\t3273\t5016\t178\t270\t6511\t223\t5391\t1342\t2377\n", + "68\t3002\t3307\t166\t275\t1989\t1611\t364\t157\t144\t3771\t1267\t3188\t3149\t156\t3454\n", + "1088\t1261\t21\t1063\t1173\t278\t1164\t207\t237\t1230\t1185\t431\t232\t660\t195\t1246\n", + "49\t1100\t136\t1491\t647\t1486\t112\t1278\t53\t1564\t1147\t1068\t809\t1638\t138\t117\n", + "158\t3216\t1972\t2646\t3181\t785\t2937\t365\t611\t1977\t1199\t2972\t201\t2432\t186\t160\n", + "244\t86\t61\t38\t58\t71\t243\t52\t245\t264\t209\t265\t308\t80\t126\t129\n", + "1317\t792\t74\t111\t1721\t252\t1082\t1881\t1349\t94\t891\t1458\t331\t1691\t89\t1724\n", + "3798\t202\t3140\t3468\t1486\t2073\t3872\t3190\t3481\t3760\t2876\t182\t2772\t226\t3753\t188\n", + "2272\t6876\t6759\t218\t272\t4095\t4712\t6244\t4889\t2037\t234\t223\t6858\t3499\t2358\t439\n", + "792\t230\t886\t824\t762\t895\t99\t799\t94\t110\t747\t635\t91\t406\t89\t157\n", + "2074\t237\t1668\t1961\t170\t2292\t2079\t1371\t1909\t221\t2039\t1022\t193\t2195\t1395\t2123\n", + "8447\t203\t1806\t6777\t278\t2850\t1232\t6369\t398\t235\t212\t992\t7520\t7304\t7852\t520\n", + "3928\t107\t3406\t123\t2111\t2749\t223\t125\t134\t146\t3875\t1357\t508\t1534\t4002\t4417''')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "46402" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(abs(max(row) - min(row)) for row in rows2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "265" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def evendiv(row): \n", + " return first(a // b for a in row for b in row if a > b and a // b == a / b)\n", + "\n", + "sum(map(evendiv, rows2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This day was also very easy. It was nice that my pre-defined `array` function did the whole job of parsing the input. In Part One, I was slowed down by a typo: I had `\"=\"` instead of `\"-\"` in `\"max(row) - min(row)\"`. I was confused by Python's misleading error message, which said `\"SyntaxError: keyword can't be an expression\"`. Later on, Alex Martelli explained to me that the message meant that in `abs(max(row)=...)` it thought that `max(row)` was a keyword argument to `abs`, as in `abs(x=-1)`.\n", + "\n", + "In Part Two, note that to check that `a/b` is an exact integer, I used `a // b == a / b`, which I think is more clear than the marginally-faster expression one would typically use here, `a % b == 0`, which requires you to think about two things: division and the modulus operator (is it `a % b` or `b % a`?)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 3](https://adventofcode.com/2017/day/3): Spiral Memory\n", + "\n", + "For today the data is just one number:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "M = 277678" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This puzzle takes some thinking, not just fast typing. I decided to break the problem into three parts:\n", + "- Generate a spiral (by writing a new function called `spiral`).\n", + "- Find the Nth square on the spiral (with my function `nth`).\n", + "- Find the distance from that square to the center (with my function `cityblock_distance`).\n", + "\n", + "I suspect many people will do all three of these in one function. That's probably the best way to get the answer really quickly, but I'd rather be clear than quick (and I'm anticipating that `spiral` will come in handy in Part Two), so I'll factor out each part, obeying the *single responsibility principle*. \n", + "\n", + "Now I need to make `spiral()` generate the coordinates of squares on an infinite spiral, in order, going out from the center square, `(0, 0)`. After the center square, the spiral goes 1 square right, then 1 square up, then 2 square left, then 2 square down, thus completing one revolution; then it does subsequent revolutions. In general if the previous revolution ended with *s* squares down, then the next revolution consists of *s*+1 squares right, *s*+1 squares up, *s*+2 squares left and *s*+2 down. A small test confirms that this matches the example diagram in the puzzle description (although I had a bug on my first try because I only incremented `s` once per revolution, not twice):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0, 0),\n", + " (0, 1),\n", + " (-1, 1),\n", + " (-1, 0),\n", + " (-1, -1),\n", + " (0, -1),\n", + " (1, -1),\n", + " (1, 0),\n", + " (1, 1),\n", + " (1, 2)]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def spiral():\n", + " \"Yield successive (x, y) coordinates of squares on a spiral.\"\n", + " x = y = s = 0 # (x, y) is the position; s is the side length.\n", + " yield (x, y)\n", + " while True:\n", + " for (dx, dy) in (RIGHT, UP, LEFT, DOWN):\n", + " if dy: s += 1 # Increment side length before RIGHT and LEFT\n", + " for _ in range(s):\n", + " x += dx; y += dy\n", + " yield (x, y)\n", + "\n", + "list(islice(spiral(), 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can find the `N`th square. As this is Python, indexes start at 0, whereas the puzzle description starts counting at 1, so I have to subtract 1. Then I can find the distance to the origin:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(263, 212)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nth(spiral(), M - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "475" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cityblock_distance(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For **Part Two** I can re-use my `spiral` generator, yay! Here's a function to sum the neighboring squares (I can use my `neighbors8` function, yay!):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def spiralsums():\n", + " \"Yield the values of a spiral where each square has the sum of the 8 neighbors.\"\n", + " value = defaultdict(int)\n", + " for p in spiral():\n", + " value[p] = sum(value[q] for q in neighbors8(p)) or 1\n", + " yield value[p]" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 1, 2, 4, 5, 10, 11, 23, 25, 26, 54, 57]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(islice(spiralsums(), 12))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looks good, so let's get the answer:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "279138" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "first(x for x in spiralsums() if x > M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 4](https://adventofcode.com/2017/day/4): High-Entropy Passphrases\n", + "\n", + "This is the first time I will have to store an input file and read it with the function `Input`. It should be straightforward, though:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "337" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def is_valid(line): return is_unique(line.split())\n", + "\n", + "def is_unique(items): return len(items) == len(set(items))\n", + "\n", + "quantify(Input(4), is_valid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "231" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def is_valid2(line): return is_unique(mapt(canon, line.split()))\n", + "\n", + "quantify(Input(4), is_valid2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy, and I started on time, but the leaders were still three times faster than me!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 5](https://adventofcode.com/2017/day/5): A Maze of Twisty Trampolines, All Alike\n", + "\n", + "Let's first make sure we can read the data/program okay:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 2, 0, 0, -2, -2, -1, -4, -5, -6)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program = mapt(int, Input(5))\n", + "\n", + "program[:10]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I'll make a little interpreter, `run`, which takes a program, loads it into memory,\n", + " and executes the instruction, maintaining a program counter, `pc`, and doing the incrementing/branching as described in the puzzle,\n", + "until the program counter no longer points to a location in memory:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "364539" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run(program):\n", + " memory = list(program)\n", + " pc = steps = 0\n", + " M = len(memory)\n", + " while 0 <= pc < M:\n", + " steps += 1\n", + " oldpc = pc\n", + " pc += memory[pc]\n", + " memory[oldpc] += 1\n", + " return steps\n", + " \n", + "run(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "Part Two seems tricky, so I'll include an optional argument, `verbose`, and check if the printout it produces matches the example in the puzzle description:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 0 [1, 3, 0, 1, -3]\n", + "2 1 [2, 3, 0, 1, -3]\n", + "3 4 [2, 2, 0, 1, -3]\n", + "4 1 [2, 2, 0, 1, -2]\n", + "5 3 [2, 3, 0, 1, -2]\n", + "6 4 [2, 3, 0, 2, -2]\n", + "7 2 [2, 3, 0, 2, -1]\n", + "8 2 [2, 3, 1, 2, -1]\n", + "9 3 [2, 3, 2, 2, -1]\n", + "10 5 [2, 3, 2, 3, -1]\n" + ] + }, + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run2(program, verbose=False):\n", + " memory = list(program)\n", + " pc = steps = 0\n", + " M = len(memory)\n", + " while 0 <= pc < M:\n", + " steps += 1\n", + " oldpc = pc\n", + " pc += memory[pc]\n", + " memory[oldpc] += (-1 if memory[oldpc] >= 3 else 1)\n", + " if verbose: print(steps, pc, memory)\n", + " return steps\n", + " \n", + "run2([0, 3, 0, 1, -3], True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks right, so I can solve the puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 6.2 s, sys: 8.37 ms, total: 6.21 s\n", + "Wall time: 6.21 s\n" + ] + }, + { + "data": { + "text/plain": [ + "27477714" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time run2(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Thanks to [Clement Sreeves](https://github.com/ClementSreeves) for the suggestion of making a distinction between the `program` and the `memory`. In my first version, `run` would mutate the argument, which was OK for a short exercise, but not best practice for a reliable API. And thanks to [Max Albert](https://github.com/maxalbert) for speeding up the loop by pulling the `len(memory)` out of the loop." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 6](https://adventofcode.com/2017/day/6): Memory Reallocation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I had to read the puzzle description carefully, but then it is pretty clear what to do. I'll keep a set of previously seen configurations, which will all be tuples. But in the function `spread`, I want to mutate the configuration of banks, so I will convert to a list at the start, then convert back to a tuple at the end." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "banks = Vector('4\t10\t4\t1\t8\t4\t9\t14\t5\t1\t14\t15\t0\t15\t3\t5')\n", + "\n", + "def realloc(banks):\n", + " \"How many cycles until we reach a configuration we've seen before?\"\n", + " seen = {banks}\n", + " for cycles in count_from(1):\n", + " banks = spread(banks)\n", + " if banks in seen:\n", + " return cycles\n", + " seen.add(banks)\n", + " \n", + "def spread(banks):\n", + " \"Find the area with the most blocks, and spread them evenly to following areas.\"\n", + " banks = list(banks)\n", + " maxi = max(range(len(banks)), key=lambda i: banks[i])\n", + " blocks = banks[maxi]\n", + " banks[maxi] = 0\n", + " for i in range(maxi + 1, maxi + 1 + blocks):\n", + " banks[i % len(banks)] += 1\n", + " return tuple(banks)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2, 4, 1, 2)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spread((0, 2, 7, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc((0, 2, 7, 0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These tests look good; let's solve the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12841" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc(banks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:** Here I will just replace the `set` of `seen` banks with a `dict` of `{bank: cycle_number}`; everything else is the same, and the final result is the current cycle number minus the cycle number of the previously-seen tuple of banks." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def realloc2(banks):\n", + " \"When we hit a cycle, what is the length of the cycle?\"\n", + " seen = {banks: 0}\n", + " for cycles in count_from(1):\n", + " banks = spread(banks)\n", + " if banks in seen:\n", + " return cycles - seen[banks]\n", + " seen[banks] = cycles\n", + "\n", + "realloc2((0, 2, 7, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8038" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc2(banks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 7](https://adventofcode.com/2017/day/7): Recursive Circus" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First I'll read the data into two dicts as follows: the input line:\n", + "\n", + " tcmdaji (40) -> wjbdxln, amtqhf\n", + " \n", + "creates:\n", + "\n", + " weight['tcmdaji'] = 40\n", + " above['tcmdaji'] = ['wjbdxln', 'amtqhf']" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def towers(lines):\n", + " \"Return (weight, above) dicts.\"\n", + " weight = {}\n", + " above = {}\n", + " for line in lines:\n", + " name, w, *rest = re.findall(r'\\w+', line)\n", + " weight[name] = int(w)\n", + " above[name] = set(rest)\n", + " return weight, above\n", + "\n", + "weight, above = towers(Input(7))\n", + "\n", + "programs = set(above)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the root progam is the one that is not above anything:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'wiapj'}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "programs - set(flatten(above.values()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "A program is *wrong* if it is the bottom of a tower that is a different weight from all its sibling towers:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def wrong(p): return tower_weight(p) not in map(tower_weight, siblings(p))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we define `tower_weight`, `siblings`, and the `below` dict:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def tower_weight(p): \n", + " \"Total weight for the tower whose root (bottom) is p.\"\n", + " return weight[p] + sum(map(tower_weight, above[p]))\n", + "\n", + "def siblings(p): \n", + " \"The other programs at the same level as this one.\"\n", + " if p not in below:\n", + " return Ø # the root has no siblings\n", + " else:\n", + " return above[below[p]] - {p}\n", + "\n", + "below = {a: b for b in programs for a in above[b]}" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'eionkb', 'lsire', 'wiapj', 'ycpcv'}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(filter(wrong, programs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So these four programs are wrong. Which one should we correct? The one that is wrong, and has no wrong program above it:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'eionkb'" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def wrongest(programs):\n", + " return first(p for p in programs\n", + " if wrong(p) \n", + " and not any(wrong(p2) for p2 in above[p]))\n", + "\n", + "wrongest(programs) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now what should we correct it to? To the weight that makes it the same weight as the sibling towers:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1072" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def correct(p):\n", + " \"Return the weight that would make p's tower's weight the same as its sibling towers.\"\n", + " delta = tower_weight(first(siblings(p))) - tower_weight(p) \n", + " return weight[p] + delta\n", + "\n", + "correct(wrongest(programs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 8](https://adventofcode.com/2017/day/8): Memory Reallocation \n", + "\n", + "This one looks easy: a simple interpreter for straight-line code where each instruction has 7 tokens. It is nice that my `Array` function parses the whole program." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6828" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program8 = Array(Input(8))\n", + "\n", + "def run8(program):\n", + " \"Run the program and return final value of registers.\"\n", + " registers = defaultdict(int)\n", + " for (r, inc, delta, _if, r2, cmp, amount) in program:\n", + " if operations[cmp](registers[r2], amount):\n", + " registers[r] += delta * (+1 if inc == 'inc' else -1)\n", + " return registers\n", + "\n", + "max(run8(program8).values())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "Here I modify the interpreter to keep track of the highest value of any register at any time." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7234" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run8_2(program):\n", + " registers = defaultdict(int)\n", + " highest = 0\n", + " for (r, inc, delta, _if, r2, cmp, amount) in program:\n", + " if operations[cmp](registers[r2], amount):\n", + " registers[r] += delta * (+1 if inc == 'inc' else -1)\n", + " highest = max(highest, registers[r])\n", + " return highest\n", + "\n", + "run8_2(program8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 9](https://adventofcode.com/2017/day/9): Stream Processing\n", + "\n", + "For this problem I could have a single finite-state machine that handles all five magic characters, `'{}'`, but I think it is easier to first clean up the garbage, using regular expressions:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'{{{{{{{},},{{},}},{{{{}},{{{{{}}},{}},},{{{{},{,{{{}}}}},},{{{}},{{}}}'" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text1 = re.sub(r'!.', '', Inputstr(9)) # Delete canceled characters\n", + "text2 = re.sub(r'<.*?>', '', text1) # Delete garbage\n", + "\n", + "text2[:70]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can deal with the nested braces (which can't be handled with regular expressions). The puzzle says \"*Each group is assigned a score which is one more than the score of the group that immediately contains it,*\" which is the same as saying that a group's score is its nesting level, a quantity that increases with each open-brace character, and decreases with each close-brace:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "9662" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def total_score(text):\n", + " \"Total of group scores; each group scores one more than the group it is nested in.\"\n", + " total = 0\n", + " level = 0 # Level of nesting\n", + " for c in text:\n", + " if c == '{':\n", + " level += 1\n", + " total += level\n", + " elif c == '}':\n", + " level -= 1\n", + " return total\n", + "\n", + "total_score(text2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "At first I thought that the amount of garbage is just the difference in lengths of `text2` and `text3`:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5989" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(text1) - len(text2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this turned out to be wrong; it counts the angle brackets themselves s being deleted, whereas the puzzle is actually asking how many character between the angle brackets are deleted. So that would be:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4903" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text3 = re.sub(r'<.*?>', '<>', text1) # Delete garbage inside brackets, but not brackets\n", + "\n", + "len(text1) - len(text3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 10](https://adventofcode.com/2017/day/10): Stream Processing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I have to do a bunch of reversals of substrings of `stream`. It looks complicated so I will include a `verbose` argument to `knothash` and confirm it works on the example puzzle. I break out the reversal into a separate function, `rev`. The way I handle reversal interacting with wraparound is that I first move all the items before the reversal position to the end of the list, then I do the reversal, then I move them back." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "stream = (63,144,180,149,1,255,167,84,125,65,188,0,2,254,229,24)\n", + "\n", + "def knothash(lengths, N=256, verbose=False):\n", + " \"Do a reversal for each of the numbers in `lengths`.\"\n", + " nums = list(range(N))\n", + " pos = skip = 0\n", + " for L in lengths:\n", + " nums = rev(nums, pos, L)\n", + " if verbose: print(nums)\n", + " pos = (pos + L + skip) % N\n", + " skip += 1\n", + " return nums[0] * nums[1]\n", + " \n", + "def rev(nums, pos, L):\n", + " \"Reverse nums[pos:pos+L], handling wrap-around.\"\n", + " # Move first pos elements to end, reverse first L, move pos elements back\n", + " nums = nums[pos:] + nums[:pos]\n", + " nums[:L] = reversed(nums[:L])\n", + " nums = nums[-pos:] + nums[:-pos]\n", + " return nums" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reverse [0, 1, 2]:\n", + "assert rev(list(range(5)), 0, 3) == [2, 1, 0, 3, 4]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reverse [4, 0, 1], wrapping around:\n", + "assert rev(list(range(5)), 4, 3) == [0, 4, 2, 3, 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 1, 0, 3, 4]\n", + "[4, 3, 0, 1, 2]\n", + "[4, 3, 0, 1, 2]\n", + "[3, 4, 2, 1, 0]\n" + ] + } + ], + "source": [ + "# Duplicate the example output\n", + "assert knothash((3, 4, 1, 5), N=5, verbose=True) == 12" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's correct, but the first time through I got it wrong because I forgot the `\"% N\"` on the update of `pos`." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4480" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "knothash(stream)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:\n", + "\n", + "Now it gets *really* complicated: string processing, the suffix, hex string output, and dense hashing. But just take them one at a time:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'c500ffe015c83b60fad2e4b7d59dabc4'" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stream2 = '63,144,180,149,1,255,167,84,125,65,188,0,2,254,229,24'\n", + "\n", + "def knothash2(lengthstr, N=256, rounds=64, suffix=(17, 31, 73, 47, 23),\n", + " verbose=False):\n", + " \"Do a reversal for each length; repeat `rounds` times.\"\n", + " nums = list(range(N))\n", + " lengths = mapt(ord, lengthstr) + suffix\n", + " pos = skip = 0\n", + " for round in range(rounds):\n", + " for L in lengths:\n", + " nums = rev(nums, pos, L)\n", + " if verbose: print(nums)\n", + " pos = (pos + L + skip) % N\n", + " skip += 1\n", + " return hexstr(dense_hash(nums))\n", + "\n", + "def hexstr(nums): \n", + " \"Convert a sequence of (0 to 255) ints into a hex str.\"\n", + " return cat(map('{:02x}'.format, nums))\n", + " \n", + "def dense_hash(nums, blocksize=16): \n", + " \"XOR each block of nums, return the list of them.\"\n", + " return [XOR(block) for block in grouper(nums, blocksize)]\n", + "\n", + "def XOR(nums):\n", + " \"Exclusive-or all the numbers together.\"\n", + " result = 0\n", + " for n in nums:\n", + " result ^= n\n", + " return result\n", + " \n", + "assert XOR([65, 27, 9, 1, 4, 3, 40, 50, 91, 7, 6, 0, 2, 5, 68, 22]) == 64\n", + "assert hexstr([255, 0, 17]) == 'ff0011'\n", + "\n", + "assert knothash2('') == 'a2582a3a0e66e6e86e3812dcb672a272'\n", + "\n", + "knothash2(stream2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I had a bug: originally I used `'{:x}'` as the format instead of `'{:02x}'`; the later correctly formats `0` as `'00'`, not `'0'`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 11](https://adventofcode.com/2017/day/11): Hex Ed\n", + "\n", + "The first thing I did was search [`[hex coordinates]`](https://www.google.com/search?source=hp&ei=Ft4xWoOqKcy4jAOs76a4CQ&q=hex+coordinates), and the #1 result (as I expected) was Amit Patel's \"[Hexagonal Grids](https://www.redblobgames.com/grids/hexagons/)\" page. I chose his \"odd-q vertical layout\" to define the six directions as (dx, dy) deltas:" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "directions6 = dict(n=(0, -1), ne=(1, 0), se=(1, 1), s=(0, 1), sw=(-1, 0), nw=(-1, -1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can read the path, follow it, and see where it ends up. If the end point is `(x, y)`, then it will take `max(abs(x), abs(y))` steps to get back to the origin, because each step can increment or decrement either `x` or `y` or both." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "705" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path = Vector(Inputstr(11))\n", + "\n", + "def follow(path):\n", + " \"Follow each step of the path; return final distance to origin.\"\n", + " x, y = (0, 0)\n", + " for (dx, dy) in map(directions6.get, path):\n", + " x += dx; y += dy\n", + " return max(abs(x), abs(y))\n", + "\n", + "follow(path)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This one seemed so easy that I didn't bother testing it on the simple examples in the puzzle; all I did was confirm that the answer for my puzzle input was correct.\n", + "\n", + "**Part Two:**\n", + "\n", + "This looks pretty easy; repeat Part One, but keep track of the maximum number of steps we get from the origin at any point in the path:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1469" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def follow2(path):\n", + " \"Follow each step of the path; return max steps to origin.\"\n", + " x = y = maxsteps = 0\n", + " for (dx, dy) in map(directions6.get, path):\n", + " x += dx; y += dy\n", + " maxsteps = max(maxsteps, abs(x), abs(y))\n", + " return maxsteps\n", + "\n", + "follow2(path)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, no tests, just the final answer.\n", + "\n", + "# [Day 12](https://adventofcode.com/2017/day/12): Digital Plumber\n", + "\n", + "First I'll parse the data, creating a dict of `{program: direct_group_of_programs}`:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def groups(lines):\n", + " \"Dict of {i: {directly_connected_to_i}\"\n", + " return {lhs: {lhs} | set(rhs)\n", + " for (lhs, _, *rhs) in Array(lines)}\n", + " \n", + "assert groups(Input(12))[0] == {0, 659, 737}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks good. I recognize this as a [Union-Find](https://en.wikipedia.org/wiki/Disjoint-set_data_structure) problem, for which there are efficient algorithms. But for this small example, I don't need efficiency, I need clarity and simplicity. So I'll write `merge` to take a dict and merge together the sets that are connected:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def merge(G):\n", + " \"Merge all indirectly connected groups together.\"\n", + " for i in G:\n", + " for j in list(G[i]):\n", + " if G[i] != G[j]:\n", + " G[i].update(G[j])\n", + " G[j] = G[i]\n", + " return G\n", + "\n", + "G = merge(groups(Input(12)))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "115" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(G[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the answer for Part One.\n", + "\n", + "**Part Two**\n", + "\n", + "I did almost all the work; I just need to count the number of distinct groups. That's a set of sets, and regular `set`s are not hashable, so I use my `Set` class:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "221" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len({Set(G[i]) for i in G})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 13](https://adventofcode.com/2017/day/13): Packet Scanners\n", + "\n", + "First thing: The puzzle says the data is *depth: range*, but `range` has a meaning in Python, so I'll use the term *width* instead.\n", + "\n", + "Second thing: I misread the puzzle description and mistakenly thought the scanners were going in a circular route,\n", + "so that they'd be at the top at any time that is 0 mod *width*. That gave the wrong answer and I realized the scanners are actually going back-and-forth, so with a width of size *n*, it takes *n* - 1 steps to get to the bottom, and *n* - 1 steps to get back to the top, so the scanner will be \n", + "at the top at times that are multiples of 2(*n* - 1). For example, with width 3, that would be times 0, 4, 8, ... " + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def trip_severity(scanners): \n", + " \"The sum of sevrities for each time the packet is caught.\"\n", + " return sum((d * w if caught(d, w) else 0) \n", + " for (d, w) in scanners)\n", + "\n", + "def caught(depth, width):\n", + " \"Does the scanner at this depth/width catch the packet?\"\n", + " return depth % (2 * (width - 1)) == 0\n", + "\n", + "example = ((0, 3), (1, 2), (4, 4), (6, 4))\n", + "assert trip_severity(example) == 24" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 3), (1, 2), (2, 4), (4, 6), (6, 4))" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scanners = mapt(Integers, Input(13))\n", + "scanners[:5]" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1504" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trip_severity(scanners)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "A packet is safe if no scanner catches it. We now have the possibility of a delay, so I update `caught` to allow for an optional delay, and define `safe_delay`: " + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def caught(depth, width, delay=0):\n", + " \"Does the scanner at this depth/width catch the packet with this delay?\"\n", + " return (depth + delay) % (2 * (width - 1)) == 0 \n", + "\n", + "def safe_delay(scanners):\n", + " \"Find the first delay such that no scanner catches the packet.\"\n", + " safe = lambda delay: not any(caught(d, w, delay) for (d, w) in scanners)\n", + " return first(filter(safe, count_from(0)))\n", + "\n", + "safe_delay(example)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3823370" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "safe_delay(scanners)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 14](https://adventofcode.com/2017/day/14): Disk Defragmentation\n", + "\n", + "I found this puzzle description confusing: are they talking about what I call `knothash`, or is it `knothash2`? I decided for the latter, which turned out to be right:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "key = 'ljoxqyyw'" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8316" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def bits(key, i):\n", + " \"The bits in the hash of this key with this row number.\"\n", + " hash = knothash2(key + '-' + str(i))\n", + " return format(int(hash, base=16), '0128b')\n", + "\n", + "sum(bits(key, i).count('1') for i in range(128))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "So as not to worry about running off the edge of the grid, I'll surround the grid with `'0'` bits:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Grid(key, N=128+2):\n", + " \"Make a grid, with a border around it.\"\n", + " return border('0', (list(bits(key, i)) for i in range(128)))\n", + "\n", + "def border(fill, grid):\n", + " \"Surround a grid with a border of fill cells.\"\n", + " rows = [[fill] + list(row) + [fill] \n", + " for row in grid]\n", + " empty = [fill] * len(rows[0])\n", + " return [empty] + rows + [empty]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To find a region, start at some `(x, y)` position and [flood fill](https://en.wikipedia.org/wiki/Flood_fill) to neighbors that have the same value (a `'1'` bit)." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def flood(grid, x, y, val, R):\n", + " \"For all cells with value val connected to grid[x][y], give them region number R.\"\n", + " if grid[y][x] == val:\n", + " grid[y][x] = R\n", + " for x2, y2 in neighbors4((x, y)):\n", + " flood(grid, x2, y2, val, R)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def flood_all(grid, val='1'):\n", + " \"Label all regions with consecutive ints starting at 1.\"\n", + " R = 0 # R is the region number\n", + " for y in range(1, len(grid) - 1):\n", + " for x in range(1, len(grid) - 1):\n", + " if grid[y][x] == val:\n", + " R += 1\n", + " flood(grid, x, y, val, R)\n", + " return R " + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1074" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "flood_all(Grid(key))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 15](https://adventofcode.com/2017/day/15): Dueling Generators\n", + "\n", + "My personalized inputs for this puzzle are `516` and `190`; the other numbers are shared by all puzzle-solvers. I decided to make infinite generators of numbers, using `gen`:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15.1 s, sys: 26.4 ms, total: 15.1 s\n", + "Wall time: 15.2 s\n" + ] + }, + { + "data": { + "text/plain": [ + "597" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@jit # This was the slowest solution; @jit helps a bit.\n", + "def gen(prev, factor, m=2147483647):\n", + " \"Generate a sequence of numbers according to the rules; stop at 0.\"\n", + " while prev:\n", + " prev = (prev * factor) % m\n", + " yield prev\n", + " \n", + "def judge(A, B, N=40*10**6, mask=2**16-1): \n", + " \"How many of the first N numbers from A and B agree in the masked bits (default last 16)?\"\n", + " return quantify(a & mask == b & mask\n", + " for (a, b, _) in zip(A, B, range(N)))\n", + "\n", + "def A(): return gen(516, 16807)\n", + "def B(): return gen(190, 48271)\n", + "\n", + "%time judge(A(), B())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice I also decided to use `@jit` (i.e. `numba.jit`) to speed things up, since this is the slowest-running day yet.\n", + "\n", + "**Part Two**\n", + "\n", + "A small change: only consider numbers that match the **criteria** of being divisible by 4 or 8, respectively;" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 9.39 s, sys: 8.62 ms, total: 9.4 s\n", + "Wall time: 9.4 s\n" + ] + }, + { + "data": { + "text/plain": [ + "303" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def criteria(m, iterable): \n", + " \"Elements of iterable that are divisible by m\"\n", + " return (n for n in iterable if n % m == 0)\n", + " \n", + "%time judge(criteria(4, A()), criteria(8, B()), 5*10**6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 16](https://adventofcode.com/2017/day/16): Permutation Promenade\n", + "\n", + "Let's read the input and check that it looks reasonable:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('x5/15',\n", + " 's15',\n", + " 'x1/3',\n", + " 'pn/f',\n", + " 'x11/2',\n", + " 's13',\n", + " 'x6/3',\n", + " 'pe/a',\n", + " 'x14/12',\n", + " 's15')" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dance = Vector(Inputstr(16))\n", + "dance[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10000" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'll define `perform` to perform the dance:" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'lbdiomkhgcjanefp'" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dancers = 'abcdefghijklmnop'\n", + "\n", + "def perform(dance, dancers=dancers):\n", + " D = deque(dancers)\n", + " def swap(i, j): D[i], D[j] = D[j], D[i]\n", + " for move in dance:\n", + " op, arg = move[0], move[1:]\n", + " if op == 's': D.rotate(int(arg))\n", + " elif op == 'x': swap(*Integers(arg))\n", + " elif op == 'p': swap(D.index(arg[0]), D.index(arg[2]))\n", + " return cat(D)\n", + " \n", + "perform(dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "My first thought was to define a dance as a permutation: a list of numbers `[11, 1, 9, ...]` which says that the net effect of the dance is that the first dancer (`a`) ends up in position, the second (`b`) stays in position 1, and so on. Applying that permutation once is a lot faster than interpreting all 10,000 moves of the dance, and it is feasible to apply the permutation a billion times. I tried that (code not shown here), but that was a mistake: it took 15 minutes to run, and it got the wrong answer. The problem is that a dance is *not* just a permutation, because a dance can reference dancer *names*, not just positions.\n", + "\n", + "It would take about 10,000 times 20 minutes to perform a billion repetitions of the dance, so that's out. But even though the dance is not a permutation, it might repeat after a short period. Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "abcdefghijklmnop is seen in iterations (0, 56)\n" + ] + } + ], + "source": [ + "seen = {dancers: 0}\n", + "d = dancers\n", + "for i in range(1, 1000):\n", + " d = perform(dance, d)\n", + " if d in seen:\n", + " print(d, 'is seen in iterations', (seen[d], i))\n", + " break" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So we get back to the start position after 56 repetitions of the dance. What happens after a billion repetitions?" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "48" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1000000000 % 56" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The end position after a billion repetitions is the same as after 48:" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ejkflpgnamhdcboi'" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def whole(N, dance, dancers=dancers):\n", + " \"Repeat `perform(dance)` N times.\"\n", + " for i in range(N):\n", + " dancers = perform(dance, dancers)\n", + " return dancers\n", + " \n", + "whole(48, dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# [Day 17](https://adventofcode.com/2017/day/17): Spinlock\n", + "\n", + "This one looks pretty easy:" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "355" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "step = 314\n", + "\n", + "def spinlock(step=step, N=2017):\n", + " \"Make N inserts into the buffer, skipping ahead by `step` each time.\"\n", + " buf = [0]\n", + " pos = 0\n", + " for i in ints(1, N):\n", + " pos = (pos + step) % i + 1\n", + " buf[pos:pos] = [i]\n", + " return buf\n", + " \n", + "buf = spinlock()\n", + "\n", + "buf[buf.index(2017)+1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "But Part Two is not so easy, if we care about the run time. Insertion into a `list` has to move all the elements after the insertion down, so insertion is O(N) and `spinlock` is O(N2). That's no problem when N = 2017, but when N is 50 million? We're gonna need a bigger boat, where by \"boat\" I mean algorithm or data structure. My first thought is a (circular) linked list, because insertion is O(1). I can implement the three key methods: `skip` to move ahead, `insert` to add a new node after the current one, and `find` to find a piece of data (with a linear search):" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Node:\n", + " \"A Node in a singly-linked list\"\n", + " \n", + " __slots__ = ('data', 'next') # Declaring slots makes it more efficient\n", + " \n", + " def __init__(self, data, next): self.data, self.next = data, next\n", + " \n", + " def skip(self, n):\n", + " \"Skip ahead n nodes, and return that node.\"\n", + " node = self\n", + " for i in range(n):\n", + " node = node.next\n", + " return node\n", + " \n", + " def insert(self, value):\n", + " \"Insert a new node with the given value after this node.\"\n", + " self.next = Node(value, self.next)\n", + " return self.next\n", + " \n", + " def find(self, value):\n", + " \"Find the node with the given data value.\"\n", + " node = self\n", + " while node.data != value:\n", + " node = node.next\n", + " return node" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can rewrite `spinlock` to use this class:" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def spinlock2(step=step, N=2017):\n", + " node = Node(0, None)\n", + " node.next = node # Make node be a circular linked list\n", + " for i in ints(1, N):\n", + " node = node.skip(step).insert(i)\n", + " return node" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's replicate the Part One results:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "355" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spinlock2().find(2017).next.data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Good news! We get the same answer. But how fast/slow is it?" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.35 s, sys: 5.54 ms, total: 1.35 s\n", + "Wall time: 1.35 s\n" + ] + }, + { + "data": { + "text/plain": [ + "<__main__.Node at 0x110c44be0>" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time spinlock2(N=100000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bad news! It takes over a second to do just 100,000 insertions, which means about 10 minutes for 50 million insertions. I did in fact try\n", + "\n", + " spinlock2(N=50000000).find(0).next.data\n", + " \n", + "and it eventually gave the right answer, but while it was running I had plenty of time to think.\n", + "I realized that, if we go back to the original `spinlock` version, the value `0` will always be in `buf[0]`, and the value we are looking for will always be in `buf[1]`. So I can create a version of `spinlock` that only keeps track of `buf[0:2]`. That should run in a few seconds, not minutes:" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 5.47 s, sys: 6.62 ms, total: 5.48 s\n", + "Wall time: 5.48 s\n" + ] + }, + { + "data": { + "text/plain": [ + "6154117" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def spinlock3(step=step, N=2017):\n", + " \"Make N inserts into a simulated buffer, but ignore all except buf[0:2].\"\n", + " pos = 0\n", + " buf = [0, 0]\n", + " for i in ints(1, N):\n", + " pos = (pos + step) % i + 1\n", + " if pos <= 1:\n", + " buf[pos] = i\n", + " return buf\n", + "\n", + "%time spinlock3(N=50000000)[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The moral of the story is *keep your eyes on the prize*. I got distracted because I asked the wrong question. I asked myself \"how can I make my solution in `spinlock` faster?\" and answered myself \"insertion is O(N2) and it should be O(N).\" I knew how to do that, with a linked list, but that was the right answer to the wrong question. I should have asked myself \"how do I solve Part Two quickly,\" concentrating on solving the actual problem. Once I did that, I realized I didn't need all those insertions: not doing them at all is a better idea than doing them faster." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 18](https://adventofcode.com/2017/day/17): Duet\n", + "\n", + "First, read the input, and take a peak at it:" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(('set', 'i', 31),\n", + " ('set', 'a', 1),\n", + " ('mul', 'p', 17),\n", + " ('jgz', 'p', 'p'),\n", + " ('mul', 'a', 2),\n", + " ('add', 'i', -1),\n", + " ('jgz', 'i', -2),\n", + " ('add', 'a', -1),\n", + " ('set', 'i', 127),\n", + " ('set', 'p', 826))" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program18 = Array(Input(18))\n", + "program18[:10]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now write an interpreter for the assembly language:" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7071" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run18(program):\n", + " \"Interpret the assembly language program; return recovered `snd`.\"\n", + " regs = defaultdict(int)\n", + " pc = snd = 0\n", + " while True:\n", + " instr = program[pc]\n", + " pc += 1\n", + " op, x, y = instr[0], instr[1], instr[-1]\n", + " vy = value(regs, y)\n", + " if op == 'snd': snd = regs[x]\n", + " elif op == 'set': regs[x] = vy\n", + " elif op == 'add': regs[x] += vy\n", + " elif op == 'mul': regs[x] *= vy\n", + " elif op == 'mod': regs[x] %= vy\n", + " elif op == 'jgz' and regs[x] > 0: pc += vy - 1\n", + " elif op == 'rcv' and regs[x] != 0: return snd\n", + " \n", + "def value(regs, y): return (y if isinstance(y, int) else regs[y])\n", + "\n", + "run18(program18)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy. (One tricky bit: the `pc` is incremented by 1 every time through the loop, regardless of the instruction. Therefore, the `'jgz'` jump instruction increments by \"`vy - 1`\" so that the net increment is \"`vy`\".)\n", + "\n", + "**Part Two**\n", + "\n", + "In Part Two we have to run two copies of the program, and send messages between them. I'll break up the loop in `run18` into\n", + "two functions. First, `run18_2`, creates (in `ps`) two structures to hold the state variables necessary to run a program:\n", + "- `id`: The id number (0 or 1) of this copy of the program.\n", + "- `pc`: The program counter.\n", + "- `sends`: A count of the number of `snd` instructions executed.\n", + "- `regs`: A dict of the program registers (`a` to `z`).\n", + "- `status`: A program has a status which can be:\n", + " * `'run'` when it is ready to execute an instruction, \n", + " * `'wait'` when it is waiting for a value to arrive in its input queue, or \n", + " * `'end'` when the `pc` has run off the end of the program and it has terminated.\n", + "\n", + "`run18_2` repeatedly calls the second function, `step18(program, p)` to execute one instruction of `program` with the state variables in `p`. I choose randomly which of the two programs to step on each iteration. The function exits when neither copy of the program can run, according to their status. " + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run18_2(program):\n", + " \"Run two copies of program, with different state variables. Return final states.\"\n", + " Qs = [deque(), deque()]\n", + " ps = [Struct(id=id, pc=0, sends=0, regs=defaultdict(int, p=id), status='run')\n", + " for id in (0, 1)]\n", + " while any(p.status == 'run' for p in ps):\n", + " step18(program, Qs, random.choice(ps))\n", + " return ps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`step18` has most of the guts of thee previous `run18` function, but with a few changes:\n", + "- State variables are accessed indirectly: `p.pc` instead of just `pc`.\n", + "- If the `pc` is out of bounds, the program terminates; the status is set to `'end'`.\n", + "- The `snd` instruction sends a value to the other program's queue.\n", + "- The `rcv` instruction pops a value off the queue if there is one, otherwise the status is set to `'wait'`.\n", + "- The \"`X`\" in \"`jgz X Y`\" might be an integer, not a register name, so use `vx = value(p.regs, x)`. I was stuck for a *long* time before I realized this. Finally I tried the strategy of *look carefully at the input*. I noticed the instruction `\"jgz 1 3\"`, and it was a simple change to make the program work." + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8001" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def step18(program, Qs, p):\n", + " \"Execute one instruction in program, using state variables in p.\"\n", + " if p.pc < 0 or p.pc > len(program):\n", + " p.status = 'end'\n", + " else:\n", + " instr = program[p.pc]\n", + " op, x, y = instr[0], instr[1], instr[-1]\n", + " vx, vy = value(p.regs, x), value(p.regs, y)\n", + " if op == 'snd': Qs[1-p.id].append(vy); p.sends += 1\n", + " elif op == 'set': p.regs[x] = vy\n", + " elif op == 'add': p.regs[x] += vy\n", + " elif op == 'mul': p.regs[x] *= vy\n", + " elif op == 'mod': p.regs[x] %= vy\n", + " elif op == 'jgz' and vx > 0: p.pc += vy - 1\n", + " elif op == 'rcv': \n", + " if not Qs[p.id]:\n", + " p.status = 'wait'\n", + " return # don't update pc; try again next time\n", + " else:\n", + " p.regs[x] = Qs[p.id].popleft()\n", + " p.status = 'run'\n", + " p.pc += 1\n", + " \n", + "run18_2(program18)[1].sends" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 19](https://adventofcode.com/2017/day/19): A Series of Tubes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At first I was confused; I thought this was a maze-following problem where I had to make a choice of directions at every turn. Actually, the direction is always determined: keep going in the current direction as long as possible, but when we hit a `'+'` character, find the new direction to go in (there will only be one possibility). Leave breadcrumbs (the `'.'` character) so that we don't back up along a previously-followed path. As in Day 14, the grid is surrounded by a border of space characters so that we don't have to worry about `(x, y)` going off the edge." + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "diagram = Inputstr(19)\n", + "\n", + "def follow_tubes(diagram):\n", + " \"Follow [-+|] lines, yielding characters along the path.\"\n", + " grid = border(' ', diagram.splitlines())\n", + " x, y = grid[1].index('|'), 1\n", + " dx, dy = 0, 1\n", + " while grid[y][x] != ' ':\n", + " yield grid[y][x]\n", + " if grid[y][x] == '+':\n", + " dx, dy = new_direction(grid, x, y)\n", + " grid[y][x] = '.' # Leave a breadcrumb\n", + " x += dx; y += dy\n", + " \n", + "def new_direction(grid, x, y):\n", + " \"Find a direction that continues the path.\"\n", + " for (dx, dy) in (UP, DOWN, RIGHT, LEFT):\n", + " if grid[y+dy][x+dx] not in (' ', '.'):\n", + " return dx, dy" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'VEBTPXCHLI'" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cat(filter(str.isalpha, follow_tubes(diagram)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "This is a surprisingly easy Part Two; I already generated the characters in the path; all I have to do is count them: " + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "18702" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "length(follow_tubes(diagram))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 20](https://adventofcode.com/2017/day/20): Particle Swarm\n", + "\n", + "I'll create structures for particles, each will have fields for particle's number (`id`), position (`p`), velocity(`v`), and acceleration (`a`):" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[Struct(a=(-7, 8, -10), id=0, p=(1199, -2918, 1457), v=(-13, 115, -8)),\n", + " Struct(a=(-6, -5, 6), id=1, p=(2551, 2418, -1471), v=(-106, -108, 39)),\n", + " Struct(a=(-6, 2, -9), id=2, p=(-73, 1626, 1321), v=(58, -118, -8)),\n", + " Struct(a=(3, 3, 11), id=3, p=(-3297, -894, -551), v=(183, 31, -61)),\n", + " Struct(a=(7, -12, -1), id=4, p=(-1425, 4298, 617), v=(32, -166, -32))]" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def particles(lines=list(Input(20))):\n", + " \"Parse the list of particles.\"\n", + " return [Particle(id, *grouper(Integers(line), 3)) \n", + " for id, line in enumerate(lines)]\n", + "\n", + "def Particle(id, p, v, a): return Struct(id=id, p=p, v=v, a=a) \n", + "\n", + "particles()[:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'm not quite sure how to determine what \"in the long run\" means, so I'll just interpret it as meaning \"after 1000 time steps.\" On each step we update velocity and position of each particle. At the end, we determine the id number of the particle closest to the origin. Note that `evolve` generates an infinite sequence of particles, and we use `nth` to pick out the 1000th generation." + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "243" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def evolve(particles):\n", + " \"Continually update particles, yielding them after each time step.\"\n", + " while True:\n", + " yield particles\n", + " for p in particles:\n", + " p.v = add(p.v, p.a)\n", + " p.p = add(p.p, p.v)\n", + " \n", + "def add(A, B): \n", + " \"Add two n-dimensional vectors.\"\n", + " return mapt(sum, zip(A, B))\n", + "\n", + "def closest(particles):\n", + " \"Find the particle closest to origin.\"\n", + " return min(particles, key=lambda p: sum(map(abs, p.p)))\n", + "\n", + "# Answer: the id of the particle closest to origin in the 1000th generation of `evolve`\n", + "closest(nth(evolve(particles()), 1000)).id" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "I can still use `evolve` unchanged, and I will add the function `remove_collisions` to eliminate particles that are in the same position as another particle. I use `map` to apply this to every generation. Note that `remove_collisions` both mutates the argument, `particles`, and also returns it. " + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "648" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def remove_collisions(particles):\n", + " \"Mutate (and return) particles, keep only ones that have a unique position.\"\n", + " poscount = Counter(p.p for p in particles)\n", + " particles[:] = [p for p in particles if poscount[p.p] == 1]\n", + " return particles\n", + " \n", + "# Answer: remove collisions from every generation of evolving particles, \n", + "# select the 1000th generation, and say how many particles are in that generation.\n", + "len(nth(map(remove_collisions, evolve(particles())), 1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 21](https://adventofcode.com/2017/day/21): Fractal Art\n", + "\n", + "First I'll create a `dict` of enhancement rules. I'll translate `'#'` and `'.'` pixels to 1 and 0, and represent a grid as a tuple of tuples (e.g. `((0, 0), (1, 1))`), so that it can be a `dict` key. I have to deal with rotations and flips; I could do that at lookup time, but it will be faster to do it at rule creation time:" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Enhancements(lines):\n", + " \"Create a dict of {square: enhanced_square}\"\n", + " enhancements = {}\n", + " for line in lines:\n", + " lhs, rhs = map(Key, line.split('=>'))\n", + " for r in range(4):\n", + " enhancements[lhs] = enhancements[flip(lhs)] = rhs\n", + " lhs = rotate(lhs)\n", + " return enhancements\n", + " \n", + "def Key(line): \n", + " \"Key('../##') => ((0, 0), (1, 1))\"\n", + " bits = {'#': 1, '.': 0}\n", + " return tuple(tuple(bits[p] for p in row.strip())\n", + " for row in line.split('/'))\n", + " \n", + "def rotate(key): return tuple(zip(*reversed(key)))\n", + "\n", + "def flip(L): return tuple(tuple(reversed(row)) for row in L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's test this on just the enhancement rules with 2x2 squares; with rotations and flips there should be 16 entries:" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{((0, 0), (0, 0)): ((0, 0, 0), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 0), (0, 1)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 0), (1, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 0), (1, 1)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 1), (0, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 1), (0, 1)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 1), (1, 0)): ((1, 1, 0), (1, 1, 0), (0, 0, 0)),\n", + " ((0, 1), (1, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 0), (0, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((1, 0), (0, 1)): ((1, 1, 0), (1, 1, 0), (0, 0, 0)),\n", + " ((1, 0), (1, 0)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((1, 0), (1, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (0, 0)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((1, 1), (0, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (1, 0)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (1, 1)): ((0, 1, 1), (1, 0, 0), (1, 1, 0))}" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Enhancements('''\n", + "../.. => .../.#./.#.\n", + "#./.. => .../#../#..\n", + "##/.. => #.#/.#./.#.\n", + ".#/#. => ##./##./...\n", + "##/#. => .##/###/#..\n", + "##/## => .##/#../##.\n", + "'''.strip().splitlines())" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looks good; let's create my complete table. There should be 24 + 29 entries:" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "enhancements = Enhancements(Input(21))\n", + "\n", + "assert len(enhancements) == 2 ** 4 + 2 ** 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now on each iteration we `enhance` the grid by first `expand`-ing it (looking up each `slice` in the `enhancements` rules) and then `stitch` the pieces together:" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def enhance(grid): \n", + " \"Expand small pieces into bigger ones and stitch them together.\"\n", + " return stitch(expand(grid))\n", + "\n", + "def expand(grid):\n", + " \"Slice the grid into d x d pieces and enhance each piece.\"\n", + " N = len(grid[0])\n", + " d = (2 if N % 2 == 0 else 3 if N % 3 == 0 else error())\n", + " return [[enhancements[slice(grid, r, c, d)]\n", + " for c in range(0, N, d)]\n", + " for r in range(0, N, d)]\n", + "\n", + "def stitch(pieces): \n", + " \"Stitch the pieces back into one big grid.\"\n", + " N = sum(map(len, pieces[0]))\n", + " return tuple(tuple(get(pieces, r, c) \n", + " for c in range(N))\n", + " for r in range(N))\n", + "\n", + "def get(pieces, r, c):\n", + " \"The pixel at location (r, c), from a matrix of d x d pieces.\"\n", + " d = len(pieces[0][0])\n", + " row = pieces[r // d]\n", + " cell = row[c // d]\n", + " return cell[r % d][c % d]\n", + "\n", + "def slice(grid, r, c, d):\n", + " \"The d x d slice of grid starting at position (r, c)\"\n", + " return tuple(row[c:c+d] for row in grid[r:r+d])" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 1, 0), (0, 0, 1), (1, 1, 1))" + ] + }, + "execution_count": 94, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid = Key('.#./..#/###')\n", + "grid" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[((1, 0, 1, 0), (0, 0, 1, 0), (0, 1, 0, 1), (0, 1, 0, 0))]]" + ] + }, + "execution_count": 95, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((1, 0, 1, 0), (0, 0, 1, 0), (0, 1, 0, 1), (0, 1, 0, 0))" + ] + }, + "execution_count": 96, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stitch(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[((0, 0, 0), (1, 0, 0), (1, 0, 0)), ((1, 0, 1), (0, 1, 0), (0, 1, 0))],\n", + " [((1, 0, 1), (0, 1, 0), (0, 1, 0)), ((0, 0, 0), (1, 0, 0), (1, 0, 0))]]" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 0, 0, 1, 0, 1),\n", + " (1, 0, 0, 0, 1, 0),\n", + " (1, 0, 0, 0, 1, 0),\n", + " (1, 0, 1, 0, 0, 0),\n", + " (0, 1, 0, 1, 0, 0),\n", + " (0, 1, 0, 1, 0, 0))" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stitch(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(_))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks right; Let's try to solve the puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "147" + ] + }, + "execution_count": 100, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(repeat(5, enhance, grid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "It looked like I didn't need to change any code to do Part Two, just change the `5` to an `18`. I ran it, and got an answer in a few seconds—but the answer was wrong. I went back and carefully looked over my code, and realized there was a place in `expand` where I had swapped the order of `r` and `c` (the code there is fixed now). Apparently there is some symmetry over the first 5 enhancements that yields the correct answer either way, but that breaks down over 18 enhancements. (Also: if I had guessed that `sum(flatten(repeat(n, enhance, grid)))` would be used in both parts, I probably would have created a function for it. But I was guessing that Part Two would involve `enhance`, but not necessarily in the same way as Part One.)" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1936582" + ] + }, + "execution_count": 101, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(repeat(18, enhance, grid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Note on Reuse\n", + "\n", + "One interesting question about these two-part problems: how does the code in Part Two use the code in Part One? \n", + "Here are my answers:\n", + "\n", + "* **All new**: All the code for Part Two (except possibly reading and parsing the input) is brand new: \n", + "
Days 1, 2, 4, 7\n", + "\n", + "* **Reuse as is**: The major function defined in Part One is called again in Part Two (and some new code\n", + "is also written):\n", + "
Days 3 (`spiral`), 6 (`spread`, but `realloc2` is copy-paste-edit), 9, 12, 14 (`bits`), \n", + "15 (`A, B, gen, judge`), 16 (`perform`), 19 (`follow_tubes`), 20 (`evolve, particles`), 21 (`expands`, `gridsum`)\n", + "\n", + "* **Generalize**: A major function from Part One is generalized in Part Two (e.g. by adding an optional parameter):\n", + "
Days 13 (`caught`)\n", + "\n", + "* **Copy-paste-edit**: The major function from Part One is copied and edited for Part Two:\n", + "
Days 5 (`run2`), 8 (`run82`), 10 (`knothash2`), 11 (`follow2`), 17 (`spinlock2`), 18 (`step18`)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Wrapping Up: Verification and Timing\n", + "\n", + "Here is a little test harness to verify that I still get the right answers (even if I refactor some of the code):" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 54.6 s, sys: 156 ms, total: 54.7 s\n", + "Wall time: 54.9 s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "def day(d, compute1, answer1, compute2, answer2):\n", + " \"Assert that we get the right answers for this day.\"\n", + " assert compute1 == answer1\n", + " assert compute2 == answer2\n", + "\n", + "day(1, sum(digits[i] for i in range(N) if digits[i] == digits[i - 1]), 1158,\n", + " sum(digits[i] for i in range(N) if digits[i] == digits[i - N // 2]), 1132)\n", + "day(2, sum(abs(max(row) - min(row)) for row in rows2), 46402, \n", + " sum(map(evendiv, rows2)), 265)\n", + "day(3, cityblock_distance(nth(spiral(), M - 1)), 475, \n", + " first(x for x in spiralsums() if x > M), 279138)\n", + "day(4, quantify(Input(4), is_valid), 337, \n", + " quantify(Input(4), is_valid2), 231)\n", + "day(5, run(program), 364539, \n", + " run2(program), 27477714)\n", + "day(6, realloc(banks), 12841, \n", + " realloc2(banks), 8038)\n", + "day(7, first(programs - set(flatten(above.values()))), 'wiapj', \n", + " correct(wrongest(programs)), 1072)\n", + "day(8, max(run8(program8).values()), 6828, \n", + " run8_2(program8), 7234)\n", + "day(9, total_score(text2), 9662, \n", + " len(text1) - len(text3), 4903)\n", + "day(10, knothash(stream), 4480, \n", + " knothash2(stream2), 'c500ffe015c83b60fad2e4b7d59dabc4')\n", + "day(11, follow(path), 705, \n", + " follow2(path), 1469)\n", + "day(12, len(G[0]), 115, \n", + " len({Set(G[i]) for i in G}), 221)\n", + "day(13, trip_severity(scanners), 1504, \n", + " safe_delay(scanners), 3823370)\n", + "day(14, sum(bits(key, i).count('1') for i in range(128)), 8316, \n", + " flood_all(Grid(key)), 1074)\n", + "day(15, judge(A(), B()), 597, \n", + " judge(criteria(4, A()), criteria(8, B()), 5*10**6), 303)\n", + "day(16, perform(dance), 'lbdiomkhgcjanefp', \n", + " whole(48, dance), 'ejkflpgnamhdcboi')\n", + "day(17, spinlock2().find(2017).next.data, 355,\n", + " spinlock3(N=50*10**6)[1], 6154117)\n", + "day(18, run18(program18), 7071, \n", + " run18_2(program18)[1].sends, 8001)\n", + "day(19, cat(filter(str.isalpha, follow_tubes(diagram))), 'VEBTPXCHLI', \n", + " quantify(follow_tubes(diagram)), 18702)\n", + "day(20, closest(nth(evolve(particles()), 1000)).id, 243,\n", + " len(nth(map(remove_collisions, evolve(particles())), 1000)), 648)\n", + "day(21, sum(flatten(repeat(5, enhance, grid))), 147,\n", + " sum(flatten(repeat(18, enhance, grid))), 1936582)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is a plot of the time taken to program solutions to both parts of each puzzle each day, for me, the first person to finish, and the hundredth person. On days when I started late, the times are my estimates, not official times (these include days 1, 3, 8, 13, 14, 17, 18, 21)." + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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AIOAgfKo847OrRJesrZvB09MGFhbBAAALi2B4etrA2lqzFVwkEuDIEcBAhwle\nLsdcRs/veqLq1ap6lWqhXZ128Ggzv1x+njQh9yGwp6cnAPa2rvgiMAzD4ODBg6UWGhQUBIZhcPPm\nTbx48QKLFi1Campq4ftZWVmlzidISEhQ+hcozwQCQYU+F9OmrUFsrPSVcmzsPEybtgAHDnjqKCrN\n5eQwEArt8P33qxEUZA57+9twcJit9L91aZ+LwEAgSYcjHbPTszHm+zGonVIb3b7upvbnNzHRAK9e\nGcHOrvR+elX+Rsrr50kjRAkpKSnk4cOH5OPHj8rsLsXV1ZW8efOGTJs2jURERBBCCPH09CTnzp2T\nuX9kZKTKdZRX8fHxug5Bp16/fkOsrLwImxmG/bGy8iKvX7/RdWgaiYkhZNkyQvLy8kjDhkvIv//m\nqXR8RfhcPHpEyJo1ivdT9lyciDpBnr18US4/TwXU+e5UeLN4/vx5jB07Ftu3b4eTkxNOnjypVkOz\naNEibNq0CWPHjkV+fj769++vVjlUxcFXV4muWVkBK1YAJiYmePfOF40bm3BSbmwscPs2J0VprN+h\nfviQ9UHt4zt0ABYu5CYWoViIoGdBaNWiRbn8PGlEUQsxZswYkpmZSQghRCAQkJEjR6reNKmA3gEU\nqQhXeoqIRISMH+9FDAwukW++8dZ1OHpB3uciLIyQwEAtB1PMq4+vyMprKwkhhDxKekTy8lW7s1GH\nqn8jZ84QMmyYFzE0DCVubuXr88TLHQDDMIUJ4KpWrYpKlSrx3ihRVIHHj4GYmKUYOPAsDh1aoutw\nNDZrFvDsWdHrjAzg3j1uyu7Zky1fV8yMzWBTzwYA0MGyA0wMNbuzOXeOzQvEpQ8fgF9+WQo3t8vY\nubPsf540pXAmcOPGjbF69WrY2toiMjISTXQxxZCqsDp2BMLCTJCcvAANGnDTVaJLo0ezXUAF3r0D\n9uwBOnXSWUicqW9eH4PMB3FW3tu3QIMGmpdzIuoEvm38Leqb18fEiQBggs6dfTUvuBxQeAfg5+eH\nxo0b49atW2jcuDFWrFihjbgoqpChoa4j4E7PnmzO+wLt2rFj3rlw+TKQmMhNWZpKyUlBh20dpEYQ\nqurHH9m1jTX1KuUVRBKR5gWVQ6U2AM+fP4eRkRFGjx6N5s2bw8TEBIbl6a+R0mtCIftgs4CTE/D0\nqc7C0UhODvv78CkiAvj4kd865CGEYMwfYyAUs79kjco1cH78ed0E85nFPRajiUUTXLjANpJUEbkN\nwL59+7CO6iClAAAgAElEQVR8+XLk5+dj7dq1uHXrFl68eAFfX3rrRGlHdDQwY0bR6xUrAGtr3cWj\niVOngNlyJvo+eQK8eqV5HUuWAF98oXk56hATMSZ8NaGw359hGDSq1kijiWAZGcC2bVxFyN55Fb/7\nokp5BvDXX3/h2LFjYBgGZ86cwcWLF1GtWjWMHTtWm/FRFVjbtmxSsAKtWukuFk05OQEj5WRFiIhg\nUzi3bKndmLhkZGCEwa0Gl9gulohhaKBer4GRkeZdWudfnUfNKjXRtVFX2NlpVlZ5JPcOwMzMDIaG\nhnj27BkaN25cOHNXkz49iqrIjI1lb580CRiuYSbonBzg2DHNyuDa9bjrGPj7QLWPNzUFfHw0i4F8\n+h8lm9wGgGEYxMTEIDg4GH369AEAxMbG0mcAlFbk5gJhYdLbkpLK5miZY8eAvDx+68jKYu8kdGXm\nuZm4n3hfalu3Rt1wetxpHUXEGthyILo16oabN4EdO3Qail6S2wDMnj0bCxcuRHx8PCZMmICIiAi4\nublhIVfT8yiqFImJwKFD0tvq1gXUnIiuM3l5wLVrikcyHT8OZGeXvk9patcG/P3VP15TU76eAusa\n0g9ojA2NNZ4LcPUq+6OpevXYEVeUNLnPAL788kv88ccfha9tbGwQGhoKY3n3sRTFoWbNgM+XnjAw\nABo10k086qpUSbkHmXfvAnZ2bLdHWfRVva9kbpcQCbJF2ahqUlWtcjVJJhqZEIkn759gos1EWFuX\n3QEEfFI4EayAiUnZn4RDlQ+EaPbFoI/WrdPs+H/+AcRi4NOSG3pjS8QWvM96j5V9Vqp1fO/e6tdt\nbmKO+lU5XFSgHNJh5nCKki07Gzh8WPZ7Bw9KDw3VZwEB0qOY+JSQwM6c1YXA24HYdlf2bc7MLjPV\n/vLXVOvareHQwgHPn+s2RYY+U6oBSEtLw6NHj5CSksJ3PJQO6NsaqWlp8sfFjxrFfrGWBf37A19+\nqdy+ycmajeIZNAgYMUL94zXh8qULRrSVXTkXC8IsX67Z85F69QBnZ43DKJcUNgDnzp2Dk5OTxumg\nKf2lb2ukNmgA/Pqr7PdMTeUPp9Q3bdoAyqbOys/nPvGZttQyrYV6VevJfT8lJwXpuelql9+4serL\nXP6X/R9mnGNvFatXB7p1U7v6ck1hA3DgwAEEBQVh69atCA4OVrgaGFW2lMU1UiUS3a57qwghQLqK\n33cNG7IzedV19ChQbNE9vbIybCWuxFxR+/gffgBKWUBQJhNDEwxoMUDtOisKmg66AtPHNXczM4FV\nq0rfx9ERuHRJO/Go4/lzYKD685/U8vQp+xBY28LiwjD6j9Gl7uPv4C+3i4gv1SpVw6BWg5CRAfTo\nwTbKVEk0HXQF5u4eiNhY6Qd0sbHzMGfOcpw+rZuO9rw8Ni1CaY4f1+9uoLZtgb//Vv24q1fZ9Ac9\ne6p+7ErdPGdF98bd0bZ2W17rePAACA8Hpk9X/VhTU2D79vI3aowrKqeDXqmrTxrFuT59ZsPSUnqR\nbCurDQgIkJO1TAtq1VL8h67PX/4F1IlRLNbNVbwmDA0MUcesjsL9HiY9RI4oR606qleXXkNBGaOO\nj0JqTiqMjHSXIK8sUNgA+Pr6Yvz48fD09MT48eOxdOlSbcRF8eSff4r+29u7Gfz8yuYaqWlpuo5A\ntrNn2VWn1GFvr96498RE9q5IF8QS5VqsDeEbEJcep1YdVlbAABW68wkhmG47HdUrV1ervopEbgNw\n5MgR9OjRA8ePH0ePHj0Kf5KTk7UZH8WhnBx2oW2BoGibu/twDBv2EIaGlzF8+CO4u2uYlUwDAgG7\nCIgiIhHbzSLSwzU+wsPZ86xN2dnsPABty8vPQ70N9SASK/6HODjiINrUbqOFqNjnln2b9wXAoG1b\n3a2RUCYoWjR427ZtKi80TAghYrGYLFmyhIwdO5Y4OzuTV69ekbi4ODJu3Dgyfvx44u0te0Fmuih8\nEXUWhc/LyyOTJi0heXnsgtz5+YQkJSk+ZvToJWTtWv4X8S6NQEDIyZOy3/v8XEgkWghIBZ+fd3X5\n+hLy4UPp+6jzueBLtjBbK/WsWUPIw4cltys6F4mJPAWkh3hZFH7atGlqNSxXrlwBwzA4evQoZs+e\nDX9/f/j5+cHDwwOHDx+GRCJBaGioWmVT8n0+pv/ECUDRGj4mJibYssUXjRvrNt1H1arA0KHK7atv\nD/W4mktRv37ZGrFSxVi5FVbyJfk4+/Ks2vV06sQ+H1LGz2d/xo1/bwBgJ4FR8vGWCsLe3r5w/eCE\nhARYWFggKioKtp+SldjZ2SE8PJyv6iskWWP6lZ05W7cuUJbW+snL05/1b/fuDcaJE9zMpZg4Eaij\n+JmqlIsXgceP1a5SbZnCTKXXBzFkDLH/4X7k5ueqVVffvuxcCWXM+3YeOtTtoJddhPqG11xABgYG\nWLx4MVauXInBgwdLfVjMzMwgKN4ZTWlE3pj+mJgYvbtaliU9nU2doOzV77VrbIoAXSs471lZuptL\nkZrKrgegbSP/NxK33t5Sal+GYfDH6D9Q2agyz1EBzWs0h0VlC3z/PZtllZKPIQqa8Fu3biE/Px+E\nEKxYsQKzZ8/GkCFDVKrk48ePGDVqFLKzs3Hnzh0AwOXLlxEeHo5ly5ZJ7Xvv3j3Ur08z+AGAQCCA\nubm5Uvu6ufkgNHQ9gOJpdwWwt1+AAwc8lSojLMwE//5rBBcXDRKvqEkoBKKijGFjI/uyTZVzoU1c\nnPfiEhIMcPSoGebNk39xpC/nghB2tS0Dhv+cku/fG2DDBnOsWSM9xbq0c5Gfz3YVVpQ1rBITE9FJ\n1RWTFD0kGDVqFImLiyOTJk0i79+/J87Ozko9XAgJCSE7duwghBAiEAhInz59yKRJk8idO3cIIYR4\nenqSc+fOlTiOPgQuosrDvtev3xArKy/CXkOzP1ZWXuT16zdKl/HqFSEREepEyj99evBZHBfnvbj0\ndEKOHi19H309F4r8l/UfCYoKUuvYnBxCzp4tuf3zc7Hu5jrif8tfrTrKOl4eAleuXBm1atWCkZER\n6tSpo3R2v379+iEqKgouLi6YMmUKli1bBk9PT2zevBljx45Ffn4++vfvr1prRcllbd0Mjo42MDVV\nf0x/ixZA5858Rci9+Hj1x9xzxdq6GaysNDvvxVWrpvqzmA0btD8kNiUnBdki1e4URRIRIhMi1aqv\ncmXl0mv81PknTPhqAlJSyt6kOl1QmAqiatWqmDJlCpycnHDkyBHUVDRP/5MqVaogQMbTx0Ofr/NH\nccbNbTiePvXGpUvVPo3p99J1SEpJSwO6dweePFFtdM+uXWy65ZEj+YtNGefPD8ekSd44flz7510i\nYRtBI6WXduLGvn/2gWEYeHzjofQx9arWw6q+ChI9acjU2BSmxqaYvYS9mHFx4bW6sk/RLUJeXh55\n9eoVIYSQFy9eaDzOWRHaBVSEi3kAqtq4kZDgYLUOVZtEQsi7d6Xvo+/dHlzNAyCEkD//LL0bSN/P\nBV/27CHk99+ltxU/F2KJmEiKTRDRt7kifFPnu1PhdUNqaiq2b9+OlJQU9O/fHzk5OfjqK9nrf1K6\nZ2Jigj17FAz8L0X//qqn3tUUwyg/xE/fpKez50vT815cmzbczQWY6zkX9+PuS3XdEkLwddOvsdFn\nIzeVqODJ+yeITonGsDbDVD62Rw+gtJVpL7+5jN/u/oaQseww3LIw+k3XFD4DWL58ORwdHSESiWBr\na4tVinL1Ujpx6BCwZ4/m5bRpwy7Iok256g0NBwBcv67bvt4FC7jPw9O+vfIJzJ48AUJKmXbQ3bY7\nIg0jca3ZtcKfSINI9OjcQ+34BHkCvEl9o9axYolY5WcHBVq1Kj0pnH1zexwZeQRJScB//6lVRYWj\nsAHIzc3FN998A4Zh0Lx5c7oegJ7q3Ruws9N1FKoTCABra/W/xAMDAV2uVLpjBzC69HT4vMrPZ4fQ\nyuM4xBEdBB2AgjsKAnTI7ICRg9V/cPL0w1OsvrFarWO/qvcVxnUYp3bdpWEYBmYmZjhzhr0gohRT\n2ABUqlQJ169fh0QiwYMHD2BS2j0YpTONGwMtW3JTlosLcP8+N2UpYm7OLoWo7ljtP/9UfeYslxgG\nMOBhGPy0acAbJS6ybWyAMWPkv88wDOa7zofpv6YAANM4UyyYsECjtXq7NeqGnUN2qn28ughhM6bK\nm/SWJWTfmDIFmDtXi4GVYQo/uitWrEBQUBBSU1Oxd+9e/CpvsVaq3PD2Btq10159ZfWaIjqaXcGM\nD66uQO3a3JQ1eMBgfJHxBSdX/1w4/eI0Lr+5rPJxDMPmtZK11kJ6bjpabWmldGoKiqWwAbh+/To2\nbtyIs2fPYtOmTbhyRf21PSl+rF4NbNnCXXktWrDjrrUhLk6zB56pqeqtvsWFrVuBW8plQlBZ9+7K\nPYw/eJBtiEpz/vV5GLY0hOElQ8weP1ujq38A+Dv2b0iIRO3jq1euDovKFmod26WL7AsGi8oWeDv3\nLd6/Z3SSF6mskjsK6MyZM7hy5Qru3LmD27dvAwAkEglevnyJCRMmaC1ASrGZM9V7kKrrESLZ2ezk\nnocPZY9jLx5fXl4eKlWqVCK+1FT2Iag6C6loasMG9Y7j8rwToni0y4i2IzBoxSB4rvLE2GGaZfzL\nEeVg7c216NW0l9pl9GyqxpqXSjBgDPD8OXtB0KEDL1WUO3IbgJ49e6JOnTpIS0uDk5MTADa5W+PG\njbUWHKUcMzP2R1Xdbbtj57udyG5aNCrDNNYUMzvNQvPm7BcznylnTE3ZxcxVjW9W51mFr5s3Vy7b\nqT5R5vd6+5btx/7zz9LLcnNTrk4TIxOs9lLvwW1xVYyr4Nz4cxqXo64LF4DQUGDdOuntCYIEWJpZ\nolcvQ/RSv22qcOR2AVlYWKBr165YuXIlGjVqhEaNGqFBgwYQ0/nVeiU3V/0uFHkjRByHjsTt22x+\nfl3iYwQLV27eBJKS1DtWmd/L0hJYvFjzON9nvceHrKJ8GVdjruLAgwOaF6whv+t+eJT8SOXjOndm\n73g/N+7EOMSkaS8Da3mh8BnA3Llz4eHhgTlz5mDUqFGYN2+eNuKilLRqlfpXwKWNEKlbl/+JNDdu\nlD78U9kRLA8esD/adPWq+sswMgyD/g79YfiGHfok6/cyMQE+LZ0hl0DAPv8pTeibUGyL3Fb4ur55\nfbSspf5wsSsxV/AxW/M1Frs26orapqo/5a5ZE2jSpOT2axOvoa5RC5w6pXFoFYsq04bT09PJrFmz\nVJ5urAqaCqKIMlP+JRJCNMk+IJFISBfHLgReIJ1GdJKaSi8Uql+uIrm5hDg4sEtWKoqv66iuBF4g\nXUd1lYqvQFAQ+6PviqcqyBfnk84jO5f6e8lT8LlITSUkMJCXUOVadGkRefXxlXYrLUXxv5E3bwhZ\nulSHwegYL9lAizM3N8fbt2/5aosoNTCMZsMoBUIBXtd8DfOr5ljivqTwKjQmBuAz40elSsBffyke\n/19wF1D1SlW549dHjGB/9N3UU1NxMfoiAMDQwBAL3RaiypUqGD10tMzfa98+YO1a+eVVrw7MmiX/\n/dLkS/LVOm61/Wq0qNlCvUo54uwMfBqXAgCISY1BWm4amjVj74gp5SnMBeTk5ASGYUAIQUpKCr75\n5httxKV3dD1iRpakJHaooKmp+mVUq1QNb7e8hY+fj1QftJWV9rtVZNl1bxeMGxvDrasbHld9jNbv\nW+OLukrmSeDJ//4HdO1aeloCWXy+80G9qkWL1DoOccThS4fRvXd3mfsPGqRZN9yT909gYmiCVrVa\nlXiv9/7e2DlkJ9rV0eKEj884HnfEnqF7UL1ydZWOW7OGXcK0wL4H+9Cpfie18gtVdAobAH9//8L/\nrlSpEmpzNTuljFFm5Ia27dnD/iFMnapZOaYmpljttRr3E+/ji7pfwMTQROM7C0WOHgUcHRXXMaDl\nAAjFQvSb2w8v8l6gjqnsab+HD7OJ7LTx8fz4kU3DrMiHrA+YdGoSgp2CYWRghIbVpDPeMQyDkM3y\nE/kU/5KT5fJlNhWEg4Ps9x8lP4KxgbHMBuD0uNOoUaWGwt+huNvvbqOyUWXY1LNR6Th55nSdg0qG\nqqeW+Xwgos93PpBIgI0bgdmz+ZmZXV4pbAAMDAxw5swZ5OXlFW6bMWMGr0HpI8chjlh/aD3ukDsA\nA70YkfLLL5odLxQLkSBIgFV1KwDAulvrsPK7lbCuaQ2A/ZJLTwdqqPY9oZBIxH55fRpdXKpG1RoB\nABJyEvBds+/k7peczKYI0EYD8NNPRf9d2p2h/6/+WG63HEYG/CTrr1KFbQDkce7gLPc9Vb/8ASA+\nIx5mJmqMN5aDy/kAOTlsTij65a8ahadr9uzZyMzMRO3atQt/KiI+cqroWnRKNGaeLxpTd9TxaOGX\nPwCcOgV4KL/eh9KMjYHduxX/sebl58ncTmSMe503D2jalIvoVCMr2+Yd5g56dO4BhmHQpWEXhWVc\njbmKbXe3yXxvyBDg3j3Zx337rWYJADOFmbj97rbiHT9xbOeI/i10v4rf69dsamgAiM+Mx/P/nsPM\nDFixQrdxlUUKGwAzMzPMnTsXY8eOLfypqDIaZYC8Jnpx9f/kCbskoiba1mmL0+NOy31/2DD2QSSX\nhEIhJk9eCmFpKSzBfsl33NER8RnSv+TZl2cx+dRkboNSwbp1wKtXRa9ljelvldpKpc9G0+pN0amB\n7MW8d+1S72H8uVfn8CCp9Ic4CYIE7PuH439gFfyX/R++OyD/rk4eKysgmF2BE08/PsWF1xe4DawC\nUdgAtGzZEmfPnsWbN28QExODmJiKO9liUKtB2DB9A8yvmuv86j80lJ+MnedencP7rPcA+JkHMHWq\nL/bvt8ekSX6l7scwDO79cK9Ev3lvq94I7B9YYv+0NLYPmG/Nm7OjbwowDINZ42ZJ3Rl6TfFS6bPR\nvEZzuXcK9erJX+5x9Wrg/XvZ7+WIchSO9GlVqxV2DNmhVIxvUt/g6OOjSu2rrFpVaiGwf6DKCdwW\n+MzFqPm90Htib+zYtAPB24PR7LtemLaApgBVlcLOyWfPnuHZs2eFrxmGwcGDB3kNSl9ZVrXEtLHT\nEPcyTuezUefM0ez4dxnvEJ8Rj66Nukptf5T8CFbVrVDXjH0CmZrK5pu3tNSsPgDYuzcYJ0/aQCLp\ngzNn0rFvXwjc3YfL3b+KcZUS2+T1QVeqBOTJ7jHilKNjyW01OtRAld+qILtJNi93hvLy/dSqxf7e\nMuNsJyNQDQjFQgjFpd+1qYphGHxp+aXKx8kakGEiNkXvb3Q3IKPM4nQmwicikYgsWLCAODs7k9Gj\nR5PLly+TuLg4Mm7cODJ+/Hji7e0t91h9nQhWMFEnLy+PjJsyizxLesZ7nXyu/Xoj7gZZd3Odwv02\nbiRk61bN63v9+g2xsvIi7NcZ+2Nl5UVev35TYt/03HTyKOmR1LbPz8WblJLH6dLxkOPE3M6c/Hnq\nT7WOf/nfS+JwyKHE9vh4Qlq2/Hwbt5+LXfd2kbDYME7L5JNEIiH1u7CTA+ENtSbTlUfqfHfKbQBm\nzpxJCCGke/fuJX4UOXHiBPH19SWEsLOHe/fuTaZNm0bu3r1LCCHE09OTXLp0ibNfQhsWXVpEdkTu\nIBMmeBHGZjHpMnMA73XK+0MPDSXk+XPeq+fU4MGzCSCQagCADDJ48OwS+96Nv0tmnJ0hta34uRCJ\nRaTj9o4kPTed97iL+/FH+eddIpGQRd6L1P4Syhfnk+iUaBnlEpKRIb1NUQOwMXwjuZdwT+m6r8Ve\n09ns3utx18nI/41U+bhD//uDmE40JfAGMZ1oqnbDW55w2gBoIjs7m2RlZRFCCElJSSF9+/YldnZ2\nhe+HhoYSHx8fmcfqawOQl59Htuw6QiwsgglAiIVFENm7N5jXOuX9oe/bR0h4OH/1Hn54uMQVuKZe\nv35DGjVS7g5AFmWuem/eJOTYMU0jle/WLUIyM6W3XY+7TpIzk/mrVIb4+HgSHU2Iv7/s9y9FXyLv\n0t9xVl++OJ8svLiQiCVizsoskC3MJinZKUrvn5yZTJIESVIpQhp/05U8flyxr/4JUe+7U+4zgCVL\nlsjtNvLzK/0BXpUqbN9tZmYmZs+ejblz52LNmjWF75uZmUEgEKjaW6VTb2PjsX7VS6SnewMA0tNH\nwMfHG3Z2X8HauplWY5k4UbPjr8Veg4RI5I6rNzMxg6FBUY6Gp0/ZZwCajAC2tm6GpUttsHBhMDIz\nR8DCIhienjacnjtzc7ZfnC+yJsFffnMZpsamhc9MNJUpzERVk5JpWIVC6UlzlSqVnBBVwL65vVp1\n50vyZc5ZEIqFaGzRGAYM94PsqxhXkfmsR57d93ejqUVTjP9yPDzGz8dkf3dM6L8AdeuW3eHYusQQ\nIvsR/JAhQ5Cbm4uhQ4eiY8eOUk/qe/ZUPIEjMTERM2bMgIuLC0aMGIHevXvj709LN12+fBnh4eFY\ntmxZiePu3buH+vXrq/nr8CM1NxWzf9yEy6EbAHz646z9HDD6CPsvDuHAAU9e6hUIBDDnISH/rYRb\nkBAJejTsodT+fn7m6Ns3D126aP4QcPbsAAQH98OIEZcQGDi7xPvnYs6huUVztKnZRmq7rHMRmRwJ\nc2NztK7ZWuO49IFYIsa3//sWlxwvoZpJ0XJg+/ebIi7OCF5eGQD4+Vxki7LxfdD3uOx4GZWNtLQc\nXDHyGh8A+JjzEbWqSLfsEgnQvr0lHF2mY8VS1UZdlVeJiYno1En2cGK5Srs9ePHiBVm3bh1xdXUl\nmzZtIrGxsUrdVnz48IEMGDCAhBfrp5g2bRqJiIgghLDPAM6dOyfzWH3sAvrpzE9k46UA6YeYbYJJ\n7e9GKt2FoQ5Z3R4HDxJy/z5vVfIm/VN3fV5eHpk0aQnJk5PC9PdHv5MnyU9KbJd1Lg4/PExCo0M5\njVOevn0JefmS/3qE+SVTsAqF7LOAAqV1h7mHuJPHyY/VqluVrhgubb6zmSy8uFDme3n5eaTD1g7k\nY/bHku/l8TtQoqzh9RlAREQEmTlzJhk9erTCfVeuXEm6d+9OXF1diYuLC3F1dSXPnz8nLi4uxMnJ\niSxdulTuwzJ9bAAIYR/yTZ8eTCwsgnT6DODkSUJevOC1WkIIOzLk9IvTnJXXvTshT5+qf7yyf+j+\n/oQ8eKB+PfK8fUuISFT0OluYTeZfmK+TkSfx8fHk0CFCbtwo+d7DpIckS5jFaX2//v2rzAfUXMkV\n5ZY4j7mi3ML/FolFnx9CCGEvJmxs5pGQEA3yoZcjnD4DKJCZmYlLly7hzJkzyMnJwdChQxXeVfzy\nyy/4RUaimkOHDql2e6JHJBIGYvFwDB7sjWPHqmHw4Edwd/fSehxKnP5SBdwOQKf6nRTmYbFtYItq\nlYq6IU6fBvr1kz/uXJGrV9kUEHzr0IH73EUA0KiR9GuRRIQv6n7BS9fDsw/P0LBaQ6nzn53NTggr\neA7QsKHs31OdcfXFJWUm4WP2R7Sv216qTFUzdipLVi6lj9kfITYSI+r3KACQ2zU0ZYovHj0agEOH\n/DBsmPb/FssFeS3D2bNnyc8//0xGjBhBtm3bRt6+fatR66QsfbsDeJz8mGTkFo3Dy8vLI926LSEL\nF+aRG3E3yLXYa7zVzcft7e23t0lcWpzKx/38MzsmnS9Zwiwy6MggmV0ghMg/F29S3pAloUv4C4yw\ni9do0/Qz00nEuwipbf36FY38kncuuLgbCYoKIoG3tbfKzB8n/yCm7uxwzoIf04mm5PCJw6Uet2dP\nEKlSRXsj8soCdb475T4EbtOmDZo3b442bdiHccVb6A0bNvDWIN27d0/1Bxk8mnV+Fpw7OKNbo26F\n20Qi9mrsSsxl5Evy4dBCTj5eDSUkJKBBgwaFr319gb592Vz0ZcXLl2yWxm7dSt9PJBbhTvwd9Ggi\n+8H05+eiQLYoGxejL2J4G/kzijX1xRfAmTOq5//nUvHZwPLOhc12G5wcexJNq+sgK56aCCH4Zsw3\nuNO+KMtu16ddEX48XO7dVXR0DOztDyA21rtwm5WVN0JD3bQ+Ik+fqPPdKbcBiIiIkHtQly6KMxyq\nS98aAAB48wY4dgxYulS79X7+h377NvslVK+e/GO4tOveLmTkZWDet+qvA33lChAXB7i7axaLvC+9\nz4lEwPjx7L8XV6mB8/LYrpeC76MtEVvAgMHPXX7mpgIVJSQkYOXKBggIkB4ampKTghqVa3DaLbXn\n/h7UMq3FawP756k/4Rbihuym2TCNNcXBkQfhOER+KoshQ+bgzJmVKByRBwAQYPDg5Th9Ws0FsssB\ntb47ub0J0Zy+dQERQkhCAiGnTklvy84m5LF6gy2UxnUX0IhjI1QaIZIoSCwcfZGdTcjevZyGUygv\nP09h94WicyGRSArLOHVK+oEt19Jy0jidaCVLxLsIcjf+buFrsZh9EE0IIW/fxpNdu6RHBnFt4cWF\nJEmQRJ4kP+F9lrAy6z4Xp0pakYqE9zWBK5pTL07hY/ZH1K/P5mUv7tUrYP16dp+zL8/qJkAVbei3\nAS1rtlR6/3pV66FmlZoA2Ae4//yj3EpYqtr3zz4sCl2kURn9j/TH4/ePAbD/VvIyaKoqLq7k72xR\n2aJEllKuJWYmFmZlBdhspwMHsv9tYABMmSKdIC4lJ4Wzuud6zsXZnWcxcvpI/LzwZ0zxmIJebr0w\n15OfbJsFa20om2XX2roZPD1tYGHB5oTmY1JhhcFDQ6QRfboDWHxpMYnPKP3K8867OyQynp+Yi1/1\nTp7MpjrQBXkPZkuTm0vIyJGE5OQo3lcikSgcuqjoDiAhI4HzIZkSCSFdurB3gAVkjUfXts/PRb44\nnzQLaMZZbiR5D2b5zLejTi6lCRO8iKHhJeLmJj+5ZEWiN7mANKFPDQAhhPj5EXLggG7qLv6HHhtb\nMimYKnJESnwTy3DgwQHy05mfVD5OJCLk8mW1qpRJle6wW7cIWbyYu7oLSCQSYrPdhsSmKjchki8n\nT2jBS+gAAB/gSURBVL4n27dLb+Oy8SveJaPP2Tbz8vKIk9MsuZMKKxraBcSDKVPY8e+y5OUB+/dr\nJ46mTdlcN+qQEAlabW6FtNw0lY8d034MNg3YBACIjQX27lXuOCMjoE8fxfs9SHqA3PxcleOSJS8/\nD4mCRLRsCYwbx0mRUhiGQeTUSK2NsnmU/Aib7mwqfJ2WBrx9C9SuLUEb6UwZnD74LSvLn5qYmMDf\nfxFMij8Jp1RCGwA51txYg5ScFNSuLX/UjbExuyrXzrv7cOzJMd5iEYs1O96AMcCrma/UmsxT2ahy\nYWI4I6PSFyEvkJ7OPppTxtqba/Eu453Kccly+NFh7Li3A7VrA19qNh8KABAWVnKRmeJJ8vhWq0ot\ntKjZovD1+fPsBYeVlRi9ehXtFxEfAQnh9uFM8aUudb38KcUjHu5ENKIPXUASiYSsv7mefExT7tby\n2YdnvCxQUtDt0a8f262hKyKxSOGzkOJmzWJzFnFJmS4gbrtBCBk6lBCBgH2dmpNK/o75m7PyNVH8\nXGTkZhD7g/a8pGr+4+QfGi1yow00F1AR2gXEEYZhMO/beejX1wQvXyrev03tNmhWg78RCCEhgK2t\nescSQvD8v+cqr7ta3MXoi/D+21vp/QMC+OmCUaR4F8WqVcDx45qUBZw8CVT9NNT83/R/cSFaPxYf\n37KlKh6zA55gXskcl1wv8ZKq2XGII37q8xO9+i/HaANQivBwoKUSoyZXrGD7ZvlSpYr6eXT+y/4P\nU09P1aj+gS0HYueQnQCAa9fYSValYRjFwzBTclKw9e5WjeKSJTc/F0cfH8X48cD333NX7peWX8K3\nry93BSopJScFfQ/2LWzAnzwBrKzyUacO/3UzDIPVXqv1ru+f4g5tAD4jIRKMOzEOOaIcGBvLXoz7\nc198AeyOWo9d93ZxHs+HD8r3p8tSx6wOrrtf5+yPuFYtQN6EXIEACApSrpwsYRYn8XzOyMAIYXFh\naNhYBDMzISZPXgqhUPV1DA4cYBOw6VqNyjWw/vv1ha+3bxfizz9XoGZNdpH23x//rsPoqLKONgCf\nkRAJnNo540Gk8qsUjRgB/PitM8a0H8N5PBMmAJGRnBersvTcdNx5dwdffAHY2cneJzkZhV0TijS2\naIyfOv/EXYCfGBkYYdvgbTA2NMbUqb44cMAeP/xQ+gp2nxOL2XNeMLjk4MODuBt/l/NYlcEwDDrW\n71jYgAsEvrhyZTB++MEPKTkpeJD0QCdxUeUDbQA+Y2RghE5VhyBAxZQiDcwbwKKyBWdxCIVCeHis\nQUiIUO3+/9ScVFyKvsRJPAmCBBx6VHo67xYtAC89ycq7d28wDh+2gVjcByEhX2LfvhCljhMKhfjh\nh6XYsEFY2I1Vx7SOVGpmXRCKhdizJwgnT9pALO6LkJAvcf6P21j7/VqdxkWVcVw/idaUPowCUseG\nDYQcOsTOyuQCO8sxVKNZjk/fPyXLryznJJ7itm8n5MIF1Y6Zs3wOsZtgR3q59SLNhzcn7Ue3J3YT\n7Mic5XOUOl6V0R4TZ7oTw441CFrZEDTtRdC0FzFu2ZSMmeyu8Fj2vF/Wu9mlbQPbkoZfzKL5bz5D\nRwEVoaOANJSWm4Zuu7upNWJm+HAg0mIJtkdu1ziOvXuDpa70lL16/Vy7Ou3g852PxvF8rlOnkg/H\np01j8yPJ0922OyINI3Gt2TW8sXmDp+2fItIgEj06K7cusSoe3U2GuFU24PwAcL8GuF+DqOMHPL5b\nlFvnt99KPrgvOu+q3TVog9Xl7xD/ZFXRhqqJiLWsgjlzAnUXFFXm0QagGHMTcyxoeQCXL6v+wLR5\nc2Clwy8a92tHR8dgxYqHSE9n0++mp4+Aj88DREfHaFQuF1JyUnD40WHY2gLNPhv1Om4cO1tZnuIT\niwDwOsHof4c2wySytlRdJvdq4NSJolm1JibSq5uNHBkDb2/p8+7tG4Gvf+sEoVj1h8hc2+w/H1ZW\nRQ+DYSBG7aq3ERAwW3dBUWUebQCKMTQwhKVha2Rmqnd8VZOqyM/XbLTNnDmBiI2dL7UtNnaeyld6\n9xPvI/hZsEaxfM6QMcSzD89kvterl3Ru+s8xDAOnoU6oEsc+XOczvUCLFs0xZYgz8OzTN/xzY0wZ\nMh4tWjQv3GfqVKBu3aJjEhIC8fat9Hn/9/ViVPu7HUwMdZ9qwNq6GWb/0hTV6rLPYSyYu1g7vmIv\ngEJpjtcG4OHDh3B1dQUA/Pvvv3B2doaLiwt+/fVXPqtVCyEEIrEIPXqw3TnqCA4G3KfkIVOoZgsC\nICBgtvSVHgArqw0qX+kxYDhPW2BR2QKr+rLdED/+CERFsUMllR1lWefLOmj0vpFW0gts8V+D2i/Z\nuwCLVxbY4r+61P2PHJF13v2xZzX3XWjqetv4CWxHnoehYSiGD38Ed3f+FmmhKgbeGoDdu3dj2bJl\nEIlEAAA/Pz94eHjg8OHDkEgkCA0N5atqtbxKeYVuexSsW6jAwIFADaeFGl15W1s3Q6NGNqhaVbNc\n5x3rd8TQ1hquIF+KH38ELC2F6N9/KebNU64FcPnKBb4/+iqd910TDMNg8/L1MD5vgh2/bAHDMBCJ\nRbjwWvZs3s9zzFerdRRLl7fXqyvsDQ4bcD5wP/q47EYzN11HQ5UHvDUATZs2xW+//Vb4+unTp7D9\nNJ7Rzs4O4eHhfFWtlla1WsEh/joeaDCsulIlYNOAALh+5apRLNu2DcewYQ+1dqVHCMHaxYuVevgt\nyBNg0aVF+PprwMPDF7du2SM9Xf44e59rPlKJ8rSZXsBphBM8Bs7FmBHs/Ix3Ge9w6sUpub+nu3vB\neb+ML8f+gSf1b/Aeo7Lmes5FL7de6PdDP6TkvEbIjhBeF2nRhCqfJ13Q9/i0irtBSCW9e/eOODk5\nEUII6dGjR+H28PBwsmDBApnH6HIY6LVrhPz3n2ZliMWEvOJgBT1Ncp3v+2cfCX4WrPT+5//4g8wx\nNyd//ak46ZdEIiHb7m4ju3b/QSwsgglAiIVFENm7V3Z9MakxJCNXg4UMPuFjuN/T909LDNvNy8sj\nkyYtIXl5eZwN6eWCLhZpUZcqnydNqfO50GZ82qTXw0ANiq3QnZWVhWrVdDuxprjc/FwkZybDzo5N\ndaCJxETAdcY7fMj6oNJxEgkQGAjkfkqNr0mu884NOqNdnXZK7UsIwYW1a+EvEOCvdesUXhUxDIPv\nazhg1conckcqvfjvReFzEKvqVjCvpOZCBjzzueaDqA9RUttMTEywZ48vTExMtJr6WRFtjqLSBMnM\nxIV585T+PGkbIQQX1q/X2/i0jaOVUxVr164d7t69i86dOyMsLAzdusnvb09ISNBWWACABx8eYPM/\nW7Cn326Ny2IYoNtPG3D20Vfo11TOSjIy5OQwePfODB8+ZMLw0/eOQCBQ+lx4rffCk8QnJbZ/Uf8L\n/Dpf/kP3v8+cQb8nT8AA+P7RIxzbvRu9Bg0qta5p09YgNlb6gWls7DxMm7YABw54IuBOAHo36o2e\nDXsqFbsyVDkXyvL/1h8Qs5+3X9b+gqeJT2FoYIgMYQbMjM1gyBgqPH/aNGnQJDy+9hjZVtkwjTPF\n5MGTkZiYqOuwpIQdPAiHxET28/T4sVKfJ02o8rkwCQvD1StX0O/xY63Fp/e4vQmRVrwLKCYmhri4\nuBAnJyeydOlSubnbddEFlJlJSOvWhAhVX/qWV6rc3qrTRSCRSMicrl2J5NPUUgnAvlaQV//5y5ek\nyuSWBIa5WpuVyveMT4/NHsRogpFed7EUX6pRH5doVPfzpAlVPheSBw/InHbttBqfNuldF1DDhg1x\n7FPuYCsrKxw6dAjHjh3DqlWr9CrFrJkZcPWq+imXP0cI8L//sd06iohEQAwHc7zU6SK4sGYN+t+/\nj4J/CQaAw+PHuKggpef2Q1tRO04EA6uOQNPeMLRuj/TmW+C1dbnmv4iOrP95PTpldfp/e+ceFmW1\n/fHvoJBy0bKDpT8M0MRLPWGAl7KUPBr4WBZQ3lLQg6Wdc1LwjjwiZYKlZSfT8nbShDBxIq+IWiIp\npKhxEYU8KqGiIHkdQBjmXb8/Xph3RgaYd+ZlLsz+PA/P48vsy2K75917rb3W2hZtYmm4qtH5F2fL\nuqKxrg5YsQJpSUkIrN9dA/Xz6cyZFudTq0HEh3xX8pln0y5cQGBxsej53pYxmQnIUilTlOGG4ga8\nu3lL1qZMBsizTqHPoK4Y4PlUs2XPnAG+/BJITDS2T/7lEJoSimqPar0CrfKvXIHi2WeRpXEeQ3l5\ncJbLERAS0mS9oX5DseHqBnAvVQE4DxWA6ssdEDg00Lg/wozIZDLMC52HsJ/CUOVeZbH34Ia8HoL0\nX9MtamECADg4ID8rCwo/P2Q1jBnHgVQqOB871ux8ajVkMqC6Grh3D3ByQv7x49rygT8TMJt8loD0\niohxmNoEdOD8UYo68KHk7a7OWk1HLh/Rq2xTGqi+6u3JqyepWlktjYng+vWmBapHsx/EwiQmCVMk\n/bJ0E0sDVpkA7e5d3kVOYhqNxZ07RIcPS96PNWBxJiBrQFYyDNe+j5G83YghEfD38G/yc03zkLGb\nzG9zvkVhRaFaC2gx0CozEzivO6UDnnyyRYEa+pFd4stZ6m5ZLHqPH4Pnww+BggL9ys6ZA+zZI2n3\nRISv4+K0PXnKy4HUVEn7adNIvgwZiTkOgVtro7dxI1FBge7Pli0j+vrr5usbstPjOI4Wxi5sfvea\nmNhyPucffyRKaTqWwNS7ZVPtevUaPzNjMRpAairR7dv6la2ulvyLlpqcTLOcnenAunVEt25J2rY1\nwjQAEdTW1iJo5nQcunDI6B14U1x22Isr1UU6P4uIAMaPN6xdIsK0XdNw8dbFRp/pdY/rpEnAqy24\nqLq78ylOm6Ct7pbZPbgiCAwEHn1Uv7IdOgiapQReD1Tvz/+FQoEDy5aBMjONbtMWsepD4MiYSJz5\n84zWl5WI4OPug9UfrW62TmHRnyi/0x4/5+7C8179m61jKH28b+FvrroTwzk7G96uTCbD9Oen46nO\nzR8wN+L6daBbN/3K+vi0WCTk9RCc+v1Uqx9IUr2q/9GaNRb7YiYirIyKwvz4eIuVURI2buRf5NOn\nG1af44CwMOD77wE3N8PaqKhAWny82uMo4O5dHHzwAAGGtWbTWLUGoHnJSMNPS5eMDPUbit/oBMpH\n/wlMvIj7gRX4jTvRKheThHqHwre7r9bvVqwwfAN0+bZQcehTQ2HfToTfKhG/8y/SrZE0SWUlf2ag\nA1PtltPkctzbutWi3fXS5HJcX7fOomWUhNGjgQAjXrV2dsDRo+Jf/hp2fiJC2vbteLWqCgAQUFXF\nonoNxKoXgKZ83/3/7o8tOVvU5W5V31I/D+jvA2R10aqDrL/Bu9/zrSLj9u3AV1/VIjx8MWpra+Hm\nZli6CRWnQuhPoSi9b2A0rEwGHD4M9Okjrl5xMR/UYCa0VH0L/ZKTZnqBFSssUkajafib3NyAHj2M\na6thw0AE/Pabfn0PHQqUlAAA0o4eReCdO8yfXwKsegFosEM7ljgCELxR6rg6XL8vhMgrVUr18/vv\nf4naG9FAUf3u+bwjaktWIDLyy0btS0Fxl81IyZyFrVtH4r334jF5MtBcGqSGrI/+U/0RMjcE/lP9\nMTxsOObFzkPG1Ax0d+luuDDtDMht88wzfJIiU8NxQEkJ0uRyQdXPybG8L3l1tbaMv/8uyFhaCpxt\nnJ6jATJhVkpD+lLXyczktUepuXEDWLkSUKkay5eXJ9wxKpPxm5D6hSf/+HFk+vkhdvhwRA0Zgtjh\nw5Hl54e8Y5aTvdVqMProWWLEnmTr441y5YrgglxUdIlcXWMIbvV+7G6Dyd09ptXSGMz6ajE5u69t\nMWtmA5JnfSwrI3rlFSKl0rD6migUxrehL8ePEzduXNOpBSorTSdLM3DBwRTRr59uGQ8fJoqPFwqf\nPEn088/qR0OzUpoqA6a6TnIyUXGx6D7F0Ei+jRuJ9u5tsZ7FeERZAIZ4AVn9AkBElCRPIvtBDrRd\nvl3n5yNHEp07Jzz/978p5Nh5PuF5F3LsPL/Fl7Kh/O9/l8jDY6k6X44+OXNuVd0i3yBfrSCrQSGD\nDHdL5LimfVHFUFVF1Lcv0T3jUzvrRKkk+ve/iRrSX3Mcpe7YQQccHUlzAFMdHenAqlVEI0a0jhwi\nSd26VbeMul606elEu3cTUX3enKefNigfjdiXHsdxFNG3r3ZfWVlEX3whFHromcvMpAh3d5Pky+E4\njiIGDDDJWLRlbNYNdP9P51GXH4z9u/jgpj17tGNODh4E+vUTnqdNexMhYztCVjgGb73hKOrCFRKh\nSo8KDkYxHQbc/dU/xXQYo4IFr5miiiIUlAvBNJ9nfY4h/kO0zFoLwhYYftAqkwH99UsN3SwdOwKn\nTgEuxqV21hq/6mr+BwDatweGDOHzygCATIb8zEzdqv7Vq8Du3UKj+iRdkpIdO/j0AgDyf/9dLWPD\nT5PmiOHDgddfB8AfGgdevWoS+3WaXI7AkhLtvrp31/b0eug5LScHgWVlppOvqIjZ8s2BxIuQ0Yhd\nxTZv/rHRxSQnTxK11IzmxR9iEKNKr1m/ljDBXsucgwnt6b24Geoy2/O3U2JeolY9SYKsCguJEhLE\n12tltMYvPJwPONODJnd6HMdrA0VFEkrZAsuWEV0y3GSoM2vmwIHExcXpFSyl96530iTizp4VnaHT\nlFk9je2LaQACNmcCMsTEYgzcsWONVenmynMc9RzmpWXO+b+Xn6Jd53e12FfyrmRyftlZtO2f4zj6\nZOFC4s6eJfrhB1F19WbOHKJTp4S+9PyycocOaZsVROTfbvaLXlKi88UpVr5mkfDll5qcrNts9O67\netXX+6WXk0Op27frb6JqSb5WuEHL2L7YAiBgyAJg1YFgERH/QXHxx1q/Ky6ei4iIJdiz5wvJ+0tL\nT0fg5cuCqrp5MwKaCYiRyWT4ZO5yTPhhElReSrT7wx7/mf85xvZt+bJ2Q7M+qv3RBw5EwLhxourq\nzfjxQJ8+2n2FhPBfX4VCMBOlpwNbtvA/qE/Hq2lW2L1bmiyMmm6J338PlJUBkZGN5TMUjgNGjOD/\nDg8PY6VtOiulk5MQzLR3LzB4MODqqn/Dly/z6Y9X1V/W4+2N/C1bRGfANGXWTJah08xIvAgZjUVp\nABxHtGMHUU2NblXV0ZG4FkxIHMfRoOBB/GFusLjDXIMO+ww8TBMLx3EUMWiQdl8nTxL5+wuF7t/n\nvZDIhKr+X38R/fGHVn+SjIURJh+DiI0lunhR50dNjsWDB/whswXnMZIapgEI2NwhcK9enoiJGYDO\nnVMAAJ07pyAmZgB69fKUrpPsbKC8XMvXG6gPPgFwsOG0ueEw8yFkMhnmh82HyxEXLJiq/2Eu6cp0\nqIviYnVmzzS5HIEFBaY7uKu/SlLdl58f8MsvQiFnZ6BrV6H8w+PXGjJ26QL07q3tm6/Zz83m72om\nzUPq9HQhAMpTwjmlD0uXCrmYKiqAc+fU8mnNi5QUIZjqkUf4Q+a2nIqCISlWvQAAvEfPG2/kol27\nn/Hmm3miPHp08uABf0sLwH+RPv0UcHPTCj7R6e0xYwawb5/OJkNeD8E/R/xTlDmnyfQH+fm8eaCB\n7GwgM1MdjfqqUgmgdcPj1X09HIoPNPnyaXH8TCFfdTUwcKDgaaRSaS9Y0DCh7dgBfPMNcOuW5PKJ\nJjdXHY3daF44OgIODmYUjmHVSKZ/SIQhaoyhHj06yc0lmj5dfL3KSqK6OuHZCDVcy3zx7LO8d0gD\np0/rPNy1poM7QxCj6jcrn+b/S1kZ0YQJ6keuooIiPD0t9q5Yyc1abQBmAhKwuUPgBuzt7dHHlYO9\niEt9STN7419/8X7uTk7Ac8/xGQ/F4ugo/DsjA9iwAUhIaNyXrh1ydTXfPwCcPYu0f/xDMOVcuoSD\nSqVwOOjjozNTJzu4E9Bbvq5dgaQk9WPazp2NfPMt4e9pQJdZy5LkY1gh0q5BzcNxHMXExND48eNp\nypQpVFJS0qiMIauYUWHuO3cS/etfRLtads3UG5WKd03U1ZdSSXTmjFD2yhUiLy/1I1dVpT7IbW0f\nbGuitXd6pvR9NwRLl89cMA1AwOLjAA4ePEiLFi0iIqKcnBx6//33G5UxJBdQhK+v9hfi5k2itWuF\nQg89c+XlFOHhIdRphbtK1X3V1VFEly5CX9XVREOHCuYijtMyHZnDvGINtPYX3dLH3dLlMxdsARCw\neBPQ6dOn8fLLLwMAvL29cbaZTIn6kiaXI/D8eW21eNgwoP4wFAD/ddF4TtuzB4HXrgl1UlJaTZVO\nS0lBYGWl0Ne+fQjQPPiUybSydGqaL2pqavDII49YlHmlrWJNZi02LxiSIfUq1BzR0dGUkZGhfn7l\nlVdI9dDuW8wqZohazMLcrRM2FgJsLATYWAhYfByAs7MzKisr1c8cx8HOznARDPEtN5k/uon7YjAY\nDLHIiEx3fdHBgwdx5MgRxMfHIycnB+vWrcOGDRu0ypw+fdpU4jAYDEabwtfXt+VCGph0ASAixMbG\noqj+Xtr4+Hh4mjrCksFgMBgATLwAMBgMBsNysPpUEAwGg8EwDIuJBNY0Dzk4OGD58uXooZnm18YI\nDg6Gs7MzAMDNzQ1xcXFmlsj05ObmYtWqVdi2bRtKSkqwaNEi2NnZoXfv3li6dKm5xTMpmmNx/vx5\nzJgxAx71qaknTpyI0aNHm1dAE1BXV4fFixfj2rVrUCqVmDlzJp5++mmbnBe6xqJbt27i54WEXkhG\noU+QmK1QU1NDQUFB5hbDrGzcuJFee+01Gj9+PBERzZw5k7Kzs4mIKCYmhg4dOmRO8UzKw2OxY8cO\n+vbbb80rlBmQy+UUV58X6+7du+Tv72+z80JzLO7cuUP+/v6UnJwsel5YjAmoNYLErJXCwkJUVVUh\nPDwcU6dORW5urrlFMjnu7u5Yu3at+rmgoAB+fn4AgGHDhiErK8tcopkcXWORnp6OyZMnIzo6GlX1\nWU/bOqNHj8bs2bMBACqVCu3atcO5c+dscl5ojgXHcWjfvj0KCgpw5MgRUfPCYhYAhUIBF40Lx9u3\nbw/O1Jd9WwgdOnRAeHg4Nm/ejNjYWMybN8/mxmLUqFFopxEhTRq+Ck5OTrh//745xDILD4+Ft7c3\nFixYgISEBPTo0QNr1qwxo3Smo2PHjnB0dIRCocDs2bMRGRlps/Pi4bGIiIjAc889h4ULF4qaFxaz\nAEgdJGbNeHh4YOzYsep/P/roo7jZwkUmbR3NuVBZWYlOnTqZURrzMnLkSPTv3x8AvzgUFhaaWSLT\ncf36dYSFhSEoKAhjxoyx6Xnx8FgYMi8s5g3r4+ODo0ePAgBycnLg5eVlZonMh1wux4oVKwAAZWVl\nqKyshKuYu2HbIP3790d2djYAICMjQ3TAS1siPDwc+fn5AICsrCw888wzZpbINFRUVCA8PBzz589H\nUFAQAKBfv342OS90jYUh88JivIBGjRqF48ePY8KECQD4IDFb5a233kJUVBQmTZoEOzs7xMXF2aw2\n1MDChQuxZMkSKJVK9OrVC4GBgeYWyWzExsZi2bJlsLe3h6urKz766CNzi2QS1q9fj3v37mHdunVY\nu3YtZDIZoqOj8fHHH9vcvNA1FlFRUYiLixM1L1ggGIPBYNgotr2tZDAYDBuGLQAMBoNho7AFgMFg\nMGwUtgAwGAyGjcIWAAaDwbBR2ALAYDAYNgpbABhWzcmTJ/Hiiy8iNDQUU6ZMwcSJE5GammpUm1Om\nTNGKQ6mtrcWIESOMajMqKgrHjh0zqg0GQ2osJhCMwTCUF154AZ999hkAoKqqCpMnT4anpyf69u1r\ncJv79u3DyJEjMXDgQACATCZroQaDYX2wBYDRpnB0dMSECROQlpYGLy8vxMTE4MaNG7h58yZGjBiB\nWbNmISAgADt37kSnTp2QlJSkzryqSXR0NJYsWYKUlBStRGxRUVEYM2YMXnrpJfz666/Yv38/4uPj\nMWrUKPj6+qK4uBiDBw+GQqFAXl4eevbsiU8++QQAkJiYiE2bNkGlUiEuLg49evRAQkIC9u7dC5lM\nhjFjxmDy5MmIiorC7du3cffuXWzYsEErSSKDISXMBMRoczz++OO4ffs2bty4gQEDBmDTpk1ITk5G\nUlISZDIZxo4di3379gEAdu/erc6loknfvn0RFBSkd0qS0tJSREZGIiEhAdu2bcM777yD5ORknD59\nGgqFAgCf72rLli2YPn06Pv30U1y8eBH79+9HUlISEhMTcejQIVy+fBkAr9UkJSWxlz+jVWEaAKPN\nUVpaiieffBKdOnVCXl4eTpw4AScnJyiVSgD8bWtz5syBn58fXF1d0aVLF53tvPvuu5g0aRIyMjJ0\nfq6ZReWxxx7DE088AYDXQnr27AkAcHFxQU1NDQCozUk+Pj5YuXIlLly4gNLSUoSFhYGIcP/+fZSU\nlAAAPD09JRgJBqN5mAbAsHo0X8QKhQLJyckIDAxESkoKOnfujJUrV2LatGl48OABAKB79+5wcXHB\nN998g5CQkCbbtbOzQ3x8vNZ1nA4ODurU3OfOnRMlW15eHgAgOzsbXl5e8PT0RO/evfHdd99h27Zt\nCAoKQp8+fdR9MxitDdMAGFbPiRMnEBoaCjs7O6hUKsyaNQseHh6oq6vD3LlzkZOTA3t7e3h4eKC8\nvBxdu3bFuHHjsHz5cqxatapRe5oHvp6enpg6dSq2bt0KAHj77bexePFi7NmzR333anNotpWbm4uw\nsDB1htdu3bphyJAhmDhxImpra+Ht7Y2uXbsaPyAMhp6wbKAMm+TAgQO4cOECPvjgA3OLwmCYDaYB\nMGyO1atX48SJE1i/fr25RWEwzArTABgMBsNGYSdNDAaDYaOwBYDBYDBsFLYAMBgMho3CFgAGg8Gw\nUdgCwGAwGDYKWwAYDAbDRvl/rNEo9OMigxQAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_times(times):\n", + " plt.style.use('seaborn-whitegrid')\n", + " X = ints(1, len(times[0]) - 2)\n", + " for (label, mark, *Y) in times:\n", + " plt.plot(X, Y, mark, label=label)\n", + " plt.xlabel('Day Number'); plt.ylabel('Minutes to Solve Both Parts')\n", + " plt.legend(loc='upper left')\n", + "\n", + "x = None\n", + "plot_times([\n", + " ('Me', 'd:', 4, 6, 20, 5, 12, 30, 33, 10, 21, 40, 13, 12, 30, 41, 13, 64, 54, 74, 50, 18, 40),\n", + " ('100th', 'v:', 6, 6, 23, 4, 5, 9, 25, 8, 12, 25, 12, 9, 22, 25, 10, 27, 16, 41, 18, 21, 45),\n", + " ('1st', '^:', 1, 1, 4, 1, 2, 3, 10, 3, 4, 6, 3, 2, 6, 5, 2, 5, 5, 10, 5, 7, 10)])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Advent 2017.ipynb b/pytudes/ipynb/Advent 2017.ipynb new file mode 100644 index 0000000..1b5e6de --- /dev/null +++ b/pytudes/ipynb/Advent 2017.ipynb @@ -0,0 +1,3667 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# December 2017: Advent of Code Solutions\n", + "\n", + "Peter Norvig\n", + "\n", + "I'm doing the [Advent of Code](https://adventofcode.com) puzzles, just like [last year](https://github.com/norvig/pytudes/blob/master/ipynb/Advent%20of%20Code.ipynb). This time, my terms of engagement are:\n", + "\n", + "* I won't write a summary of each day's puzzle description. Follow the links in the section headers (e.g. **[Day 1](https://adventofcode.com/2017/day/1)**) to understand what each puzzle is asking. \n", + "* What you see is mostly the algorithm I first came up with first, although sometimes I go back and refactor if I think the original is unclear.\n", + "* I do clean up the code a bit even after I solve the puzzle: adding docstrings, changing variable names, changing input boxes to `assert` statements.\n", + "* I will describe my errors that slowed me down.\n", + "* Some days I start on time and try to code very quickly (although I know that people at the top of the leader board will be much faster than me); other days I end up starting late and don't worry about going quickly.\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "# Day 0: Imports and Utility Functions\n", + "\n", + "I might need these:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Python 3.x Utility Functions\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import re\n", + "import numpy as np\n", + "import math\n", + "import random\n", + "\n", + "from collections import Counter, defaultdict, namedtuple, deque, abc, OrderedDict\n", + "from functools import lru_cache\n", + "from statistics import mean, median, mode, stdev, variance\n", + "from itertools import (permutations, combinations, chain, cycle, product, islice, \n", + " takewhile, zip_longest, count as count_from)\n", + "from heapq import heappop, heappush\n", + "from numba import jit\n", + "\n", + "identity = lambda x: x\n", + "letters = 'abcdefghijklmnopqrstuvwxyz'\n", + "\n", + "cache = lru_cache(None)\n", + "\n", + "cat = ''.join\n", + "\n", + "Ø = frozenset() # Empty set\n", + "inf = float('inf')\n", + "BIG = 10 ** 999\n", + "\n", + "################ Functions for Input, Parsing\n", + "\n", + "def Input(day, year=2017):\n", + " \"Open this day's input file.\"\n", + " return open('data/advent{}/input{}.txt'.format(year, day))\n", + "\n", + "def Inputstr(day, year=2017): \n", + " \"The contents of this day's input file as a str.\"\n", + " return Input(day, year).read().rstrip('\\n')\n", + " \n", + "def Array(lines):\n", + " \"Parse an iterable of str lines into a 2-D array. If `lines` is a str, splitlines.\"\n", + " if isinstance(lines, str): lines = lines.splitlines()\n", + " return mapt(Vector, lines)\n", + "\n", + "def Vector(line):\n", + " \"Parse a str into a tuple of atoms (numbers or str tokens).\"\n", + " return mapt(Atom, line.replace(',', ' ').split())\n", + "\n", + "def Integers(text): \n", + " \"Return a tuple of all integers in a string.\"\n", + " return mapt(int, re.findall(r'-?\\b\\d+\\b', text))\n", + "\n", + "def Atom(token):\n", + " \"Parse a str token into a number, or leave it as a str.\"\n", + " try:\n", + " return int(token)\n", + " except ValueError:\n", + " try:\n", + " return float(token)\n", + " except ValueError:\n", + " return token\n", + " \n", + "def error(err=RuntimeError, *args): raise err(*args)\n", + "\n", + "################ Functions on Iterables\n", + "\n", + "def first(iterable, default=None): \n", + " \"The first item in an iterable, or default if it is empty.\"\n", + " return next(iter(iterable), default)\n", + "\n", + "def first_true(iterable, pred=None, default=None):\n", + " \"\"\"Returns the first true value in the iterable.\n", + " If no true value is found, returns *default*\n", + " If *pred* is not None, returns the first item\n", + " for which pred(item) is true.\"\"\"\n", + " # first_true([a,b,c], default=x) --> a or b or c or x\n", + " # first_true([a,b], fn, x) --> a if fn(a) else b if fn(b) else x\n", + " return next(filter(pred, iterable), default)\n", + "\n", + "def nth(iterable, n, default=None):\n", + " \"Returns the nth item of iterable, or a default value\"\n", + " return next(islice(iterable, n, None), default)\n", + "\n", + "def upto(iterable, maxval):\n", + " \"From a monotonically increasing iterable, generate all the values <= maxval.\"\n", + " # Why <= maxval rather than < maxval? In part because that's how Ruby's upto does it.\n", + " return takewhile(lambda x: x <= maxval, iterable)\n", + "\n", + "def groupby(iterable, key=identity):\n", + " \"Return a dict of {key(item): [items...]} grouping all items in iterable by keys.\"\n", + " groups = defaultdict(list)\n", + " for item in iterable:\n", + " groups[key(item)].append(item)\n", + " return groups\n", + "\n", + "def grouper(iterable, n, fillvalue=None):\n", + " \"\"\"Collect data into fixed-length chunks:\n", + " grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx\"\"\"\n", + " args = [iter(iterable)] * n\n", + " return zip_longest(*args, fillvalue=fillvalue)\n", + "\n", + "def overlapping(iterable, n):\n", + " \"\"\"Generate all (overlapping) n-element subsequences of iterable.\n", + " overlapping('ABCDEFG', 3) --> ABC BCD CDE DEF EFG\"\"\"\n", + " if isinstance(iterable, abc.Sequence):\n", + " yield from (iterable[i:i+n] for i in range(len(iterable) + 1 - n))\n", + " else:\n", + " result = deque(maxlen=n)\n", + " for x in iterable:\n", + " result.append(x)\n", + " if len(result) == n:\n", + " yield tuple(result)\n", + " \n", + "def pairwise(iterable):\n", + " \"s -> (s0,s1), (s1,s2), (s2, s3), ...\"\n", + " return overlapping(iterable, 2)\n", + "\n", + "def sequence(iterable, type=tuple):\n", + " \"Coerce iterable to sequence: leave alone if already a sequence, else make it `type`.\"\n", + " return iterable if isinstance(iterable, abc.Sequence) else type(iterable)\n", + "\n", + "def join(iterable, sep=''):\n", + " \"Join the items in iterable, converting each to a string first.\"\n", + " return sep.join(map(str, iterable))\n", + " \n", + "def powerset(iterable):\n", + " \"Yield all subsets of items.\"\n", + " items = list(iterable)\n", + " for r in range(len(items)+1):\n", + " for c in combinations(items, r):\n", + " yield c\n", + " \n", + "def quantify(ite1rable, pred=bool):\n", + " \"Count how many times the predicate is true.\"\n", + " return sum(map(pred, iterable))\n", + "\n", + "def length(iterable):\n", + " \"Same as len(list(iterable)), but without consuming memory.\"\n", + " return sum(1 for _ in iterable)\n", + "\n", + "def shuffled(iterable):\n", + " \"Create a new list out of iterable, and shuffle it.\"\n", + " new = list(iterable)\n", + " random.shuffle(new)\n", + " return new\n", + " \n", + "flatten = chain.from_iterable\n", + "\n", + "def repeat(n, fn, arg):\n", + " \"Repeat arg=fn(arg) n times.\"\n", + " for i in range(n):\n", + " arg = fn(arg)\n", + " return arg\n", + "\n", + "################ Making immutable objects\n", + " \n", + "class Set(frozenset):\n", + " \"A frozenset, but with a prettier printer.\"\n", + " def __repr__(self): return '{' + join(sorted(self), ', ') + '}'\n", + " \n", + "def canon(items, typ=None):\n", + " \"Canonicalize these order-independent items into a hashable canonical form.\"\n", + " typ = typ or (cat if isinstance(items, str) else tuple)\n", + " return typ(sorted(items))\n", + "\n", + "def mapt(fn, *args): \n", + " \"Do a map, and make the results into a tuple.\"\n", + " return tuple(map(fn, *args))\n", + " \n", + "################ Math Functions\n", + " \n", + "def transpose(matrix): return tuple(zip(*matrix))\n", + "\n", + "def isqrt(n):\n", + " \"Integer square root (rounds down).\"\n", + " return int(n ** 0.5)\n", + "\n", + "def ints(start, end):\n", + " \"The integers from start to end, inclusive: range(start, end+1)\"\n", + " return range(start, end + 1)\n", + "\n", + "def floats(start, end, step=1.0):\n", + " \"Yield floats from start to end (inclusive), by increments of step.\"\n", + " m = (1.0 if step >= 0 else -1.0)\n", + " while start * m <= end * m:\n", + " yield start\n", + " start += step\n", + " \n", + "def multiply(numbers):\n", + " \"Multiply all the numbers together.\"\n", + " result = 1\n", + " for n in numbers:\n", + " result *= n\n", + " return result\n", + "\n", + "import operator as op\n", + "\n", + "operations = {'>': op.gt, '>=': op.ge, '==': op.eq,\n", + " '<': op.lt, '<=': op.le, '!=': op.ne,\n", + " '+': op.add, '-': op.sub, '*': op.mul, \n", + " '/': op.truediv, '**': op.pow}\n", + "\n", + "################ 2-D points implemented using (x, y) tuples\n", + "\n", + "def X(point): x, y = point; return x\n", + "def Y(point): x, y = point; return y\n", + "\n", + "origin = (0, 0)\n", + "UP, DOWN, LEFT, RIGHT = (0, 1), (0, -1), (-1, 0), (1, 0)\n", + "\n", + "def neighbors4(point): \n", + " \"The four neighboring squares.\"\n", + " x, y = point\n", + " return ( (x, y-1),\n", + " (x-1, y), (x+1, y), \n", + " (x, y+1))\n", + "\n", + "def neighbors8(point): \n", + " \"The eight neighboring squares.\"\n", + " x, y = point \n", + " return ((x-1, y-1), (x, y-1), (x+1, y-1),\n", + " (x-1, y), (x+1, y),\n", + " (x-1, y+1), (x, y+1), (x+1, y+1))\n", + "\n", + "def cityblock_distance(P, Q=origin): \n", + " \"Manhatten distance between two points.\"\n", + " return sum(abs(p - q) for p, q in zip(P, Q))\n", + "\n", + "def distance(P, Q=origin): \n", + " \"Hypotenuse distance between two points.\"\n", + " return sum((p - q) ** 2 for p, q in zip(P, Q)) ** 0.5\n", + "\n", + "################ Debugging \n", + "\n", + "def trace1(f):\n", + " \"Print a trace of the input and output of a function on one line.\"\n", + " def traced_f(*args):\n", + " result = f(*args)\n", + " print('{}({}) = {}'.format(f.__name__, ', '.join(map(str, args)), result))\n", + " return result\n", + " return traced_f\n", + "\n", + "def grep(pattern, iterable):\n", + " \"Print lines from iterable that match pattern.\"\n", + " for line in iterable:\n", + " if re.search(pattern, line):\n", + " print(line)\n", + " \n", + "class Struct:\n", + " \"A structure that can have any fields defined.\"\n", + " def __init__(self, **entries): self.__dict__.update(entries)\n", + " def __repr__(self): \n", + " fields = ['{}={}'.format(f, self.__dict__[f]) \n", + " for f in sorted(self.__dict__)]\n", + " return 'Struct({})'.format(', '.join(fields))\n", + "\n", + "################ A* and Breadth-First Search (tracking states, not actions)\n", + "\n", + "def always(value): return (lambda *args: value)\n", + "\n", + "def Astar(start, moves_func, h_func, cost_func=always(1)):\n", + " \"Find a shortest sequence of states from start to a goal state (where h_func(s) == 0).\"\n", + " frontier = [(h_func(start), start)] # A priority queue, ordered by path length, f = g + h\n", + " previous = {start: None} # start state has no previous state; other states will\n", + " path_cost = {start: 0} # The cost of the best path to a state.\n", + " Path = lambda s: ([] if (s is None) else Path(previous[s]) + [s])\n", + " while frontier:\n", + " (f, s) = heappop(frontier)\n", + " if h_func(s) == 0:\n", + " return Path(s)\n", + " for s2 in moves_func(s):\n", + " g = path_cost[s] + cost_func(s, s2)\n", + " if s2 not in path_cost or g < path_cost[s2]:\n", + " heappush(frontier, (g + h_func(s2), s2))\n", + " path_cost[s2] = g\n", + " previous[s2] = s\n", + "\n", + "def bfs(start, moves_func, goals):\n", + " \"Breadth-first search\"\n", + " goal_func = (goals if callable(goals) else lambda s: s in goals)\n", + " return Astar(start, moves_func, lambda s: (0 if goal_func(s) else 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " # Functions for Input, Parsing\n", + " assert Array('''1 2 3\n", + " 4 5 6''') == ((1, 2, 3), \n", + " (4, 5, 6))\n", + " assert Vector('testing 1 2 3.') == ('testing', 1, 2, 3.0)\n", + " \n", + " # Functions on Iterables\n", + " assert first('abc') == first(['a', 'b', 'c']) == 'a'\n", + " assert first_true([0, None, False, {}, 42, 43]) == 42\n", + " assert nth('abc', 1) == nth(iter('abc'), 1) == 'b'\n", + " assert cat(upto('abcdef', 'd')) == 'abcd'\n", + " assert cat(['do', 'g']) == 'dog'\n", + " assert groupby([-3, -2, -1, 1, 2], abs) == {1: [-1, 1], 2: [-2, 2], 3: [-3]}\n", + " assert list(grouper(range(8), 3)) == [(0, 1, 2), (3, 4, 5), (6, 7, None)]\n", + " assert list(overlapping((0, 1, 2, 3, 4), 3)) == [(0, 1, 2), (1, 2, 3), (2, 3, 4)]\n", + " assert list(overlapping('abcdefg', 4)) == ['abcd', 'bcde', 'cdef', 'defg'] \n", + " assert list(pairwise((0, 1, 2, 3, 4))) == [(0, 1), (1, 2), (2, 3), (3, 4)]\n", + " assert sequence('seq') == 'seq'\n", + " assert sequence((i**2 for i in range(5))) == (0, 1, 4, 9, 16)\n", + " assert join(range(5)) == '01234'\n", + " assert join(range(5), ', ') == '0, 1, 2, 3, 4'\n", + " assert multiply([1, 2, 3, 4]) == 24\n", + " assert transpose(((1, 2, 3), (4, 5, 6))) == ((1, 4), (2, 5), (3, 6))\n", + " assert isqrt(9) == 3 == isqrt(10)\n", + " assert ints(1, 100) == range(1, 101)\n", + " assert identity('anything') == 'anything'\n", + " assert set(powerset({1, 2, 3})) == {\n", + " (), (1,), (1, 2), (1, 2, 3), (1, 3), (2,), (2, 3), (3,)}\n", + " assert quantify(['testing', 1, 2, 3, int, len], callable) == 2 # int and len are callable\n", + " assert quantify([0, False, None, '', [], (), {}, 42]) == 1 # Only 42 is truish\n", + " assert set(shuffled('abc')) == set('abc')\n", + " assert canon('abecedarian') == 'aaabcdeeinr'\n", + " assert canon([9, 1, 4]) == canon({1, 4, 9}) == (1, 4, 9)\n", + " assert mapt(math.sqrt, [1, 9, 4]) == (1, 3, 2)\n", + " \n", + " # Math\n", + " assert transpose([(1, 2, 3), (4, 5, 6)]) == ((1, 4), (2, 5), (3, 6))\n", + " assert isqrt(10) == isqrt(9) == 3\n", + " assert ints(1, 5) == range(1, 6)\n", + " assert list(floats(1, 5)) == [1., 2., 3., 4., 5.]\n", + " assert multiply(ints(1, 10)) == math.factorial(10) == 3628800\n", + " \n", + " # 2-D points\n", + " P = (3, 4)\n", + " assert X(P) == 3 and Y(P) == 4\n", + " assert cityblock_distance(P) == cityblock_distance(P, origin) == 7\n", + " assert distance(P) == distance(P, origin) == 5\n", + " \n", + " # Search\n", + " assert Astar((4, 4), neighbors8, distance) == [(4, 4), (3, 3), (2, 2), (1, 1), (0, 0)]\n", + " assert bfs((4, 4), neighbors8, {origin}) == [(4, 4), (3, 3), (2, 2), (1, 1), (0, 0)]\n", + " forty2 = always(42)\n", + " assert forty2() == forty2('?') == forty2(4, 2) == 42\n", + "\n", + " return 'pass'\n", + "\n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 1](https://adventofcode.com/2017/day/1): Inverse Captcha\n", + "\n", + "This was easier than I remember last year's puzzles being:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2014, (3, 2, 9, 4, 1, 9, 9, 4, 7, 1))" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "digits = mapt(int, Inputstr(1))\n", + "N = len(digits)\n", + "\n", + "N, digits[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1158" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(digits[i] \n", + " for i in range(N) \n", + " if digits[i] == digits[i - 1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1132" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(digits[i] \n", + " for i in range(N) \n", + " if digits[i] == digits[i - N // 2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 2](https://adventofcode.com/2017/day/2): Corruption Checksum\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "rows2 = Array('''790\t99\t345\t1080\t32\t143\t1085\t984\t553\t98\t123\t97\t197\t886\t125\t947\n", + "302\t463\t59\t58\t55\t87\t508\t54\t472\t63\t469\t419\t424\t331\t337\t72\n", + "899\t962\t77\t1127\t62\t530\t78\t880\t129\t1014\t93\t148\t239\t288\t357\t424\n", + "2417\t2755\t254\t3886\t5336\t3655\t5798\t3273\t5016\t178\t270\t6511\t223\t5391\t1342\t2377\n", + "68\t3002\t3307\t166\t275\t1989\t1611\t364\t157\t144\t3771\t1267\t3188\t3149\t156\t3454\n", + "1088\t1261\t21\t1063\t1173\t278\t1164\t207\t237\t1230\t1185\t431\t232\t660\t195\t1246\n", + "49\t1100\t136\t1491\t647\t1486\t112\t1278\t53\t1564\t1147\t1068\t809\t1638\t138\t117\n", + "158\t3216\t1972\t2646\t3181\t785\t2937\t365\t611\t1977\t1199\t2972\t201\t2432\t186\t160\n", + "244\t86\t61\t38\t58\t71\t243\t52\t245\t264\t209\t265\t308\t80\t126\t129\n", + "1317\t792\t74\t111\t1721\t252\t1082\t1881\t1349\t94\t891\t1458\t331\t1691\t89\t1724\n", + "3798\t202\t3140\t3468\t1486\t2073\t3872\t3190\t3481\t3760\t2876\t182\t2772\t226\t3753\t188\n", + "2272\t6876\t6759\t218\t272\t4095\t4712\t6244\t4889\t2037\t234\t223\t6858\t3499\t2358\t439\n", + "792\t230\t886\t824\t762\t895\t99\t799\t94\t110\t747\t635\t91\t406\t89\t157\n", + "2074\t237\t1668\t1961\t170\t2292\t2079\t1371\t1909\t221\t2039\t1022\t193\t2195\t1395\t2123\n", + "8447\t203\t1806\t6777\t278\t2850\t1232\t6369\t398\t235\t212\t992\t7520\t7304\t7852\t520\n", + "3928\t107\t3406\t123\t2111\t2749\t223\t125\t134\t146\t3875\t1357\t508\t1534\t4002\t4417''')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "46402" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(abs(max(row) - min(row)) for row in rows2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "265" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def evendiv(row): \n", + " return first(a // b for a in row for b in row if a > b and a // b == a / b)\n", + "\n", + "sum(map(evendiv, rows2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This day was also very easy. It was nice that my pre-defined `array` function did the whole job of parsing the input. In Part One, I was slowed down by a typo: I had `\"=\"` instead of `\"-\"` in `\"max(row) - min(row)\"`. I was confused by Python's misleading error message, which said `\"SyntaxError: keyword can't be an expression\"`. Later on, Alex Martelli explained to me that the message meant that in `abs(max(row)=...)` it thought that `max(row)` was a keyword argument to `abs`, as in `abs(x=-1)`.\n", + "\n", + "In Part Two, note that to check that `a/b` is an exact integer, I used `a // b == a / b`, which I think is more clear than the marginally-faster expression one would typically use here, `a % b == 0`, which requires you to think about two things: division and the modulus operator (is it `a % b` or `b % a`?)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 3](https://adventofcode.com/2017/day/3): Spiral Memory\n", + "\n", + "For today the data is just one number:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "M = 277678" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This puzzle takes some thinking, not just fast typing. I decided to break the problem into three parts:\n", + "- Generate a spiral (by writing a new function called `spiral`).\n", + "- Find the Nth square on the spiral (with my function `nth`).\n", + "- Find the distance from that square to the center (with my function `cityblock_distance`).\n", + "\n", + "I suspect many people will do all three of these in one function. That's probably the best way to get the answer really quickly, but I'd rather be clear than quick (and I'm anticipating that `spiral` will come in handy in Part Two), so I'll factor out each part, obeying the *single responsibility principle*. \n", + "\n", + "Now I need to make `spiral()` generate the coordinates of squares on an infinite spiral, in order, going out from the center square, `(0, 0)`. After the center square, the spiral goes 1 square right, then 1 square up, then 2 square left, then 2 square down, thus completing one revolution; then it does subsequent revolutions. In general if the previous revolution ended with *s* squares down, then the next revolution consists of *s*+1 squares right, *s*+1 squares up, *s*+2 squares left and *s*+2 down. A small test confirms that this matches the example diagram in the puzzle description (although I had a bug on my first try because I only incremented `s` once per revolution, not twice):" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0, 0),\n", + " (0, 1),\n", + " (-1, 1),\n", + " (-1, 0),\n", + " (-1, -1),\n", + " (0, -1),\n", + " (1, -1),\n", + " (1, 0),\n", + " (1, 1),\n", + " (1, 2)]" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def spiral():\n", + " \"Yield successive (x, y) coordinates of squares on a spiral.\"\n", + " x = y = s = 0 # (x, y) is the position; s is the side length.\n", + " yield (x, y)\n", + " while True:\n", + " for (dx, dy) in (RIGHT, UP, LEFT, DOWN):\n", + " if dy: s += 1 # Increment side length before RIGHT and LEFT\n", + " for _ in range(s):\n", + " x += dx; y += dy\n", + " yield (x, y)\n", + "\n", + "list(islice(spiral(), 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can find the `N`th square. As this is Python, indexes start at 0, whereas the puzzle description starts counting at 1, so I have to subtract 1. Then I can find the distance to the origin:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(263, 212)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nth(spiral(), M - 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "475" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cityblock_distance(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For **Part Two** I can re-use my `spiral` generator, yay! Here's a function to sum the neighboring squares (I can use my `neighbors8` function, yay!):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def spiralsums():\n", + " \"Yield the values of a spiral where each square has the sum of the 8 neighbors.\"\n", + " value = defaultdict(int)\n", + " for p in spiral():\n", + " value[p] = sum(value[q] for q in neighbors8(p)) or 1\n", + " yield value[p]" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 1, 2, 4, 5, 10, 11, 23, 25, 26, 54, 57]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(islice(spiralsums(), 12))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looks good, so let's get the answer:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "279138" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "first(x for x in spiralsums() if x > M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 4](https://adventofcode.com/2017/day/4): High-Entropy Passphrases\n", + "\n", + "This is the first time I will have to store an input file and read it with the function `Input`. It should be straightforward, though:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "337" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def is_valid(line): return is_unique(line.split())\n", + "\n", + "def is_unique(items): return len(items) == len(set(items))\n", + "\n", + "quantify(Input(4), is_valid)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "231" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def is_valid2(line): return is_unique(mapt(canon, line.split()))\n", + "\n", + "quantify(Input(4), is_valid2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy, and I started on time, but the leaders were still three times faster than me!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 5](https://adventofcode.com/2017/day/5): A Maze of Twisty Trampolines, All Alike\n", + "\n", + "Let's first make sure we can read the data/program okay:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 2, 0, 0, -2, -2, -1, -4, -5, -6)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program = mapt(int, Input(5))\n", + "\n", + "program[:10]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I'll make a little interpreter, `run`, which takes a program, loads it into memory,\n", + " and executes the instruction, maintaining a program counter, `pc`, and doing the incrementing/branching as described in the puzzle,\n", + "until the program counter no longer points to a location in memory:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "364539" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run(program):\n", + " memory = list(program)\n", + " pc = steps = 0\n", + " M = len(memory)\n", + " while 0 <= pc < M:\n", + " steps += 1\n", + " oldpc = pc\n", + " pc += memory[pc]\n", + " memory[oldpc] += 1\n", + " return steps\n", + " \n", + "run(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "Part Two seems tricky, so I'll include an optional argument, `verbose`, and check if the printout it produces matches the example in the puzzle description:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 0 [1, 3, 0, 1, -3]\n", + "2 1 [2, 3, 0, 1, -3]\n", + "3 4 [2, 2, 0, 1, -3]\n", + "4 1 [2, 2, 0, 1, -2]\n", + "5 3 [2, 3, 0, 1, -2]\n", + "6 4 [2, 3, 0, 2, -2]\n", + "7 2 [2, 3, 0, 2, -1]\n", + "8 2 [2, 3, 1, 2, -1]\n", + "9 3 [2, 3, 2, 2, -1]\n", + "10 5 [2, 3, 2, 3, -1]\n" + ] + }, + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run2(program, verbose=False):\n", + " memory = list(program)\n", + " pc = steps = 0\n", + " M = len(memory)\n", + " while 0 <= pc < M:\n", + " steps += 1\n", + " oldpc = pc\n", + " pc += memory[pc]\n", + " memory[oldpc] += (-1 if memory[oldpc] >= 3 else 1)\n", + " if verbose: print(steps, pc, memory)\n", + " return steps\n", + " \n", + "run2([0, 3, 0, 1, -3], True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks right, so I can solve the puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 6.2 s, sys: 8.37 ms, total: 6.21 s\n", + "Wall time: 6.21 s\n" + ] + }, + { + "data": { + "text/plain": [ + "27477714" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time run2(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Thanks to [Clement Sreeves](https://github.com/ClementSreeves) for the suggestion of making a distinction between the `program` and the `memory`. In my first version, `run` would mutate the argument, which was OK for a short exercise, but not best practice for a reliable API. And thanks to [Max Albert](https://github.com/maxalbert) for speeding up the loop by pulling the `len(memory)` out of the loop." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 6](https://adventofcode.com/2017/day/6): Memory Reallocation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I had to read the puzzle description carefully, but then it is pretty clear what to do. I'll keep a set of previously seen configurations, which will all be tuples. But in the function `spread`, I want to mutate the configuration of banks, so I will convert to a list at the start, then convert back to a tuple at the end." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "banks = Vector('4\t10\t4\t1\t8\t4\t9\t14\t5\t1\t14\t15\t0\t15\t3\t5')\n", + "\n", + "def realloc(banks):\n", + " \"How many cycles until we reach a configuration we've seen before?\"\n", + " seen = {banks}\n", + " for cycles in count_from(1):\n", + " banks = spread(banks)\n", + " if banks in seen:\n", + " return cycles\n", + " seen.add(banks)\n", + " \n", + "def spread(banks):\n", + " \"Find the area with the most blocks, and spread them evenly to following areas.\"\n", + " banks = list(banks)\n", + " maxi = max(range(len(banks)), key=lambda i: banks[i])\n", + " blocks = banks[maxi]\n", + " banks[maxi] = 0\n", + " for i in range(maxi + 1, maxi + 1 + blocks):\n", + " banks[i % len(banks)] += 1\n", + " return tuple(banks)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(2, 4, 1, 2)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spread((0, 2, 7, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc((0, 2, 7, 0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These tests look good; let's solve the problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12841" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc(banks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:** Here I will just replace the `set` of `seen` banks with a `dict` of `{bank: cycle_number}`; everything else is the same, and the final result is the current cycle number minus the cycle number of the previously-seen tuple of banks." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def realloc2(banks):\n", + " \"When we hit a cycle, what is the length of the cycle?\"\n", + " seen = {banks: 0}\n", + " for cycles in count_from(1):\n", + " banks = spread(banks)\n", + " if banks in seen:\n", + " return cycles - seen[banks]\n", + " seen[banks] = cycles\n", + "\n", + "realloc2((0, 2, 7, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8038" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "realloc2(banks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 7](https://adventofcode.com/2017/day/7): Recursive Circus" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First I'll read the data into two dicts as follows: the input line:\n", + "\n", + " tcmdaji (40) -> wjbdxln, amtqhf\n", + " \n", + "creates:\n", + "\n", + " weight['tcmdaji'] = 40\n", + " above['tcmdaji'] = ['wjbdxln', 'amtqhf']" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def towers(lines):\n", + " \"Return (weight, above) dicts.\"\n", + " weight = {}\n", + " above = {}\n", + " for line in lines:\n", + " name, w, *rest = re.findall(r'\\w+', line)\n", + " weight[name] = int(w)\n", + " above[name] = set(rest)\n", + " return weight, above\n", + "\n", + "weight, above = towers(Input(7))\n", + "\n", + "programs = set(above)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the root progam is the one that is not above anything:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'wiapj'}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "programs - set(flatten(above.values()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "A program is *wrong* if it is the bottom of a tower that is a different weight from all its sibling towers:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def wrong(p): return tower_weight(p) not in map(tower_weight, siblings(p))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we define `tower_weight`, `siblings`, and the `below` dict:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def tower_weight(p): \n", + " \"Total weight for the tower whose root (bottom) is p.\"\n", + " return weight[p] + sum(map(tower_weight, above[p]))\n", + "\n", + "def siblings(p): \n", + " \"The other programs at the same level as this one.\"\n", + " if p not in below:\n", + " return Ø # the root has no siblings\n", + " else:\n", + " return above[below[p]] - {p}\n", + "\n", + "below = {a: b for b in programs for a in above[b]}" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'eionkb', 'lsire', 'wiapj', 'ycpcv'}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(filter(wrong, programs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So these four programs are wrong. Which one should we correct? The one that is wrong, and has no wrong program above it:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'eionkb'" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def wrongest(programs):\n", + " return first(p for p in programs\n", + " if wrong(p) \n", + " and not any(wrong(p2) for p2 in above[p]))\n", + "\n", + "wrongest(programs) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now what should we correct it to? To the weight that makes it the same weight as the sibling towers:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1072" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def correct(p):\n", + " \"Return the weight that would make p's tower's weight the same as its sibling towers.\"\n", + " delta = tower_weight(first(siblings(p))) - tower_weight(p) \n", + " return weight[p] + delta\n", + "\n", + "correct(wrongest(programs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 8](https://adventofcode.com/2017/day/8): Memory Reallocation \n", + "\n", + "This one looks easy: a simple interpreter for straight-line code where each instruction has 7 tokens. It is nice that my `Array` function parses the whole program." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6828" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program8 = Array(Input(8))\n", + "\n", + "def run8(program):\n", + " \"Run the program and return final value of registers.\"\n", + " registers = defaultdict(int)\n", + " for (r, inc, delta, _if, r2, cmp, amount) in program:\n", + " if operations[cmp](registers[r2], amount):\n", + " registers[r] += delta * (+1 if inc == 'inc' else -1)\n", + " return registers\n", + "\n", + "max(run8(program8).values())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "Here I modify the interpreter to keep track of the highest value of any register at any time." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7234" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run8_2(program):\n", + " registers = defaultdict(int)\n", + " highest = 0\n", + " for (r, inc, delta, _if, r2, cmp, amount) in program:\n", + " if operations[cmp](registers[r2], amount):\n", + " registers[r] += delta * (+1 if inc == 'inc' else -1)\n", + " highest = max(highest, registers[r])\n", + " return highest\n", + "\n", + "run8_2(program8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 9](https://adventofcode.com/2017/day/9): Stream Processing\n", + "\n", + "For this problem I could have a single finite-state machine that handles all five magic characters, `'{}'`, but I think it is easier to first clean up the garbage, using regular expressions:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'{{{{{{{},},{{},}},{{{{}},{{{{{}}},{}},},{{{{},{,{{{}}}}},},{{{}},{{}}}'" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text1 = re.sub(r'!.', '', Inputstr(9)) # Delete canceled characters\n", + "text2 = re.sub(r'<.*?>', '', text1) # Delete garbage\n", + "\n", + "text2[:70]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can deal with the nested braces (which can't be handled with regular expressions). The puzzle says \"*Each group is assigned a score which is one more than the score of the group that immediately contains it,*\" which is the same as saying that a group's score is its nesting level, a quantity that increases with each open-brace character, and decreases with each close-brace:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "9662" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def total_score(text):\n", + " \"Total of group scores; each group scores one more than the group it is nested in.\"\n", + " total = 0\n", + " level = 0 # Level of nesting\n", + " for c in text:\n", + " if c == '{':\n", + " level += 1\n", + " total += level\n", + " elif c == '}':\n", + " level -= 1\n", + " return total\n", + "\n", + "total_score(text2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two:**\n", + "\n", + "At first I thought that the amount of garbage is just the difference in lengths of `text2` and `text3`:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5989" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(text1) - len(text2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this turned out to be wrong; it counts the angle brackets themselves s being deleted, whereas the puzzle is actually asking how many character between the angle brackets are deleted. So that would be:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4903" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text3 = re.sub(r'<.*?>', '<>', text1) # Delete garbage inside brackets, but not brackets\n", + "\n", + "len(text1) - len(text3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 10](https://adventofcode.com/2017/day/10): Stream Processing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I have to do a bunch of reversals of substrings of `stream`. It looks complicated so I will include a `verbose` argument to `knothash` and confirm it works on the example puzzle. I break out the reversal into a separate function, `rev`. The way I handle reversal interacting with wraparound is that I first move all the items before the reversal position to the end of the list, then I do the reversal, then I move them back." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "stream = (63,144,180,149,1,255,167,84,125,65,188,0,2,254,229,24)\n", + "\n", + "def knothash(lengths, N=256, verbose=False):\n", + " \"Do a reversal for each of the numbers in `lengths`.\"\n", + " nums = list(range(N))\n", + " pos = skip = 0\n", + " for L in lengths:\n", + " nums = rev(nums, pos, L)\n", + " if verbose: print(nums)\n", + " pos = (pos + L + skip) % N\n", + " skip += 1\n", + " return nums[0] * nums[1]\n", + " \n", + "def rev(nums, pos, L):\n", + " \"Reverse nums[pos:pos+L], handling wrap-around.\"\n", + " # Move first pos elements to end, reverse first L, move pos elements back\n", + " nums = nums[pos:] + nums[:pos]\n", + " nums[:L] = reversed(nums[:L])\n", + " nums = nums[-pos:] + nums[:-pos]\n", + " return nums" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reverse [0, 1, 2]:\n", + "assert rev(list(range(5)), 0, 3) == [2, 1, 0, 3, 4]" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# Reverse [4, 0, 1], wrapping around:\n", + "assert rev(list(range(5)), 4, 3) == [0, 4, 2, 3, 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 1, 0, 3, 4]\n", + "[4, 3, 0, 1, 2]\n", + "[4, 3, 0, 1, 2]\n", + "[3, 4, 2, 1, 0]\n" + ] + } + ], + "source": [ + "# Duplicate the example output\n", + "assert knothash((3, 4, 1, 5), N=5, verbose=True) == 12" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's correct, but the first time through I got it wrong because I forgot the `\"% N\"` on the update of `pos`." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4480" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "knothash(stream)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**:\n", + "\n", + "Now it gets *really* complicated: string processing, the suffix, hex string output, and dense hashing. But just take them one at a time:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'c500ffe015c83b60fad2e4b7d59dabc4'" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stream2 = '63,144,180,149,1,255,167,84,125,65,188,0,2,254,229,24'\n", + "\n", + "def knothash2(lengthstr, N=256, rounds=64, suffix=(17, 31, 73, 47, 23),\n", + " verbose=False):\n", + " \"Do a reversal for each length; repeat `rounds` times.\"\n", + " nums = list(range(N))\n", + " lengths = mapt(ord, lengthstr) + suffix\n", + " pos = skip = 0\n", + " for round in range(rounds):\n", + " for L in lengths:\n", + " nums = rev(nums, pos, L)\n", + " if verbose: print(nums)\n", + " pos = (pos + L + skip) % N\n", + " skip += 1\n", + " return hexstr(dense_hash(nums))\n", + "\n", + "def hexstr(nums): \n", + " \"Convert a sequence of (0 to 255) ints into a hex str.\"\n", + " return cat(map('{:02x}'.format, nums))\n", + " \n", + "def dense_hash(nums, blocksize=16): \n", + " \"XOR each block of nums, return the list of them.\"\n", + " return [XOR(block) for block in grouper(nums, blocksize)]\n", + "\n", + "def XOR(nums):\n", + " \"Exclusive-or all the numbers together.\"\n", + " result = 0\n", + " for n in nums:\n", + " result ^= n\n", + " return result\n", + " \n", + "assert XOR([65, 27, 9, 1, 4, 3, 40, 50, 91, 7, 6, 0, 2, 5, 68, 22]) == 64\n", + "assert hexstr([255, 0, 17]) == 'ff0011'\n", + "\n", + "assert knothash2('') == 'a2582a3a0e66e6e86e3812dcb672a272'\n", + "\n", + "knothash2(stream2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I had a bug: originally I used `'{:x}'` as the format instead of `'{:02x}'`; the later correctly formats `0` as `'00'`, not `'0'`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 11](https://adventofcode.com/2017/day/11): Hex Ed\n", + "\n", + "The first thing I did was search [`[hex coordinates]`](https://www.google.com/search?source=hp&ei=Ft4xWoOqKcy4jAOs76a4CQ&q=hex+coordinates), and the #1 result (as I expected) was Amit Patel's \"[Hexagonal Grids](https://www.redblobgames.com/grids/hexagons/)\" page. I chose his \"odd-q vertical layout\" to define the six directions as (dx, dy) deltas:" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "directions6 = dict(n=(0, -1), ne=(1, 0), se=(1, 1), s=(0, 1), sw=(-1, 0), nw=(-1, -1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can read the path, follow it, and see where it ends up. If the end point is `(x, y)`, then it will take `max(abs(x), abs(y))` steps to get back to the origin, because each step can increment or decrement either `x` or `y` or both." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "705" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path = Vector(Inputstr(11))\n", + "\n", + "def follow(path):\n", + " \"Follow each step of the path; return final distance to origin.\"\n", + " x, y = (0, 0)\n", + " for (dx, dy) in map(directions6.get, path):\n", + " x += dx; y += dy\n", + " return max(abs(x), abs(y))\n", + "\n", + "follow(path)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This one seemed so easy that I didn't bother testing it on the simple examples in the puzzle; all I did was confirm that the answer for my puzzle input was correct.\n", + "\n", + "**Part Two:**\n", + "\n", + "This looks pretty easy; repeat Part One, but keep track of the maximum number of steps we get from the origin at any point in the path:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1469" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def follow2(path):\n", + " \"Follow each step of the path; return max steps to origin.\"\n", + " x = y = maxsteps = 0\n", + " for (dx, dy) in map(directions6.get, path):\n", + " x += dx; y += dy\n", + " maxsteps = max(maxsteps, abs(x), abs(y))\n", + " return maxsteps\n", + "\n", + "follow2(path)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, no tests, just the final answer.\n", + "\n", + "# [Day 12](https://adventofcode.com/2017/day/12): Digital Plumber\n", + "\n", + "First I'll parse the data, creating a dict of `{program: direct_group_of_programs}`:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def groups(lines):\n", + " \"Dict of {i: {directly_connected_to_i}\"\n", + " return {lhs: {lhs} | set(rhs)\n", + " for (lhs, _, *rhs) in Array(lines)}\n", + " \n", + "assert groups(Input(12))[0] == {0, 659, 737}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks good. I recognize this as a [Union-Find](https://en.wikipedia.org/wiki/Disjoint-set_data_structure) problem, for which there are efficient algorithms. But for this small example, I don't need efficiency, I need clarity and simplicity. So I'll write `merge` to take a dict and merge together the sets that are connected:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def merge(G):\n", + " \"Merge all indirectly connected groups together.\"\n", + " for i in G:\n", + " for j in list(G[i]):\n", + " if G[i] != G[j]:\n", + " G[i].update(G[j])\n", + " G[j] = G[i]\n", + " return G\n", + "\n", + "G = merge(groups(Input(12)))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "115" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(G[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the answer for Part One.\n", + "\n", + "**Part Two**\n", + "\n", + "I did almost all the work; I just need to count the number of distinct groups. That's a set of sets, and regular `set`s are not hashable, so I use my `Set` class:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "221" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len({Set(G[i]) for i in G})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 13](https://adventofcode.com/2017/day/13): Packet Scanners\n", + "\n", + "First thing: The puzzle says the data is *depth: range*, but `range` has a meaning in Python, so I'll use the term *width* instead.\n", + "\n", + "Second thing: I misread the puzzle description and mistakenly thought the scanners were going in a circular route,\n", + "so that they'd be at the top at any time that is 0 mod *width*. That gave the wrong answer and I realized the scanners are actually going back-and-forth, so with a width of size *n*, it takes *n* - 1 steps to get to the bottom, and *n* - 1 steps to get back to the top, so the scanner will be \n", + "at the top at times that are multiples of 2(*n* - 1). For example, with width 3, that would be times 0, 4, 8, ... " + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def trip_severity(scanners): \n", + " \"The sum of sevrities for each time the packet is caught.\"\n", + " return sum((d * w if caught(d, w) else 0) \n", + " for (d, w) in scanners)\n", + "\n", + "def caught(depth, width):\n", + " \"Does the scanner at this depth/width catch the packet?\"\n", + " return depth % (2 * (width - 1)) == 0\n", + "\n", + "example = ((0, 3), (1, 2), (4, 4), (6, 4))\n", + "assert trip_severity(example) == 24" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 3), (1, 2), (2, 4), (4, 6), (6, 4))" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scanners = mapt(Integers, Input(13))\n", + "scanners[:5]" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1504" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "trip_severity(scanners)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "A packet is safe if no scanner catches it. We now have the possibility of a delay, so I update `caught` to allow for an optional delay, and define `safe_delay`: " + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def caught(depth, width, delay=0):\n", + " \"Does the scanner at this depth/width catch the packet with this delay?\"\n", + " return (depth + delay) % (2 * (width - 1)) == 0 \n", + "\n", + "def safe_delay(scanners):\n", + " \"Find the first delay such that no scanner catches the packet.\"\n", + " safe = lambda delay: not any(caught(d, w, delay) for (d, w) in scanners)\n", + " return first(filter(safe, count_from(0)))\n", + "\n", + "safe_delay(example)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3823370" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "safe_delay(scanners)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 14](https://adventofcode.com/2017/day/14): Disk Defragmentation\n", + "\n", + "I found this puzzle description confusing: are they talking about what I call `knothash`, or is it `knothash2`? I decided for the latter, which turned out to be right:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "key = 'ljoxqyyw'" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8316" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def bits(key, i):\n", + " \"The bits in the hash of this key with this row number.\"\n", + " hash = knothash2(key + '-' + str(i))\n", + " return format(int(hash, base=16), '0128b')\n", + "\n", + "sum(bits(key, i).count('1') for i in range(128))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "So as not to worry about running off the edge of the grid, I'll surround the grid with `'0'` bits:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Grid(key, N=128+2):\n", + " \"Make a grid, with a border around it.\"\n", + " return border('0', (list(bits(key, i)) for i in range(128)))\n", + "\n", + "def border(fill, grid):\n", + " \"Surround a grid with a border of fill cells.\"\n", + " rows = [[fill] + list(row) + [fill] \n", + " for row in grid]\n", + " empty = [fill] * len(rows[0])\n", + " return [empty] + rows + [empty]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To find a region, start at some `(x, y)` position and [flood fill](https://en.wikipedia.org/wiki/Flood_fill) to neighbors that have the same value (a `'1'` bit)." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def flood(grid, x, y, val, R):\n", + " \"For all cells with value val connected to grid[x][y], give them region number R.\"\n", + " if grid[y][x] == val:\n", + " grid[y][x] = R\n", + " for x2, y2 in neighbors4((x, y)):\n", + " flood(grid, x2, y2, val, R)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def flood_all(grid, val='1'):\n", + " \"Label all regions with consecutive ints starting at 1.\"\n", + " R = 0 # R is the region number\n", + " for y in range(1, len(grid) - 1):\n", + " for x in range(1, len(grid) - 1):\n", + " if grid[y][x] == val:\n", + " R += 1\n", + " flood(grid, x, y, val, R)\n", + " return R " + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1074" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "flood_all(Grid(key))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 15](https://adventofcode.com/2017/day/15): Dueling Generators\n", + "\n", + "My personalized inputs for this puzzle are `516` and `190`; the other numbers are shared by all puzzle-solvers. I decided to make infinite generators of numbers, using `gen`:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15.1 s, sys: 26.4 ms, total: 15.1 s\n", + "Wall time: 15.2 s\n" + ] + }, + { + "data": { + "text/plain": [ + "597" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@jit # This was the slowest solution; @jit helps a bit.\n", + "def gen(prev, factor, m=2147483647):\n", + " \"Generate a sequence of numbers according to the rules; stop at 0.\"\n", + " while prev:\n", + " prev = (prev * factor) % m\n", + " yield prev\n", + " \n", + "def judge(A, B, N=40*10**6, mask=2**16-1): \n", + " \"How many of the first N numbers from A and B agree in the masked bits (default last 16)?\"\n", + " return quantify(a & mask == b & mask\n", + " for (a, b, _) in zip(A, B, range(N)))\n", + "\n", + "def A(): return gen(516, 16807)\n", + "def B(): return gen(190, 48271)\n", + "\n", + "%time judge(A(), B())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice I also decided to use `@jit` (i.e. `numba.jit`) to speed things up, since this is the slowest-running day yet.\n", + "\n", + "**Part Two**\n", + "\n", + "A small change: only consider numbers that match the **criteria** of being divisible by 4 or 8, respectively;" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 9.39 s, sys: 8.62 ms, total: 9.4 s\n", + "Wall time: 9.4 s\n" + ] + }, + { + "data": { + "text/plain": [ + "303" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def criteria(m, iterable): \n", + " \"Elements of iterable that are divisible by m\"\n", + " return (n for n in iterable if n % m == 0)\n", + " \n", + "%time judge(criteria(4, A()), criteria(8, B()), 5*10**6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 16](https://adventofcode.com/2017/day/16): Permutation Promenade\n", + "\n", + "Let's read the input and check that it looks reasonable:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('x5/15',\n", + " 's15',\n", + " 'x1/3',\n", + " 'pn/f',\n", + " 'x11/2',\n", + " 's13',\n", + " 'x6/3',\n", + " 'pe/a',\n", + " 'x14/12',\n", + " 's15')" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dance = Vector(Inputstr(16))\n", + "dance[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10000" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'll define `perform` to perform the dance:" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'lbdiomkhgcjanefp'" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dancers = 'abcdefghijklmnop'\n", + "\n", + "def perform(dance, dancers=dancers):\n", + " D = deque(dancers)\n", + " def swap(i, j): D[i], D[j] = D[j], D[i]\n", + " for move in dance:\n", + " op, arg = move[0], move[1:]\n", + " if op == 's': D.rotate(int(arg))\n", + " elif op == 'x': swap(*Integers(arg))\n", + " elif op == 'p': swap(D.index(arg[0]), D.index(arg[2]))\n", + " return cat(D)\n", + " \n", + "perform(dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "My first thought was to define a dance as a permutation: a list of numbers `[11, 1, 9, ...]` which says that the net effect of the dance is that the first dancer (`a`) ends up in position, the second (`b`) stays in position 1, and so on. Applying that permutation once is a lot faster than interpreting all 10,000 moves of the dance, and it is feasible to apply the permutation a billion times. I tried that (code not shown here), but that was a mistake: it took 15 minutes to run, and it got the wrong answer. The problem is that a dance is *not* just a permutation, because a dance can reference dancer *names*, not just positions.\n", + "\n", + "It would take about 10,000 times 20 minutes to perform a billion repetitions of the dance, so that's out. But even though the dance is not a permutation, it might repeat after a short period. Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "abcdefghijklmnop is seen in iterations (0, 56)\n" + ] + } + ], + "source": [ + "seen = {dancers: 0}\n", + "d = dancers\n", + "for i in range(1, 1000):\n", + " d = perform(dance, d)\n", + " if d in seen:\n", + " print(d, 'is seen in iterations', (seen[d], i))\n", + " break" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So we get back to the start position after 56 repetitions of the dance. What happens after a billion repetitions?" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "48" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1000000000 % 56" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The end position after a billion repetitions is the same as after 48:" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ejkflpgnamhdcboi'" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def whole(N, dance, dancers=dancers):\n", + " \"Repeat `perform(dance)` N times.\"\n", + " for i in range(N):\n", + " dancers = perform(dance, dancers)\n", + " return dancers\n", + " \n", + "whole(48, dance)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# [Day 17](https://adventofcode.com/2017/day/17): Spinlock\n", + "\n", + "This one looks pretty easy:" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "355" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "step = 314\n", + "\n", + "def spinlock(step=step, N=2017):\n", + " \"Make N inserts into the buffer, skipping ahead by `step` each time.\"\n", + " buf = [0]\n", + " pos = 0\n", + " for i in ints(1, N):\n", + " pos = (pos + step) % i + 1\n", + " buf[pos:pos] = [i]\n", + " return buf\n", + " \n", + "buf = spinlock()\n", + "\n", + "buf[buf.index(2017)+1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "But Part Two is not so easy, if we care about the run time. Insertion into a `list` has to move all the elements after the insertion down, so insertion is O(N) and `spinlock` is O(N2). That's no problem when N = 2017, but when N is 50 million? We're gonna need a bigger boat, where by \"boat\" I mean algorithm or data structure. My first thought is a (circular) linked list, because insertion is O(1). I can implement the three key methods: `skip` to move ahead, `insert` to add a new node after the current one, and `find` to find a piece of data (with a linear search):" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Node:\n", + " \"A Node in a singly-linked list\"\n", + " \n", + " __slots__ = ('data', 'next') # Declaring slots makes it more efficient\n", + " \n", + " def __init__(self, data, next): self.data, self.next = data, next\n", + " \n", + " def skip(self, n):\n", + " \"Skip ahead n nodes, and return that node.\"\n", + " node = self\n", + " for i in range(n):\n", + " node = node.next\n", + " return node\n", + " \n", + " def insert(self, value):\n", + " \"Insert a new node with the given value after this node.\"\n", + " self.next = Node(value, self.next)\n", + " return self.next\n", + " \n", + " def find(self, value):\n", + " \"Find the node with the given data value.\"\n", + " node = self\n", + " while node.data != value:\n", + " node = node.next\n", + " return node" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can rewrite `spinlock` to use this class:" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def spinlock2(step=step, N=2017):\n", + " node = Node(0, None)\n", + " node.next = node # Make node be a circular linked list\n", + " for i in ints(1, N):\n", + " node = node.skip(step).insert(i)\n", + " return node" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's replicate the Part One results:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "355" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "spinlock2().find(2017).next.data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Good news! We get the same answer. But how fast/slow is it?" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.35 s, sys: 5.54 ms, total: 1.35 s\n", + "Wall time: 1.35 s\n" + ] + }, + { + "data": { + "text/plain": [ + "<__main__.Node at 0x110c44be0>" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time spinlock2(N=100000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bad news! It takes over a second to do just 100,000 insertions, which means about 10 minutes for 50 million insertions. I did in fact try\n", + "\n", + " spinlock2(N=50000000).find(0).next.data\n", + " \n", + "and it eventually gave the right answer, but while it was running I had plenty of time to think.\n", + "I realized that, if we go back to the original `spinlock` version, the value `0` will always be in `buf[0]`, and the value we are looking for will always be in `buf[1]`. So I can create a version of `spinlock` that only keeps track of `buf[0:2]`. That should run in a few seconds, not minutes:" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 5.47 s, sys: 6.62 ms, total: 5.48 s\n", + "Wall time: 5.48 s\n" + ] + }, + { + "data": { + "text/plain": [ + "6154117" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def spinlock3(step=step, N=2017):\n", + " \"Make N inserts into a simulated buffer, but ignore all except buf[0:2].\"\n", + " pos = 0\n", + " buf = [0, 0]\n", + " for i in ints(1, N):\n", + " pos = (pos + step) % i + 1\n", + " if pos <= 1:\n", + " buf[pos] = i\n", + " return buf\n", + "\n", + "%time spinlock3(N=50000000)[1]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The moral of the story is *keep your eyes on the prize*. I got distracted because I asked the wrong question. I asked myself \"how can I make my solution in `spinlock` faster?\" and answered myself \"insertion is O(N2) and it should be O(N).\" I knew how to do that, with a linked list, but that was the right answer to the wrong question. I should have asked myself \"how do I solve Part Two quickly,\" concentrating on solving the actual problem. Once I did that, I realized I didn't need all those insertions: not doing them at all is a better idea than doing them faster." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 18](https://adventofcode.com/2017/day/17): Duet\n", + "\n", + "First, read the input, and take a peak at it:" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(('set', 'i', 31),\n", + " ('set', 'a', 1),\n", + " ('mul', 'p', 17),\n", + " ('jgz', 'p', 'p'),\n", + " ('mul', 'a', 2),\n", + " ('add', 'i', -1),\n", + " ('jgz', 'i', -2),\n", + " ('add', 'a', -1),\n", + " ('set', 'i', 127),\n", + " ('set', 'p', 826))" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "program18 = Array(Input(18))\n", + "program18[:10]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now write an interpreter for the assembly language:" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7071" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def run18(program):\n", + " \"Interpret the assembly language program; return recovered `snd`.\"\n", + " regs = defaultdict(int)\n", + " pc = snd = 0\n", + " while True:\n", + " instr = program[pc]\n", + " pc += 1\n", + " op, x, y = instr[0], instr[1], instr[-1]\n", + " vy = value(regs, y)\n", + " if op == 'snd': snd = regs[x]\n", + " elif op == 'set': regs[x] = vy\n", + " elif op == 'add': regs[x] += vy\n", + " elif op == 'mul': regs[x] *= vy\n", + " elif op == 'mod': regs[x] %= vy\n", + " elif op == 'jgz' and regs[x] > 0: pc += vy - 1\n", + " elif op == 'rcv' and regs[x] != 0: return snd\n", + " \n", + "def value(regs, y): return (y if isinstance(y, int) else regs[y])\n", + "\n", + "run18(program18)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy. (One tricky bit: the `pc` is incremented by 1 every time through the loop, regardless of the instruction. Therefore, the `'jgz'` jump instruction increments by \"`vy - 1`\" so that the net increment is \"`vy`\".)\n", + "\n", + "**Part Two**\n", + "\n", + "In Part Two we have to run two copies of the program, and send messages between them. I'll break up the loop in `run18` into\n", + "two functions. First, `run18_2`, creates (in `ps`) two structures to hold the state variables necessary to run a program:\n", + "- `id`: The id number (0 or 1) of this copy of the program.\n", + "- `pc`: The program counter.\n", + "- `sends`: A count of the number of `snd` instructions executed.\n", + "- `regs`: A dict of the program registers (`a` to `z`).\n", + "- `status`: A program has a status which can be:\n", + " * `'run'` when it is ready to execute an instruction, \n", + " * `'wait'` when it is waiting for a value to arrive in its input queue, or \n", + " * `'end'` when the `pc` has run off the end of the program and it has terminated.\n", + "\n", + "`run18_2` repeatedly calls the second function, `step18(program, p)` to execute one instruction of `program` with the state variables in `p`. I choose randomly which of the two programs to step on each iteration. The function exits when neither copy of the program can run, according to their status. " + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run18_2(program):\n", + " \"Run two copies of program, with different state variables. Return final states.\"\n", + " Qs = [deque(), deque()]\n", + " ps = [Struct(id=id, pc=0, sends=0, regs=defaultdict(int, p=id), status='run')\n", + " for id in (0, 1)]\n", + " while any(p.status == 'run' for p in ps):\n", + " step18(program, Qs, random.choice(ps))\n", + " return ps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`step18` has most of the guts of thee previous `run18` function, but with a few changes:\n", + "- State variables are accessed indirectly: `p.pc` instead of just `pc`.\n", + "- If the `pc` is out of bounds, the program terminates; the status is set to `'end'`.\n", + "- The `snd` instruction sends a value to the other program's queue.\n", + "- The `rcv` instruction pops a value off the queue if there is one, otherwise the status is set to `'wait'`.\n", + "- The \"`X`\" in \"`jgz X Y`\" might be an integer, not a register name, so use `vx = value(p.regs, x)`. I was stuck for a *long* time before I realized this. Finally I tried the strategy of *look carefully at the input*. I noticed the instruction `\"jgz 1 3\"`, and it was a simple change to make the program work." + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "8001" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def step18(program, Qs, p):\n", + " \"Execute one instruction in program, using state variables in p.\"\n", + " if p.pc < 0 or p.pc > len(program):\n", + " p.status = 'end'\n", + " else:\n", + " instr = program[p.pc]\n", + " op, x, y = instr[0], instr[1], instr[-1]\n", + " vx, vy = value(p.regs, x), value(p.regs, y)\n", + " if op == 'snd': Qs[1-p.id].append(vy); p.sends += 1\n", + " elif op == 'set': p.regs[x] = vy\n", + " elif op == 'add': p.regs[x] += vy\n", + " elif op == 'mul': p.regs[x] *= vy\n", + " elif op == 'mod': p.regs[x] %= vy\n", + " elif op == 'jgz' and vx > 0: p.pc += vy - 1\n", + " elif op == 'rcv': \n", + " if not Qs[p.id]:\n", + " p.status = 'wait'\n", + " return # don't update pc; try again next time\n", + " else:\n", + " p.regs[x] = Qs[p.id].popleft()\n", + " p.status = 'run'\n", + " p.pc += 1\n", + " \n", + "run18_2(program18)[1].sends" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 19](https://adventofcode.com/2017/day/19): A Series of Tubes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At first I was confused; I thought this was a maze-following problem where I had to make a choice of directions at every turn. Actually, the direction is always determined: keep going in the current direction as long as possible, but when we hit a `'+'` character, find the new direction to go in (there will only be one possibility). Leave breadcrumbs (the `'.'` character) so that we don't back up along a previously-followed path. As in Day 14, the grid is surrounded by a border of space characters so that we don't have to worry about `(x, y)` going off the edge." + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "diagram = Inputstr(19)\n", + "\n", + "def follow_tubes(diagram):\n", + " \"Follow [-+|] lines, yielding characters along the path.\"\n", + " grid = border(' ', diagram.splitlines())\n", + " x, y = grid[1].index('|'), 1\n", + " dx, dy = 0, 1\n", + " while grid[y][x] != ' ':\n", + " yield grid[y][x]\n", + " if grid[y][x] == '+':\n", + " dx, dy = new_direction(grid, x, y)\n", + " grid[y][x] = '.' # Leave a breadcrumb\n", + " x += dx; y += dy\n", + " \n", + "def new_direction(grid, x, y):\n", + " \"Find a direction that continues the path.\"\n", + " for (dx, dy) in (UP, DOWN, RIGHT, LEFT):\n", + " if grid[y+dy][x+dx] not in (' ', '.'):\n", + " return dx, dy" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'VEBTPXCHLI'" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cat(filter(str.isalpha, follow_tubes(diagram)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the right answer.\n", + "\n", + "**Part Two**\n", + "\n", + "This is a surprisingly easy Part Two; I already generated the characters in the path; all I have to do is count them: " + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "18702" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "length(follow_tubes(diagram))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 20](https://adventofcode.com/2017/day/20): Particle Swarm\n", + "\n", + "I'll create structures for particles, each will have fields for particle's number (`id`), position (`p`), velocity(`v`), and acceleration (`a`):" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[Struct(a=(-7, 8, -10), id=0, p=(1199, -2918, 1457), v=(-13, 115, -8)),\n", + " Struct(a=(-6, -5, 6), id=1, p=(2551, 2418, -1471), v=(-106, -108, 39)),\n", + " Struct(a=(-6, 2, -9), id=2, p=(-73, 1626, 1321), v=(58, -118, -8)),\n", + " Struct(a=(3, 3, 11), id=3, p=(-3297, -894, -551), v=(183, 31, -61)),\n", + " Struct(a=(7, -12, -1), id=4, p=(-1425, 4298, 617), v=(32, -166, -32))]" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def particles(lines=list(Input(20))):\n", + " \"Parse the list of particles.\"\n", + " return [Particle(id, *grouper(Integers(line), 3)) \n", + " for id, line in enumerate(lines)]\n", + "\n", + "def Particle(id, p, v, a): return Struct(id=id, p=p, v=v, a=a) \n", + "\n", + "particles()[:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'm not quite sure how to determine what \"in the long run\" means, so I'll just interpret it as meaning \"after 1000 time steps.\" On each step we update velocity and position of each particle. At the end, we determine the id number of the particle closest to the origin. Note that `evolve` generates an infinite sequence of particles, and we use `nth` to pick out the 1000th generation." + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "243" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def evolve(particles):\n", + " \"Continually update particles, yielding them after each time step.\"\n", + " while True:\n", + " yield particles\n", + " for p in particles:\n", + " p.v = add(p.v, p.a)\n", + " p.p = add(p.p, p.v)\n", + " \n", + "def add(A, B): \n", + " \"Add two n-dimensional vectors.\"\n", + " return mapt(sum, zip(A, B))\n", + "\n", + "def closest(particles):\n", + " \"Find the particle closest to origin.\"\n", + " return min(particles, key=lambda p: sum(map(abs, p.p)))\n", + "\n", + "# Answer: the id of the particle closest to origin in the 1000th generation of `evolve`\n", + "closest(nth(evolve(particles()), 1000)).id" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "I can still use `evolve` unchanged, and I will add the function `remove_collisions` to eliminate particles that are in the same position as another particle. I use `map` to apply this to every generation. Note that `remove_collisions` both mutates the argument, `particles`, and also returns it. " + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "648" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def remove_collisions(particles):\n", + " \"Mutate (and return) particles, keep only ones that have a unique position.\"\n", + " poscount = Counter(p.p for p in particles)\n", + " particles[:] = [p for p in particles if poscount[p.p] == 1]\n", + " return particles\n", + " \n", + "# Answer: remove collisions from every generation of evolving particles, \n", + "# select the 1000th generation, and say how many particles are in that generation.\n", + "len(nth(map(remove_collisions, evolve(particles())), 1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 21](https://adventofcode.com/2017/day/21): Fractal Art\n", + "\n", + "First I'll create a `dict` of enhancement rules. I'll translate `'#'` and `'.'` pixels to 1 and 0, and represent a grid as a tuple of tuples (e.g. `((0, 0), (1, 1))`), so that it can be a `dict` key. I have to deal with rotations and flips; I could do that at lookup time, but it will be faster to do it at rule creation time:" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Enhancements(lines):\n", + " \"Create a dict of {square: enhanced_square}\"\n", + " enhancements = {}\n", + " for line in lines:\n", + " lhs, rhs = map(Key, line.split('=>'))\n", + " for r in range(4):\n", + " enhancements[lhs] = enhancements[flip(lhs)] = rhs\n", + " lhs = rotate(lhs)\n", + " return enhancements\n", + " \n", + "def Key(line): \n", + " \"Key('../##') => ((0, 0), (1, 1))\"\n", + " bits = {'#': 1, '.': 0}\n", + " return tuple(tuple(bits[p] for p in row.strip())\n", + " for row in line.split('/'))\n", + " \n", + "def rotate(key): return tuple(zip(*reversed(key)))\n", + "\n", + "def flip(L): return tuple(tuple(reversed(row)) for row in L)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's test this on just the enhancement rules with 2x2 squares; with rotations and flips there should be 16 entries:" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{((0, 0), (0, 0)): ((0, 0, 0), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 0), (0, 1)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 0), (1, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 0), (1, 1)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 1), (0, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((0, 1), (0, 1)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((0, 1), (1, 0)): ((1, 1, 0), (1, 1, 0), (0, 0, 0)),\n", + " ((0, 1), (1, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 0), (0, 0)): ((0, 0, 0), (1, 0, 0), (1, 0, 0)),\n", + " ((1, 0), (0, 1)): ((1, 1, 0), (1, 1, 0), (0, 0, 0)),\n", + " ((1, 0), (1, 0)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((1, 0), (1, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (0, 0)): ((1, 0, 1), (0, 1, 0), (0, 1, 0)),\n", + " ((1, 1), (0, 1)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (1, 0)): ((0, 1, 1), (1, 1, 1), (1, 0, 0)),\n", + " ((1, 1), (1, 1)): ((0, 1, 1), (1, 0, 0), (1, 1, 0))}" + ] + }, + "execution_count": 90, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Enhancements('''\n", + "../.. => .../.#./.#.\n", + "#./.. => .../#../#..\n", + "##/.. => #.#/.#./.#.\n", + ".#/#. => ##./##./...\n", + "##/#. => .##/###/#..\n", + "##/## => .##/#../##.\n", + "'''.strip().splitlines())" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 91, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looks good; let's create my complete table. There should be 24 + 29 entries:" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "enhancements = Enhancements(Input(21))\n", + "\n", + "assert len(enhancements) == 2 ** 4 + 2 ** 9" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now on each iteration we `enhance` the grid by first `expand`-ing it (looking up each `slice` in the `enhancements` rules) and then `stitch` the pieces together:" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def enhance(grid): \n", + " \"Expand small pieces into bigger ones and stitch them together.\"\n", + " return stitch(expand(grid))\n", + "\n", + "def expand(grid):\n", + " \"Slice the grid into d x d pieces and enhance each piece.\"\n", + " N = len(grid[0])\n", + " d = (2 if N % 2 == 0 else 3 if N % 3 == 0 else error())\n", + " return [[enhancements[slice(grid, r, c, d)]\n", + " for c in range(0, N, d)]\n", + " for r in range(0, N, d)]\n", + "\n", + "def stitch(pieces): \n", + " \"Stitch the pieces back into one big grid.\"\n", + " N = sum(map(len, pieces[0]))\n", + " return tuple(tuple(get(pieces, r, c) \n", + " for c in range(N))\n", + " for r in range(N))\n", + "\n", + "def get(pieces, r, c):\n", + " \"The pixel at location (r, c), from a matrix of d x d pieces.\"\n", + " d = len(pieces[0][0])\n", + " row = pieces[r // d]\n", + " cell = row[c // d]\n", + " return cell[r % d][c % d]\n", + "\n", + "def slice(grid, r, c, d):\n", + " \"The d x d slice of grid starting at position (r, c)\"\n", + " return tuple(row[c:c+d] for row in grid[r:r+d])" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 1, 0), (0, 0, 1), (1, 1, 1))" + ] + }, + "execution_count": 94, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grid = Key('.#./..#/###')\n", + "grid" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[((1, 0, 1, 0), (0, 0, 1, 0), (0, 1, 0, 1), (0, 1, 0, 0))]]" + ] + }, + "execution_count": 95, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((1, 0, 1, 0), (0, 0, 1, 0), (0, 1, 0, 1), (0, 1, 0, 0))" + ] + }, + "execution_count": 96, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stitch(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[((0, 0, 0), (1, 0, 0), (1, 0, 0)), ((1, 0, 1), (0, 1, 0), (0, 1, 0))],\n", + " [((1, 0, 1), (0, 1, 0), (0, 1, 0)), ((0, 0, 0), (1, 0, 0), (1, 0, 0))]]" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expand(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 0, 0, 1, 0, 1),\n", + " (1, 0, 0, 0, 1, 0),\n", + " (1, 0, 0, 0, 1, 0),\n", + " (1, 0, 1, 0, 0, 0),\n", + " (0, 1, 0, 1, 0, 0),\n", + " (0, 1, 0, 1, 0, 0))" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stitch(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(_))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks right; Let's try to solve the puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "147" + ] + }, + "execution_count": 100, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(repeat(5, enhance, grid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Part Two**\n", + "\n", + "It looked like I didn't need to change any code to do Part Two, just change the `5` to an `18`. I ran it, and got an answer in a few seconds—but the answer was wrong. I went back and carefully looked over my code, and realized there was a place in `expand` where I had swapped the order of `r` and `c` (the code there is fixed now). Apparently there is some symmetry over the first 5 enhancements that yields the correct answer either way, but that breaks down over 18 enhancements. (Also: if I had guessed that `sum(flatten(repeat(n, enhance, grid)))` would be used in both parts, I probably would have created a function for it. But I was guessing that Part Two would involve `enhance`, but not necessarily in the same way as Part One.)" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1936582" + ] + }, + "execution_count": 101, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum(flatten(repeat(18, enhance, grid)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Note on Reuse\n", + "\n", + "One interesting question about these two-part problems: how does the code in Part Two use the code in Part One? \n", + "Here are my answers:\n", + "\n", + "* **All new**: All the code for Part Two (except possibly reading and parsing the input) is brand new: \n", + "
Days 1, 2, 4, 7\n", + "\n", + "* **Reuse as is**: The major function defined in Part One is called again in Part Two (and some new code\n", + "is also written):\n", + "
Days 3 (`spiral`), 6 (`spread`, but `realloc2` is copy-paste-edit), 9, 12, 14 (`bits`), \n", + "15 (`A, B, gen, judge`), 16 (`perform`), 19 (`follow_tubes`), 20 (`evolve, particles`), 21 (`expands`, `gridsum`)\n", + "\n", + "* **Generalize**: A major function from Part One is generalized in Part Two (e.g. by adding an optional parameter):\n", + "
Days 13 (`caught`)\n", + "\n", + "* **Copy-paste-edit**: The major function from Part One is copied and edited for Part Two:\n", + "
Days 5 (`run2`), 8 (`run82`), 10 (`knothash2`), 11 (`follow2`), 17 (`spinlock2`), 18 (`step18`)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Wrapping Up: Verification and Timing\n", + "\n", + "Here is a little test harness to verify that I still get the right answers (even if I refactor some of the code):" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 54.6 s, sys: 156 ms, total: 54.7 s\n", + "Wall time: 54.9 s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "def day(d, compute1, answer1, compute2, answer2):\n", + " \"Assert that we get the right answers for this day.\"\n", + " assert compute1 == answer1\n", + " assert compute2 == answer2\n", + "\n", + "day(1, sum(digits[i] for i in range(N) if digits[i] == digits[i - 1]), 1158,\n", + " sum(digits[i] for i in range(N) if digits[i] == digits[i - N // 2]), 1132)\n", + "day(2, sum(abs(max(row) - min(row)) for row in rows2), 46402, \n", + " sum(map(evendiv, rows2)), 265)\n", + "day(3, cityblock_distance(nth(spiral(), M - 1)), 475, \n", + " first(x for x in spiralsums() if x > M), 279138)\n", + "day(4, quantify(Input(4), is_valid), 337, \n", + " quantify(Input(4), is_valid2), 231)\n", + "day(5, run(program), 364539, \n", + " run2(program), 27477714)\n", + "day(6, realloc(banks), 12841, \n", + " realloc2(banks), 8038)\n", + "day(7, first(programs - set(flatten(above.values()))), 'wiapj', \n", + " correct(wrongest(programs)), 1072)\n", + "day(8, max(run8(program8).values()), 6828, \n", + " run8_2(program8), 7234)\n", + "day(9, total_score(text2), 9662, \n", + " len(text1) - len(text3), 4903)\n", + "day(10, knothash(stream), 4480, \n", + " knothash2(stream2), 'c500ffe015c83b60fad2e4b7d59dabc4')\n", + "day(11, follow(path), 705, \n", + " follow2(path), 1469)\n", + "day(12, len(G[0]), 115, \n", + " len({Set(G[i]) for i in G}), 221)\n", + "day(13, trip_severity(scanners), 1504, \n", + " safe_delay(scanners), 3823370)\n", + "day(14, sum(bits(key, i).count('1') for i in range(128)), 8316, \n", + " flood_all(Grid(key)), 1074)\n", + "day(15, judge(A(), B()), 597, \n", + " judge(criteria(4, A()), criteria(8, B()), 5*10**6), 303)\n", + "day(16, perform(dance), 'lbdiomkhgcjanefp', \n", + " whole(48, dance), 'ejkflpgnamhdcboi')\n", + "day(17, spinlock2().find(2017).next.data, 355,\n", + " spinlock3(N=50*10**6)[1], 6154117)\n", + "day(18, run18(program18), 7071, \n", + " run18_2(program18)[1].sends, 8001)\n", + "day(19, cat(filter(str.isalpha, follow_tubes(diagram))), 'VEBTPXCHLI', \n", + " quantify(follow_tubes(diagram)), 18702)\n", + "day(20, closest(nth(evolve(particles()), 1000)).id, 243,\n", + " len(nth(map(remove_collisions, evolve(particles())), 1000)), 648)\n", + "day(21, sum(flatten(repeat(5, enhance, grid))), 147,\n", + " sum(flatten(repeat(18, enhance, grid))), 1936582)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is a plot of the time taken to program solutions to both parts of each puzzle each day, for me, the first person to finish, and the hundredth person. On days when I started late, the times are my estimates, not official times (these include days 1, 3, 8, 13, 14, 17, 18, 21)." + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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AIOAgfKo847OrRJesrZvB09MGFhbBAAALi2B4etrA2lqzFVwkEuDIEcBAhwle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\nUdgCwGAwGDYKWwAYDAbDRvl/rNEo9OMigxQAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_times(times):\n", + " plt.style.use('seaborn-whitegrid')\n", + " X = ints(1, len(times[0]) - 2)\n", + " for (label, mark, *Y) in times:\n", + " plt.plot(X, Y, mark, label=label)\n", + " plt.xlabel('Day Number'); plt.ylabel('Minutes to Solve Both Parts')\n", + " plt.legend(loc='upper left')\n", + "\n", + "x = None\n", + "plot_times([\n", + " ('Me', 'd:', 4, 6, 20, 5, 12, 30, 33, 10, 21, 40, 13, 12, 30, 41, 13, 64, 54, 74, 50, 18, 40),\n", + " ('100th', 'v:', 6, 6, 23, 4, 5, 9, 25, 8, 12, 25, 12, 9, 22, 25, 10, 27, 16, 41, 18, 21, 45),\n", + " ('1st', '^:', 1, 1, 4, 1, 2, 3, 10, 3, 4, 6, 3, 2, 6, 5, 2, 5, 5, 10, 5, 7, 10)])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Advent of Code.ipynb b/pytudes/ipynb/Advent of Code.ipynb new file mode 100644 index 0000000..812fe73 --- /dev/null +++ b/pytudes/ipynb/Advent of Code.ipynb @@ -0,0 +1,3226 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# December 2016: Advent of Code Solutions\n", + "\n", + "## Peter Norvig\n", + "\n", + "From Dec. 1 to Dec. 25, [I](http://norvig.com) will be solving the puzzles that appear each day at *[Advent of Code](http://adventofcode.com/)*. The two-part puzzles are released at midnight EST (9:00PM PST); points are awarded to the first 100 people to solve the day's puzzles. The code shown here basically represents what I did to solve the problem, but slightly cleaned up:\n", + "- On days when I start at 9:00PM and am competing against the clock, I take shortcuts. I use shorter names, because I'm not a fast typist. I run test cases in the Jupyter Notebook, but don't make them into `assert` statements. Even then, I'm not really competitive with the fastest solvers.\n", + "- On days when I didn't get a chance to start until after all the points are gone, what you see here is pretty much exactly what I did, or at least what I ended up with after correcting typos and other errors. \n", + "\n", + "To understand the problems completely, you will have to read the full description in the **\"[Day 1](http://adventofcode.com/2016/day/1):\"** link in each day's section header.\n", + "\n", + "# Day 0: Getting Ready\n", + "\n", + "On November 30th, I spent some time preparing: \n", + "\n", + "- I'll import my favorite modules and functions, so I don't have to do it each day.\n", + "\n", + "- From looking at [last year's](http://adventofcode.com/2015) puzzles, I knew that there would be a data file on many days, so I defined the function `Input` to open the file (and for those using this notebook on a remote machine, to fetch the file from the web). My data files are at [http://norvig.com/ipython/advent2016/](http://norvig.com/ipython/advent2016/).\n", + "\n", + "- From working on another puzzle site, [Project Euler](https://projecteuler.net/), I had built up a collection of utility functions, shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Python 3.x\n", + "import re\n", + "import numpy as np\n", + "import math\n", + "import urllib.request\n", + "\n", + "from collections import Counter, defaultdict, namedtuple, deque\n", + "from functools import lru_cache\n", + "from itertools import permutations, combinations, chain, cycle, product, islice\n", + "from heapq import heappop, heappush\n", + "\n", + "def Input(day):\n", + " \"Open this day's input file.\"\n", + " filename = 'advent2016/input{}.txt'.format(day)\n", + " try:\n", + " return open(filename)\n", + " except FileNotFoundError:\n", + " return urllib.request.urlopen(\"http://norvig.com/ipython/\" + filename)\n", + "\n", + "def transpose(matrix): return zip(*matrix)\n", + "\n", + "def first(iterable): return next(iter(iterable))\n", + "\n", + "def nth(iterable, n, default=None):\n", + " \"Returns the nth item of iterable, or a default value\"\n", + " return next(islice(iterable, n, None), default)\n", + "\n", + "cat = ''.join\n", + "\n", + "Ø = frozenset() # Empty set\n", + "inf = float('inf')\n", + "BIG = 10 ** 999\n", + "\n", + "def grep(pattern, lines):\n", + " \"Print lines that match pattern.\"\n", + " for line in lines:\n", + " if re.search(pattern, line):\n", + " print(line)\n", + "\n", + "def groupby(iterable, key=lambda it: it):\n", + " \"Return a dic whose keys are key(it) and whose values are all the elements of iterable with that key.\"\n", + " dic = defaultdict(list)\n", + " for it in iterable:\n", + " dic[key(it)].append(it)\n", + " return dic\n", + "\n", + "def powerset(iterable):\n", + " \"Yield all subsets of items.\"\n", + " items = list(iterable)\n", + " for r in range(len(items)+1):\n", + " for c in combinations(items, r):\n", + " yield c\n", + "\n", + "# 2-D points implemented using (x, y) tuples\n", + "def X(point): return point[0]\n", + "def Y(point): return point[1]\n", + "\n", + "def neighbors4(point): \n", + " \"The four neighbors (without diagonals).\"\n", + " x, y = point\n", + " return ((x+1, y), (x-1, y), (x, y+1), (x, y-1))\n", + "\n", + "def neighbors8(point): \n", + " \"The eight neighbors (with diagonals).\"\n", + " x, y = point \n", + " return ((x+1, y), (x-1, y), (x, y+1), (x, y-1),\n", + " (x+1, y+1), (x-1, y-1), (x+1, y-1), (x-1, y+1))\n", + "\n", + "def cityblock_distance(p, q=(0, 0)): \n", + " \"City block distance between two points.\"\n", + " return abs(X(p) - X(q)) + abs(Y(p) - Y(q))\n", + "\n", + "def euclidean_distance(p, q=(0, 0)): \n", + " \"Euclidean (hypotenuse) distance between two points.\"\n", + " return math.hypot(X(p) - X(q), Y(p) - Y(q))\n", + "\n", + "def trace1(f):\n", + " \"Print a trace of the input and output of a function on one line.\"\n", + " def traced_f(*args):\n", + " result = f(*args)\n", + " print('{}({}) = {}'.format(f.__name__, ', '.join(map(str, args)), result))\n", + " return result\n", + " return traced_f\n", + "\n", + "def astar_search(start, h_func, moves_func):\n", + " \"Find a shortest sequence of states from start to a goal state (a state s with h_func(s) == 0).\"\n", + " frontier = [(h_func(start), start)] # A priority queue, ordered by path length, f = g + h\n", + " previous = {start: None} # start state has no previous state; other states will\n", + " path_cost = {start: 0} # The cost of the best path to a state.\n", + " while frontier:\n", + " (f, s) = heappop(frontier)\n", + " if h_func(s) == 0:\n", + " return Path(previous, s)\n", + " for s2 in moves_func(s):\n", + " new_cost = path_cost[s] + 1\n", + " if s2 not in path_cost or new_cost < path_cost[s2]:\n", + " heappush(frontier, (new_cost + h_func(s2), s2))\n", + " path_cost[s2] = new_cost\n", + " previous[s2] = s\n", + " return dict(fail=True, front=len(frontier), prev=len(previous))\n", + " \n", + "def Path(previous, s): \n", + " \"Return a list of states that lead to state s, according to the previous dict.\"\n", + " return ([] if (s is None) else Path(previous, previous[s]) + [s])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some tests/examples for these:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "assert tuple(transpose(((1, 2, 3), (4, 5, 6)))) == ((1, 4), (2, 5), (3, 6))\n", + "assert first('abc') == first(['a', 'b', 'c']) == 'a'\n", + "assert cat(['a', 'b', 'c']) == 'abc'\n", + "assert (groupby(['test', 'one', 'two', 'three', 'four'], key=len) \n", + " == {3: ['one', 'two'], 4: ['test', 'four'], 5: ['three']})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 1](http://adventofcode.com/2016/day/1): No Time for a Taxicab\n", + "\n", + "Given a sequence of moves, such as `\"R2, L3\"`, which means turn 90° to the right and go forward 2 blocks, then turn 90° left and go 3 blocks, how many blocks do we end up away from the start? I make the following choices:\n", + "* **Intersection Points** in the city grid will be represented as points on the complex plane. \n", + "* **Headings and turns** can be represented by unit vectors in the complex plane: if you are heading east (along the positive real axis), then a left turn means you head north, and a right turn means you head south, and [in general](https://betterexplained.com/articles/understanding-why-complex-multiplication-works/) a left or right turn is a multiplication of your current heading by the `North` or `South` unit vectors, respectively. \n", + "* **Moves** of the form `\"R53\"` will be parsed into a `(turn, distance)` pair, e.g. `(South, 53)`.\n", + "\n", + "To solve the puzzle with the function `how_far(moves)`, I initialize the starting location as the origin and the starting heading as North, and follow the list of moves, updating the heading and location on each step, before returning the distance from the final location to the origin." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "250.0" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Point = complex \n", + "N, S, E, W = 1j, -1j, 1, -1 # Unit vectors for headings\n", + "\n", + "def distance(point): \n", + " \"City block distance between point and the origin.\"\n", + " return abs(point.real) + abs(point.imag)\n", + "\n", + "def how_far(moves):\n", + " \"After following moves, how far away from the origin do we end up?\"\n", + " loc, heading = 0, N # Begin at origin, heading North\n", + " for (turn, dist) in parse(moves):\n", + " heading *= turn\n", + " loc += heading * dist\n", + " return distance(loc)\n", + "\n", + "def parse(text):\n", + " \"Return a list of (turn, distance) pairs from text of form 'R2, L42, ...'\"\n", + " turns = dict(L=N, R=S)\n", + " return [(turns[RL], int(d))\n", + " for (RL, d) in re.findall(r'(R|L)(\\d+)', text)]\n", + "\n", + "assert distance(Point(3, 4)) == 7 # City block distance; Euclidean distance would be 5\n", + "assert parse('R2, L42') == [(S, 2), (N, 42)]\n", + "assert how_far(\"R2, L3\") == 5\n", + "assert how_far(\"R2, R2, R2\") == 2\n", + "assert how_far(\"R5, L5, R5, R3\") == 12\n", + "\n", + "how_far(Input(1).read())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two** of this puzzle, I have to find the first point that is visited twice. To support that, I keep track of the set of visited points. My first submission was wrong, because I didn't consider that the first point visited twice might be in the middle of a move, not the end, so I added the \"`for i`\" loop to iterate over the path of a move, one point at a time." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "151.0" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def visited_twice(text):\n", + " \"Following moves in text, find the first location we visit twice, and return the distance to it.\"\n", + " loc, heading = 0, N # Begin at origin, heading North\n", + " visited = {loc}\n", + " for (turn, dist) in parse(text):\n", + " heading *= turn\n", + " for i in range(dist):\n", + " loc += heading\n", + " if loc in visited:\n", + " return distance(loc)\n", + " visited.add(loc)\n", + "\n", + "assert visited_twice(\"R8, R4, R4, R8\") == 4\n", + "assert visited_twice(\"R8, R4, R4, L8\") == None\n", + "assert visited_twice(\"R8, R0, R1\") == 7\n", + "\n", + "visited_twice(Input(1).read())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 2](http://adventofcode.com/2016/day/2): Bathroom Security\n", + "\n", + "Given instructions in the form of a sequence of Up/Down/Right/Left moves, such as `'ULL'`, output the keys on the bathroom lock keypad that the instructions correspond to. Start at the 5 key. Representation choices:\n", + "* **Keypad**: a keypad is an array of strings: `keypad[y][x]` is a key. The character `'.'` indicates a location that is `off` the keypad; by surrounding the keys with a border of `off` characters, I avoid having to write code that checks to see if we hit the edge.\n", + "* **Key**: A key is a character other than `'.'`.\n", + "* **Instructions**: A sequence of lines of `\"UDRL\"` characters, where each line leads to the output of one key." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'97289'" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Keypad = str.split\n", + "\n", + "keypad = Keypad(\"\"\"\n", + ".....\n", + ".123.\n", + ".456.\n", + ".789.\n", + ".....\n", + "\"\"\")\n", + "\n", + "assert keypad[2][2] == '5'\n", + "\n", + "off = '.'\n", + "\n", + "def decode(instructions, x=2, y=2):\n", + " \"\"\"Follow instructions, keeping track of x, y position, and\n", + " yielding the key at the end of each line of instructions.\"\"\"\n", + " for line in instructions:\n", + " for C in line:\n", + " x, y = move(C, x, y)\n", + " yield keypad[y][x]\n", + "\n", + "def move(C, x, y):\n", + " \"Make the move corresponding to this character (L/R/U/D)\"\n", + " if C == 'L' and keypad[y][x-1] is not off: x -= 1\n", + " elif C == 'R' and keypad[y][x+1] is not off: x += 1\n", + " elif C == 'U' and keypad[y-1][x] is not off: y -= 1\n", + " elif C == 'D' and keypad[y+1][x] is not off: y += 1\n", + " return x, y\n", + "\n", + "assert move('U', 2, 2) == (2, 1)\n", + "assert move('U', 2, 1) == (2, 1)\n", + "assert cat(decode(\"ULL RRDDD LURDL UUUUD\".split())) == '1985'\n", + "\n", + "cat(decode(Input(2)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we have to deal with a different keypad. I won't need any new functions, but I will need to redefine the global variable `keypad`, and provide `decode` with the new `x` and `y` coordinates of the `5` key:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'9A7DC'" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "keypad = Keypad(\"\"\"\n", + ".......\n", + "...1...\n", + "..234..\n", + ".56789.\n", + "..ABC..\n", + "...D...\n", + ".......\n", + "\"\"\")\n", + "\n", + "assert keypad[3][1] == '5'\n", + "\n", + "cat(decode(Input(2), x=1, y=3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 3](http://adventofcode.com/2016/day/3): Squares With Three Sides\n", + "\n", + "From a file of numbers, three to a line, count the number that represent valid triangles; that is, numbers that satisfy the [triangle inequality](https://en.wikipedia.org/wiki/Triangle_inequality)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "983" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def is_triangle(sides):\n", + " \"Do these side lengths form a valid triangle?\"\n", + " x, y, z = sorted(sides)\n", + " return z < x + y\n", + "\n", + "def parse_ints(text): \n", + " \"All the integers anywhere in text.\"\n", + " return [int(x) for x in re.findall(r'\\d+', text)]\n", + "\n", + "triangles = [parse_ints(line) for line in Input(3)]\n", + "\n", + "sum(map(is_triangle, triangles))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, the triangles are denoted not by three sides in the same line, but by three sides in the same column. For example, given the text:\n", + "\n", + " 101 301 501\n", + " 102 302 502\n", + " 103 303 503\n", + " 201 401 601\n", + " 202 402 602\n", + " 203 403 603\n", + " \n", + "The triangles are:\n", + "\n", + " [101, 102, 103]\n", + " [301, 302, 303]\n", + " [501, 502, 503]\n", + " [201, 202, 203]\n", + " [401, 402, 403]\n", + " [601, 602, 603]\n", + " \n", + "The task is still to count the number of valid triangles." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1836" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def invert(triangles):\n", + " \"Take each 3 lines and transpose them.\"\n", + " for i in range(0, len(triangles), 3):\n", + " yield from transpose(triangles[i:i+3])\n", + "\n", + "sum(map(is_triangle, invert(triangles)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 4](http://adventofcode.com/2016/day/4): Security Through Obscurity\n", + "\n", + "Given a list of room names like `\"aaaaa-bbb-z-y-x-123[abxyz]\"`, consisting of an encrypted name followed by a dash, a sector ID, and a checksum in square brackets, compute the sum of the sectors of the valid rooms. A room is valid if the checksum is the five most common characters, in order (ties listed in alphabetical order)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "185371" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def parse(line): \n", + " \"Return (name, sector, checksum).\"\n", + " return re.match(r\"(.+)-(\\d+)\\[([a-z]+)\\]\", line).groups()\n", + "\n", + "def sector(line):\n", + " \"Return the sector number if valid, or 0 if not.\"\n", + " name, sector, checksum = parse(line)\n", + " return int(sector) if valid(name, checksum) else 0\n", + "\n", + "def valid(name, checksum):\n", + " \"Determine if name is valid according to checksum.\"\n", + " counts = Counter(name.replace('-', '')) \n", + " # Note: counts.most_common(5) doesn't work because it breaks ties arbitrarily.\n", + " letters = sorted(counts, key=lambda L: (-counts[L], L))\n", + " return checksum == cat(letters[:5])\n", + "\n", + "assert parse('aaaaa-bbb-z-y-x-123[abxyz]') == ('aaaaa-bbb-z-y-x', '123', 'abxyz')\n", + "assert sector('aaaaa-bbb-z-y-x-123[abxyz]') == 123\n", + "assert valid('aaaaa-bbb-z-y-x', 'abxyz')\n", + "\n", + "sum(map(sector, Input(4)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Initially I had a bug: I forgot the `name.replace('-', '')` to make sure that we don't count hyphens. \n", + "\n", + "In **part two**, we are asked *\"What is the sector ID of the room where North Pole objects are stored?\"* We are told that names are to be decrypted by a shift cipher, shifting each letter forward in the alphabet by the sector number." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "northpole-object-storage 984\n" + ] + } + ], + "source": [ + "def decrypt(line):\n", + " \"Decrypt the line (shift the name by sector; discard checksum).\"\n", + " name, sector, _ = parse(line)\n", + " return shift(name, int(sector)) + ' ' + sector\n", + "\n", + "def shift(text, N, alphabet='abcdefghijklmnopqrstuvwxyz'):\n", + " \"Shift cipher: letters in text rotate forward in alphabet by N places.\"\n", + " N = N % len(alphabet)\n", + " tr = str.maketrans(alphabet, alphabet[N:] + alphabet[:N])\n", + " return text.translate(tr)\n", + "\n", + "assert shift('hal', 1) == 'ibm'\n", + "assert shift('qzmt-zixmtkozy-ivhz', 343) == 'very-encrypted-name'\n", + "\n", + "grep(\"north\", map(decrypt, Input(4)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 5](http://adventofcode.com/2016/day/5): How About a Nice Game of Chess?\n", + "\n", + "This puzzle involves md5 hashes and byte encodings; it took me a while to look up how to do that. What I have to do, for integers starting at 0, is concatenate my door ID string with the integer, get the md5 hex hash, and if the first five digits of the hash are 0, collect the sixth digit; repeat until I have collected eight digits:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "515840 00000c6c3f533fe4f7b0cb6d851185a8 c\n", + "844745 000006a94bb1c9322cbb56dd8564e76e c6\n", + "2968550 000006c8c9090315b0fb38154a947c86 c66\n", + "4034943 00000970faef6424564944d5e8a59618 c669\n", + "5108969 000007b2e0e83dfeade14ebe09f9e6a7 c6697\n", + "5257971 00000bc5fdee6506b09262247ceb63f0 c6697b\n", + "5830668 0000051079ac6b44fc3a5266a1630d42 c6697b5\n", + "5833677 00000537192966c3ee924306195faede c6697b55\n" + ] + }, + { + "data": { + "text/plain": [ + "'c6697b55'" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import hashlib\n", + "\n", + "door = \"ffykfhsq\"\n", + "\n", + "def find_password(door):\n", + " \"First 8 sixth digits of md5 hashes of door+i that begin with '00000'.\"\n", + " password = ''\n", + " for i in range(BIG):\n", + " x = hashlib.md5(bytes(door + str(i), 'utf-8')).hexdigest()\n", + " if x.startswith('00000'):\n", + " password += x[5]\n", + " print(i, x, password) # Just to see something happen\n", + " if len(password) == 8: \n", + " return password\n", + "\n", + "find_password(door)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, the sixth digit of the hash that starts with `'00000'` is to be treated as an index that tells where in the password to place the *seventh* digit of the hash. For example, if the sixth digit is `2` and the seventh digit is `a`, then place `a` as the second digit of the final password. Do nothing if the sixth digit is not less than 8, or if a digit has already been placed at that index location." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "844745 000006a94bb1c9322cbb56dd8564e76e ......a.\n", + "5108969 000007b2e0e83dfeade14ebe09f9e6a7 ......ab\n", + "5830668 0000051079ac6b44fc3a5266a1630d42 .....1ab\n", + "6497076 0000008239d1bbf480ea541e9da1e494 8....1ab\n", + "8962195 00000351ce68ffb449644d4bfa4cee5d 8..5.1ab\n", + "23867827 000001c3c28bcbacf0f543a33548ef24 8c.5.1ab\n", + "24090051 000004d57fc545f376c09f27383b2c88 8c.5d1ab\n", + "26383109 0000023d12c49f028699d4679ba91780 8c35d1ab\n", + "CPU times: user 30.4 s, sys: 48.7 ms, total: 30.4 s\n", + "Wall time: 30.4 s\n" + ] + }, + { + "data": { + "text/plain": [ + "'8c35d1ab'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def find_tougher_password(door):\n", + " \"For md5 hashes that begin with '00000', the seventh digit goes in the sixth-digit slot of the password.\"\n", + " password = [off] * 8\n", + " for i in range(BIG):\n", + " x = hashlib.md5(bytes(door + str(i), 'utf-8')).hexdigest()\n", + " if x.startswith('00000'):\n", + " index = int(x[5], 16)\n", + " if index < 8 and password[index] is off:\n", + " password[index] = x[6]\n", + " print(i, x, cat(password)) # Just to see something happen\n", + " if off not in password:\n", + " return cat(password)\n", + "\n", + "%time find_tougher_password(door)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 6](http://adventofcode.com/2016/day/6): Signals and Noise\n", + "\n", + "Given a file, where each line is a string of letters and every line has the same length, find the most common letter in each column. We can easily do this with the help of `Counter.most_common`. (Note I use `Input(6).read().split()` instead of just `Input(6)` so that I don't get the `'\\n'` at the end of each line.)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'tsreykjj'" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counts = [Counter(col) for col in transpose(Input(6).read().split())]\n", + "cat(c.most_common(1)[0][0] for c in counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just to make it clear, here's how we ask for the most common character (and its count) in the first column:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('t', 24)]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = counts[0]\n", + "c.most_common(1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is how we pick out the `'t'` character:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'t'" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c.most_common(1)[0][0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we ask for the *least* common character in each column. Easy-peasy:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'hnfbujie'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cat(c.most_common()[-1][0] for c in counts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 7](http://adventofcode.com/2016/day/7): Internet Protocol Version 7\n", + "\n", + "Given input lines of the form `'abcd[1234]fghi[56789]zz[0]z'`, count the number of lines that are a *TLS*, meaning they have an *ABBA* outside of square brackets, but no *ABBA* inside brackets. An *ABBA* is a 4-character subsequence where the first two letters are the same as the last two, but not all four are the same.\n", + "\n", + "I assume brackets are in proper pairs, and are never nested. Then if I do a `re.split` on brackets, the even-indexed pieces of the split will be outside the brackets, and the odd-indexed will be inside. For example:\n", + "- Given the line `'abcd[1234]fghi[56789]zz'`\n", + "- Split on brackets to get `['abcd', '1234', 'fghi', '56789', 'zz']`\n", + "- Outsides of brackets are `'abcd, fghi, zz'` at indexes 0, 2, 4.\n", + "- Insides of brackets are `'1234, 56789'` at indexes 1, 3." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "110" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def abba(text): return any(a == d != b == c for (a, b, c, d) in subsequences(text, 4))\n", + "def subsequences(seq, n): return [seq[i:i+n] for i in range(len(seq) + 1 - n)]\n", + "def segment(line): return re.split(r'\\[|\\]', line)\n", + "def outsides(segments): return ', '.join(segments[0::2])\n", + "def insides(segments): return ', '.join(segments[1::2])\n", + "def tls(segments): return abba(outsides(segments)) and not abba(insides(segments))\n", + "\n", + "sum(tls(segment(line)) for line in Input(7))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some tests:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "assert abba('abba') and not abba('aaaa') and not abba('abbc')\n", + "assert subsequences('abcdefg', 4) == ['abcd', 'bcde', 'cdef', 'defg']\n", + "assert segment('abcd[1234]fghi[56789]zz') == ['abcd', '1234', 'fghi', '56789', 'zz']\n", + "assert outsides(['abcd', '1234', 'fghi', '56789', 'zz']) == 'abcd, fghi, zz'\n", + "assert insides(['abcd', '1234', 'fghi', '56789', 'zz']) == '1234, 56789'\n", + "assert tls(['abba', '123']) \n", + "assert not tls(['bookkeeper', '123']) and not tls(['abba', 'xxyyx'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we are asked to count the number of *SSL* lines: an *SSL* is when there is an *ABA* outside brackets, and the corresponding *BAB* inside brackets. An *ABA* is a three-character sequence with first and third (but not all three) the same. The corresponding *BAB* has the first character of the *ABA* surrounded by two copies of the second character." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "242" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alphabet = 'abcdefghijklmnopqrstuvwxyz'\n", + "\n", + "def ssl(segments): \n", + " \"Is there an ABA outside brackets, and the corresponding BAB inside?\"\n", + " outs, ins = outsides(segments), insides(segments)\n", + " return any(a+b+a in outs and b+a+b in ins\n", + " for a in alphabet for b in alphabet if a != b)\n", + "\n", + "sum(ssl(segment(line)) for line in Input(7))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 8](http://adventofcode.com/2016/day/8): Two-Factor Authentication\n", + "\n", + "Given an array of pixels on a screen, follow commands that can:\n", + "- Turn on a sub-rectangle of pixels in the upper left corner: `rect 3x2`\n", + "- Rotate a row of pixels: `rotate row y=0 by 4`\n", + "- Rotate a column of pixels: `rotate column x=1 by 1`\n", + "\n", + "Then count the total number of `1` pixels in the screen.\n", + "\n", + "I will use `numpy` two-dimensional arrays, mostly because of the `screen[:, A]` notation for getting at a column." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "128" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def interpret(cmd, screen):\n", + " \"Interpret this command to mutate screen.\"\n", + " A, B = map(int, re.findall(r'(\\d+)', cmd)) # There should be 2 numbers on every command line\n", + " if cmd.startswith('rect'):\n", + " screen[:B, :A] = 1\n", + " elif cmd.startswith('rotate row'):\n", + " screen[A, :] = rotate(screen[A, :], B)\n", + " elif cmd.startswith('rotate col'):\n", + " screen[:, A] = rotate(screen[:, A], B)\n", + "\n", + "def rotate(items, n): return np.append(items[-n:], items[:-n])\n", + "\n", + "def Screen(): return np.zeros((6, 50), dtype=np.int)\n", + "\n", + "def run(commands, screen):\n", + " \"Do all the commands and return the final pixel array.\"\n", + " for cmd in Input(8):\n", + " interpret(cmd, screen) \n", + " return screen\n", + "\n", + "screen = run(Input(8), Screen())\n", + "np.sum(screen)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we are asked what message is on the screen. I won't try to do OCR; I'll just print the screen and look at the output:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "@@@@ @@ @@ @@@ @@ @@@ @ @ @ @ @@ @@ \n", + "@ @ @ @ @ @ @ @ @ @ @ @ @ @ @@ @ @ @ \n", + "@@@ @ @ @ @ @ @ @ @ @ @@@@ @ @ @ @ @ @ \n", + "@ @ @ @@@@ @@@ @ @@ @@@ @ @ @ @@@@ @ @ \n", + "@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ \n", + "@@@@ @@ @ @ @ @ @@@ @ @ @ @ @ @ @@ \n" + ] + } + ], + "source": [ + "for row in screen:\n", + " print(cat(' @'[pixel] for pixel in row))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "My answer is `EOARGPHYAO`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 9](http://adventofcode.com/2016/day/9): Explosives in Cyberspace\n", + "\n", + "In this puzzle we are asked to decompress text of the form `'A(2x5)BCD'`, where the `'(2x5)'` means to make 5 copies of the next 2 characters, yielding `'ABCBCBCBCBCD'`. We'll go through the input text, a character at a time, and if a `re` matcher detects a `'(CxR)'` pattern, process it; otherwise just collect the character. Note that the `C` characters that are to be repeated `R` times are taken literally; even if they contain an embedded `'(1x5)'`." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "138735" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "matcher = re.compile(r'[(](\\d+)x(\\d+)[)]').match # e.g. matches \"(2x5)\" as ('2', '5')\n", + "\n", + "def decompress(s):\n", + " \"Decompress string s by interpreting '(2x5)' as making 5 copies of the next 2 characters.\"\n", + " s = re.sub(r'\\s', '', s) # \"whitespace is ignored\"\n", + " result = []\n", + " i = 0\n", + " while i < len(s):\n", + " m = matcher(s, i)\n", + " if m:\n", + " i = m.end() # Advance to end of '(CxR)' match\n", + " C, R = map(int, m.groups())\n", + " result.append(s[i:i+C] * R) # Collect the C characters, repeated R times\n", + " i += C # Advance past the C characters \n", + " else:\n", + " result.append(s[i]) # Collect 1 regular character\n", + " i += 1 # Advance past it\n", + " return cat(result)\n", + "\n", + "len(decompress(Input(9).read()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, the copied characters *are* recursively decompressed. So, given `'(8x2)(3x3)ABC'`, the `(8x2)` directive picks out the 8 characters `'(3x3)ABC'`, which would then be decompressed to get `'ABCABCABC'` and then the `'x2'` is applied to get `'ABCABCABCABCABCABC'`. However, for this part, we are not asked to actually build up the decompressed string, just to compute its length:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "11125026826" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def decompress_length(s):\n", + " \"\"\"Decompress string s by interpreting '(2x5)' as making 5 copies of the next 2 characters.\n", + " Recursively decompress these next 5 characters. Return the length of the decompressed string.\"\"\"\n", + " s = re.sub(r'\\s', '', s) # \"whitespace is ignored\"\n", + " length = 0\n", + " i = 0\n", + " while i < len(s):\n", + " m = matcher(s, i)\n", + " if m:\n", + " C, R = map(int, m.groups())\n", + " i = m.end(0) # Advance to end of '(CxR)'\n", + " length += R * decompress_length(s[i:i+C]) # Decompress C chars and add to length\n", + " i += C # Advance past the C characters \n", + " else:\n", + " length += 1 # Add 1 regular character to length\n", + " i += 1 # Advance past it\n", + " return length\n", + "\n", + "decompress_length(Input(9).read())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some tests:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "assert decompress('A(2x5)BCD') == 'ABCBCBCBCBCD'\n", + "assert decompress('ADVENT') == 'ADVENT'\n", + "assert decompress('(3x3)XYZ') == 'XYZXYZXYZ'\n", + "assert decompress('(5x4)(3x2)') == '(3x2)(3x2)(3x2)(3x2)'\n", + "assert decompress('X(8x2)(3x3)ABCY') == 'X(3x3)ABC(3x3)ABCY'\n", + " \n", + "assert decompress_length('(8x2)(3x3)ABC') == 18\n", + "assert decompress_length('(25x3)(3x3)ABC(2x3)XY(5x2)PQRSTX(18x9)(3x2)TWO(5x7)SEVEN') == 445\n", + "assert decompress_length('(9x999)(2x999)xx') == 999 * 999 * 2 == 1996002" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 10](http://adventofcode.com/2016/day/10): Balance Bots\n", + "\n", + "In this puzzle, a fleet of robots exchange some chips from input bins, \n", + "passing them among themselves, and eventually putting them in output bins. We are given instructions like this:\n", + "\n", + " value 5 goes to bot 2\n", + " bot 2 gives low to bot 1 and high to bot 0\n", + " value 3 goes to bot 1\n", + " bot 1 gives low to output 1 and high to bot 0\n", + " bot 0 gives low to output 2 and high to output 0\n", + " value 2 goes to bot 2\n", + " \n", + "At first I thought I just had to interpret these instructions sequentially, but then I realized this is actually a *data flow* problem: *whenever* a bot acquires two chips, it passes the low number chip to one destination and the high number to another. So my representation choices are:\n", + "- Bots and bins are represented as strings: `'bot 1'` and `'output 2'`.\n", + "- Chips are represented by ints. (Not strings, because we want 9 to be less than 10).\n", + "- Keep track of which bot currently has which chip(s) with a dict: `has['bot 2'] = {5}`\n", + "- Keep track of what a bot does when it gets 2 chips with a dict: `gives['bot 1'] = ('output 1', 'bot 0')`\n", + "- Pull this information from instructions with `re.findall`. The order of instructions is not important.\n", + "- A function, `give`, moves a chip to a recipient, and if the recipient now has two chips, that triggers two more `give` calls." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bot 113 has {17, 61}\n" + ] + } + ], + "source": [ + "def bots(instructions, goal={17, 61}):\n", + " \"Follow the data flow instructions, and if a bot gets the goal, print it.\"\n", + " def give(giver, chip, recip):\n", + " \"Pass the chip from giver to recipient.\"\n", + " has[giver].discard(chip)\n", + " has[recip].add(chip)\n", + " chips = has[recip]\n", + " if chips == goal:\n", + " print(recip, 'has', goal)\n", + " if len(chips) == 2:\n", + " give(recip, min(chips), gives[recip][0])\n", + " give(recip, max(chips), gives[recip][1])\n", + " \n", + " has = defaultdict(set) # who has what\n", + " gives = {giver: (dest1, dest2) # who will give what\n", + " for (giver, dest1, dest2) \n", + " in re.findall(r'(bot \\d+) gives low to (\\w+ \\d+) and high to (\\w+ \\d+)', instructions)}\n", + " for (chip, recip) in re.findall(r'value (\\d+) goes to (\\w+ \\d+)', instructions):\n", + " give('input bin', int(chip), recip)\n", + " return has\n", + "\n", + "has = bots(Input(10).read())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we are asked for the product of three output bins:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "12803" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def out(i): return has['output ' + str(i)].pop()\n", + "\n", + "out(0) * out(1) * out(2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 11](http://adventofcode.com/2016/day/11): Radioisotope Thermoelectric Generators \n", + "\n", + "I *knew* my `astar_search` function would come in handy! To search for the shortest path to the goal, I need to provide an initial state of the world, a heuristic function (which estimates how many moves away from the goal a state is), and a function that says what states can be reached by moving the elevator up or down, and carrying some stuff. I will make these choices:\n", + "* The state of the world is represented by the `State` type, which says what floor the elevator is on, and for a tuple of floors, the set of objects that are on the floor. We use frozensets so that a state will be hashable.\n", + "* To figure out what moves can be made, consider both directions for the elevator (up or down); find all combinations of one or two items on each floor, and keep all of those moves, as long as they don't violate the constraint that we can't have a chip on the same floor as an RTG, unless the chip's own RTG is there.\n", + "* To calculate the heuristic, add up the number of floors away each item is from the top floor and divide by two (since a move might carry two items).\n", + "\n", + "Here is my input: \n", + "\n", + "* The first floor contains a thulium generator, a thulium-compatible microchip, a plutonium generator, and a strontium generator.\n", + "* The second floor contains a plutonium-compatible microchip and a strontium-compatible microchip.\n", + "* The third floor contains a promethium generator, a promethium-compatible microchip, a ruthenium generator, and a ruthenium-compatible microchip.\n", + "* The fourth floor contains nothing relevant." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "State = namedtuple('State', 'elevator, floors')\n", + "\n", + "def fs(*items): return frozenset(items)\n", + "\n", + "legal_floors = {0, 1, 2, 3}\n", + "\n", + "def combos(things):\n", + " \"All subsets of 1 or 2 things.\"\n", + " for s in chain(combinations(things, 1), combinations(things, 2)):\n", + " yield fs(*s)\n", + "\n", + "def moves(state):\n", + " \"All legal states that can be reached in one move from this state\"\n", + " L, floors = state\n", + " for L2 in {L + 1, L - 1} & legal_floors:\n", + " for stuff in combos(floors[L]):\n", + " newfloors = tuple((s | stuff if i == L2 else \n", + " s - stuff if i == state.elevator else \n", + " s)\n", + " for (i, s) in enumerate(state.floors))\n", + " if legal_floor(newfloors[L]) and legal_floor(newfloors[L2]):\n", + " yield State(L2, newfloors)\n", + "\n", + "def legal_floor(floor):\n", + " \"Floor is legal if no RTG, or every chip has its corresponding RTG.\"\n", + " rtgs = any(r.endswith('G') for r in floor)\n", + " chips = [c for c in floor if c.endswith('M')]\n", + " return not rtgs or all(generator_for(c) in floor for c in chips)\n", + "\n", + "def generator_for(chip): return chip[0] + 'G'\n", + "\n", + "def h_to_top(state):\n", + " \"An estimate of the number of moves needed to move everything to top.\"\n", + " total = sum(len(floor) * i for (i, floor) in enumerate(reversed(state.floors)))\n", + " return math.ceil(total / 2) # Can move two items in one move." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try it out on an easy sample problem:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[State(elevator=0, floors=(frozenset({'RG'}), frozenset(), frozenset({'RM'}), frozenset())),\n", + " State(elevator=1, floors=(frozenset(), frozenset({'RG'}), frozenset({'RM'}), frozenset())),\n", + " State(elevator=2, floors=(frozenset(), frozenset(), frozenset({'RG', 'RM'}), frozenset())),\n", + " State(elevator=3, floors=(frozenset(), frozenset(), frozenset(), frozenset({'RG', 'RM'})))]" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "easy = State(0, (fs('RG'), Ø, fs('RM'), Ø))\n", + "\n", + "astar_search(easy, h_to_top, moves)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to solve the real problem. The answer we need is the number of elevator moves, which is one less than the path length (because the path includes the initial state)." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 11.9 s, sys: 72.3 ms, total: 12 s\n", + "Wall time: 12 s\n" + ] + }, + { + "data": { + "text/plain": [ + "31" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "part1 = State(0, (fs('TG', 'TM', 'PG', 'SG'), fs('PM', 'SM'), fs('pM', 'pG', 'RM', 'RG'), Ø))\n", + "\n", + "%time path = astar_search(part1, h_to_top, moves)\n", + "len(path) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we add four more items. Now, in part one there were 10 items, each of which could be on any of the 4 floors, so that's 410 ≈ 1 million states. Adding 4 more items yields ≈ 260 million states. We won't visit every state, but the run time could be around 100 times longer. I think I'll start this running, take the dog for a walk, and come back to see if it worked." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 14min 34s, sys: 11.4 s, total: 14min 46s\n", + "Wall time: 14min 52s\n" + ] + }, + { + "data": { + "text/plain": [ + "55" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "part2 = State(0, (fs('TG', 'TM', 'PG', 'SG', 'EG', 'EM', 'DG', 'DM'), \n", + " fs('PM', 'SM'), fs('pM', 'pG', 'RM', 'RG'), Ø))\n", + "\n", + "%time path = astar_search(part2, h_to_top, moves)\n", + "len(path) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It worked. And it took about 60 times longer. If I wanted to make it more efficient, I would focus on *symmetry*: when there are two symmetric moves, we only need to consider one. For example, in terms of finding the shortest path, it is the same to move, say `{'TG', 'TM'}` or `{'EG', 'EM'}` or `{'DG', 'DM'}` when they are all on the ground floor." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 12](http://adventofcode.com/2016/day/12): Leonardo's Monorail\n", + "\n", + "This one looks pretty easy: an interpreter for an assembly language with 4 op codes and 4 registers. We start by parsing a line like `\"cpy 1 a\"` into a tuple, `('cpy', 1, 'a')`. Then to `interpret` the code, we set the program counter, `pc`, to 0, and interpret the instruction at `code[0]`, and continue until the `pc` is past the end of the code:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'a': 318007, 'b': 196418, 'c': 0, 'd': 0}" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def interpret(code, regs):\n", + " \"Execute instructions until pc goes off the end.\"\n", + " def val(x): return (regs[x] if x in regs else x)\n", + " pc = 0\n", + " while pc < len(code):\n", + " inst = code[pc]\n", + " op, x, y = inst[0], inst[1], inst[-1]\n", + " pc += 1\n", + " if op == 'cpy': regs[y] = val(x)\n", + " elif op == 'inc': regs[x] += 1\n", + " elif op == 'dec': regs[x] -= 1\n", + " elif op == 'jnz' and val(x): pc += y - 1\n", + " return regs\n", + "\n", + "def parse(line): \n", + " \"Split line into words, and convert to int where appropriate.\"\n", + " return tuple((x if x.isalpha() else int(x)) \n", + " for x in line.split())\n", + "\n", + "code = [parse(line) for line in Input(12)]\n", + "\n", + "interpret(code, dict(a=0, b=0, c=0, d=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I had a bug initially: in the `jnz` instruction, I had `pc += y`, to do the relative jump, but I forgot the `-1` to offset the previous `pc += 1`.\n", + "\n", + "In **part two** all we have to do is initialize register `c` to 1, not 0:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'a': 9227661, 'b': 5702887, 'c': 0, 'd': 0}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "interpret(code, dict(a=0, b=0, c=1, d=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 13](http://adventofcode.com/2016/day/13): A Maze of Twisty Little Cubicles \n", + "\n", + "This is a maze-solving puzzle, where the maze is infinite in the non-negative (x, y) quarter-plane. Each space in that infinite grid is open or closed according to this computation:\n", + "> Find `x*x + 3*x + 2*x*y + y + y*y`.\n", + "Add the office designer's favorite number (your puzzle input).\n", + "Find the binary representation of that sum; count the number of bits that are 1.\n", + "If the number of bits that are 1 is even, it's an open space (denoted `'.'`).\n", + "If the number of bits that are 1 is odd, it's a wall (denoted `'#'`).\n", + "\n", + "The problem is to find the length of the shortest path to the goal location, (31, 39). So I'll be using `astar_search` again." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "82" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "favorite = 1362\n", + "goal = (31, 39)\n", + "\n", + "def is_open(location):\n", + " \"Is this an open location?\"\n", + " x, y = location\n", + " num = x*x + 3*x + 2*x*y + y + y*y + favorite\n", + " return x >= 0 and y >= 0 and bin(num).count('1') % 2 == 0\n", + "\n", + "def open_neighbors(location): return filter(is_open, neighbors4(location))\n", + "\n", + "path = astar_search((1, 1), lambda p: cityblock_distance(p, goal), open_neighbors)\n", + "len(path) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see a portion of the maze:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "#..###.#...#..#....##.#...#....#....#..#.#.##...##.##.##.#####.#####.####.#.##..#..#.#.#.#\n", + "#.#..#.##.#######.#.#.####.##.###...##.#..#.###...#.#..#.##...#..###....##...##.#.##.#.#..\n", + "#..#.#.##.#....##...#..#.####.####...#..#..#..#.#...##......#.....######.#.#...##.##.#..##\n", + "##..##.##.#..#...###.#.....#.....##.######....#..###########.####..##....#...#......###..#\n", + "..#.##..########.#.#####...#..##.##.#.....##.###.#..#...##.###..#....####.#######.#.#.####\n", + "#............###.....#####.#####....#..##..#.###....#....#......#..#.##.#....##.###.###..#\n", + "###.##.####...#.##....#..#.#..#.##.####.##....####.###.#.##.##.###......###........#...#..\n", + "#.#..#.##.#.#.######..#.##..#.####..#.#######..###..##..#.##.#.##########.#####..#.#.#....\n", + ".###......#..#..#..####.###..#..#.#.##..#.......###...#....#....##...#......#####..#..##.#\n", + ".####..###.#.##.#.#...#..#.#.##.##......#..####..#.######.#####....#...##.......#.###..#.#\n", + "..######.###..###..##.#..###..##.#..##.####...#..##....##.#...#.###.######.######.#.##....\n", + "#..##..#.......###.#..###......#.#####..#.#...#...#..#....#...#...###....#.##..##.######..\n", + ".......##.##.#.....#....#.##.#.###..#.#.####..##.###########..##.#....##.....#..##..#..##.\n", + "#####.#.#.##...###.##...##.#..#..##.##...#######.....##..#######.#########.#.....##.#.#.#.\n", + "...##..##.#.###..#.###.#.##.#..#..##.#.....#..#####....#..##..##...#..##.#..##.#..###..##.\n", + ".#.###.#..#...#.##...#..#.#..#.......##..#.##..##.#.##.....#.....#..#...###..#......##.#..\n", + "##..#..#.######.#####.#..###..##.###.####...#.....#.#.##.#.##.#####...#.####..##.##.#..#.#\n", + "....##.#.##..#...##.#.##.####..#.###....#...#..###..#..#..#.#....#.##.#..#######.#..##.#..\n", + "##...#.......#......#.....#.###...########.#####.#..##..#..####..##.#.#...##..#..#...#..#.\n", + "###.#######.########.##.#.###.##...##..#.#.##..#.#########.##.###.##..###.....##.##.######\n", + ".##.#...###.##...#.##.#..#.....##....#.##......#.#..#........#..##.#......##.#.#.##.#...#.\n", + ".##.#.....#....#..#.##.#.####.#.#.##..#.#####.##.#..#..#####......###..##..#..##.#..#...##\n", + "...###.##.#.###.#.##.###...##..##.#.#......##.#..#.####.....##.##.#####.##..#.#..#####...#\n", + ".#..##.#..##..##...#.....#..##.#..#..##..#.##.#.##..#.#..##..#.#....#.#######.#.#....##.##\n", + "###....#...###.#...##.#####.#..#..##.#####..###.#.#.#####.###..#.##.##..#...###...##.##.##\n", + ".#.##.###.#..#.##.#.###..#..##.#####..........#.##...##.###.##.#.#....#.#.....######.#....\n", + ".####..##..#.#.##..#.....#...#.#..#####.##.##.##.#.....#.....#...#.##..###.##..#..#..#..##\n", + "...#.#...#..##..##...###.##.##..#..##.#.##.#...#.##..#.#.##.###..#.#.#..##.#.#..#.#.###...\n", + "#..##.##..#.###.#.####.#.##.###.#.....#....#.#.######..#.##.#.###..##.#....####..##.#####.\n", + "##..#######..#..#.....##.....#..######.##..#..#.....#.##.#..###.##..##.##.#..#.#..#..##.#.\n" + ] + } + ], + "source": [ + "for y in range(30):\n", + " print(cat(('.' if is_open((x, y)) else '#') for x in range(90)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we're asked how many locations we can reach in 50 moves or less. I'll grab the `breadth_first` search function from [aima-python](https://github.com/aimacode/aima-python/blob/master/search-4e.ipynb) and modify it to find all the states within N steps:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "138" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def count_locations_within(start, N, neighbors):\n", + " \"Find how many locations are within N steps from start.\"\n", + " frontier = deque([start]) # A queue of states\n", + " distance = {start: 0} # distance to start; also tracks all states seen\n", + " while frontier:\n", + " s = frontier.popleft()\n", + " if distance[s] < N:\n", + " for s2 in neighbors(s):\n", + " if s2 not in distance:\n", + " frontier.append(s2)\n", + " distance[s2] = distance[s] + 1\n", + " return len(distance)\n", + " \n", + "count_locations_within((1, 1), 50, open_neighbors)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# [Day 14](http://adventofcode.com/2016/day/14): One-Time Pad \n", + "\n", + "For this problem I again have to take the md5 hash of a string with increasing integers appended. The puzzle is to find the integer that yields the 64th key, where a hash is a key if:\n", + "- It contains three of the same character in a row, like 777. Only consider the first such triplet in a hash.\n", + "- One of the next 1000 hashes in the stream contains that same character five times in a row, like 77777.\n", + "\n", + "I'll use `lru_cache` to avoid repeating the hashing of the next 1000." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "25427" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "salt = 'yjdafjpo'\n", + "\n", + "@lru_cache(1001)\n", + "def hashval(i): return hashlib.md5(bytes(salt + str(i), 'utf-8')).hexdigest()\n", + "\n", + "def is_key(i):\n", + " \"A key has a triple like '777', and then '77777' in one of the next thousand hashval(i).\"\n", + " three = re.search(r'(.)\\1\\1', hashval(i))\n", + " if three:\n", + " five = three.group(1) * 5\n", + " return any(five in hashval(i+delta) for delta in range(1, 1001))\n", + " \n", + "def nth_key(N): return nth(filter(is_key, range(BIG)), N)\n", + "\n", + "nth_key(63)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we do *key stretching*, hashing an additional 2016 times. Eeverything else is the same:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 36.4 s, sys: 314 ms, total: 36.7 s\n", + "Wall time: 37 s\n" + ] + }, + { + "data": { + "text/plain": [ + "22045" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@lru_cache(1001)\n", + "def hashval(i, stretch=2016): \n", + " h = hashlib.md5(bytes(salt + str(i), 'utf-8')).hexdigest()\n", + " for i in range(stretch):\n", + " h = hashlib.md5(bytes(h, 'utf-8')).hexdigest()\n", + " return h\n", + "\n", + "%time nth_key(63)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This was my highest-scoring day, finishing #20 on part two." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 15](http://adventofcode.com/2016/day/15): Timing is Everything\n", + "\n", + "In this puzzle rotating discs with a slot in position 0 spin around. We are asked at what time will all the slots be lined up for a capsule to fall through the slots. The capsule takes one time unit to fall through each disc (not clear why it doesn't accelerate as it falls) and the discs spin one position per time unit." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "376777" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def parse(inputs): \n", + " \"Parse an input string into (disc#, positions, pos) triples.\"\n", + " return [tuple(map(int, triple))\n", + " for triple in re.findall(r'#(\\d+).* (\\d+) positions.* (\\d+)[.]', inputs)]\n", + " \n", + "discs = parse('''\n", + "Disc #1 has 13 positions; at time=0, it is at position 1.\n", + "Disc #2 has 19 positions; at time=0, it is at position 10.\n", + "Disc #3 has 3 positions; at time=0, it is at position 2.\n", + "Disc #4 has 7 positions; at time=0, it is at position 1.\n", + "Disc #5 has 5 positions; at time=0, it is at position 3.\n", + "Disc #6 has 17 positions; at time=0, it is at position 5.\n", + "''')\n", + "\n", + "def falls(t, discs):\n", + " \"If we drop the capsule at time t, does it fall through all slots?\"\n", + " return all((pos + t + d) % positions == 0 \n", + " for (d, positions, pos) in discs)\n", + "\n", + "first(t for t in range(BIG) if falls(t, discs))" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "assert discs == [(1, 13, 1), (2, 19, 10), (3, 3, 2), (4, 7, 1), (5, 5, 3), (6, 17, 5)]\n", + "assert falls(5, [(1, 5, 4), (2, 2, 1)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For **part two**, we add a 7th disc, with 11 positions, at position 0 at time 0. I coud go through all the possible times, just as in part one, but I see a way to get a 19-fold speedup: Disc #2 is the largest, with 19 positions, so we only need consider every 19 values of `t`. But what is the first one to consider? Disc @2 starts at position 10, so to get back to position 0, we have to release at `t=7`, because 10 + 2 + 7 = 19 = 0 mod 19. So we will iterate `t` over `range(7, BIG, 19)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3903937" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "discs.append((7, 11, 0))\n", + "\n", + "first(t for t in range(7, BIG, 19) if falls(t, discs))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 16](http://adventofcode.com/2016/day/16) Dragon Checksum\n", + "\n", + "Given a bit string of the form `'01...'`, expand it until it fills N bits, then report the checksum.\n", + "\n", + "The rules for expanding:\n", + "- Call the data you have at this point \"a\".\n", + "- Make a copy of \"a\"; call this copy \"b\".\n", + "- Reverse the order of the characters in \"b\".\n", + "- In \"b\", replace all instances of 0 with 1 and all 1s with 0.\n", + "- The resulting data is \"a\", then a single 0, then \"b\".\n", + "- If this gives N or more bits, take the first N; otherwise repeat the process.\n", + "\n", + "The rules for the checksum:\n", + "- Assume the string is 110010110100\n", + "- Consider each pair: 11, 00, 10, 11, 01, 00.\n", + "- These are same, same, different, same, different, same, producing 110101.\n", + "- The resulting string has length 6, which is even, so we repeat the process.\n", + "- The pairs are 11 (same), 01 (different), 01 (different).\n", + "- This produces the checksum 100, which has an odd length, so we stop." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'10010110010011110'" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def expand(a, N):\n", + " \"Expand seed `a` until it has length N.\"\n", + " while len(a) < N:\n", + " b = flip(a[::-1])\n", + " a = a + '0' + b\n", + " return a[:N]\n", + "\n", + "def flip(text, table=str.maketrans('10', '01')): return text.translate(table)\n", + "\n", + "def checksum(a):\n", + " \"Compute the checksum of `a` by comparing pairs until len is odd.\"\n", + " while len(a) % 2 == 0:\n", + " a = cat(('1' if a[i] == a[i+1] else '0') \n", + " for i in range(0, len(a), 2))\n", + " return a\n", + " \n", + "seed = '10010000000110000'\n", + "\n", + "checksum(expand(seed, 272))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we take the same seed, but expand it to fill 35Mb of space:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 6.17 s, sys: 326 ms, total: 6.49 s\n", + "Wall time: 6.54 s\n" + ] + }, + { + "data": { + "text/plain": [ + "'01101011101100011'" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time checksum(expand(seed, 35651584)) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 17](http://adventofcode.com/2016/day/17) Two Steps Forward\n", + "\n", + "In this puzzle, we move through a 4x4 grid/maze, starting at position (0, 0) and trying to reach (3, 3), but the door from one position to the next is open or not depending on the hash of the path to get there (and my passcode), so doors open and lock themselves as you move around. I'll represent a state as a tuple of `(position, path)` and use `astar_search` to find the shortest path to the goal:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[((0, 0), ''),\n", + " ((1, 0), 'R'),\n", + " ((1, 1), 'RD'),\n", + " ((1, 0), 'RDU'),\n", + " ((2, 0), 'RDUR'),\n", + " ((3, 0), 'RDURR'),\n", + " ((3, 1), 'RDURRD'),\n", + " ((3, 2), 'RDURRDD'),\n", + " ((2, 2), 'RDURRDDL'),\n", + " ((3, 2), 'RDURRDDLR'),\n", + " ((3, 3), 'RDURRDDLRD')]" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "passcode = 'awrkjxxr'\n", + "\n", + "openchars = 'bcdef'\n", + "\n", + "grid = set((x, y) for x in range(4) for y in range(4))\n", + "\n", + "start, goal = (0, 0), (3, 3)\n", + "\n", + "def to_goal(state): \n", + " \"City block distance between state's position and goal.\"\n", + " pos, path = state\n", + " return cityblock_distance(pos, goal)\n", + "\n", + "directions = [(0, 'U', (0, -1)), (1, 'D', (0, 1)), (2, 'L', (-1, 0)), (3, 'R', (1, 0))]\n", + "\n", + "def moves(state):\n", + " \"All states reachable from this state.\"\n", + " (x, y), path = state\n", + " hashx = hashlib.md5(bytes(passcode + path, 'utf-8')).hexdigest()\n", + " for (i, p, (dx, dy)) in directions:\n", + " pos2 = (x+dx, y+dy)\n", + " if hashx[i] in openchars and pos2 in grid:\n", + " yield (pos2, path+p)\n", + " \n", + "astar_search((start, ''), to_goal, moves)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we're asked for the longest path to the goal. We have to stop when we reach the goal, but we can make repeated visits to positions along the way, as long as the doors are open. I'll use a depth-first search, and keep track of the longest path length:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "526" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def longest_search(state, goal, moves):\n", + " \"Find the longest path to goal by depth-first search.\"\n", + " longest = 0\n", + " frontier = [state]\n", + " while frontier:\n", + " state = (pos, path) = frontier.pop()\n", + " if pos == goal:\n", + " longest = max(longest, len(path))\n", + " else:\n", + " frontier.extend(moves(state))\n", + " return longest\n", + " \n", + "longest_search((start, ''), goal, moves)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 18](http://adventofcode.com/2016/day/18) Like a Rogue\n", + "\n", + "Here we have a cellular automaton, where a cell is a \"trap\" iff the 3 tiles in the row above, (one to the left above, directly above, and one to the right above) are one of the set `{'^^.', '.^^', '^..', '..^'}`; in other words if the first of the three is different from the last of the three. Given an initial row, we're asked for the count of all the safe tiles in the first 40 rows:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1951" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "safe, trap = '.', '^' \n", + "initial = '.^^.^^^..^.^..^.^^.^^^^.^^.^^...^..^...^^^..^^...^..^^^^^^..^.^^^..^.^^^^.^^^.^...^^^.^^.^^^.^.^^.^.'\n", + "\n", + "def rows(n, row=initial):\n", + " \"The first n rows of tiles (given the initial row).\"\n", + " result = [row]\n", + " for i in range(n-1):\n", + " previous = safe + result[-1] + safe\n", + " result.append(cat((trap if previous[i-1] != previous[i+1] else safe)\n", + " for i in range(1, len(previous) - 1)))\n", + " return result\n", + "\n", + "cat(rows(40)).count(safe)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here I reproduce the simple example from the puzzle page:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['.^^.^.^^^^',\n", + " '^^^...^..^',\n", + " '^.^^.^.^^.',\n", + " '..^^...^^^',\n", + " '.^^^^.^^.^',\n", + " '^^..^.^^..',\n", + " '^^^^..^^^.',\n", + " '^..^^^^.^^',\n", + " '.^^^..^.^^',\n", + " '^^.^^^..^^']" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rows(10, '.^^.^.^^^^')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we just have to run longer (but only a few seconds):" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 7.92 s, sys: 90.6 ms, total: 8.01 s\n", + "Wall time: 8.08 s\n" + ] + }, + { + "data": { + "text/plain": [ + "20002936" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time cat(rows(400000)).count(safe)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 19](http://adventofcode.com/2016/day/19) An Elephant Named Joseph\n", + "\n", + "Elves numbered 1 to *N* sit in a circle. Each Elf brings a present. Then, starting with the first Elf, they take turns stealing all the presents from the Elf to their left. An Elf with no presents is removed from the circle and does not take turns. So, if *N* = 5, then:\n", + "\n", + " Elf 1 takes Elf 2's present.\n", + " Elf 2 has no presents and is skipped.\n", + " Elf 3 takes Elf 4's present.\n", + " Elf 4 has no presents and is also skipped.\n", + " Elf 5 takes Elf 1's two presents.\n", + " Neither Elf 1 nor Elf 2 have any presents, so both are skipped.\n", + " Elf 3 takes Elf 5's three presents, ending the game.\n", + " \n", + "Who ends up with all the presents for general case of *N*?\n", + "First, I note that I only need to keep track of the Elf number of the remaining elves,\n", + "I don't need to count how many presents each one has. I see two representation choices:\n", + "- Represent the circle of elves as a list of elf numbers, and everytime an Elf's presents are taken, delete the elf from the list. But this is O(*N*2), where *N* = 3 million, so this will be slow.\n", + "- Represent the elves by a range, and instead of deleting elf-by-elf, instead limit the range round-by-round.\n", + "If there is an even number of elves, then the elf in position 0 takes from position 1; position 2 takes from position 3, and so on, leaving only the even positions, which we denote `elves[0::2]`. If there is an odd number of elves, then it is the same, except that the last elf takes from the one in position 0, leaving `elves[2::2]`. Here's the code:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1842613" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def Elves(N=3018458): return range(1, N+1) \n", + "\n", + "def winner(elves): return (elves[0] if (len(elves) == 1) else winner(one_round(elves)))\n", + "\n", + "def one_round(elves): return (elves[0::2] if (len(elves) % 2 == 0) else elves[2::2])\n", + "\n", + "assert winner(Elves(5)) == 3\n", + "\n", + "winner(Elves())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a cool thing about representing the elves with a range: the total storage is O(1), not O(*N*).\n", + "We never need to make a list of 3 million elements.\n", + "Here we see a trace of the calls to `one_round`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "one_round(range(1, 3018459)) = range(1, 3018459, 2)\n", + "one_round(range(1, 3018459, 2)) = range(5, 3018459, 4)\n", + "one_round(range(5, 3018459, 4)) = range(5, 3018461, 8)\n", + "one_round(range(5, 3018461, 8)) = range(21, 3018461, 16)\n", + "one_round(range(21, 3018461, 16)) = range(53, 3018469, 32)\n", + "one_round(range(53, 3018469, 32)) = range(53, 3018485, 64)\n", + "one_round(range(53, 3018485, 64)) = range(181, 3018485, 128)\n", + "one_round(range(181, 3018485, 128)) = range(437, 3018549, 256)\n", + "one_round(range(437, 3018549, 256)) = range(437, 3018677, 512)\n", + "one_round(range(437, 3018677, 512)) = range(1461, 3018677, 1024)\n", + "one_round(range(1461, 3018677, 1024)) = range(3509, 3019189, 2048)\n", + "one_round(range(3509, 3019189, 2048)) = range(7605, 3020213, 4096)\n", + "one_round(range(7605, 3020213, 4096)) = range(7605, 3022261, 8192)\n", + "one_round(range(7605, 3022261, 8192)) = range(7605, 3022261, 16384)\n", + "one_round(range(7605, 3022261, 16384)) = range(7605, 3022261, 32768)\n", + "one_round(range(7605, 3022261, 32768)) = range(7605, 3022261, 65536)\n", + "one_round(range(7605, 3022261, 65536)) = range(7605, 3022261, 131072)\n", + "one_round(range(7605, 3022261, 131072)) = range(269749, 3022261, 262144)\n", + "one_round(range(269749, 3022261, 262144)) = range(794037, 3153333, 524288)\n", + "one_round(range(794037, 3153333, 524288)) = range(1842613, 3415477, 1048576)\n", + "one_round(range(1842613, 3415477, 1048576)) = range(1842613, 3939765, 2097152)\n" + ] + }, + { + "data": { + "text/plain": [ + "1842613" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "one_round = trace1(one_round)\n", + "winner(Elves())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two** the rules have changed, and each elf now takes from the elf *across* the circle. If there is an even number of elves, take from the elf directly across. Fo example, with 12 elves in a circle (like a clock face), Elf 1 takes from Elf 7. With an odd number of elves, directly across the circle falls between two elves, so choose the one that is earlier in the circle. For example, with 11 elves, Elf 2 takes from the Elf at position 7. Now who ends up with the presents?\n", + "\n", + "This is tougher. I can't think of a simple `range` expression to describe who gets eliminated in a round. But I can represent the circle as a list and write a loop to eliminate elves one at a time. Again, if I did that with a `del` statement for each elf, it would be O(*N*2). But if instead I do one round at a time, replacing each eliminated elf with `None` in the list, and then filtering out the `None` values, then each round is only O(*N*), and sine there will be log(*N*) rounds, the whole thing is only O(*N* log(*N*)). That should be reasonably fast.\n", + "\n", + "It is still tricky to know which elf to eliminate. If there are *N* elves, then the elf at position *i* should elminate the one at position *i* + *N* // 2. But we have to skip over the already-eliminated spaces; we can do that by keeping track of the number of eliminated elves in the variable `eliminated`. We also need to keep track of the current value of `N`, since it will change. And, since I don't want to deal with the headaches of wrapping around the circletconn, I will only deal with the first third of the elves: the first third all eliminate elves in the other two-thirds; if we went more than 1/3 of the way through, we would have to worry about wrapping around. (I had a bug here: at first I just iterated through `N // 3`. But when `N` is 2, that does no iteration at all, which is wrong; with two elves, the first should eliminate the other. It turns out it is safe to iterate through `ceil(N /3)` on each round.)\n", + "\n", + "I will change the `Elves` function to return a `list`, not a `range`. The function `winner` stays the same. The `one_round` function is where the work goes:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.26 s, sys: 74.7 ms, total: 1.33 s\n", + "Wall time: 1.34 s\n" + ] + }, + { + "data": { + "text/plain": [ + "1424135" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def Elves(N=3018458): return list(range(1, N+1))\n", + "\n", + "def one_round(elves):\n", + " \"The first third of elves eliminate ones across the circle from them; who is left?\"\n", + " N = len(elves)\n", + " eliminated = 0\n", + " for i in range(int(math.ceil(N / 3))):\n", + " across = i + eliminated + (N // 2) \n", + " elves[across] = None\n", + " N -= 1\n", + " eliminated += 1\n", + " return list(filter(None, elves[i+1:] + elves[:i+1]))\n", + "\n", + "assert winner(Elves(5)) == 2\n", + "\n", + "assert one_round(Elves(5)) == [4, 1, 2]\n", + "\n", + "%time winner(Elves())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I was worried that this solution might take over a minute to run, but it turns out to only take about a second." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 20](http://adventofcode.com/2016/day/20) Firewall Rules\n", + "\n", + "We are given a list of blocked IP addresses, in the form `\"2365712272-2390766206\"`, indicating the low and high numbers that are blocked by the firewall. I will parse the numbers into `(low, high)` pairs, and sort them by the low number first (and peek at the first 5 to see if I got it right): " + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[[0, 97802],\n", + " [5682, 591077],\n", + " [591078, 868213],\n", + " [868214, 1216244],\n", + " [1216245, 1730562]]" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pairs = sorted(map(parse_ints, Input(20)))\n", + "\n", + "pairs[:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We are asked what is the lowest non-negative integer that is not blocked. I will generate all the unblocked numbers, and just ask for the first one. (Why do it that way? Because it feels like `unblocked` is the fundamental issue of the problem, and we already have a function to compute `first`; there's no need for a `first_unblocked` function that conflates two ideas.) To find unblocked numbers, start a counter, `i` at zero, and increment it past the high value of each range, after yielding any numbers from `i` to the low value of the range:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4793564" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def unblocked(pairs):\n", + " \"Find the lowest unblocked integer, given the sorted pairs of blocked numbers.\"\n", + " i = 0\n", + " for (low, high) in pairs:\n", + " yield from range(i, low)\n", + " i = max(i, high + 1)\n", + " \n", + "first(unblocked(pairs)) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two** we are asked how many numbers are unblocked:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "146" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(list(unblocked(pairs)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# [Day 21](http://adventofcode.com/2016/day/21) Scrambled Letters and Hash \n", + "\n", + "In this puzzle we are asked to take a password string, scramble it according to a list of instructions, and output the result, which will be a permutation of the original password. This is tedious because there are seven different instructions, but each one is pretty straightforward. I make the following choices:\n", + "- I'll transform `password` (a `str`) into `pw` (a `list`), because lists are mutable and easier to manipulate. At the end I'll turn it back into a `str`.\n", + "- I'll define functions `rot` and `swap` because they get used multiple times by different instructions.\n", + "- I use the variables `A, B` to denote the first two integers anywhere in a line. If there is only one integer (or none), then `B` (and `A`) get as a default value `0`. I accept ill-formed instructions, such as `\"move 1 to 4\"` instead of requiring `\"move position 1 to position 4\"`. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'gcedfahb'" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def scramble(password, instructions=list(Input(21)), verbose=False):\n", + " \"Scramble the password according to the instructions.\"\n", + " pw = list(password) \n", + " def rot(N): pw[:] = pw[-N:] + pw[:-N]\n", + " def swap(A, B): pw[A], pw[B] = pw[B], pw[A] \n", + " for line in instructions:\n", + " words = line.split()\n", + " A, B, = parse_ints(line + ' 0 0')[:2]\n", + " cmd = line.startswith\n", + " if cmd('swap position'): swap(A, B)\n", + " elif cmd('swap letter'): swap(pw.index(words[2]), pw.index(words[5]))\n", + " elif cmd('rotate right'): rot(A)\n", + " elif cmd('rotate left'): rot(-A)\n", + " elif cmd('reverse'): pw[A:B+1] = pw[A:B+1][::-1]\n", + " elif cmd('move'): pw[A:A+1], pw[B:B] = [], pw[A:A+1]\n", + " elif cmd('rotate based'):\n", + " i = pw.index(words[6])\n", + " rot((i + 1 + (i >= 4)) % len(pw))\n", + " if verbose: \n", + " print(line + ': ' + cat(pw))\n", + " return cat(pw)\n", + "\n", + "scramble('abcdefgh')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When I ran the first version of this code the answer I got was incorrect, and I couldn't see where I went wrong, so I implemented the test case from the problem description and inspected the results line by line." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "swap position 4 with position 0: ebcda\n", + "swap letter d with letter b: edcba\n", + "reverse positions 0 through 4: abcde\n", + "rotate left 1 step: bcdea\n", + "move position 1 to position 4: bdeac\n", + "move position 3 to position 0: abdec\n", + "rotate based on position of letter b: ecabd\n", + "rotate based on position of letter d: decab\n" + ] + }, + { + "data": { + "text/plain": [ + "'decab'" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "test = '''swap position 4 with position 0\n", + "swap letter d with letter b\n", + "reverse positions 0 through 4\n", + "rotate left 1 step\n", + "move position 1 to position 4\n", + "move position 3 to position 0\n", + "rotate based on position of letter b\n", + "rotate based on position of letter d'''.splitlines()\n", + "\n", + "scramble('abcde', test, verbose=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was enough to show me that I had two bugs (which are fixed above): \n", + "- For `\"reverse\"`, I thought `\"positions 0 through 4\"` meant `[0:4]`, when actually it means `[0:5]`.\n", + "- For `\"rotate based\"`, in the case where the rotation is longer than the password, I need to take the modulo of the password length.\n", + "\n", + "For **part two**, the task is to find the password that, when scrambled, yields `'fbgdceah'`. I think the puzzle designer was trying to tempt solvers into implementing an `unscramble` function, which would be another 20 or 30 lines of code. Fortunately, I was too lazy to go down that path. I realized there are only 40 thousand permutations of an 8-character password, so we can just brute force them all (which would be infeasible with a 20-character password):" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'hegbdcfa'}" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{cat(p) for p in permutations('fbgdceah') \n", + " if scramble(p) == 'fbgdceah'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# [Day 22](http://adventofcode.com/2016/day/22) Grid Computing\n", + "\n", + "We are given a description of files across a grid computing cluster, like this:\n", + "\n", + " root@ebhq-gridcenter# df -h\n", + " Filesystem Size Used Avail Use%\n", + " /dev/grid/node-x0-y0 92T 70T 22T 76%\n", + " /dev/grid/node-x0-y1 86T 65T 21T 75%\n", + "\n", + "For part one, we are asked how many pairs of nodes can viably make a transfer of data. The pair (A, B) is viable if\n", + "- Node A is not empty (its Used is not zero).\n", + "- Nodes A and B are not the same node.\n", + "- The data on node A (its Used) would fit on node B (its Avail).\n", + "\n", + "I'll represent a node as a `namedtuple` of six integers; the rest is easy:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "903" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Node = namedtuple('Node', 'x, y, size, used, avail, pct')\n", + "\n", + "nodes = [Node(*parse_ints(line)) for line in Input(22) if line.startswith('/dev')]\n", + "\n", + "def viable(A, B): return A != B and 0 < A.used <= B.avail\n", + "\n", + "sum(viable(A, B) for A in nodes for B in nodes)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That worked, but let's make sure the nodes look reasonable:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[Node(x=0, y=0, size=92, used=70, avail=22, pct=76),\n", + " Node(x=0, y=1, size=86, used=65, avail=21, pct=75),\n", + " Node(x=0, y=2, size=88, used=73, avail=15, pct=82),\n", + " Node(x=0, y=3, size=91, used=67, avail=24, pct=73),\n", + " Node(x=0, y=4, size=87, used=70, avail=17, pct=80)]" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nodes[:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we are asked to move data from the node in the upper right (the one with maximum `x` value and `y=0`) to the upper left (x=0, y=0). At first I worried about all sorts of complications: could we split the data into two or more pieces, copying different pieces into different nodes, and then recombining them? I spent many minutes thinking about these complications. Eventually, after a more careful reading of the rules, I decided such moves were not allowed, and the answer had to just involve moving the empty square around. So to proceed, we need to find the initial position of the empty node, and the maximum x value, so we know where the data is: " + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(Node(x=35, y=21, size=91, used=0, avail=91, pct=0), 37)" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "empty = first(node for node in nodes if node.used == 0)\n", + "maxx = max(node.x for node in nodes)\n", + "\n", + "empty, maxx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will also define the `grid` as a dict of `{(x, y): node}` entries (which will enable me to find neighbors of a node):" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "grid = {(node.x, node.y): node \n", + " for node in nodes}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An `astar_search` seems appropriate. Each state of the search keeps track of the position of the data we are trying to get, and the position of the currently empty node. The heuristic is the city block distance of the data to the origin:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "215" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "State = namedtuple('State', 'datapos, emptypos')\n", + "\n", + "def distance(state): return cityblock_distance(state.datapos)\n", + "\n", + "def moves(state):\n", + " \"Try moving any neighbor we can into the empty position.\"\n", + " for pos in neighbors4(state.emptypos):\n", + " if pos in grid:\n", + " # Try to move contents of `node` at pos into `empty` at emptypos\n", + " node, empty = grid[pos], grid[state.emptypos]\n", + " if node.used <= empty.size:\n", + " newdatapos = (state.emptypos if pos == state.datapos else state.datapos)\n", + " yield State(newdatapos, pos)\n", + " \n", + "path = astar_search(State((maxx, 0), (empty.x, empty.y)), distance, moves)\n", + "len(path) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# [Day 23](http://adventofcode.com/2016/day/23) Safe Cracking\n", + "\n", + "This day's puzzle is just like Day 12, except there is one more instruction, `tgl`. I made four mistakes in the process of coding this up:\n", + "- At first I didn't read the part that says register `'a'` should initially be 7.\n", + "- I wasn't sure exactly what constitutes an invalid instruction; it took me a few tries to get that right:\n", + "the only thing that is invalid is a `cpy` that does not copy into a register.\n", + "- I forgot to subtract one from the `pc` (again!) in the `tgl` instruction.\n", + "- I forgot that I had `parse` return instructions as immutable tuples; I had to change that to mutable lists." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def interpret(code, regs):\n", + " \"Execute instructions until pc goes off the end.\"\n", + " def val(x): return (regs[x] if x in regs else x)\n", + " pc = 0\n", + " while 0 <= pc < len(code):\n", + " inst = code[pc]\n", + " op, x, y = inst[0], inst[1], inst[-1]\n", + " pc += 1\n", + " if op == 'cpy' and y in regs: regs[y] = val(x)\n", + " elif op == 'inc': regs[x] += 1 \n", + " elif op == 'dec': regs[x] -= 1 \n", + " elif op == 'jnz' and val(x): pc += val(y) - 1 \n", + " elif op == 'tgl': toggle(code, pc - 1 + val(x))\n", + " return regs\n", + "\n", + "def toggle(code, i):\n", + " \"Toggle the instruction at location i.\"\n", + " if 0 <= i < len(code): \n", + " inst = code[i]\n", + " inst[0] = ('dec' if inst[0] == 'inc' else \n", + " 'inc' if len(inst) == 2 else\n", + " 'cpy' if inst[0] == 'jnz' else \n", + " 'jnz')\n", + "\n", + "def parse(line): \n", + " \"Split line into words, and convert to int where appropriate.\"\n", + " return [(x if x.isalpha() else int(x)) \n", + " for x in line.split()]" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'a': 11340, 'b': 1, 'c': 0, 'd': 0}" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text = '''\n", + "cpy a b\n", + "dec b\n", + "cpy a d\n", + "cpy 0 a\n", + "cpy b c\n", + "inc a\n", + "dec c\n", + "jnz c -2\n", + "dec d\n", + "jnz d -5\n", + "dec b\n", + "cpy b c\n", + "cpy c d\n", + "dec d\n", + "inc c\n", + "jnz d -2\n", + "tgl c\n", + "cpy -16 c\n", + "jnz 1 c\n", + "cpy 84 c\n", + "jnz 75 d\n", + "inc a\n", + "inc d\n", + "jnz d -2\n", + "inc c\n", + "jnz c -5\n", + "'''.strip()\n", + "\n", + "code = [parse(line) for line in text.splitlines()]\n", + "\n", + "regs = dict(a=7, b=0, c=0, d=0)\n", + "\n", + "interpret(code, regs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two**, we are told to run the same computation, but with register `a` set to 12. We are also warned that this will take a long time, and we might consider implementing a multiply instruction, but I was too lazy to make sense of the assembly code, and just let my interpreter run to completion, even if it takes a while." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 25min 21s, sys: 5.37 s, total: 25min 27s\n", + "Wall time: 25min 31s\n" + ] + }, + { + "data": { + "text/plain": [ + "{'a': 479007900, 'b': 1, 'c': 0, 'd': 0}" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "code = [parse(line) for line in text.splitlines()]\n", + "\n", + "regs = dict(a=12, b=0, c=0, d=0)\n", + "\n", + "%time interpret(code, regs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Well, it completed, and gave me the right answer. But I feel like the intent of *Advent of Code* is like *Project Euler*: all code should run in about a minute or less. So I don't think this counts as a \"real\" solution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 24](http://adventofcode.com/2016/day/24) Air Duct Spelunking \n", + "\n", + "This is another maze-solving problem; it should be easy for my `astar_search`. First the maze:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "maze = tuple(Input(24))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The tricky part is that we have to visit all the digits in the maze, starting at `0`, and not necessarily going in order. How many digits are there?" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'\\n', '#', '.', '0', '1', '2', '3', '4', '5', '6', '7'}" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(cat(maze))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "OK, there are 8 digits. What is the start square (the square that currently holds a `'0'`)?" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(33, 11)" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "zero = first((x, y) for y, row in enumerate(maze) for x, c in enumerate(row) if c == '0')\n", + "zero" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I'm ready to go. The state of the search will include the x, y position, and also the digits visited so far, which I can represent as a sorted string (a `frozenset` would also work):" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "448" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def h(state):\n", + " \"Heuristic: the number of digits not yet visited.\"\n", + " _, visited = state\n", + " return 8 - len(visited) # Note: 8 == len('01234567')\n", + " \n", + "def moves(state):\n", + " \"Move to any neighboring square that is not a wall. Track the digits visited.\"\n", + " pos, visited = state\n", + " for x1, y1 in neighbors4(pos):\n", + " c = maze[y1][x1]\n", + " if c != '#':\n", + " visited1 = (visited if c in visited or c == '.' else cat(sorted(visited + c)))\n", + " yield (x1, y1), visited1\n", + "\n", + "path = astar_search((zero, '0'), h, moves)\n", + "len(path) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In **part two** we need to get the robot back to the start square. I'll do that by creating a new heuristic function that still requires us to collect all the digits, and also measures the distance back to the start (`zero`) square." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "672" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def h2(state):\n", + " \"Heuristic: the number of digits not yet visited, plus the distance back to start.\"\n", + " pos, visited = state\n", + " return 8 - len(visited) + cityblock_distance(pos, zero)\n", + "\n", + "path2 = astar_search((zero, '0'), h2, moves)\n", + "len(path2) - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# [Day 25](http://adventofcode.com/2016/day/25) Clock Signal\n", + "\n", + "This is another assembly language interpreter puzzle. This time there is one more instruction, `out`, which transmits a signal. We are asked to find the lowest positive integer value for register `a` that causes the program to output an infinite series of `0, 1, 0, 1, 0, 1, ...` signals. Dealing with infinity is difficult, so I'll approximate that by asking: what is the lowest value for register `a` that causes the program to output at least 100 elements in the `0, 1, 0, 1, 0, 1, ...` series, within the first million instructions executed?\n", + "\n", + "To do that, I'll change `interpret` to be a generator that yields signals, and change it to take an argument saying the number of steps to execute before halting:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def interpret(code, regs, steps=BIG):\n", + " \"Execute instructions until pc goes off the end, or until we execute the given number of steps.\"\n", + " def val(x): return (regs[x] if x in regs else x)\n", + " pc = 0\n", + " for _ in range(steps):\n", + " if not (0 <= pc < len(code)):\n", + " return\n", + " inst = code[pc]\n", + " op, x, y = inst[0], inst[1], inst[-1]\n", + " pc += 1\n", + " if op == 'cpy' and y in regs: regs[y] = val(x)\n", + " elif op == 'inc': regs[x] += 1 \n", + " elif op == 'dec': regs[x] -= 1 \n", + " elif op == 'jnz' and val(x): pc += val(y) - 1 \n", + " elif op == 'tgl': toggle(code, pc - 1 + val(x))\n", + " elif op == 'out': yield val(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is my program, and the function `repeats`, which returns True if the code repeats with a given value of the register `a`. Then all we need to do is iterate through integer values for register `a` until we find one that repeats:" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "198" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "text = '''\n", + "cpy a d\n", + "cpy 4 c\n", + "cpy 633 b\n", + "inc d\n", + "dec b\n", + "jnz b -2\n", + "dec c\n", + "jnz c -5\n", + "cpy d a\n", + "jnz 0 0\n", + "cpy a b\n", + "cpy 0 a\n", + "cpy 2 c\n", + "jnz b 2\n", + "jnz 1 6\n", + "dec b\n", + "dec c\n", + "jnz c -4\n", + "inc a\n", + "jnz 1 -7\n", + "cpy 2 b\n", + "jnz c 2\n", + "jnz 1 4\n", + "dec b\n", + "dec c\n", + "jnz 1 -4\n", + "jnz 0 0\n", + "out b\n", + "jnz a -19\n", + "jnz 1 -21\n", + "'''.strip()\n", + "\n", + "code = [parse(line) for line in text.splitlines()]\n", + "\n", + "def repeats(a, code, steps=10**6, minsignals=100):\n", + " \"Does this value for register a cause code to repeat `out` signals of 0, 1, 0, 1, ...?\"\n", + " signals = interpret(code, dict(a=a, b=0, c=0, d=0), steps)\n", + " expecteds = cycle((0, 1))\n", + " for (i, (signal, expected)) in enumerate(zip(signals, expecteds)):\n", + " if signal != expected:\n", + " return False\n", + " # We'll say \"yes\" if the code outputs at least a minimum number of 0, 1, ... signals, and nothing else.\n", + " return i >= minsignals\n", + " \n", + "first(a for a in range(1, BIG) if repeats(a, code))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's all folks! Thank you [Eric Wastl](http://was.tl/), that was fun!" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/BASIC.ipynb b/pytudes/ipynb/BASIC.ipynb new file mode 100644 index 0000000..71f7b70 --- /dev/null +++ b/pytudes/ipynb/BASIC.ipynb @@ -0,0 +1,1957 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Peter Norvig, Feb 2017
\n", + "\n", + "# BASIC Interpreter\n", + "\n", + "[Years ago](http://norvig.com/lispy.html), I showed how to write an Interpreter for a dialect of Lisp. Some readers appreciated it, and some asked about an interpreter for a language that isn't just a bunch of parentheses. In 2014 I saw a [celebration](http://time.com/69316/basic/) of the 50th anniversary of the 1964 [Dartmouth BASIC](http://web.archive.org/web/20120716185629/http://www.bitsavers.org/pdf/dartmouth/BASIC_Oct64.pdf) interpreter, and thought that I could show how to implement such an interpreter. I never quite finished in 2014, but in 2017 I rediscovered my unfinished file and completed it. For those of you unfamiliar with BASIC, here is a sample program:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "program = '''\n", + "10 REM POWER TABLE\n", + "11 DATA 8, 4\n", + "15 READ N0, P0\n", + "20 PRINT \"N\",\n", + "25 FOR P = 2 to P0\n", + "30 PRINT \"N ^\" P,\n", + "35 NEXT P\n", + "40 PRINT \"SUM\"\n", + "45 LET S = 0\n", + "50 FOR N = 2 TO N0\n", + "55 PRINT N,\n", + "60 FOR P = 2 TO P0\n", + "65 LET S = S + N ^ P\n", + "70 PRINT N ^ P,\n", + "75 NEXT P\n", + "80 PRINT S\n", + "85 NEXT N\n", + "99 END\n", + "'''" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course I don't have to build everything from scratch in assembly language, and I don't have to worry about every byte of storage, like [Kemeny](http://www.dartmouth.edu/basicfifty/basic.html), [Gates](http://www.pagetable.com/?p=774), and [Woz](http://www.retrothing.com/2008/07/restoring-wozs.html) did, so my job is much easier. The interpreter consists of three phases: \n", + "* **Tokenization**: breaking a text into a list of tokens, for example: `\"10 READ N\"` becomes `['10', 'READ', 'N']`.\n", + "* **Parsing**: building an executable representation from the tokens, so this statement becomes: `Stmt(num=10, typ='READ', args=['N'])`.\n", + "* **Execution**: follow the flow of the program and do what each statement says; in this case an assignment: `variables['N'] = data.popleft()`.\n", + "\n", + "\n", + "\n", + "# Tokenization\n", + "\n", + "One way to turn a line of text into a list of tokens is with the `findall` method of a regular expression that defines all the legal tokens:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import re \n", + "\n", + "tokenize = re.compile(\n", + " r'''\\d* \\.? \\d+ (?: E -? \\d+)? | # number \n", + " SIN|COS|TAN|ATN|EXP|ABS|LOG|SQR|RND|INT|FN[A-Z]| # functions (including user-defined FNA-FNZ)\n", + " LET|READ|DATA|PRINT|GOTO|IF|FOR|NEXT|END|STOP | # keywords\n", + " DEF|GOSUB|RETURN|DIM|REM|TO|THEN|STEP | # more keywords\n", + " [A-Z]\\d? | # variable names (letter optionally followed by a digit)\n", + " \" .*? \" | # labels (strings in double quotes)\n", + " <>|>=|<= | # multi-character relational operators\n", + " \\S # any non-space single character ''', \n", + " re.VERBOSE).findall" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The only complicated part is the syntax for numbers: optional digits followed by an optional decimal point, some digits, and optionally a power of 10 marked by `\"E\"` and followed by an (optional) minus sign and some digits. \n", + "Example usage of `tokenize`:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['10', 'READ', 'N']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tokenize('10 READ N')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['100', 'PRINT', '\"SIN(X)^2 = \"', ',', 'SIN', '(', 'X', ')', '^', '2']" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tokenize('100 PRINT \"SIN(X)^2 = \", SIN(X) ^ 2')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "That looks good. Note that my tokens are just strings; it will be the parser's job, not the tokenizer's, to recognize that `'2'` is a number and `'X'` is the name of a variable. (In some interpreters, the tokenizer makes distinctions like these.)\n", + "\n", + "There's one important complication: spaces don't matter in BASIC programs, so the following should all be equivalent:\n", + "\n", + " 10 GOTO 99\n", + " 10GOTO99\n", + " 10 GO TO 99\n", + " \n", + "The problem is that `tokenize` gets the last one wrong:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['10', 'G', 'O', 'TO', '99']" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tokenize('10 GO TO 99')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "My first thought was to remove all white space from the input. That would work for this example, but it would change the token `\"HELLO WORLD\"` to `\"HELLOWORLD\"`, which is wrong. To remove spaces everywhere *except* between double quotes, I can tokenize the line and join the tokens back together. Then I can re-tokenize to get the final list of tokens; I do that in my new function below called `tokenizer`. \n", + "\n", + "Once I have a list of tokens, I access them through this interface:\n", + "* `peek()`: returns the next token in `tokens` (without changing `tokens`), or `None` if there are no more tokens.\n", + "* `pop()`: removes and returns the next token. \n", + "* `pop(`*string*`)`: removes and returns the next token if it is equal to the string; else return `None` and leave `tokens` unchanged.\n", + "* `pop(`*predicate*`)`: removes and returns the next token if *predicate*(*token*) is true; else return `None` and leave `tokens` unchanged." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "tokens = [] # Global variable to hold a list of tokens\n", + "\n", + "def tokenizer(line):\n", + " \"Return a list of the tokens on this line, handling spaces properly, and upper-casing.\"\n", + " return tokenize(remove_spaces(line).upper())\n", + "\n", + "def peek(): \n", + " \"Return the first token in the global `tokens`, or None if we are at the end of the line.\"\n", + " return (tokens[0] if tokens else None)\n", + "\n", + "def pop(constraint=None):\n", + " \"\"\"Remove and return the first token in `tokens`, or return None if first token fails a constraint.\n", + " `constraint` can be None, a literal string (e.g. pop('=')), or a predicate (e.g. pop(is_varname)).\"\"\"\n", + " if constraint is None or (peek() == constraint) or (callable(constraint) and constraint(peek())):\n", + " return tokens.pop(0)\n", + " \n", + "def remove_spaces(line): \n", + " \"Remove white space from line, except space inside double quotes.\"\n", + " return ''.join(tokenize(line))\n", + "\n", + "def lines(text): \n", + " \"A list of the non-empty lines in a text.\"\n", + " return [line for line in text.splitlines() if line]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(Note: if I expected program lines to contain many tokens, I would use a `deque` instead of a `list` of tokens.) \n", + "\n", + "We can test `tokenizer` and the related functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_tokenizer():\n", + " global tokens\n", + " assert tokenizer('X-1') == ['X', '-', '1'] # Numbers don't have a leading minus sign, so this isn't ['X', '-1']\n", + " assert tokenizer('PRINT \"HELLO WORLD\"') == ['PRINT', '\"HELLO WORLD\"']\n", + " assert tokenizer('10 GOTO 99') == tokenizer('10GOTO99') == tokenizer('10 GO TO 99') == ['10', 'GOTO', '99']\n", + " assert (tokenizer('100 PRINT \"HELLO WORLD\", SIN(X) ^ 2') == \n", + " ['100', 'PRINT', '\"HELLO WORLD\"', ',', 'SIN', '(', 'X', ')', '^', '2'])\n", + " assert (tokenizer('100IFX1+123.4+E1-12.3E4 <> 1.2E-34*-12E34+1+\"HI\" THEN99') ==\n", + " ['100', 'IF', 'X1', '+', '123.4', '+', 'E1', '-', '12.3E4', '<>', \n", + " '1.2E-34', '*', '-', '12E34', '+', '1', '+', '\"HI\"', 'THEN', '99'])\n", + " assert remove_spaces('10 GO TO 99') == '10GOTO99'\n", + " assert remove_spaces('100 PRINT \"HELLO WORLD\", SIN(X) ^ 2') == '100PRINT\"HELLO WORLD\",SIN(X)^2'\n", + " assert lines('one line') == ['one line']\n", + " assert lines(program) == [\n", + " '10 REM POWER TABLE',\n", + " '11 DATA 8, 4',\n", + " '15 READ N0, P0',\n", + " '20 PRINT \"N\",',\n", + " '25 FOR P = 2 to P0',\n", + " '30 PRINT \"N ^\" P,',\n", + " '35 NEXT P',\n", + " '40 PRINT \"SUM\"',\n", + " '45 LET S = 0',\n", + " '50 FOR N = 2 TO N0',\n", + " '55 PRINT N,',\n", + " '60 FOR P = 2 TO P0',\n", + " '65 LET S = S + N ^ P',\n", + " '70 PRINT N ^ P,',\n", + " '75 NEXT P',\n", + " '80 PRINT S',\n", + " '85 NEXT N',\n", + " '99 END']\n", + " assert [tokenizer(line) for line in lines(program)] == [\n", + " ['10', 'REM', 'P', 'O', 'W', 'E', 'R', 'T', 'A', 'B', 'L', 'E'],\n", + " ['11', 'DATA', '8', ',', '4'],\n", + " ['15', 'READ', 'N0', ',', 'P0'],\n", + " ['20', 'PRINT', '\"N\"', ','],\n", + " ['25', 'FOR', 'P', '=', '2', 'TO', 'P0'],\n", + " ['30', 'PRINT', '\"N ^\"', 'P', ','],\n", + " ['35', 'NEXT', 'P'],\n", + " ['40', 'PRINT', '\"SUM\"'],\n", + " ['45', 'LET', 'S', '=', '0'],\n", + " ['50', 'FOR', 'N', '=', '2', 'TO', 'N0'],\n", + " ['55', 'PRINT', 'N', ','],\n", + " ['60', 'FOR', 'P', '=', '2', 'TO', 'P0'],\n", + " ['65', 'LET', 'S', '=', 'S', '+', 'N', '^', 'P'],\n", + " ['70', 'PRINT', 'N', '^', 'P', ','],\n", + " ['75', 'NEXT', 'P'],\n", + " ['80', 'PRINT', 'S'],\n", + " ['85', 'NEXT', 'N'],\n", + " ['99', 'END']]\n", + "\n", + " tokens = tokenizer('10 GO TO 99') \n", + " assert peek() == '10'\n", + " assert pop() == '10'\n", + " assert peek() == 'GOTO'\n", + " assert pop() == 'GOTO'\n", + " assert peek() == '99'\n", + " assert pop(str.isalpha) == None # '99' is not alphabetic\n", + " assert pop('98.6') == None # '99' is not '98.6'\n", + " assert peek() == '99'\n", + " assert pop(str.isnumeric) == '99' # '99' is numeric\n", + " assert peek() is None and not tokens \n", + " \n", + " return 'ok'\n", + " \n", + "test_tokenizer()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: Grammar of Statements\n", + "\n", + "Parsing is the process of transforming the text of a program into an internal representation, which can then be executed.\n", + "For BASIC, the representation will be an ordered list of statements, and we'll need various data types to represent the parts of the statements.\n", + "I'll start by showing the grammar of BASIC statements, as seen on pages 56-57 of [the manual](http://web.archive.org/web/20120716185629/http://www.bitsavers.org/pdf/dartmouth/BASIC_Oct64.pdf) (see also pages 26-30 for a simpler introduction). A statement starts with a line number, and then can be one of the following 15 types of statements, each \n", + "type introduced by a distinct keyword:\n", + "\n", + "- **`LET`** `` **=** ``\n", + "- **`READ`** ``\n", + "- **`DATA`** ``\n", + "- **`PRINT`** ``\n", + "- **`GOTO`** ``\n", + "- **`IF`** ` ` **`THEN`** ``\n", + "- **`FOR`** `` **=** `` **`TO`** ` [`**`STEP`** `]`\n", + "- **`NEXT`** ``\n", + "- **`END`**\n", + "- **`STOP`**\n", + "- **`DEF`** ``**(**``**) = **``\n", + "- **`GOSUB`** ``\n", + "- **`RETURN`**\n", + "- **`DIM`** ``\n", + "- **`REM`** ``\n", + " \n", + "The notation `` means any variable and `` means zero or more variables, separated by commas. `[STEP ]` means that the literal string `\"STEP\"`, followed by an expression, is optional. \n", + "\n", + "Rather than use one of the many [language parsing frameworks](https://wiki.python.org/moin/LanguageParsing), I will show how to build a parser from scratch. First I'll translate the grammar above into Python. Not character-for-character (because it would take a lot of work to get Python to understand how to handle those characters), but almost word-for-word (because I can envision a straightforward way to get Python to handle the following format):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Grammar(): \n", + " return {\n", + " 'LET': [variable, '=', expression],\n", + " 'READ': [list_of(variable)],\n", + " 'DATA': [list_of(number)],\n", + " 'PRINT': [labels_and_expressions],\n", + " 'GOTO': [linenumber],\n", + " 'IF': [expression, relational, expression, 'THEN', linenumber],\n", + " 'FOR': [varname, '=', expression, 'TO', expression, step],\n", + " 'NEXT': [varname],\n", + " 'END': [],\n", + " 'STOP': [],\n", + " 'DEF': [funcname, '(', varname, ')', '=', expression],\n", + " 'GOSUB': [linenumber],\n", + " 'RETURN': [],\n", + " 'DIM': [list_of(variable)], \n", + " 'REM': [anycharacters]\n", + " }" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing Strategy\n", + "\n", + "The grammar of BASIC is designed so that at every point, the next token tells us unambiguously how to parse. For example, the first token after the line number defines the type of statement; also, in an expression we know that all three-letter names are functions while all 1-letter names are variables. So in writing the various grammatical category functions, a common pattern is to either `peek()` at the next token or try a `pop(`*constraint*`)`, and from that decide what to parse next, and never have to back up or undo a `pop()`. Here is my strategy for parsing statements:\n", + "\n", + "* The grammatical categories, like `variable` and `expression` (and also `statement`), will be defined as functions\n", + "(with no argument) that pop tokens from the global variable `tokens`, and return a data object. For example, calling `linenumber()` will pop a token, convert it to an `int`, and return that. \n", + "\n", + "* Consider parsing the statement `\"20 LET X = X + 1\"`. \n", + "\n", + "* First tokenize to get: `tokens = ['20', 'LET', 'X', '=', 'X', '+', '1']`.\n", + "\n", + "* Then call `statement()` (defined below).\n", + "\n", + " * `statement` first calls `linenumber()`, getting back the integer `20` (and removing `'20'` from `tokens`).\n", + "\n", + " * Then it calls `pop()` to get `'LET'` (and removing `'LET'` from `tokens`).\n", + " * Then it indexes into the grammar with `'LET'`, retrieving the grammar rule `[variable, '=', expression]`.\n", + "\n", + " * Then it processes the 3 constituents of the grammar rule:\n", + " * First, call `variable()`, which removes and returns `'X'`.\n", + " * Second, call `pop('=')`, which removes `'='` from `tokens`, and discard it.\n", + " * Third, call `expression()`, which returns a representation of `X + 1`; let's write that as `Opcall('X', '+', 1.0)`.\n", + "\n", + " * Finally, `statement` assembles the pieces and returns `Stmt(num=20, typ='LET', args=['X', Opcall('X', '+', 1.0)])`.\n", + "* If anything goes wrong, call `fail(\"`*error message*`\")`, which raises an error.\n", + "\n", + "Here is the definition of `statement`:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def statement():\n", + " \"Parse a BASIC statement from `tokens`.\"\n", + " num = linenumber()\n", + " typ = pop(is_stmt_type) or fail('unknown statement type')\n", + " args = []\n", + " for c in grammar[typ]: # For each constituent of rule, call if callable or match if literal string\n", + " if callable(c):\n", + " args.append(c())\n", + " else:\n", + " pop(c) or fail('expected ' + repr(c))\n", + " return Stmt(num, typ, args)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some of the grammatical categories, like `expression`, are complex. But many of the categories are easy one-liners:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def linenumber(): return (int(pop()) if peek().isnumeric() else fail('missing line number'))\n", + "def number(): return (-1 if pop('-') else +1) * float(pop()) # Optional minus sign before number\n", + "def step(): return (expression() if pop('STEP') else 1) # 1 is the default step\n", + "def relational(): return pop(is_relational) or fail('expected a relational operator')\n", + "def varname(): return pop(is_varname) or fail('expected a variable name')\n", + "def funcname(): return pop(is_funcname) or fail('expected a function name')\n", + "def anycharacters(): tokens.clear() # The tokens in a REM statement don't matter, so just clear them" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the predicates that distinguish different types of tokens:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def is_stmt_type(x): return isinstance(x, str) and x in grammar # LET, READ, ...\n", + "def is_funcname(x): return isinstance(x, str) and len(x) == 3 and x.isalpha() # SIN, COS, FNA, FNB, ...\n", + "def is_varname(x): return isinstance(x, str) and len(x) in (1, 2) and x[0].isalpha() # A, A1, A2, B, ...\n", + "def is_label(x): return isinstance(x, str) and x.startswith('\"') # \"HELLO WORLD\", ...\n", + "def is_relational(x): return isinstance(x, str) and x in ('<', '=', '>', '<=', '<>', '>=')\n", + "def is_number(x): return isinstance(x, str) and x and x[0] in '.0123456789' # '3', '.14', ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that `varname` means an unsubscripted variable name (a letter by itself, like `X`, or followed by a digit, like `X3`), and that `variable` is a `varname` optionally followed by index expressions in parentheses, like `A(I)` or `M(2*I, 3)`: " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def variable(): \n", + " \"Parse a possibly subscripted variable e.g. 'X3' or 'A(I)' or 'M(2*I, 3)'.\"\n", + " V = varname()\n", + " if pop('('):\n", + " indexes = list_of(expression)()\n", + " pop(')') or fail('expected \")\" to close subscript')\n", + " return Subscript(V, indexes) # E.g. 'A(I)' => Subscript('A', ['I'])\n", + " else: \n", + " return V # E.g. 'X3' " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`list_of` is tricky because it works at two different times. When I write `list_of(number)` in the grammar, this returns an object of class `list_of`. When this object is called (just as other grammatical categories like `variable` are called), the effect is that it will parse a list of `number`. That list can be empty (if there are no more tokens on the line), or can be a single number, or can be several numbers separated by comma tokens. I could have defined `list_of` as a function that returns a function, but I thought that it would be clearer to define it as a class, so I can clearly separate what happens at the two different times: first the `__init__` method determines what category to parse, and later the `__call__` method does the actual parsing." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class list_of:\n", + " \"list_of(category) is a callable that parses a comma-separated list of \"\n", + " def __init__(self, category): self.category = category\n", + " def __call__(self):\n", + " result = ([self.category()] if tokens else [])\n", + " while pop(','):\n", + " result.append(self.category())\n", + " return result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: Top Level `parse`, and Handling Errors\n", + "\n", + "Most of the parsing action happens inside the function `statement()`, but at the very top level, `parse(program)` takes a program text (that is, a string), and parses each line by calling `parse_line`, sorting the resulting list of lines by line number. If we didn't have to handle errors, this would be simple:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def parse(program): return sorted(map(parse_line, lines(program)))\n", + "\n", + "def parse_line(line): global tokens; tokens = tokenizer(line); return statement()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To handle syntactic errors, I add to `parse_line` a `try/except` that catches exceptions raised by calls to `fail`. I acknowledge the interpreter isn't very thorough about handling all errors, and the error messages could be more helpful." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def parse_line(line):\n", + " \"Return a Stmt(linenumber, statement_type, arguments).\"\n", + " global tokens\n", + " tokens = tokenizer(line)\n", + " try:\n", + " stmt = statement()\n", + " if tokens: fail('extra tokens at end of line')\n", + " return stmt\n", + " except SyntaxError as err:\n", + " print(\"Error in line '{}' at '{}': {}\".format(line, ' '.join(tokens), err))\n", + " return Stmt(0, 'REM', []) # Have to return something: a dummy statement\n", + " \n", + "def fail(message): raise SyntaxError(message)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: Building A Representation of the Program\n", + "\n", + "A program is represented by various data structures: a list of statements, where each statement contains various components: subscripted variable references, user-defined functions, function calls, operation calls, variable names, numbers, and labels. Here I define these data structures with `namedtuple`s:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import namedtuple, defaultdict, deque\n", + "\n", + "Stmt = namedtuple('Stmt', 'num, typ, args') # Statement: '20 GOTO 99' => Stmt(20, 'GOTO', 99)\n", + "Subscript = namedtuple('Subscript', 'var, indexes') # Subscripted reference: 'A(I)' => Subscript('A', ['I'])\n", + "Funcall = namedtuple('Funcall', 'f, x') # Function call: 'SQR(X)' => Funcall('SQR', 'X')\n", + "Opcall = namedtuple('Opcall', 'x, op, y') # Infix operation: 'X + 1' => Opcall('X', '+', 1)\n", + "ForState = namedtuple('ForState', 'continu, end, step') # Data used to control a FOR loop variable\n", + "\n", + "class Function(namedtuple('_', 'parm, body')):\n", + " \"User-defined callable function; 'DEF FNC(X) = X ^ 3' => functions['FNC'] = Function('X', Opcall('X', '^', 3))\"\n", + " def __call__(self, value): \n", + " variables[self.parm] = value # Global assignment to the parameter\n", + " return evalu(self.body)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first four namedtuples should be self-explanatory. The next one, `ForState`, is used to represent the state of a `FOR` loop variable while the program is running, but does not appear in the static representation of the program.\n", + "`Function` is used to represent the definition of a user defined function. When the user writes `\"DEF FNC(X) = X ^ 3\"`, we create an object with `Function(parm='X', body=Opcall('X', '^', 3))`, and whenever the program calls, say, `FNC(2)` in an expression, the call returns 8, and also assigns 2 to the *global* variable `X` (whereas in modern languages, it would temporarily bind a new *local* variable named `X`). BASIC has no local variables. Note the technique of making `Function` be a subclass of a `namedtuple`; we are then free to add the `__call__` method to the subclass." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: Grammar of `PRINT` Statements\n", + "\n", + "On page 26 of the manual, it appears that the grammar rule for `PRINT` should be `[list_of(expression)]`. But in section 3.1, **More about PRINT**, some complications are introduced:\n", + "\n", + "* Labels (strings enclosed in double quotes) are allowed, as well as expressions.\n", + "* The `\",\"` is not a separator. A line can end with `\",\"`.\n", + "* Optionally, `\";\"` can be used instead of `\",\"`.\n", + "* Optionally, the `\",\"` or `\";\"` can be omitted—we can have a label immediately followed by an expression.\n", + "\n", + "The effect of a comma is to advance the output to the next column that is a multiple of 15 (and to a new line if this goes past column 75). The effect of a semicolon is similar, but works in multiples of 3, not 15. (Note that column numbering starts at 0, not 1.) Normally, at the end of a `PRINT` statement we advance to a new line, but this is not done if the statement ends in `\",\"` or `\";\"`. Here are some examples:\n", + "\n", + "* `10 PRINT X, Y`\n", + "
Prints the value of `X` in column 0 and `Y` in column 15. Advances to new line.\n", + "\n", + "* `20 PRINT \"X =\", X`\n", + "
Prints the string `\"X =\"` in column 0 and the value of `X` in column 15. Advances to new line.\n", + "\n", + "* `30 PRINT \"X = \" X`\n", + "
Prints the string `\"X =\"` in column 0 and the value of `X` immediately after. Advances to new line.\n", + "\n", + "* `40 PRINT X; Y,`\n", + "
Prints the value of `X` in column 0, and the value of `Y` in the column that is the first available multiple of 3 after that.\n", + "For example, if `X` is `'0'`, then print `Y` in column 3, but if `X` is `'12345'`, then we've gone past column 3, so print `Y` in column 6.\n", + "Then, because the statement ends in a comma, advance to the next column that is a multiple of 15, but not to a new line.\n", + "\n", + "That explanation was long, but the implementation is short (at least for the parsing part; later we will see the execution part):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def labels_and_expressions():\n", + " \"Parse a sequence of label / comma / semicolon / expression (for PRINT statement).\"\n", + " result = []\n", + " while tokens:\n", + " item = pop(is_label) or pop(',') or pop(';') or expression()\n", + " result.append(item)\n", + " return result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: Grammar of Expressions\n", + "\n", + "Now for the single most complicated part of the grammar: the `expression`. The biggest complication is operator precedence: the string `\"A + B * X + C\"` should be parsed as if it were `\"A + (B * X) + C\"`, and not as `\"(A + B) * (X + C),\"` because multiplication binds more tightly than addition. There are [many schemes](https://en.wikipedia.org/wiki/Operator-precedence_parser) for parsing expressions, I'll use [an approach](https://groups.google.com/forum/#!topic/comp.compilers/ruJLlQTVJ8o) attributed to Keith Clarke.\n", + "\n", + "Like all our grammatical categories, calling `expression()` pops off some tokens and returns a data object. The first thing it does is parse one of five types of simple \"primary\" expressions: \n", + "a number like `1.23`; \n", + "a possibly-subscripted variable like `X` or `A(I)`;\n", + "a function call like `SIN(X)`;\n", + "a unary negation like `-X`;\n", + "or a parenthesied expression like `(X + 1)`. \n", + "\n", + "Next, `expression` looks for infix operators. To parse `'X + 1'` as an expression, first `primary()` would parse `'X'`, then it would pop off the `'+'` operator, then a recursive call to `expression()` would parse `1`, and the results can then be combined into an `Opcall('X', '+', 1)`. If there are multiple infix operators, they can all be handled, as in `'X+1+Y+2'`, which gets parsed as `Opcall(Opcall(Opcall('X', '+', 1), '+', 'Y'), '+', 2)`.\n", + "\n", + "When there are multiple infix operators of *different* precedence, as in `\"A + B * X + C\"`, the trick is to know which operators are parsed by the top-level call to `expression`, and which by recursive calls. When we first call `expression()`, the optional parameter `prec` gets the default value, 1, which is the precedence of addition and subtraction. When `expression` makes a recursive call, it passes the precedence of the current operator, and we only parse off operator/expression pairs at an equal or higher precedence. So, in parsing `\"A + B * X + C\"`, when we pop off the `'*'` operator (which has precedence 2), we then recursively call `expression(2)`, which parses off an expression containing operators of precedence 2 or higher, which means the recursive call will parse `X`, but it won't pop off the `'+'`, because that is at a lower precedence. So we correctly get the structure `\"(A + ((B * X) + C)\"`.\n", + "\n", + "The function `associativity` ensures that the operator `'^'` is right associative, meaning `10^2^3` = `(10^(2^3))`, whereas the other operators are left associative, so `10-2-3` = `((10-2)-3)`.\n", + "\n", + "Here is the implementation of `expression`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def expression(prec=1): \n", + " \"Parse an expression: a primary and any [op expression]* pairs with precedence(op) >= prec.\"\n", + " exp = primary() # 'A' => 'A'\n", + " while precedence(peek()) >= prec:\n", + " op = pop()\n", + " rhs = expression(precedence(op) + associativity(op))\n", + " exp = Opcall(exp, op, rhs) # 'A + B' => Opcall('A', '+', 'B')\n", + " return exp\n", + "\n", + "def primary():\n", + " \"Parse a primary expression (no infix op except maybe within parens).\"\n", + " if is_number(peek()): # '1.23' => 1.23 \n", + " return number()\n", + " elif is_varname(peek()): # X or A(I) or M(I+1, J)\n", + " return variable()\n", + " elif is_funcname(peek()): # SIN(X) => Funcall('SIN', 'X')\n", + " return Funcall(pop(), primary())\n", + " elif pop('-'): # '-X' => Funcall('NEG', 'X')\n", + " return Funcall('NEG', primary())\n", + " elif pop('('): # '(X + 1)' => Opcall('X', '+', 1)\n", + " exp = expression()\n", + " pop(')') or fail('expected \")\" to end expression')\n", + " return exp\n", + " else:\n", + " return fail('unknown expression')\n", + "\n", + "def precedence(op): return (3 if op == '^' else 2 if op in ('*', '/') else 1 if op in ('+', '-') else 0)\n", + "\n", + "def associativity(op): return (0 if op == '^' else 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parsing: The Complete Parser in Action\n", + "\n", + "I've now written all the grammatical categories, so I can now safely instantiate the global variable `grammar` by calling `Grammar()`, and parse a program:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[Stmt(num=10, typ='REM', args=[None]),\n", + " Stmt(num=11, typ='DATA', args=[[8.0, 4.0]]),\n", + " Stmt(num=15, typ='READ', args=[['N0', 'P0']]),\n", + " Stmt(num=20, typ='PRINT', args=[['\"N\"', ',']]),\n", + " Stmt(num=25, typ='FOR', args=['P', 2.0, 'P0', 1]),\n", + " Stmt(num=30, typ='PRINT', args=[['\"N ^\"', 'P', ',']]),\n", + " Stmt(num=35, typ='NEXT', args=['P']),\n", + " Stmt(num=40, typ='PRINT', args=[['\"SUM\"']]),\n", + " Stmt(num=45, typ='LET', args=['S', 0.0]),\n", + " Stmt(num=50, typ='FOR', args=['N', 2.0, 'N0', 1]),\n", + " Stmt(num=55, typ='PRINT', args=[['N', ',']]),\n", + " Stmt(num=60, typ='FOR', args=['P', 2.0, 'P0', 1]),\n", + " Stmt(num=65, typ='LET', args=['S', Opcall(x='S', op='+', y=Opcall(x='N', op='^', y='P'))]),\n", + " Stmt(num=70, typ='PRINT', args=[[Opcall(x='N', op='^', y='P'), ',']]),\n", + " Stmt(num=75, typ='NEXT', args=['P']),\n", + " Stmt(num=80, typ='PRINT', args=[['S']]),\n", + " Stmt(num=85, typ='NEXT', args=['N']),\n", + " Stmt(num=99, typ='END', args=[])]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grammar = Grammar()\n", + "\n", + "parse(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some more tests:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_parse(text, result, category=expression):\n", + " \"Test that text can be parsed as a category to yield the semantic result, with no tokens left over.\"\n", + " global tokens\n", + " tokens = tokenizer(text)\n", + " return category() == result and not tokens\n", + " \n", + "def test_parser():\n", + " assert is_funcname('SIN') and is_funcname('FNZ') # Function names are three letters\n", + " assert not is_funcname('X') and not is_funcname('')\n", + " assert is_varname('X') and is_varname('A2') # Variables names are one letter and an optional digit\n", + " assert not is_varname('FNZ') and not is_varname('A10') and not is_varname('')\n", + " assert is_relational('>') and is_relational('>=') and not is_relational('+')\n", + " \n", + " assert test_parse('A + B * X + C', Opcall(Opcall('A', '+', Opcall('B', '*', 'X')), '+', 'C'))\n", + " assert test_parse('A + B + X + C', Opcall(Opcall(Opcall('A', '+', 'B'), '+', 'X'), '+', 'C'))\n", + " assert test_parse('SIN(X)^2', Opcall(Funcall('SIN', 'X'), '^', 2))\n", + " assert test_parse('10 ^ 2 ^ 3', Opcall(10, '^', Opcall(2, '^', 3))) # right associative\n", + " assert test_parse('10 - 2 - 3', Opcall(Opcall(10, '-', 2), '-', 3)) # left associative\n", + " assert test_parse('A(I)+M(I, J)', Opcall(Subscript(var='A', indexes=['I']), '+', \n", + " Subscript(var='M', indexes=['I', 'J'])))\n", + " assert test_parse('X * -1', Opcall('X', '*', Funcall('NEG', 1.0)))\n", + " assert test_parse('X--Y--Z', Opcall(Opcall('X', '-', Funcall('NEG', 'Y')), '-', Funcall('NEG', 'Z')))\n", + " assert test_parse('((((X))))', 'X')\n", + " return 'ok'\n", + "\n", + "test_parser()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Execution\n", + "\n", + "Now that we can parse programs, we're ready to execute them. I'll first define `run` to `parse` and `execute` a program:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def run(program): execute(parse(program))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `execute(stmts)` first calls `preprocess(stmts)` to handle *declarations*: `DATA` and `DEF` statements that are processed one time only, before the program runs, regardless of their line numbers. (`DIM` statements are also declarations, but I decided that all lists/tables can have any number of elements, so I can ignore `DIM` declarations.)\n", + "`execute` keeps track of the state of the program, partially in three globals:\n", + "\n", + "* `variables`: A mapping of the values of all BASIC variables (both subscripted and unsubscripted).
For example, `{'P1': 3.14, ('M', (1, 1)): 42.0}` says that the value of `P1` is `3.14` and `M(1, 1)` is `42.0`.\n", + "* `functions`: A mapping of the values of all BASIC functions (both built-in and user-defined).
For example, `{'FNC': Function('X', Opcall('X', '^', 3)), 'SIN': math.sin}` \n", + "* `column`: The column that `PRINT` will print in next.\n", + "\n", + "And also with these local variables:\n", + "\n", + "* `data`: a queue of all the numbers in `DATA` statements.\n", + "* `pc`: program counter; the index into the list of statements.\n", + "* `ret`: the index where a `RETURN` statement will return to.\n", + "* `fors`: a map of `{varname: ForState(...)}` which gives the state of each `FOR` loop variable.\n", + "* `goto`: a mapping of `{linenumber: index}`, for example `{10: 0, 20: 1}` for a program with two line numbers, 10 and 20.\n", + "\n", + "\n", + "Running the program means executing the statement that the program counter (`pc`) is currently pointing at, repeatedly, until we hit an `END` or `STOP` statement (or a `READ` statement when there is no more data). \n", + "The variable `pc` is initialized to `0` (the index of the first statement in the program) and is then incremented by `1` each cycle to go to the following statement; but a branching statement (`GOTO`, `IF`, `GOSUB`, or `RETURN`) can change the `pc` to something other than the following statement. Note that branching statements refer to line numbers, but the `pc` refers to the *index* number within the list of statements. The variable `goto` maps from line numbers to index numbers. In BASIC there is no notion of a *stack*, neither for variables nor return addresses. If I do a `GOSUB` to a subroutine that itself does a `GOSUB`, then the original return address is lost, because BASIC has only one return address register (which we call `ret`).\n", + "\n", + "The main body of `execute` checks the statement type, and takes appropriate action. All the statement types are straightforward, except for `FOR` and `NEXT`, which are explained a bit later." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def execute(stmts): \n", + " \"Parse and execute the BASIC program.\"\n", + " global variables, functions, column\n", + " functions, data = preprocess(stmts) # {name: function,...}, deque[number,...]\n", + " variables = defaultdict(float) # mapping of {variable: value}, default 0.0\n", + " column = 0 # column to PRINT in next\n", + " pc = 0 # program counter\n", + " ret = 0 # index (pc) that a GOSUB returns to\n", + " fors = {} # runtime map of {varname: ForState(...)}\n", + " goto = {stmt.num: i # map of {linenumber: index}\n", + " for (i, stmt) in enumerate(stmts)}\n", + " while pc < len(stmts):\n", + " (_, typ, args) = stmts[pc] # Fetch and decode the instruction\n", + " pc += 1 # Increment the program counter\n", + " if typ in ('END', 'STOP') or (typ == 'READ' and not data): \n", + " return\n", + " elif typ == 'LET':\n", + " V, exp = args\n", + " let(V, evalu(exp))\n", + " elif typ == 'READ':\n", + " for V in args[0]:\n", + " let(V, data.popleft())\n", + " elif typ == 'PRINT':\n", + " basic_print(args[0])\n", + " elif typ == 'GOTO':\n", + " pc = goto[args[0]]\n", + " elif typ == 'IF':\n", + " lhs, relational, rhs, dest = args\n", + " if functions[relational](evalu(lhs), evalu(rhs)):\n", + " pc = goto[dest]\n", + " elif typ == 'FOR':\n", + " V, start, end, step = args\n", + " variables[V] = evalu(start)\n", + " fors[V] = ForState(pc, evalu(end), evalu(step))\n", + " elif typ == 'NEXT':\n", + " V = args[0]\n", + " continu, end, step = fors[V]\n", + " if ((step >= 0 and variables[V] + step <= end) or\n", + " (step < 0 and variables[V] + step >= end)):\n", + " variables[V] += step\n", + " pc = continu\n", + " elif typ == 'GOSUB':\n", + " ret = pc\n", + " pc = goto[args[0]]\n", + " elif typ == 'RETURN':\n", + " pc = ret" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the functions referenced by `execute`:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import math\n", + "import random\n", + "import operator as op\n", + "\n", + "def preprocess(stmts):\n", + " \"\"\"Go through stmts and return two values extracted from the declarations: \n", + " functions: a mapping of {name: function}, for both built-in and user-defined functions,\n", + " data: a queue of all the numbers in DATA statements.\"\"\"\n", + " functions = { # A mapping of {name: function}; first the built-ins:\n", + " 'SIN': math.sin, 'COS': math.cos, 'TAN': math.tan, 'ATN': math.atan, \n", + " 'ABS': abs, 'EXP': math.exp, 'LOG': math.log, 'SQR': math.sqrt, 'INT': int,\n", + " '>': op.gt, '<': op.lt, '=': op.eq, '>=': op.ge, '<=': op.le, '<>': op.ne, \n", + " '^': pow, '+': op.add, '-': op.sub, '*': op.mul, '/': op.truediv, \n", + " 'RND': lambda _: random.random(), 'NEG': op.neg}\n", + " data = deque() # A queue of numbers that READ can read from\n", + " for (_, typ, args) in stmts:\n", + " if typ == 'DEF':\n", + " name, parm, body = args\n", + " functions[name] = Function(parm, body)\n", + " elif typ == 'DATA':\n", + " data.extend(args[0])\n", + " return functions, data\n", + "\n", + "def evalu(exp):\n", + " \"Evaluate an expression, returning a number.\"\n", + " if isinstance(exp, Opcall):\n", + " return functions[exp.op](evalu(exp.x), evalu(exp.y))\n", + " elif isinstance(exp, Funcall):\n", + " return functions[exp.f](evalu(exp.x))\n", + " elif isinstance(exp, Subscript):\n", + " return variables[exp.var, tuple(evalu(x) for x in exp.indexes)]\n", + " elif is_varname(exp):\n", + " return variables[exp]\n", + " else: # number constant\n", + " return exp\n", + " \n", + "def let(V, value):\n", + " \"Assign value to the variable name or Subscripted variable.\"\n", + " if isinstance(V, Subscript): # A subsscripted variable\n", + " variables[V.var, tuple(evalu(x) for x in V.indexes)] = value \n", + " else: # An unsubscripted variable\n", + " variables[V] = value" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Execution: `FOR/NEXT` Statements\n", + "\n", + "I have to admit I don't completely understand `FOR` loops. My questions include:\n", + "\n", + "* Are the `END` and `STEP` expressions evaluated once when we first enter the `FOR` loop, or each time through the loop?\n", + "* After executing `\"FOR V = 1 TO 10\"`, is the value of `V` equal to 10 or 11? (Answer: the manual says 10.)\n", + "* Does `\"FOR V = 0 TO -2\"` execute zero times? Or do all loops execute at least once, with the termination test done by the `NEXT`?\n", + "* What if control branches into the middle of a loop and hits the `NEXT` statement, without ever executing the corresponding `FOR` statement? \n", + "* What if control branches into the middle of a loop and hits the `NEXT` statement, without ever executing the corresponding `FOR` statement, but we have previously\n", + "executed a `FOR` statement of a *different* loop that happens to use the same variable name?\n", + "\n", + "I chose a solution that is easy to implement, and correctly runs all the examples in the manual, but I'm not certain that my solution is true to the original intent. Consider this program:\n", + "\n", + " 10 PRINT \"TABLE OF SQUARES\"\n", + " 20 LET N = 10\n", + " 30 FOR V = 1 to N STEP N/5\n", + " 40 PRINT V, V * V\n", + " 50 NEXT V\n", + " 60 END\n", + " \n", + " \n", + "* When control hits the `\"FOR V\"` statement in line 30, I assign:\n", + "
`variables['V'] = 1`\n", + "
` fors['V'] = ForState(continu=3, end=10, step=2)`\n", + "
where `3` is the index of line 40 (the line right after the `FOR` statement); `10` is the value of `N`; and `2` is the value of `N/5`.\n", + "* When control hits the `\"NEXT V\"` statement in line 50, I do the following:\n", + "
Examine `fors['V']` to check if `V` incremented by the step value, `2`, is within the bounds defined by the end, `10`. \n", + "
If it is, increment `V` and assign `pc` to be `3`, the `continu` value. \n", + "
If not, continue on to the following statement, `60`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Execution: Printing\n", + "\n", + "We showed how to parse a `PRINT` statement with `labels_and_expressions()`; now it is time to execute a `PRINT` statement, printing each of the labels and expressions, and keeping track of what column to print at next, using the global variable `column`." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def basic_print(items): \n", + " \"Print the items (',' / ';' / label / expression) in appropriate columns.\"\n", + " for item in items:\n", + " if item == ',': pad(15)\n", + " elif item == ';': pad(3)\n", + " elif is_label(item): print_string(item.replace('\"', ''))\n", + " else: print_string(\"{:g} \".format(evalu(item)))\n", + " if (not items) or items[-1] not in (',', ';'):\n", + " newline()\n", + " \n", + "def print_string(s): \n", + " \"Print a string, keeping track of column, and advancing to newline if at or beyond column 75.\"\n", + " global column\n", + " print(s, end='')\n", + " column += len(s)\n", + " if column >= 75: newline()\n", + " \n", + "def pad(width): \n", + " \"Pad out to the column that is the next multiple of width.\"\n", + " while column % width != 0: \n", + " print_string(' ')\n", + "\n", + "def newline(): global column; print(); column = 0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Running the First Sample Program\n", + "\n", + "Let's re-examine, parse, and run our first sample program:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "10 REM POWER TABLE\n", + "11 DATA 8, 4\n", + "15 READ N0, P0\n", + "20 PRINT \"N\",\n", + "25 FOR P = 2 to P0\n", + "30 PRINT \"N ^\" P,\n", + "35 NEXT P\n", + "40 PRINT \"SUM\"\n", + "45 LET S = 0\n", + "50 FOR N = 2 TO N0\n", + "55 PRINT N,\n", + "60 FOR P = 2 TO P0\n", + "65 LET S = S + N ^ P\n", + "70 PRINT N ^ P,\n", + "75 NEXT P\n", + "80 PRINT S\n", + "85 NEXT N\n", + "99 END\n", + "\n" + ] + } + ], + "source": [ + "print(program)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[Stmt(num=10, typ='REM', args=[None]),\n", + " Stmt(num=11, typ='DATA', args=[[8.0, 4.0]]),\n", + " Stmt(num=15, typ='READ', args=[['N0', 'P0']]),\n", + " Stmt(num=20, typ='PRINT', args=[['\"N\"', ',']]),\n", + " Stmt(num=25, typ='FOR', args=['P', 2.0, 'P0', 1]),\n", + " Stmt(num=30, typ='PRINT', args=[['\"N ^\"', 'P', ',']]),\n", + " Stmt(num=35, typ='NEXT', args=['P']),\n", + " Stmt(num=40, typ='PRINT', args=[['\"SUM\"']]),\n", + " Stmt(num=45, typ='LET', args=['S', 0.0]),\n", + " Stmt(num=50, typ='FOR', args=['N', 2.0, 'N0', 1]),\n", + " Stmt(num=55, typ='PRINT', args=[['N', ',']]),\n", + " Stmt(num=60, typ='FOR', args=['P', 2.0, 'P0', 1]),\n", + " Stmt(num=65, typ='LET', args=['S', Opcall(x='S', op='+', y=Opcall(x='N', op='^', y='P'))]),\n", + " Stmt(num=70, typ='PRINT', args=[[Opcall(x='N', op='^', y='P'), ',']]),\n", + " Stmt(num=75, typ='NEXT', args=['P']),\n", + " Stmt(num=80, typ='PRINT', args=[['S']]),\n", + " Stmt(num=85, typ='NEXT', args=['N']),\n", + " Stmt(num=99, typ='END', args=[])]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "parse(program)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N N ^2 N ^3 N ^4 SUM\n", + "2 4 8 16 28 \n", + "3 9 27 81 145 \n", + "4 16 64 256 481 \n", + "5 25 125 625 1256 \n", + "6 36 216 1296 2804 \n", + "7 49 343 2401 5597 \n", + "8 64 512 4096 10269 \n" + ] + } + ], + "source": [ + "run(program)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Running More Programs\n", + "\n", + "Rather than put together a suite of unit tests for `execute`, I'll run integration tests—additional whole programs. I've also added a few assertions." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4 -5.5 \n", + "0.666667 0.166667 \n", + "-3.66667 3.83333 \n" + ] + } + ], + "source": [ + "# Linear equation solver (page 3 and 19 of the manual)\n", + "\n", + "run('''\n", + "10 READ A1, A2, A3, A4\n", + "15 LET D = A1 * A4 - A3 * A2\n", + "20 IF D = 0 THEN 65\n", + "30 READ B1, B2\n", + "37 LET X1 = (B1*A4 - B2 * A2) / D\n", + "42 LET X2 = ( A1 * B2 - A3 * B1)/D\n", + "55 PRINT X1, X2\n", + "60 GOTO 30\n", + "65 PRINT \"NO UNIQUE SOLUTION\"\n", + "70 DATA 1, 2, 4\n", + "80 DATA 2, -7, 5\n", + "85 DATA 1, 3, 4, -7\n", + "90 END\n", + "''')\n", + "\n", + "assert variables['D'] != 0\n", + "assert variables['X1'] == -11/3" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X VALUE SINE RESOLUTION\n", + "1.6 0.999574 0.1 \n", + "1.57 1 0.01 \n", + "1.571 1 0.001 \n", + "1.5708 1 0.0001 \n" + ] + } + ], + "source": [ + "# Find max(sin(x)) for 0 <= x <= 3 (page 25)\n", + "\n", + "run('''\n", + "5 PRINT \"X VALUE\", \"SINE\", \"RESOLUTION\"\n", + "10 READ D\n", + "20 LET M = -1\n", + "30 FOR X = 0 TO 3 STEP D\n", + "40 IF SIN(X) <= M THEN 80\n", + "50 LET X0 = X\n", + "60 LET M = SIN(X)\n", + "80 NEXT X\n", + "85 PRINT X0, M, D\n", + "90 GO TO 10\n", + "95 DATA .1, .01, .001, .0001\n", + "99 END\n", + "''')\n", + "\n", + "assert abs(variables['X0'] - math.pi / 2) < 0.00001" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 2 3 4 5 \n", + "6 7 8 9 10 \n", + "11 12 " + ] + } + ], + "source": [ + "# Printing (page 32)\n", + "\n", + "run('''\n", + "10 FOR I = 1 TO 12\n", + "20 PRINT I,\n", + "30 NEXT I\n", + "40 END''')\n", + "\n", + "assert variables['I'] == 12" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "THIS PROGRAM COMPUTES AND PRINTS THE NTH POWERS\n", + "OF THE NUMBERS LESS THAN OR EQUAL TO N FOR VARIOUS\n", + "N FROM 1 TO 7\n", + "\n", + "N = 1 I^N:\n", + "1 \n", + "\n", + "N = 2 I^N:\n", + "1 4 \n", + "\n", + "N = 3 I^N:\n", + "1 8 27 \n", + "\n", + "N = 4 I^N:\n", + "1 16 81 256 \n", + "\n", + "N = 5 I^N:\n", + "1 32 243 1024 3125 \n", + "\n", + "\n", + "N = 6 I^N:\n", + "1 64 729 4096 15625 \n", + "46656 \n", + "\n", + "N = 7 I^N:\n", + "1 128 2187 16384 78125 \n", + "279936 823543 \n", + "\n" + ] + } + ], + "source": [ + "# Powers (page 33)\n", + "\n", + "run('''\n", + " 5 PRINT \"THIS PROGRAM COMPUTES AND PRINTS THE NTH POWERS\"\n", + " 6 PRINT \"OF THE NUMBERS LESS THAN OR EQUAL TO N FOR VARIOUS\"\n", + " 7 PRINT \"N FROM 1 TO 7\"\n", + " 8 PRINT\n", + "10 FOR N = 1 TO 7\n", + "15 PRINT \"N = \"; N; \"I^N:\"\n", + "20 FOR I = 1 TO N\n", + "30 PRINT I^N,\n", + "40 NEXT I\n", + "50 PRINT\n", + "60 PRINT\n", + "70 NEXT N\n", + "80 END''')\n", + "\n", + "assert variables['N'] ** variables['I'] == 7 ** 7" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1e+06 941192 884736 830584 778688 729000 681472 636056 592704 \n", + "551368 512000 474552 438976 405224 373248 343000 314432 287496 \n", + "262144 238328 216000 195112 175616 157464 140608 125000 110592 \n", + "97336 85184 74088 64000 54872 46656 39304 32768 27000 21952 17576 13824 10648 \n", + "8000 5832 4096 2744 1728 1000 512 216 64 8 0 " + ] + } + ], + "source": [ + "# Cubes (page 35; but with STEP -2 because I haven't tested negative step yet)\n", + "\n", + "run('''\n", + "10 FOR I = 100 TO 0 STEP -2\n", + "20 PRINT I*I*I;\n", + "30 NEXT I\n", + "40 END\n", + "''')\n", + "\n", + "assert variables['I'] == 0" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TOTAL SALES FOR SALESMAN1 $180.5 \n", + "TOTAL SALES FOR SALESMAN2 $211.3 \n", + "TOTAL SALES FOR SALESMAN3 $131.65 \n", + "TOTAL SALES FOR SALESMAN4 $166.55 \n", + "TOTAL SALES FOR SALESMAN5 $169.4 \n" + ] + } + ], + "source": [ + "# Sales ledger (page 37; cleaned up a bit)\n", + "\n", + "run('''\n", + "10 FOR I = 1 TO 3\n", + "20 READ P(I)\n", + "30 NEXT I\n", + "40 FOR I = 1 TO 3\n", + "50 FOR J = 1 TO 5\n", + "60 READ S(I, J)\n", + "70 NEXT J\n", + "80 NEXT I\n", + "90 FOR J = 1 TO 5\n", + "100 LET S = 0\n", + "110 FOR I = 1 TO 3\n", + "120 LET S = S + P(I) * S(I, J)\n", + "130 NEXT I\n", + "140 PRINT \"TOTAL SALES FOR SALESMAN\"J, \"$\"S\n", + "150 NEXT J\n", + "190 DIM S(3, 5)\n", + "200 DATA 1.25, 4.30, 2.50\n", + "210 DATA 40, 20, 37, 29, 42\n", + "220 DATA 10, 16, 3, 21, 8\n", + "230 DATA 35, 47, 29, 16, 33\n", + "300 END\n", + "''')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can look at the variables that have been stored for this program:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(float,\n", + " {'J': 5.0,\n", + " ('S', (1.0, 1.0)): 40.0,\n", + " ('S', (2.0, 4.0)): 21.0,\n", + " ('P', (1.0,)): 1.25,\n", + " ('S', (3.0, 2.0)): 47.0,\n", + " ('S', (2.0, 2.0)): 16.0,\n", + " ('S', (3.0, 3.0)): 29.0,\n", + " ('S', (3.0, 5.0)): 33.0,\n", + " ('S', (1.0, 5.0)): 42.0,\n", + " ('S', (3.0, 4.0)): 16.0,\n", + " 'I': 3.0,\n", + " ('P', (3.0,)): 2.5,\n", + " ('S', (1.0, 4.0)): 29.0,\n", + " ('S', (2.0, 3.0)): 3.0,\n", + " ('S', (1.0, 3.0)): 37.0,\n", + " ('S', (2.0, 1.0)): 10.0,\n", + " ('S', (1.0, 2.0)): 20.0,\n", + " ('S', (2.0, 5.0)): 8.0,\n", + " ('S', (3.0, 1.0)): 35.0,\n", + " 'S': 169.4,\n", + " ('P', (2.0,)): 4.3})" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "variables" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "6 3 2 6 9 0 0 3 3 6 9 2 7 9 1 2 1 4 4 1 2 7 3 7 8 \n", + "5 2 5 4 4 9 7 7 0 5 4 9 7 7 5 5 4 9 3 8 6 2 6 4 5 \n", + "8 7 6 0 3 4 1 4 2 2 8 1 1 9 2 4 0 1 0 2 1 3 4 0 2 \n", + "9 0 2 7 4 1 8 4 3 2 8 3 9 3 9 3 2 4 6 8 9 0 9 5 9 \n" + ] + } + ], + "source": [ + "# Random number generator (page 40)\n", + "\n", + "run('''\n", + "10 FOR I = 1 TO 100\n", + "20 PRINT INT(10 * RND(X));\n", + "30 NEXT I\n", + "40 END\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "D SIN(D) COS(D) SIN(D)^2 + COS(D)^2\n", + "0 0 1 1 \n", + "15 0.258819 0.965926 1 \n", + "30 0.5 0.866025 1 \n", + "45 0.707107 0.707107 1 \n", + "60 0.866025 0.5 1 \n", + "75 0.965926 0.258819 1 \n", + "90 1 6.12323e-17 1 \n" + ] + } + ], + "source": [ + "# DEF example: table of SIN(X) and COS(X) in degrees (page 41, expanded some)\n", + "\n", + "run('''\n", + " 5 PRINT \"D\"; \"SIN(D)\", \"COS(D)\", \"SIN(D)^2 + COS(D)^2\"\n", + "20 LET P = 3.1415926535897932 / 180\n", + "30 FOR X = 0 TO 90 STEP 15\n", + "40 PRINT X; FNS(X), FNC(X), FNS(X)^2 + FNC(X)^2\n", + "50 NEXT X\n", + "97 DEF FNS(D) = SIN(D * P)\n", + "98 DEF FNC(D) = COS(D * P)\n", + "99 END\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9 27 120 \n", + "25 125 780 \n", + "Z = 2615 \n" + ] + } + ], + "source": [ + "# GOSUB (page 43)\n", + "\n", + "run('''\n", + "100 LET X = 3\n", + "110 GOSUB 400\n", + "120 PRINT U, V, W\n", + "200 LET X = 5\n", + "210 GOSUB 400\n", + "215 PRINT U, V, W\n", + "220 LET Z = U + 2*V + 3*W\n", + "230 PRINT \"Z = \" Z\n", + "240 STOP\n", + "400 LET U = X*X\n", + "410 LET V = X*X*X\n", + "420 LET W = X*X*X*X + X*X*X + X*X + X\n", + "430 RETURN\n", + "440 END\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "21 \n" + ] + } + ], + "source": [ + "# Sum of non-negative multiples of 0.1 less than or equal to 2, two ways (page 47)\n", + "\n", + "run('''\n", + " 5 LET S = 0\n", + "10 LET N = 0\n", + "20 LET S = S + N/10\n", + "30 IF N >= 20 THEN 60\n", + "40 LET N = N + 1\n", + "50 GOTO 20\n", + "60 PRINT S\n", + "70 END\n", + "''')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "21 \n" + ] + } + ], + "source": [ + "run('''\n", + "20 FOR N = 1 TO 20\n", + "40 LET S = S + N/10\n", + "50 NEXT N\n", + "60 PRINT S\n", + "70 END\n", + "''')\n", + "\n", + "assert variables['S'] == sum(N/10 for N in range(1, 21))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Checking for Syntax Errors\n", + "\n", + "Here we show a collection of syntax errors, and the messages they generate:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error in line '10 X = 1' at 'X = 1': unknown statement type\n", + "Error in line '20 GO TO JAIL' at 'J A I L': missing line number\n", + "Error in line '30 FOR I = 1 ' at '': expected 'TO'\n", + "Error in line '40 IF X > 0 & X < 10 GOTO 999' at '& X < 10 GOTO 999': expected 'THEN'\n", + "Error in line '50 LET Z = (Z + 1' at '': expected \")\" to end expression\n", + "Error in line '60 PRINT \"OH CANADA\", EH?' at '?': unknown expression\n", + "Error in line '70 LET Z = +3' at '+ 3': unknown expression\n", + "Error in line '80 LET X = Y ** 2' at '* 2': unknown expression\n", + "Error in line '90 LET A(I = 1' at '= 1': expected \")\" to close subscript\n", + "Error in line '100 IF A = 0 THEN 900 + 99' at '+ 99': extra tokens at end of line\n", + "Error in line '110 NEXT A(I)' at '( I )': extra tokens at end of line\n", + "Error in line '120 DEF F(X) = X ^ 2 + 1' at 'F ( X ) = X ^ 2 + 1': expected a function name\n", + "Error in line '130 IF X != 0 THEN 999' at '! = 0 THEN 999': expected a relational operator\n", + "Error in line '140 DEF FNS(X + 2*P1) = SIN(X)' at '+ 2 * P1 ) = SIN ( X )': expected ')'\n", + "Error in line '150 DEF FNY(M, B) = M * X + B' at ', B ) = M * X + B': expected ')'\n", + "Error in line '160 LET 3 = X' at '3 = X': expected a variable name\n", + "Error in line '170 LET SIN = 7 * DEADLY' at 'SIN = 7 * D E A D L Y': expected a variable name\n", + "Error in line '180 LET X = A-1(I)' at '( I )': extra tokens at end of line\n", + "Error in line 'STOP' at 'STOP': missing line number\n", + "Error in line '200 STOP IT, ALREADY' at 'I T , A L READ Y': extra tokens at end of line\n", + "PROGRAM STILL EXECUTES: 2 + 2 = 4 \n" + ] + } + ], + "source": [ + "run('''\n", + "10 X = 1\n", + "20 GO TO JAIL\n", + "30 FOR I = 1 \n", + "40 IF X > 0 & X < 10 GOTO 999\n", + "50 LET Z = (Z + 1\n", + "60 PRINT \"OH CANADA\", EH?\n", + "70 LET Z = +3\n", + "80 LET X = Y ** 2\n", + "90 LET A(I = 1\n", + "100 IF A = 0 THEN 900 + 99\n", + "110 NEXT A(I)\n", + "120 DEF F(X) = X ^ 2 + 1\n", + "130 IF X != 0 THEN 999\n", + "140 DEF FNS(X + 2*P1) = SIN(X)\n", + "150 DEF FNY(M, B) = M * X + B\n", + "160 LET 3 = X\n", + "170 LET SIN = 7 * DEADLY\n", + "180 LET X = A-1(I)\n", + "STOP\n", + "200 STOP IT, ALREADY\n", + "998 PRINT \"PROGRAM STILL EXECUTES: 2 + 2 = \" 2 + 2\n", + "999 END\n", + "''')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Final Program\n", + "\n", + "Now for a final, longer example, Conway's Game of [Life](https://en.wikipedia.org/wiki/Conway's_Game_of_Life),\n", + "which shows that BASIC is capable of handling a non-trivial problem—but I wouldn't want to rely on it for anything much bigger. This should give us some added confidence in the validity of the interpreter, but I would say the interpreter needs more work before I would trust it. I hope you found working through the interpreter informative, and maybe you have ideas for how to improve it, or to develop an interpreter for another language." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " GENERATION 0 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . O . . . . . . . \n", + ". . O . . O O . . . \n", + ". . O . . O O . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 1 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". O O O . O O . . . \n", + ". . . . . O O . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 2 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . O . . . . . . . \n", + ". . O . O O O . . . \n", + ". . O . O O O . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 3 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . O . O . . . . \n", + ". O O . O . O . . . \n", + ". . . . O . O . . . \n", + ". . . . . O . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 4 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . O O O O . . . . \n", + ". . O . O . O . . . \n", + ". . . O O . O . . . \n", + ". . . . . O . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 5 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . O O . . . . . \n", + ". . O . O O . . . . \n", + ". . O . . . O . . . \n", + ". . . O O . O . . . \n", + ". . . . O O . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 6 \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . O O O . . . . \n", + ". . O . O O . . . . \n", + ". . O . . . O . . . \n", + ". . . O O . O . . . \n", + ". . . O O O . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 7 \n", + ". . . . . . . . . . \n", + ". . . . O . . . . . \n", + ". . . O . O . . . . \n", + ". . O . . . O . . . \n", + ". . O . . . O . . . \n", + ". . O . . . O . . . \n", + ". . . O . O . . . . \n", + ". . . . O . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 8 \n", + ". . . . . . . . . . \n", + ". . . . O . . . . . \n", + ". . . O O O . . . . \n", + ". . O O . O O . . . \n", + ". O O O . O O O . . \n", + ". . O O . O O . . . \n", + ". . . O O O . . . . \n", + ". . . . O . . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 9 \n", + ". . . . . . . . . . \n", + ". . . O O O . . . . \n", + ". . O . . . O . . . \n", + ". O . . . . . O . . \n", + ". O . . . . . O . . \n", + ". O . . . . . O . . \n", + ". . O . . . O . . . \n", + ". . . O O O . . . . \n", + ". . . . . . . . . . \n", + ". . . . . . . . . . \n", + " GENERATION 10 \n", + ". . . . O . . . . . \n", + ". . . O O O . . . . \n", + ". . O O O O O . . . \n", + ". O O . . . O O . . \n", + "O O O . . . O O O . \n", + ". O O . . . O O . . \n", + ". . O O O O O . . . \n", + ". . . O O O . . . . \n", + ". . . . O . . . . . \n", + ". . . . . . . . . . \n" + ] + } + ], + "source": [ + "run('''\n", + "100 REM CONWAY'S GAME OF LIFE\n", + "102 REM G IS NUMBER OF GENERATIONS, M IS MATRIX SIZE (M X M)\n", + "104 REM A(X, Y) IS 1 IFF CELL AT (X, Y) IS LIVE\n", + "106 REM L(SELF_ALIVE, NEIGHBORS_ALIVE) IS 1 IFF CELL WITH THOSE COUNTS SHOULD LIVE ON\n", + "110 LET G = 10\n", + "120 LET M = 10\n", + "125 READ A(3,4), A(3,5), A(3,6), A(6,5), A(6,6), A(7,5), A(7,6)\n", + "130 DATA 1, 1, 1, 1, 1, 1, 1\n", + "140 READ L(0, 3), L(1, 3), L(1, 2)\n", + "145 DATA 1, 1, 1\n", + "\n", + "150 REM MAIN LOOP: PRINT, THEN REPEAT G TIMES: UPDATE / COPY / PRINT\n", + "155 LET I = 0\n", + "160 GOSUB 700\n", + "170 FOR I = 1 TO G\n", + "180 GOSUB 300\n", + "190 GOSUB 500\n", + "200 GOSUB 700\n", + "210 NEXT I\n", + "220 STOP\n", + "\n", + "300 REM SUBROUTINE: UPDATE B = NEXT_GENERATION(A)\n", + "310 FOR Y = 1 TO M\n", + "320 FOR X = 1 TO M\n", + "325 LET N = A(X-1,Y)+A(X+1,Y)+A(X,Y-1)+A(X,Y+1)+A(X-1,Y-1)+A(X+1,Y+1)+A(X-1,Y+1)+A(X+1,Y-1)\n", + "330 LET B(X, Y) = L(A(X, Y), N)\n", + "340 NEXT X\n", + "350 NEXT Y\n", + "360 RETURN\n", + "\n", + "500 REM SUBROUTINE: COPY A = B\n", + "510 FOR Y = 1 TO M\n", + "520 FOR X = 1 TO M\n", + "530 LET A(X, Y) = B(X, Y)\n", + "540 NEXT X\n", + "550 NEXT Y\n", + "560 RETURN\n", + "\n", + "700 REM SUBROUTINE: PRINT A\n", + "705 PRINT \" GENERATION \" I\n", + "710 FOR Y = 1 TO M\n", + "720 FOR X = 1 TO M\n", + "730 IF A(X, Y) = 0 THEN 750\n", + "740 PRINT \"O\";\n", + "750 IF A(X, Y) = 1 THEN 770\n", + "760 PRINT \".\";\n", + "770 NEXT X\n", + "780 PRINT\n", + "790 NEXT Y\n", + "795 RETURN\n", + "\n", + "999 END \n", + "''')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Beal.ipynb b/pytudes/ipynb/Beal.ipynb new file mode 100644 index 0000000..71cad1f --- /dev/null +++ b/pytudes/ipynb/Beal.ipynb @@ -0,0 +1,1070 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "
Peter Norvig 22 October 2015, revised 28 October 2015, 4 July 2017
\n", + "\n", + "# Beal's Conjecture Revisited\n", + "\n", + "In 1637, Pierre de Fermat wrote in the margin of a book that he had a proof of his famous \"[Last Theorem](https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem)\":\n", + "\n", + "> If $A^n + B^n = C^n$,\n", + ">
where $A, B, C, n$ are positive integers\n", + ">
then $n \\le 2$.\n", + "\n", + "Centuries passed before [Andrew Beal](https://en.wikipedia.org/wiki/Andrew_Beal), a businessman and amateur mathematician,\n", + "made his conjecture in 1993:\n", + "\n", + "> If $A^x + B^y = C^z$, \n", + ">
where $A, B, C, x, y, z$ are positive integers and $x, y, z$ are all greater than $2$, \n", + ">
then $A, B$ and $C$ must have a common prime factor.\n", + "\n", + "[Andrew Wiles](https://en.wikipedia.org/wiki/Andrew_Wiles) proved Fermat's theorem in 1995, but Beal's conjecture remains unproved, and Beal has offered [$1,000,000](http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize) for a proof or disproof. I don't have the mathematical skills of Wiles, so I could never find a proof, but I can write a program to search for counterexamples. I first wrote [that program in 2000](http://norvig.com/beal2000.html), and [my name got associated](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=beal%20conjecture) with Beal's Conjecture, which means I get a lot of emails with purported proofs or counterexamples (many asking how they can collect their prize money). So far, all the emails have been wrong. This page catalogs some of the more common errors and updates my 2000 program." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# How to Not Win A Million Dollars\n", + "\n", + "\n", + "* A proof must show that there are no examples that satisfy the conditions. A common error is to show how a certain pattern generates an infinite collection of numbers that satisfy $A^x + B^y = C^z$ and then show that in all of these, $A, B, C$ have a common factor. But that's not good enough, unless you can also prove that no other pattern exists.\n", + "\n", + "

\n", + "\n", + "* It is valid to use proof by contradiction: assume the conjecture is true, and show that that leads to a contradiction. It is not valid to use proof by circular reasoning: assume the conjecture is true, put in some irrelevant steps, and show that it follows that the conjecture is true.\n", + "\n", + "\n", + "

\n", + "\n", + "* A valid counterexample needs to satisfy all four conditions—don't leave one out:\n", + "\n", + "> $A, B, C, x, y, z$ are positive integers
\n", + "$x, y, z > 2$
\n", + "$A^x + B^y = C^z$
\n", + "$A, B, C$ have no common prime factor.\n", + "\n", + "(If you think you might have a valid counterexample, before you share it with Andrew Beal or anyone else, you can check it with my [Online Beal Counterexample Checker](http://norvig.com/bealcheck.html).)\n", + "\n", + "

\n", + "\n", + "* One correspondent claimed that $27^4 + 162 ^ 3 = 9 ^ 7$ was a solution, because the first three conditions hold, and the common factor is 9, which isn't a prime. But of course, if $A, B, C$ have 9 as a common factor, then they also have 3, and 3 is prime. The phrase \"no common prime factor\" means the same thing as \"no common factor greater than 1.\"\n", + "\n", + "

\n", + "\n", + "* Another claimed that $2^3+2^3=2^4$ was a counterexample, because all the bases are 2, which is prime, and prime numbers have no prime factors. But that's not true; a prime number has itself as a factor.\n", + "\n", + "

\n", + "\n", + "* A creative person offered $1359072^4 - 940896^4 = 137998080^3$, which fails both because $3^3 2^5 11^2$ is a common factor, and because it has a subtraction rather than an addition (although, as Julius Jacobsen pointed out, that can be rectified by adding $940896^4$ to both sides).\n", + "\n", + "

\n", + "\n", + "* Mustafa Pehlivan came up with an example involving 76-million-digit numbers, which took some work to prove wrong (by using modulo arithmetic). \n", + "\n", + "

\n", + "\n", + "* Another Beal fan started by saying \"Let $C = 43$ and $z = 3$. Since $43 = 21 + 22$, we have $43^3 = (21^3 + 22^3).$\" But of course $(a + b)^3 \\ne (a^3 + b^3)$. This fallacy is called [the freshman's dream](https://en.wikipedia.org/wiki/Freshman%27s_dream) (although I remember having different dreams as a freshman).\n", + "\n", + "

\n", + "\n", + "* Multiple people proposed answers similar to this one:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import gcd #### In Python versions < 3.5, use \"from fractions import gcd\"" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A, B, C = 60000000000000000000, 70000000000000000000, 82376613842809255677\n", + "\n", + "x = y = z = 3.\n", + "\n", + "A ** x + B ** y == C ** z and gcd(gcd(A, B), C) == 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**WOW! The result is `True`!** Is this a real counterexample to Beal? And also a disproof of Fermat?\n", + "\n", + "Alas, it is not. Notice the decimal point in \"`3.`\", indicating a floating point number, with inexact, limited precision. Change the inexact \"`3.`\" to an exact \"`3`\" and the result changes to \"`False`\". Below we see that the two sides of the equation are the same for the first 18 digits, but differ starting with the 19th: " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(559000000000000000000000000000000000000000000000000000000000,\n", + " 559000000000000000063037470301555182935702892172500189973733)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(A ** 3 + B ** 3,\n", + " C ** 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "They say \"close\" only counts in horseshoes and hand grenades, and if you threw two horseshoes at a stake on the planet [Kapteyn-b](https://en.wikipedia.org/wiki/Kapteyn_b) (a possibly habitable and thus possibly horseshoe-playing exoplanet 12.8 light years from Earth) and the two paths differed in the 19th digit, the horseshoes would end up [less than an inch](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=12.8%20light%20years%20*%201e-19%20in%20inches) apart. That's really, really close, but close doesn't count in number theory.\n", + "\n", + "\n", + "# *The Simpsons* and Fermat\n", + "\n", + "In two different [episodes of *The Simpsons*](http://www.npr.org/sections/krulwich/2014/05/08/310818693/did-homer-simpson-actually-solve-fermat-s-last-theorem-take-a-look), close counterexamples to Fermat's Last Theorem are shown: \n", + "$1782^{12} + 1841^{12} = 1922^{12}$ and $3987^{12} + 4365^{12} = 4472^{12}$. These were designed by *Simpsons* writer David X. Cohen to be correct up to the precision found in most handheld calculators. Cohen found the equations with a program that must have been something like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from itertools import combinations\n", + "\n", + "def simpsons(bases, powers):\n", + " \"\"\"Find the integers (A, B, C, n) that come closest to solving \n", + " Fermat's equation, A ** n + B ** n == C ** n. \n", + " Let A, B range over all pairs of bases and n over all powers.\"\"\"\n", + " equations = ((A, B, iroot(A ** n + B ** n, n), n)\n", + " for A, B in combinations(bases, 2)\n", + " for n in powers)\n", + " return min(equations, key=relative_error)\n", + "\n", + "def iroot(i, n): \n", + " \"The integer closest to the nth root of i.\"\n", + " return int(round(i ** (1./n)))\n", + "\n", + "def relative_error(equation):\n", + " \"Error between LHS and RHS of equation, relative to RHS.\" \n", + " (A, B, C, n) = equation\n", + " LHS = A ** n + B ** n\n", + " RHS = C ** n\n", + " return abs(LHS - RHS) / RHS" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1782, 1841, 1922, 12)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simpsons(range(1000, 2000), [11, 12, 13])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3987, 4365, 4472, 12)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simpsons(range(3000, 5000), [12])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Back to Beal\n", + "\n", + "In October 2015 I looked back at my original [program from 2000](http://norvig.com/beal2000.html).\n", + "I ported it from Python 1.5 to 3.5 (by putting parens around the argument to `print` and adding `long = int`). The program runs 250 times faster today than it did in 2000, a tribute to both computer hardware engineers and the developers of the Python interpreter.\n", + "\n", + "I found that I was a bit confused about the definition of [the problem in 2000](https://web.archive.org/web/19991127081319/http://bealconjecture.com/). I thought then that, *by definition*, $A$ and $B$ could not have a common factor, but actually, the definition of the conjecture only rules out examples where all three of $A, B, C$ share a common factor. Mark Tiefenbruck (and later Edward P. Berlin and Shen Lixing) wrote to point out that my thought was actually correct, not by definition, but by derivation: if $A$ and $B$ have a commmon prime factor $p$, then the sum of $A^x + B^y$ must also have that factor $p$, and since $A^x + B^y = C^z$, then $C^z$ and hence $C$ must have the factor $p$. So I was wrong twice, and in this case two wrongs did make a right.\n", + "\n", + "Mark Tiefenbruck also suggested an optimization: only consider exponents that are odd primes, or 4. The idea is that a number like 512 can be expressed as either $2^9$ or $8^3$, and my program doesn't need to consider both. In general, any time we have a composite exponent, such as $b^{qp}$, where $p$ is prime, we should ignore $b^{(qp)}$, and instead consider only $(b^q)^p$. There's one complication to this scheme: 2 is a prime, but 2 is not a valid exponent for a Beal counterexample. So we will allow 4 as an exponent, as well as all odd primes up to `max_x`.\n", + "\n", + "Here is the complete, updated, refactored, optimized program:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import gcd, log\n", + "from itertools import combinations, product\n", + "\n", + "def beal(max_A, max_x):\n", + " \"\"\"See if any A ** x + B ** y equals some C ** z, with gcd(A, B) == 1.\n", + " Consider any 1 <= A,B <= max_A and x,y <= max_x, with x,y prime or 4.\"\"\"\n", + " Apowers = make_Apowers(max_A, max_x)\n", + " Czroots = make_Czroots(Apowers)\n", + " for (A, B) in combinations(Apowers, 2):\n", + " if gcd(A, B) == 1:\n", + " for (Ax, By) in product(Apowers[A], Apowers[B]): \n", + " Cz = Ax + By\n", + " if Cz in Czroots:\n", + " C = Czroots[Cz]\n", + " x, y, z = exponent(Ax, A), exponent(By, B), exponent(Cz, C)\n", + " print('{} ** {} + {} ** {} == {} ** {} == {}'\n", + " .format(A, x, B, y, C, z, C ** z))\n", + "\n", + "def make_Apowers(max_A, max_x): \n", + " \"A dict of {A: [A**3, A**4, ...], ...}.\"\n", + " exponents = exponents_upto(max_x)\n", + " return {A: [A ** x for x in (exponents if (A != 1) else [3])]\n", + " for A in range(1, max_A+1)}\n", + "\n", + "def make_Czroots(Apowers): return {Cz: C for C in Apowers for Cz in Apowers[C]} \n", + " \n", + "def exponents_upto(max_x):\n", + " \"Return all odd primes up to max_x, as well as 4.\"\n", + " exponents = [3, 4] if max_x >= 4 else [3] if max_x == 3 else []\n", + " for x in range(5, max_x, 2):\n", + " if not any(x % p == 0 for p in exponents):\n", + " exponents.append(x)\n", + " return exponents\n", + "\n", + "def exponent(Cz, C): \n", + " \"\"\"Recover z such that C ** z == Cz (or equivalently z = log Cz base C).\n", + " For exponent(1, 1), arbitrarily choose to return 3.\"\"\"\n", + " return 3 if (Cz == C == 1) else int(round(log(Cz, C)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "It takes less than a second to verify that there are no counterexamples for combinations up to $100^{100}$, a computation that took Andrew Beal thousands of hours on his 1990s-era computers:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 256 ms, sys: 1.44 ms, total: 257 ms\n", + "Wall time: 256 ms\n" + ] + } + ], + "source": [ + "%time beal(100, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The execution time goes up roughly with the square of `max_A`, so the following should take about 100 times longer:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 29.1 s, sys: 25.2 ms, total: 29.2 s\n", + "Wall time: 29.2 s\n" + ] + } + ], + "source": [ + "%time beal(1000, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# How `beal` Works\n", + "\n", + "The function `beal` first does some precomputation, creating two data structures:\n", + "* `Apowers`: a dict of the form `{A: [A**3, A**4, ...]}` giving the\n", + "nonredundant powers (prime and 4th powers) of each base, `A`, from 3 to `max_x`.\n", + "* `Czroots`: a dict of `{C**z : C}` pairs, giving the zth root of each power in `Apowers`.\n", + "\n", + "Here is a very small example Apowers table:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{1: [1],\n", + " 2: [8, 16, 32, 128],\n", + " 3: [27, 81, 243, 2187],\n", + " 4: [64, 256, 1024, 16384],\n", + " 5: [125, 625, 3125, 78125],\n", + " 6: [216, 1296, 7776, 279936]}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Apowers = make_Apowers(6, 10)\n", + "Apowers" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Then we enumerate all combinations of two bases, `A` and `B`, from `Apowers`. Consider the combination where `A` is `3` and `B` is `6`. Of course `gcd(3, 6) == 3`, so the program would not consider them further, but imagine if they did not share a common factor. Then we would look at all possible `Ax + By` sums, for `Ax` in `[27, 81, 243, 2187]` and `By` in `[216, 1296, 7776, 279936].` One of these would be `27 + 216`, which sums to `243`. We look up `243` in `Czroots`:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{1: 1,\n", + " 8: 2,\n", + " 16: 2,\n", + " 27: 3,\n", + " 32: 2,\n", + " 64: 4,\n", + " 81: 3,\n", + " 125: 5,\n", + " 128: 2,\n", + " 216: 6,\n", + " 243: 3,\n", + " 256: 4,\n", + " 625: 5,\n", + " 1024: 4,\n", + " 1296: 6,\n", + " 2187: 3,\n", + " 3125: 5,\n", + " 7776: 6,\n", + " 16384: 4,\n", + " 78125: 5,\n", + " 279936: 6}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Czroots = make_Czroots(Apowers)\n", + "Czroots" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Czroots[243]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see that `243` is in `Czroots`, with value `3`, so this would be a counterexample (except for the common factor). The program uses the `exponent` function to recover the values of `x, y, z`, and prints the results.\n", + "\n", + "# Is the Program Correct?\n", + "\n", + "Can we gain confidence in the program? It is difficult to test `beal`, because the expected output is nothing, for all known inputs.\n", + "One thing we can do is verify that `beal` finds cases like `3 ** 3 + 6 ** 3 == 3 ** 5 == 243` that would be a counterexample except for the common factor `3`. We can test this by temporarily replacing the `gcd` function with a mock function that always reports no common factors:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3 ** 3 + 6 ** 3 == 3 ** 5 == 243\n", + "7 ** 7 + 49 ** 3 == 98 ** 3 == 941192\n", + "8 ** 4 + 16 ** 3 == 2 ** 13 == 8192\n", + "8 ** 5 + 32 ** 3 == 16 ** 4 == 65536\n", + "9 ** 3 + 18 ** 3 == 9 ** 4 == 6561\n", + "16 ** 5 + 32 ** 4 == 8 ** 7 == 2097152\n", + "17 ** 4 + 34 ** 4 == 17 ** 5 == 1419857\n", + "19 ** 4 + 38 ** 3 == 57 ** 3 == 185193\n", + "27 ** 3 + 54 ** 3 == 3 ** 11 == 177147\n", + "28 ** 3 + 84 ** 3 == 28 ** 4 == 614656\n", + "34 ** 5 + 51 ** 4 == 85 ** 4 == 52200625\n" + ] + } + ], + "source": [ + "def gcd(a, b): return 1\n", + "\n", + "beal(100, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's make sure all those expressions are true:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{True}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{3 ** 3 + 6 ** 3 == 3 ** 5 == 243,\n", + " 7 ** 7 + 49 ** 3 == 98 ** 3 == 941192,\n", + " 8 ** 4 + 16 ** 3 == 2 ** 13 == 8192,\n", + " 8 ** 5 + 32 ** 3 == 16 ** 4 == 65536,\n", + " 9 ** 3 + 18 ** 3 == 9 ** 4 == 6561,\n", + " 16 ** 5 + 32 ** 4 == 8 ** 7 == 2097152,\n", + " 17 ** 4 + 34 ** 4 == 17 ** 5 == 1419857,\n", + " 19 ** 4 + 38 ** 3 == 57 ** 3 == 185193,\n", + " 27 ** 3 + 54 ** 3 == 3 ** 11 == 177147,\n", + " 28 ** 3 + 84 ** 3 == 28 ** 4 == 614656,\n", + " 34 ** 5 + 51 ** 4 == 85 ** 4 == 52200625}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I get nervous having an incorrect version of `gcd` around; let's change it back, quick!" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import gcd\n", + "\n", + "beal(100, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can also provide some test cases for the subfunctions of `beal`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'tests pass'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " assert make_Apowers(6, 10) == {\n", + " 1: [1],\n", + " 2: [8, 16, 32, 128],\n", + " 3: [27, 81, 243, 2187],\n", + " 4: [64, 256, 1024, 16384],\n", + " 5: [125, 625, 3125, 78125],\n", + " 6: [216, 1296, 7776, 279936]}\n", + " \n", + " assert make_Czroots(make_Apowers(5, 8)) == {\n", + " 1: 1, 8: 2, 16: 2, 27: 3, 32: 2, 64: 4, 81: 3,\n", + " 125: 5, 128: 2, 243: 3, 256: 4, 625: 5, 1024: 4,\n", + " 2187: 3, 3125: 5, 16384: 4, 78125: 5}\n", + " Czroots = make_Czroots(make_Apowers(100, 100))\n", + " assert 3 ** 3 + 6 ** 3 in Czroots\n", + " assert 99 ** 97 in Czroots\n", + " assert 101 ** 100 not in Czroots\n", + " assert Czroots[99 ** 97] == 99\n", + " \n", + " assert exponent(10 ** 5, 10) == 5\n", + " assert exponent(7 ** 3, 7) == 3\n", + " assert exponent(1234 ** 999, 1234) == 999\n", + " assert exponent(12345 ** 6789, 12345) == 6789\n", + " assert exponent(3 ** 10000, 3) == 10000\n", + " assert exponent(1, 1) == 3\n", + " \n", + " assert exponents_upto(2) == []\n", + " assert exponents_upto(3) == [3]\n", + " assert exponents_upto(4) == [3, 4]\n", + " assert exponents_upto(40) == [3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]\n", + " assert exponents_upto(100) == [\n", + " 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, \n", + " 67, 71, 73, 79, 83, 89, 97]\n", + " \n", + " assert gcd(3, 6) == 3\n", + " assert gcd(3, 7) == 1\n", + " assert gcd(861591083269373931, 94815872265407) == 97\n", + " assert gcd(2*3*5*(7**10)*(11**12), 3*(7**5)*(11**13)*17) == 3*(7**5)*(11**12)\n", + " \n", + " return 'tests pass'\n", + " \n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The program is mostly straightforward, but relies on the correctness of these arguments: \n", + "\n", + "* Are we justified in taking `combinations` without replacements from the `Apowers` table? In other words, are we sure there are no solutions of the form $A^x + A^x = C^z$? Yes, we can be sure, because then $2\\;A^x = C^z$, and all the factors of $A$ would also be factors of $C$.\n", + "\n", + "

\n", + "* Are we justified in having a single value for each key in the `Czroots` table? Consider that $81 = 3^4 = 9^2$. We put `{81: 3}` in the table and discard `{81: 9}`, because any number that has 9 as a factor will always have 3 as a factor as well, so 3 is all we need to know. But what if a number could be formed with two bases where neither was a multiple of the other? For example, what if $2^7 = 5^3 = s$; then wouldn't we have to have both 2 and 5 as values for $s$ in the table? Fortunately, that can never happen, because of the [fundamental theorem of arithmetic](https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic).\n", + "\n", + "

\n", + "* Could there be a rounding error involving the `exponent` function that was not caught by the tests? Possibly; but `exponent` is not used to find counterexamples, only to print them, so any such error wouldn't cause us to miss a counterexample.\n", + "\n", + "

\n", + "* Are we justified in only considering exponents that are odd primes, or the number 4? In one sense, yes, because when we consider the two terms $A^{(qp)}$ and $(A^q)^p$, we find they are always equal, and always have the same prime factors (the factors of $A$), so for the purposes of the Beal problem, they are equivalent, and we only need consider one of them. In another sense, there is a difference. With this optimization, when we run `beal(6, 10)`, we are no longer testing $512$ as a value of $A$ or $B$, even though $512 = 2^9$ and both $2$ and $9$ are within range, because the program chooses to express $512$ as $8^3$, and $8$ is not in the specified range. So the program is still correctly searching for counterexamples, but the space that it searches for given `max_A` and `max_x` is different with this optimization.\n", + "\n", + "

\n", + "* Are we really sure that when $A$ and $B$ have a common factor greater than 1, then\n", + "$C$ also shares that common factor? Yes, because if $p$ is a factor of both $A$ and $B$, then it is a factor of $A^x + B^y$, and since we know this is equal to $C^z$, then $p$ must also be a factor of $C^z$, and thus a factor of $C$.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "# Faster Arithmetic (mod *p*)\n", + "\n", + "Arithmetic is slow with integers that have thousands of digits. If we want to explore much further, we'll have to make the program more efficient. An obvious improvement would be to do all the arithmetic modulo some number $m$. Then we know:\n", + "\n", + "$$\\mbox{if} ~~ \n", + "A^x + B^y = C^z\n", + "~~ \\mbox{then} ~~\n", + "(A^x (\\mbox{mod} ~ m) + B^y (\\mbox{mod} ~ m)) (\\mbox{mod} ~ m) = C^z \\;(\\mbox{mod} ~ m)$$\n", + "\n", + "\n", + "So we can do efficient tests modulo $m$, and then do the full arithmetic only for combinations that work modulo $m$. Unfortunately there will be collisions (two numbers that are distinct, but are equal mod $m$), so the tables will have to have lists of values. Here is a simple, unoptimized implementation:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import gcd\n", + "from itertools import combinations, product\n", + "from collections import defaultdict\n", + " \n", + "def beal_modm(max_A, max_x, m=2**31-1):\n", + " \"\"\"See if any A ** x + B ** y equals some C ** z (mod p), with gcd(A, B) == 1.\n", + " If so, verify that the equation works without the (mod m).\n", + " Consider any 1 <= A,B <= max_A and x,y <= max_x, with x,y prime or 4.\"\"\"\n", + " assert m >= max_A\n", + " Apowers = make_Apowers_modm(max_A, max_x, m)\n", + " Czroots = make_Czroots_modm(Apowers)\n", + " for (A, B) in combinations(Apowers, 2):\n", + " if gcd(A, B) == 1:\n", + " for (Axm, x), (Bym, y) in product(Apowers[A], Apowers[B]): \n", + " Czm = (Axm + Bym) % m\n", + " if Czm in Czroots:\n", + " lhs = A ** x + B ** y\n", + " for (C, z) in Czroots[Czm]:\n", + " if lhs == C ** z:\n", + " print('{} ** {} + {} ** {} == {} ** {} == {}'\n", + " .format(A, x, B, y, C, z, C ** z)) \n", + " \n", + "\n", + "def make_Apowers_modm(max_A, max_x, m): \n", + " \"A dict of {A: [(A**3 (mod m), 3), (A**4 (mod m), 4), ...]}.\"\n", + " exponents = exponents_upto(max_x)\n", + " return {A: [(pow(A, x, m), x) for x in (exponents if (A != 1) else [3])]\n", + " for A in range(1, max_A+1)}\n", + "\n", + "def make_Czroots_modm(Apowers): \n", + " \"A dict of {C**z (mod m): [(C, z),...]}\"\n", + " Czroots = defaultdict(list)\n", + " for A in Apowers:\n", + " for (Axm, x) in Apowers[A]:\n", + " Czroots[Axm].append((A, x))\n", + " return Czroots " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here we see that each entry in the `Apowers` table is a list of `(A**x (mod p), x)` pairs.\n", + "For example, $6^7 = 279,936$, so in our (mod 1000) table we have the pair `(936, 7)` under `6`." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{1: [(1, 3)],\n", + " 2: [(8, 3), (16, 4), (32, 5), (128, 7)],\n", + " 3: [(27, 3), (81, 4), (243, 5), (187, 7)],\n", + " 4: [(64, 3), (256, 4), (24, 5), (384, 7)],\n", + " 5: [(125, 3), (625, 4), (125, 5), (125, 7)],\n", + " 6: [(216, 3), (296, 4), (776, 5), (936, 7)]}" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Apowers = make_Apowers_modm(6, 10, 1000)\n", + "Apowers" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And each item in the `Czroots` table is of the form `{C**z (mod m): [(C, z), ...]}`.\n", + "For example, `936: [(6, 7)]`." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(list,\n", + " {1: [(1, 3)],\n", + " 8: [(2, 3)],\n", + " 16: [(2, 4)],\n", + " 24: [(4, 5)],\n", + " 27: [(3, 3)],\n", + " 32: [(2, 5)],\n", + " 64: [(4, 3)],\n", + " 81: [(3, 4)],\n", + " 125: [(5, 3), (5, 5), (5, 7)],\n", + " 128: [(2, 7)],\n", + " 187: [(3, 7)],\n", + " 216: [(6, 3)],\n", + " 243: [(3, 5)],\n", + " 256: [(4, 4)],\n", + " 296: [(6, 4)],\n", + " 384: [(4, 7)],\n", + " 625: [(5, 4)],\n", + " 776: [(6, 5)],\n", + " 936: [(6, 7)]})" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "make_Czroots_modm(Apowers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's run the program:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 35.5 s, sys: 44.1 ms, total: 35.5 s\n", + "Wall time: 35.5 s\n" + ] + } + ], + "source": [ + "%time beal_modm(1000, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We don't see a speedup here, but the idea is that as we start dealing with much larger integers, this version should be faster. I could improve this version by caching certain computations, managing the memory layout better, moving some computations out of loops, considering using multiple different numbers as the modulus (as in a Bloom filter), finding a way to parallelize the program, and re-coding in a faster compiled language (such as C++ or Go or Julia). Then I could invest thousands (or millions) of CPU hours searching for counterexamples. \n", + "\n", + "But [Witold Jarnicki](https://plus.sandbox.google.com/+WitoldJarnicki/posts) and [David Konerding](http://www.konerding.com/~dek/) already did that: they wrote a C++ program that, in parallel across thousands of machines, searched for $A, B$ up to 200,000 and $x, y$ up to 5,000, but found no counterexamples. So I don't think it is worthwhile to continue on that path.\n", + "\n", + "# Conclusion\n", + "\n", + "This was fun, but I can't recommend anyone spend a serious amount of computer time looking for counterexamples to the Beal Conjecture—the money you would have to spend in computer time would be more than the expected value of your prize winnings. I suggest you work on a proof rather than a counterexample, or work on some other interesting problem instead!" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Bike Speed versus Grade.ipynb b/pytudes/ipynb/Bike Speed versus Grade.ipynb new file mode 100644 index 0000000..5791e61 --- /dev/null +++ b/pytudes/ipynb/Bike Speed versus Grade.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Bike Speed versus Grade\n", + "\n", + "Like most people, I bike slower when I'm going up a steep hill than on a flat road. But how much slower?\n", + "To answer that, I downloaded data on my past rides \n", + "from [Strava](https://www.strava.com/athletes/575579) and manipulated the `data` to create two lists: \n", + "\n", + "- `X`: the *grade* of each ride, in feet of ascent per mile. \n", + "- `Y`: the *speed* of each (corresponding) ride, in miles per hour.\n", + "\n", + "I omit rides shorter than 30 miles, because on some short rides I was sprinting at an unsustainable speed, and on others I was slowed by city traffic. Here is the code to collect and plot the X:Y data:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import csv\n", + "\n", + "def hours(sec): return float(sec) / 60 / 60\n", + "def feet(meters): return float(meters) * 100 / 2.54 / 12\n", + "def miles(meters): return feet(meters) / 5280\n", + "\n", + "# Read data file with three fields: distance (m), climb (m), elapsed time (sec)\n", + "X, Y = [], []\n", + "for (dist, climb, time) in csv.reader(open('dist-climb-time.csv')):\n", + " if miles(dist) > 30:\n", + " X.append(feet(climb) / miles(dist))\n", + " Y.append(miles(dist) / hours(time))\n", + "\n", + "plt.plot(X, Y, 'o');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the speeds get slower as the grade gets steeper. The data has a lot of variance, and I can say that it \n", + "looks more like a curve than a straight line, so I'll fit a cubic (degree two) polynomial to the data,\n", + "and make the plot prettier:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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uqYWoEVhmVWO1w2azwWKxIH/ROndhgqrmRoybuwrrZ0xERkZGp23p8XPhkpycjHXT8rH8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def poly(X, Y, n):\n", + " \"Best-fit degree-n polynomial for X, Y data.\"\n", + " C = np.polyfit(X, Y, n)[::-1] # Array of coefficients, reversed\n", + " return lambda x: sum(C[i] * x ** i for i in range(n + 1)) \n", + "\n", + "F = poly(X, Y, 2) # defines y = F(x); x in ft/mile, y in mph\n", + "\n", + "def show(X, Y, F=F): \n", + " plt.rcParams[\"figure.figsize\"] = (12, 8)\n", + " plt.style.use('fivethirtyeight')\n", + " plt.plot(X, Y, 'o')\n", + " X1 = list(range(int(max(X))))\n", + " plt.plot(X1, [F(x) for x in X1], 'o')\n", + " plt.ylabel('Speed (mph)')\n", + " plt.xlabel('Grade (feet/mile)')\n", + " plt.minorticks_on()\n", + " plt.grid(True, which='major')\n", + " plt.grid(True, which='minor', alpha=0.2)\n", + " \n", + "show(X, Y) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, I average about 14 mph when the road is fairly flat, with a lot of variability from 12 to 16 mph, depending more on my level of effort than on the grade of the road. But from 60 ft/mile and up, speed falls off quickly at 1 mph for every 20 ft/mile, and by 140 ft/mile, I'm down around 8 mph. Note that 140 ft/mile is only 2.7% grade, but if you figure a typical route is 1/3 up, 1/3 down, and 1/3 flatish, then that's 8% grade on the up part.\n", + "\n", + "I can use the polynomial `F` to estimate the duration of a route:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def duration(dist, climb, F=F):\n", + " \"Given a distance in miles and total climb in feet, return estimated time in minutes.\"\n", + " return dist / F(climb / dist) * 60" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example, to get to Pescadero from La Honda, I could take the flatter [coast route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.4039496!2d37.3116594!3s0x808f062b7d7585e7:0x942480c22f110b74!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1), or the shorter [creek route](https://www.google.com/maps/dir/La+Honda,+California/Pescadero,+California/@37.2905834,-122.3896683,12z/data=!4m19!4m18!1m10!1m1!1s0x808faed4dc6265bd:0x51a109d3306a7219!2m2!1d-122.274227!2d37.3190255!3m4!1m2!1d-122.3658887!2d37.2538867!3s0x808f00acf265bd43:0xb7e2a0c9ee355c3a!1m5!1m1!1s0x808f00b4b613c4c1:0x43c609077878b77!2m2!1d-122.3830152!2d37.2551636!3e1):" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6.7314081227852185" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "coast = duration(15.7, 344)\n", + "creek = duration(13.5, 735)\n", + "\n", + "coast - creek" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This says the coast route takes 6.7 minutes longer. Good to know, but other factors are probably more important in making the choice." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Cheryl-and-Eve.ipynb b/pytudes/ipynb/Cheryl-and-Eve.ipynb new file mode 100644 index 0000000..29864bd --- /dev/null +++ b/pytudes/ipynb/Cheryl-and-Eve.ipynb @@ -0,0 +1,1202 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# When Cheryl Met Eve: A Birthday Story" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Peter Norvig, May 2015\n", + "\n", + "The \"Cheryl's Birthday\" logic puzzle [made the rounds](https://www.google.com/webhp?#q=cheryl%27s+birthday),\n", + "and I wrote [code](Cheryl.ipynb) that solves it. There I said that one reason for solving the problem with code rather than pencil and paper is that you can do more with code. [Gabe Gaster](http://www.gabegaster.com/) proved me right when he [tweeted](https://twitter.com/gabegaster/status/593976413314777089/photo/1) that he had extended my code to generate a new list of dates that satisfies the constraints of the puzzle:\n", + "\n", + " January 15, January 4,\n", + " July 13, July 24, July 30,\n", + " March 13, March 24,\n", + " May 11, May 17, May 30\n", + "\n", + "In this notebook, I verify Gabe's result, and find some other variations on the puzzle.\n", + "\n", + "First, let's recap [the puzzle](https://en.wikipedia.org/wiki/Cheryl%27s_Birthday):\n", + "\n", + "> Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:\n", + "\n", + "> May 15 16 19\n", + "> June 17 18\t\n", + "> July 14 16\t\t\t\n", + "> August 14 15 17\t\t\n", + "\n", + "> Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.\n", + "\n", + ">**Albert**: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\n", + "\n", + ">**Bernard**: At first I don't know when Cheryl's birthday is, but I know now.\n", + "\n", + ">**Albert**: Then I also know when Cheryl's birthday is.\n", + "\n", + ">So when is Cheryl's birthday?\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Code for Original Cheryl's Birthday Puzzle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a slight modification of my [previous code](Cheryl.ipynb), and I'll give a slight modification of the explanation. The puzzle concerns these concepts:\n", + "\n", + "- **Possible dates** that might be Cheryl's birthday.\n", + "- **Knowing** which dates are still possible; knowing for sure when only one is possible.\n", + "- **Telling** Albert and Bernard specific facts about the birthday.\n", + "- **Statements** about knowledge.\n", + "- **Hearing** the statements about knowledge.\n", + "\n", + "I implement them as follows:\n", + "- `DATES` is a set of all possible dates (each date is a string); we also consider subsets of `DATES`.\n", + "- `know(possible_dates)` is a function that returns `True` when there is only one possible date.\n", + "- `tell(part)` is a function that returns the set of possible dates after Cheryl tells a part (month or day).\n", + "- *`statement`*`(date)` returns true for dates that satisfy the statement.\n", + "- `hear(possible_dates, statement,...)` returns a subset of possible_dates that are still possible after hearing the statements.\n", + "\n", + "For example, `albert1` is Albert's first statement, which says in part that he knows that Bernard\n", + "does not yet know Cheryl's birthday. So `albert1('May 19')` should be `False`, because if May 19 were Cheryl's birthday, then she would have told Bernard `'19'`, he would know that `'May 19'` is the only possibility.\n", + "\n", + "`tell('17')` returns `{'June 17', 'August 17'}`, the set of possible dates after Bernard is told `'17'`. \n", + "\n", + " `know(tell('17'))` is `False` because if Bernard was told `'17'` he would not know Cheryl's birthday for sure; there would be two possibilities. But `know(tell('19'))` is `True` because there would be only one possibility.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. \n", + "# Cheryl gives them a set of 10 possible dates:\n", + "\n", + "cheryl_dates = DATES = {\n", + " 'May 15', 'May 16', 'May 19',\n", + " 'June 17', 'June 18',\n", + " 'July 14', 'July 16',\n", + " 'August 14', 'August 15', 'August 17'}\n", + "\n", + "def month(date): return date.split()[0]\n", + "\n", + "def day(date): return date.split()[1]\n", + "\n", + "# Cheryl then tells Albert and Bernard separately \n", + "# the month and the day of the birthday respectively.\n", + "\n", + "def tell(part):\n", + " \"Cheryl tells a part of her birthdate; return a subset of DATES that match the part.\"\n", + " return {date for date in DATES if part in date}\n", + "\n", + "def know(possible_dates):\n", + " \"A person knows the birthdate if they know there is exactly one possible date.\"\n", + " return len(possible_dates) == 1\n", + "\n", + "def hear(possible_dates, *statements):\n", + " \"Return the subset of possible dates that are consistent with all the statements.\"\n", + " return {date for date in possible_dates\n", + " if all(stmt(date) for stmt in statements)}\n", + "\n", + "# Albert and Bernard make three statements:\n", + "\n", + "def albert1(date):\n", + " \"Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\"\n", + " after_being_told = tell(month(date))\n", + " return (not know(after_being_told) \n", + " and all(not know(tell(day(d)))\n", + " for d in after_being_told))\n", + "\n", + "def bernard1(date):\n", + " \"Bernard: At first I don't know when Cheryl's birthday is, but I know now.\"\n", + " at_first = tell(day(date))\n", + " return (not know(at_first)\n", + " and know(hear(at_first, albert1)))\n", + "\n", + "def albert2(date):\n", + " \"Albert: Then I also know when Cheryl's birthday is.\"\n", + " return know(hear(tell(month(date)), bernard1))\n", + " \n", + "# So when is Cheryl's birthday?\n", + "\n", + "def cheryls_birthday(dates):\n", + " \"Return a list of the possible dates after hearing the three statements.\"\n", + " return hear(using(dates), albert1, bernard1, albert2)\n", + "\n", + "def using(dates):\n", + " \"Make dates be the value of the global variable DATES.\"\n", + " global DATES # This is necessary because `tell` looks at `DATES`\n", + " DATES = dates\n", + " return dates\n", + "\n", + "# Some tests\n", + "\n", + "assert month('May 19') == 'May'\n", + "assert day('May 19') == '19'\n", + "assert albert1('May 19') == False\n", + "assert albert1('July 14') == True\n", + "assert know(tell('17')) == False\n", + "assert know(tell('19')) == True" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 16'}" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cheryls_birthday(cheryl_dates)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'August 14', 'August 15', 'August 17', 'July 14', 'July 16'}" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(DATES, albert1)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'August 15', 'August 17', 'July 16'}" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(DATES, albert1, bernard1)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 16'}" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(DATES, albert1, bernard1, albert2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Verifying Gabe's Version" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gabe tweeted these ten dates:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "gabe_dates = [\n", + " 'January 15', 'January 4',\n", + " 'July 13', 'July 24', 'July 30',\n", + " 'March 13', 'March 24',\n", + " 'May 11', 'May 17', 'May 30']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can verify that they do indeed make the puzzle work, giving a single known birthdate:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 30'}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cheryls_birthday(gabe_dates)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Creating Our Own Versions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If Gabe can do it, we can do it! Our strategy will be to repeatedly pick a random sample of dates, and check if they solve the puzzle. We'll limit ourselves to a subset of dates (not all 366) to make it more likely that a random selection will have multiple dates with the same month and day (otherwise Albert and Bernard would know right away):" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "some_dates = {mo + ' ' + d1 + d2\n", + " for mo in ('March', 'April', 'May', 'June', 'July')\n", + " for d1 in '12'\n", + " for d2 in '56789'}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need to cycle through random samples of these possible dates until we hit one that works. I anticipate wanting to solve other puzzles besides the original `cheryls_birthday`, so I'll make the `puzzle` be a parameter of the function `pick_dates`. Note that `pick_dates` returns two things: the one date that is the solution (the birthday), and the `k` (default 10) dates that form the puzzle." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "\n", + "def pick_dates(puzzle=cheryls_birthday, k=10):\n", + " \"Pick a set of dates for which the puzzle has a unique solution.\"\n", + " while True:\n", + " dates = set(random.sample(some_dates, k))\n", + " solutions = puzzle(dates)\n", + " if know(solutions):\n", + " return solutions.pop(), dates" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('June 27',\n", + " {'April 19',\n", + " 'April 28',\n", + " 'June 19',\n", + " 'June 27',\n", + " 'June 28',\n", + " 'March 15',\n", + " 'March 28',\n", + " 'May 16',\n", + " 'May 19',\n", + " 'May 27'})" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pick_dates()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Great! We can make a new puzzle, just like Gabe. But how often do we get a unique solution to the puzzle (that is, the puzzle returns a set of size 1)? How often do we get a solution where Albert and Bernard know, but we the puzzle solver doesn't (that is, a set of size greater than 1)? How often is there no solution (size 0)? Let's make a Counter of the number of times each length-of-solution occurs:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "from collections import Counter\n", + "\n", + "def counter(puzzle=cheryls_birthday, N=10000, k=10):\n", + " \"Try N random samples and count how often each possible length-of-solution appears.\"\n", + " return Counter(len(puzzle(set(random.sample(some_dates, k))))\n", + " for _ in range(N))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 8700, 1: 614, 2: 684, 3: 2})" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counter(cheryls_birthday)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This says that about 6% of the time we get a unique solution (a set of `len` 1). With similar frequency we get an ambiguous solution (with 2 or more possible birth dates). And most of the time, the sample of dates leads to no solution.\n", + "\n", + "What happens if Cheryl changes the number of possible dates?" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 9972, 1: 11, 2: 17})" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counter(cheryls_birthday, k=6)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 7532, 1: 1394, 2: 1030, 3: 44})" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counter(cheryls_birthday, k=12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is really hard (but not impossible) to find a set of 6 dates that work for the puzzle, and much easier to find a solution with 12 dates." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A New Puzzle: All About Eve" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's see if we can create a more complicated puzzle. We'll introduce a new character, Eve, give her a statement, and alter the rest of the puzzle slightly:\n", + "\n", + "> *Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl wrote down a list of 10 possible dates for all to see.*\n", + " \n", + "> *Cheryl then writes down the month and shows it just to Albert, and also writes down the day and shows it just to Bernard.*\n", + "\n", + "> **Albert**: *I don't know when Cheryl's birthday is, but I know that Bernard does not know either.*\n", + "\n", + "> **Bernard**: *At first I didn't know when Cheryl's birthday is, but I know now.*\n", + " \n", + "> **Albert**: *Then I also know when Cheryl's birthday is.*\n", + "\n", + "> **Eve**: *Hi, my name is Eve and I'm an evesdropper. It's what I do! I peeked and saw the first letter of the month and the first digit of the day. When I peeked, I didn't know Cheryl's birthday, but after listening to Albert and Bernard I do. And it's a good thing I peeked, because otherwise I couldn't have\n", + "figured it out.*\n", + " \n", + "> *So when is Cheryl's birthday?*\n", + "\n", + "We can easily code this up:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def cheryls_birthday_with_eve(dates):\n", + " \"Return a set of the dates for which Albert, Bernard, and Eve's statements are true.\"\n", + " return hear(using(dates), albert1, bernard1, albert2, eve1)\n", + "\n", + "def eve1(date):\n", + " \"\"\"Eve: I peeked and saw the first letter of the month and the first digit of the day. \n", + " When I peeked, I didn't know Cheryl's birthday, but after listening to Albert and Bernard \n", + " I do. And it's a good thing I peeked, because otherwise I couldn't have figured it out.\"\"\"\n", + " at_first = tell(first(day(date))) & tell(first(month(date)))\n", + " otherwise = tell('')\n", + " return (not know(at_first) and\n", + " know(hear(at_first, albert1, bernard1, albert2)) and\n", + " not know(hear(otherwise, albert1, bernard1, albert2)))\n", + "\n", + "def first(seq): return seq[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Note*: I admit I \"cheated\" a bit here. Remember that the function `tell` tests for `(part in date)`. For that to work for Eve, we have to make sure that the first letter is distinct from any other character in the date (it is—because only the first letter is uppercase) and that the first digit is distinct from any other character (it is—because in `some_dates` I carefully made sure that the first digit is always 1 or 2, and the second digit is never 1 or 2). Also note that `tell('')` denotes the hypothetical situation where Cheryl \"told\" Eve nothing.\n", + "\n", + "I have no idea if it is possible to find a set of dates that works for this puzzle. But I can try:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('July 17',\n", + " {'April 18',\n", + " 'April 25',\n", + " 'April 29',\n", + " 'July 17',\n", + " 'July 18',\n", + " 'June 18',\n", + " 'June 29',\n", + " 'March 27',\n", + " 'May 17',\n", + " 'May 28'})" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pick_dates(puzzle=cheryls_birthday_with_eve)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy. How often is a random sample of dates a solution to this puzzle?" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 9492, 1: 258, 2: 250})" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counter(cheryls_birthday_with_eve)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "About half as often as for the original puzzle." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# An Even More Complex Puzzle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make the puzzle even more complicated by making Albert wait one more time before he finally knows:\n", + "\n", + "> *Albert and Bernard just became friends with Cheryl, and they want to know when her birtxhday is. Cheryl wrote down a list of 10 possible dates for all to see.*\n", + " \n", + "> *Cheryl then writes down the month and shows it just to Albert, and also writes down the day and shows it just to Bernard.*\n", + " \n", + "> **Albert**: *I don't know when Cheryl's birthday is, but I know that Bernard does not know either.*\n", + " \n", + "> **Bernard**: *At first I didn't know when Cheryl's birthday is, but I know now.*\n", + " \n", + "> **Albert**: *I still don't know.*\n", + "\n", + "> **Eve**: *Hi, my name is Eve and I'm an evesdropper. It's what I do! I peeked and saw the first letter of the month and the first digit of the day. When I peeked, I didn't know Cheryl's birthday, but after listening to Albert and Bernard I do. And it's a good thing I peeked, because otherwise I couldn't have figured it out.*\n", + "\n", + "> **Albert**: *OK, now I know.*\n", + " \n", + "> *So when is Cheryl's birthday?*\n", + "\n", + "Let's be careful in coding this up; Albert's second statement is different; he has a new third statement; and Eve's statement uses the same words, but it now implicitly refers to a different statement by Albert. We'll use the names `albert2c`, `eve1c`, and `albert3c` (`c` for \"complex\") to represent the new statements:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def cheryls_birthday_complex(dates):\n", + " \"Return a set of the dates for which Albert, Bernard, and Eve's statements are true.\"\n", + " return hear(using(dates), albert1, bernard1, albert2c, eve1c, albert3c)\n", + "\n", + "def albert2c(date):\n", + " \"Albert: I still don't know.\"\n", + " return not know(hear(tell(month(date)), bernard1))\n", + "\n", + "def eve1c(date):\n", + " \"\"\"Eve: I peeked and saw the first letter of the month and the first digit of the day. \n", + " When I peeked, I didn't know Cheryl's birthday, but after listening to Albert and Bernard \n", + " I do. And it's a good thing I peeked, because otherwise I couldn't have figured it out.\"\"\"\n", + " at_first = tell(first(day(date))) & tell(first(month(date)))\n", + " otherwise = tell('')\n", + " return (not know(at_first)\n", + " and know(hear(at_first, albert1, bernard1, albert2c)) and\n", + " not know(hear(otherwise, albert1, bernard1, albert2c)))\n", + "\n", + "def albert3c(date):\n", + " \"Albert: OK, now I know.\"\n", + " return know(hear(tell(month(date)), eve1c))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, I don't know if it is possible to find dates that works with this story, but I can try:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('July 29',\n", + " {'April 29',\n", + " 'July 15',\n", + " 'July 18',\n", + " 'July 29',\n", + " 'June 25',\n", + " 'March 15',\n", + " 'March 19',\n", + " 'March 25',\n", + " 'May 18',\n", + " 'May 27'})" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pick_dates(puzzle=cheryls_birthday_complex)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It worked! Were we just lucky, or are there many sets of dates that work?" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 9047, 1: 951, 2: 2})" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counter(cheryls_birthday_complex)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Interesting. It was actually easier to find dates that work for this story than for either of the other stories." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analyzing a Solution to the Complex Puzzle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will go through a solution step-by-step. We'll use a set of dates selected in a previous run:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "DATES = {\n", + " 'April 28',\n", + " 'July 27',\n", + " 'June 19',\n", + " 'June 16',\n", + " 'July 15',\n", + " 'April 15',\n", + " 'June 29',\n", + " 'July 16',\n", + " 'May 24',\n", + " 'May 27'}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's find the solution:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27'}" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cheryls_birthday_complex(DATES)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the first step is that Albert was told \"July\":" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 15', 'July 16', 'July 27'}" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tell('July')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And no matter which of these three dates is the actual birthday, Albert knows that Bernard would not know the birthday, because each of the days (15, 16, 27) appears twice in the list of possible dates." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all(not know(tell(day(d)))\n", + " for d in tell('July'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, Bernard is told the day:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27', 'May 27'}" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tell('27')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are two dates with a 27, so Bernard did not know then. But only one of these dates is still consistent after hearing Albert's statement:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27'}" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(tell('27'), albert1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So after Albert's statement, Bernard knows. Poor Albert still doesn't know (after being told `'July'` and hearing Bernard's statement):" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 15', 'July 16', 'July 27'}" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(tell('July'), bernard1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then along comes Eve. She evesdrops the \"J\" and the \"2\":" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27', 'June 29'}" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tell('J') & tell('2')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Two dates, so Eve doesn't know yet. But only one of the dates works after hearing the three statements made by Albert and Bernard:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27'}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(tell('J') & tell('2'), albert1, bernard1, albert2c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But Eve wouldn't have known if she had been told nothing:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 15', 'July 16', 'July 27'}" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(tell(''), albert1, bernard1, albert2c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about Albert? After hearing Eve's statement he finally knows:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'July 27'}" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(tell('July'), eve1c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Three Children\n", + "\n", + "Here's another puzzle:\n", + "\n", + "> *A parent has the following conversation with a friend:*\n", + "\n", + "> **Parent:** the product of my three childrens' ages is 36.\n", + "\n", + "> **Friend**: I don't know their ages.\n", + "\n", + "> **Parent**: The sum of their ages is the same as the number of people in this room.\n", + "\n", + "> **Friend**: I still don't know their ages.\n", + "\n", + "> **Parent**: The oldest one likes bananas.\n", + "\n", + "> **Friend**: Now I know their ages.\n", + "\n", + "Let's follow the same methodology to solve this puzzle. Except this time, we're not dealing with sets of possible dates, we're dealing with set of possible *states* of the world. We'll define a state as a tuple of 4 numbers: the ages of the three children (in increasing order), and the number of people in the room. (We'll limit the children's ages to be below 30 and the number of people in the room to be below 90.)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(2, 2, 9, 13)}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "N = 30\n", + "states = {(a, b, c, n) \n", + " for a in range(1, N)\n", + " for b in range(a, N)\n", + " for c in range(b, N) if a * b * c == 36\n", + " for n in range(2, 90)}\n", + "\n", + "def ages(state): return state[:-1]\n", + "def room(state): return state[-1]\n", + "\n", + "def parent1(state): \n", + " \"The product of my three childrens' ages is 36.\"\n", + " a, b, c = ages(state)\n", + " return a * b * c == 36\n", + "\n", + "def friend1(state): \n", + " \"I don't know their ages.\"\n", + " return not know({ages(s) for s in hear(states, parent1)})\n", + "\n", + "def parent2(state):\n", + " \"The sum of their ages is the same as the number of people in this room.\"\n", + " return sum(ages(state)) == room(state)\n", + "\n", + "def friend2(state, possibilities=hear(states, parent1, friend1, parent2)): \n", + " \"I still don't know their ages.\"\n", + " # Given there are room(state) people in the room, I still don't know the ages.\n", + " return not know({ages(s) for s in possibilities if room(s) == room(state)})\n", + "\n", + "def parent3(state):\n", + " \"The oldest one likes bananas.\"\n", + " # I.e., there is an oldest one (and not twins of the same age)\n", + " a, b, c = ages(state)\n", + " return c > b\n", + "\n", + "def friend3(state, possibilities=hear(states, parent1, friend1, parent2, friend2, parent3)): \n", + " \"Now I know their ages.\"\n", + " return know({ages(s) for s in possibilities})\n", + "\n", + "def child_age_puzzle(states):\n", + " return hear(states, parent1, friend1, parent2, friend2, parent3, friend3)\n", + "\n", + "child_age_puzzle(states)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The tricky part of this puzzle comes after the `parent2` statement:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2, 18, 21),\n", + " (1, 3, 12, 16),\n", + " (1, 4, 9, 14),\n", + " (1, 6, 6, 13),\n", + " (2, 2, 9, 13),\n", + " (2, 3, 6, 11),\n", + " (3, 3, 4, 10)}" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hear(states, parent1, friend1, parent2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that out of these 7 possibilities, if the number of people in the room (the last number in each tuple) \n", + "were anything other than 13, then the friend (who can observe the number of people in the room) would know the ages. Since the `friend2` statement professes continued ignorance, it must be that the number of people in the room is 13. Then the `parent3` statement makes it clear that there can't be 6-year-old twins as the oldest children; it must be 2-year-old twins with an oldest age 9." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# What Next?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you like, there are many other directions you could take this:\n", + "\n", + "- Could you create a puzzle that goes one or two rounds more before everyone knows?\n", + "- Could you add new characters: Faith, and then George, and maybe even a new Hope?\n", + "- Would it be more interesting with a different number of possible dates (not 10)?\n", + "- Should we include the year or the day of the week, as well as the month and day?\n", + "- Perhaps a puzzle that starts with [Richard Smullyan](http://en.wikipedia.org/wiki/Raymond_Smullyan) announcing that one of the characters is a liar.\n", + "- Or you could make a puzzle harder than [the hardest logic puzzle ever](https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever).\n", + "- Try the \"black and white hats\" [Riddler Express](https://fivethirtyeight.com/features/can-you-solve-these-colorful-puzzles/) stumper.\n", + "- It's up to you ..." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Cheryl.ipynb b/pytudes/ipynb/Cheryl.ipynb new file mode 100644 index 0000000..f4af940 --- /dev/null +++ b/pytudes/ipynb/Cheryl.ipynb @@ -0,0 +1,504 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:b9e2e6c3f7e82432833f1416dd0552c13753f683e1888682faf2910ef7d9f8ff" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When is Cheryl's Birthday?\n", + "===\n", + "\n", + "Peter Norvig, April 2015\n", + "\n", + "This logic puzzle has been [making the rounds](https://www.google.com/webhp?#q=cheryl%27s+birthday):\n", + "\n", + "\n", + "1. Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gave them a list of 10 possible dates:\n", + "

\n",
+      "       May 15     May 16     May 19\n",
+      "      June 17    June 18\n",
+      "      July 14    July 16\n",
+      "    August 14  August 15  August 17\n",
+      "
\n", + " \n", + "2. Cheryl then tells Albert and Bernard separately the month and the day of the birthday respectively.\n", + " \n", + "3. **Albert**: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\n", + " \n", + "4. **Bernard**: At first I don't know when Cheryl's birthday is, but I know now.\n", + " \n", + "5. **Albert**: Then I also know when Cheryl's birthday is.\n", + " \n", + "6. So when is Cheryl's birthday?\n", + "\n", + "Problem-Solving Tools\n", + "---\n", + "\n", + "Cheryl's puzzle was designed to be solved with a pencil, the greatest problem-solving tool in the history of mathematics (although some prefer a pen, chalk, marker, or a [stick for drawing in the sand](http://www.hellenicaworld.com/Greece/Science/en/Archimedes.html)). But I will show how to solve it with another tool: **computer code**. I choose this tool for four reasons: \n", + "- It is a more direct way to find the solution. All I have to do is faithfully describe the problem with code that says: *\"for each of the 10 possible dates, tell Albert the month and Bernard the day and check if statements 3 through 5 are true.\"* The intended [pencil and paper solution](https://scontent-iad.xx.fbcdn.net/hphotos-xpa1/v/t1.0-9/s720x720/11111802_983395601695416_3208022346737572922_n.jpg?oh=15fcb7edc4689dd9c71385b613446465&oe=55DD4488) requires not just understanding the *problem*, but also creatively discovering the steps of the *solution*—a harder task.\n", + "- With tested, debugged code, you're less likely to make a mistake that leads you to a [wrong answer](http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/15/why-the-cheryl-birthday-problem-turned-into-the-maths-version-of-thatdress).\n", + "- You'll learn how to solve problems that are similar, but can't be solved with pencil and paper because they have millions of possibilities rather than just 10.\n", + "- Solving puzzles is fun; programming is fun; solving puzzles with programs is double fun.\n", + "\n", + "We will translate each of the 6 statements in the puzzle into Python code:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Cheryl gave them a list of 10 possible dates:\n", + "---\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "DATES = ['May 15', 'May 16', 'May 19',\n", + " 'June 17', 'June 18',\n", + " 'July 14', 'July 16',\n", + " 'August 14', 'August 15', 'August 17']" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll also define accessor functions for the month and day of a date:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def Month(date): return date.split()[0]\n", + "\n", + "def Day(date): return date.split()[1]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "Month('May 15')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 3, + "text": [ + "'May'" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "Day('May 15')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "'15'" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Cheryl then tells Albert and Bernard separately the month and the day of the birthday respectively.\n", + "---\n", + "\n", + "We can define the idea of **telling**, and while we're at it, the idea of **knowing** a birthdate:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def tell(part, possible_dates=DATES):\n", + " \"Cheryl tells a part of her birthdate to someone; return a new list of possible dates that match the part.\"\n", + " return [date for date in possible_dates if part in date]\n", + "\n", + "def know(possible_dates):\n", + " \"A person knows the birthdate if they have exactly one possible date.\"\n", + " return len(possible_dates) == 1" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that we use a *list of dates* to represent someone's knowledge of the possible birthdates, and that someone *knows* the birthdate when they get down to only one possibility. For example: If Cheryl tells Albert that her birthday is in May, he would have a list of three possible birthdates:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "tell('May')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 6, + "text": [ + "['May 15', 'May 16', 'May 19']" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And if she tells Bernard that her birthday is on the 15th, he would end up with two possibilities:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "tell('15')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 7, + "text": [ + "['May 15', 'August 15']" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With two possibilities, Bernard does not know the birthdate:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "know(tell('15'))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 8, + "text": [ + "False" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Overall Strategy\n", + "---\n", + "\n", + "When Cheryl tells Albert `'May'` then *he* knows there are three possibilities, but *we* (the puzzle solvers) don't, because we don't know what Cheryl said. So what can we do? We will consider *all* of the possible dates, one at a time. For example, first consider `'May 15'`. Cheryl tells Albert `'May'` and Bernard `'15'`, giving them the lists of possible birthdates shown above. We can then check whether statements 3 through 5 are true in this scenario. If they are, then `'May 15'` is a solution to the puzzle. Repeat the process for each of the possible dates. If all goes well, there should be exactly one solution. \n", + "\n", + "Here is the main function, `cheryls_birthday`:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def cheryls_birthday(possible_dates=DATES):\n", + " \"Return a list of the possible dates for which statements 3 to 5 are true.\"\n", + " return filter(statements3to5, possible_dates)\n", + "\n", + "def statements3to5(date): return statement3(date) and statement4(date) and statement5(date)\n", + "\n", + "## TO DO: define statement3, statement4, statement5" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " (*Python note:* `filter(predicate, items)` returns a list of all items for which `predicate(item)` is true.)\n", + " \n", + " 3. Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `statement3` takes as input a possible birthdate and returns true if Albert's statement is true for that birthdate. How do we go from Albert's English statement to a Python function? Let's paraphrase in a form that is closer to Python code:\n", + "\n", + "> **Albert**: After Cheryl told me the month of her birthdate, I didn't know her birthday. I don't know which day Cheryl told Bernard, but I know that for all of the possible dates, if Bernard is told that day, he wouldn't know the birthdate.\n", + "\n", + "That I can translate directly into code:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def statement3(date):\n", + " \"Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.\"\n", + " possible_dates = tell(Month(date))\n", + " return (not know(possible_dates) \n", + " and all(not know(tell(Day(d)))\n", + " for d in possible_dates))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can try the function on a date:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "statement3('May 15')" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 11, + "text": [ + "False" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In fact, we can see all the dates that satisfy statement 3:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "filter(statement3, DATES)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 12, + "text": [ + "['July 14', 'July 16', 'August 14', 'August 15', 'August 17']" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. Bernard: At first I don't know when Cheryl's birthday is, but I know now.\n", + "---\n", + "\n", + "Again, a paraphrase:\n", + "\n", + "> **Bernard:** At first Cheryl told me the day, and I didn't know. Then I considered just the dates for which Albert's statement 3 is true, and now I know." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def statement4(date):\n", + " \"Bernard: At first I don't know when Cheryl's birthday is, but I know now.\"\n", + " at_first = tell(Day(date))\n", + " return (not know(at_first)\n", + " and know(filter(statement3, at_first)))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see which dates satisfy both statement 3 and statement 4:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "filter(statement4, filter(statement3, DATES))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 14, + "text": [ + "['July 16', 'August 15', 'August 17']" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wait a minute—I thought that Bernard **knew**?! Why are there three possible dates remaining? Bernard does indeed know the birthdate,\n", + "because he knows something we don't know: the day. We won't know the birthdate until after statement 5.\n", + "\n", + "5. Albert: Then I also know when Cheryl's birthday is.\n", + "---\n", + "\n", + "Albert is saying that after hearing the month and Bernard's statement 4, he now knows Cheryl's birthday:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def statement5(date):\n", + " \"Albert: Then I also know when Cheryl's birthday is.\"\n", + " return know(filter(statement4, tell(Month(date))))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "6. So when is Cheryl's birthday?\n", + "---\n", + "\n", + "Let's see:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cheryls_birthday()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 16, + "text": [ + "['July 16']" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Success!** We have deduced that Cheryl's birthday is **July 16**. It is now `True` that we know Cheryl's birthday:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "know(cheryls_birthday())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 17, + "text": [ + "True" + ] + } + ], + "prompt_number": 17 + } + ], + "metadata": {} + } + ] +} diff --git a/pytudes/ipynb/Coin Flip.ipynb b/pytudes/ipynb/Coin Flip.ipynb new file mode 100644 index 0000000..ff1c312 --- /dev/null +++ b/pytudes/ipynb/Coin Flip.ipynb @@ -0,0 +1,1191 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Devil and the Coin Flip Game\n", + "\n", + ">You're playing a game with the devil, with your soul at stake. You're sitting at a circular table which has 4 coins, arranged in a diamond, at the 12, 3, 6, and 9 o'clock positions. You are blindfolded, and can never see the coins or the table.\n", + "\n", + ">Your goal is to get all 4 coins showing heads, by telling the devil the position(s) of some coins to flip. We call this a \"move\" on your part. The devil must faithfully perform the requested flips, but may first sneakily rotate the table any number of quarter-turns, so that the coins are in different positions. You keep making moves, and the devil keeps rotating and flipping, until all 4 coins show heads.\n", + "\n", + "> Example: You tell the devil tthe 12 o'clock and 6 o'clock positions. The devil could leave the table unrotated (or could rotate it a half-turn), and then flip the two coins that you specified. Or the devil could rotate the table a quarter turn in either direction, and then flip the coins that are now in the 12 o'clock and 6 o'clock positions (which were formerly at 3 o'clock and 9 o'clock). You won't know which of these actions the devil took.\n", + "\n", + "> What is a shortest sequence of moves that is *guaranteed* to win, no matter what the initial state of the coins, and no matter what rotations the devil applies?\n", + "\n", + "# Analysis\n", + "\n", + "The player, being blindfolded, does not know the true state of the coins. So the player should represent what is known: the *set of possible states* of the coins. We call this a *belief state*. At the start of the game, each of the four coins could be either heads or tails, so that's 24 = 16 possibilities in the belief state. \n", + "\n", + "A move updates the belief state as follows: for every coin sequence in the current belief state, rotate it in every possible way, and then flip the coins specified by the position(s) in the move. Collect all these results together to form the new belief state. Solving the game means coming up with a sequence of moves that ends in a belief state consisting of just `{'HHHH'}`. It must be a shortest possible sequence, so a breadth-first search seems right. The search space will be tiny, so compute time will be trivial; the only issue is specifying the domain correctly. To increase the chance of getting it correct, I won't try to do anything fancy, such as noticing that some coin sequences are rotational variants of other sequences.\n", + "\n", + "\n", + "# Implementation Choices\n", + "\n", + "Here are the main concepts, and my implementation choices:\n", + "\n", + "- `Coins`: A *coin sequence* is represented as a `str` of four characters, such as `'HTTT'`. \n", + "- `Belief`: A *belief state* is represented as a `frozenset` of `Coins` (frozen so that it can be hashed in a `set`).\n", + "- `Move`: A *move* is a set of positions to flip. A position will be an integer index into the coin sequence, so a move is a set of these such as `{0, 2}`, which we can interpret as \"flip the 12 o'clock and 6 o'clock positions.\" \n", + "- `all_coins`: Set of all possible coin sequences: `{'HHHH', 'HHHT', ...}`.\n", + "- `rotations`: The function `rotations(coins)` returns the set of all 4 rotations of the coin sequence.\n", + "- `update`: The function `update(belief, move)` returns an updated belief state, representing all the possible coin sequences that could result from any devil rotation followed by the specified flip(s). (But don't flip `'HHHH'`, because the game would have already ended.)\n", + "- `flip`: The function `flip(coins, move)` flips the specified positions within the coin sequence." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from collections import deque, Counter\n", + "from itertools import product, combinations\n", + "import random\n", + "\n", + "Coins = ''.join # A coin sequence, such as 'HHHT'.\n", + "Belief = frozenset # A belief state is a set of possible coin sequences.\n", + "all_coins = Belief(map(Coins, product('HT', repeat=4)))\n", + "\n", + "def rotations(coins) -> [Coins]: \n", + " \"A list of all possible rotations of a coin sequence.\"\n", + " return [coins[r:] + coins[:r] for r in range(4)]\n", + "\n", + "def update(belief, move) -> Belief:\n", + " \"Update belief: consider all possible rotations, then flip.\"\n", + " return Belief((c if c == 'HHHH' else flip(c, move))\n", + " for coins in belief\n", + " for c in rotations(coins))\n", + "\n", + "def flip(coins, move) -> Coins:\n", + " \"Flip the coins in the positions specified by the move.\"\n", + " coins = list(coins) # Need a mutable sequence\n", + " for i in move:\n", + " coins[i] = ('H' if coins[i] == 'T' else 'T')\n", + " return Coins(coins)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try out these functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'THTT'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "flip('HHHT', {0, 2})" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['HHHT', 'HHTH', 'HTHH', 'THHH']" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rotations('HHHT')" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({'HHHH',\n", + " 'HHHT',\n", + " 'HHTH',\n", + " 'HHTT',\n", + " 'HTHH',\n", + " 'HTHT',\n", + " 'HTTH',\n", + " 'HTTT',\n", + " 'THHH',\n", + " 'THHT',\n", + " 'THTH',\n", + " 'THTT',\n", + " 'TTHH',\n", + " 'TTHT',\n", + " 'TTTH',\n", + " 'TTTT'})" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all_coins" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see there are 16 coin sequences in the `all_coins` belief state. Now if we update this belief state by flipping all 4 positions, we should get a new belief state where we have eliminated the possibility of 4 tails, leaving 15 possible coin sequences:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({'HHHH',\n", + " 'HHHT',\n", + " 'HHTH',\n", + " 'HHTT',\n", + " 'HTHH',\n", + " 'HTHT',\n", + " 'HTTH',\n", + " 'HTTT',\n", + " 'THHH',\n", + " 'THHT',\n", + " 'THTH',\n", + " 'THTT',\n", + " 'TTHH',\n", + " 'TTHT',\n", + " 'TTTH'})" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "update(all_coins, {0, 1, 2, 3})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Everything looks good so far. One more thing: we need to find all subsets of the 4 positions; these are the possible moves:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def powerset(sequence): \n", + " \"All subsets of a sequence.\"\n", + " return [set(c) \n", + " for r in range(len(sequence) + 1)\n", + " for c in combinations(sequence, r)]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[set(),\n", + " {0},\n", + " {1},\n", + " {2},\n", + " {3},\n", + " {0, 1},\n", + " {0, 2},\n", + " {0, 3},\n", + " {1, 2},\n", + " {1, 3},\n", + " {2, 3},\n", + " {0, 1, 2},\n", + " {0, 1, 3},\n", + " {0, 2, 3},\n", + " {1, 2, 3},\n", + " {0, 1, 2, 3}]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "powerset(range(4))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Search for a Solution\n", + "\n", + "The function `search` does a breadth-first search starting\n", + "from a `belief` state consisting of `all_coins`, and applying a sequences of moves, trying to\n", + "find a sequence that leads to the goal belief state in which the only possibility is 4 heads: `{'HHHH'}`.\n", + "As is typical for search algorithms, we build a search tree, keeping a queue of tree `nodes` to consider, where each \n", + "node consists of a path (a sequence of moves) and a resulting belief state. We also keep track, in `explored`, of\n", + "the states we have already explored, so that we don't have to revisit them." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def search():\n", + " \"Breadth-first search from all_coins to all heads.\"\n", + " explored = set()\n", + " queue = deque([Node([], all_coins)])\n", + " while queue:\n", + " (path, belief) = queue.popleft()\n", + " if belief == {'HHHH'}:\n", + " return path\n", + " for move in powerset(range(4)):\n", + " belief2 = update(belief, move)\n", + " if belief2 not in explored:\n", + " explored.add(belief2)\n", + " queue.append(Node(path + [move], belief2))\n", + " \n", + "def Node(path, belief) -> tuple: return (path, belief)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Solution" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[{0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3}]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "search()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a 15-move sequence that is guaranteed to lead to a win. You can stop reading here if all you want is the answer to the puzzle. Or you can continue on ...\n", + "\n", + "# Verifying the Solution\n", + "\n", + "Can I verify that the solution is correct? Exploring with paper and pencil, it does appear to work. A colleague did the puzzle and got the same answer. And here's further validation: The function `random_devil` takes an initial coin sequence and a sequence of moves, and plays those moves with a devil that chooses rotations randomly, returning the number of moves it takes until the player wins:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def random_devil(coins, moves) -> int or None:\n", + " \"\"\"A random devil responds to moves starting from coins; \n", + " return the number of moves until win, or None.\"\"\"\n", + " if coins == 'HHHH': return 0\n", + " for (i, move) in enumerate(moves, 1):\n", + " coins = flip(random.choice(list(rotations(coins))), move)\n", + " if coins == 'HHHH': \n", + " return i" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will let the `random_devil` play 1000 times from each possible starting coin sequence:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({0: 1000,\n", + " 1: 1000,\n", + " 2: 986,\n", + " 3: 1014,\n", + " 4: 1052,\n", + " 5: 1004,\n", + " 6: 976,\n", + " 7: 968,\n", + " 8: 964,\n", + " 9: 1014,\n", + " 10: 985,\n", + " 11: 1003,\n", + " 12: 1056,\n", + " 13: 983,\n", + " 14: 1021,\n", + " 15: 974})" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "moves = search()\n", + "\n", + "Counter(random_devil(coins, moves) \n", + " for coins in all_coins\n", + " for _ in range(1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This says that the player won all 16,000 times. (If the player had ever lost, there would have been an entry for `None` in the Counter.)\n", + "The remarkable thing, which I can't explain, is that there are very nearly exactly 1,000 results for each of the move counts from 0 to 15. Can you explain that?\n", + "\n", + "# Canonical Coin Sequences and Moves\n", + "\n", + "Consider the four coin sequences `{'HHHT', 'HHTH', 'HTHH', 'THHH'}`. In a sense, these are all the same: they all denote the same sequence of coins with the table rotated to different degrees. Since the devil is free to rotate the table any amount at any time, we could be justified in treating all four of these as equivalent, and collapsing them into one representative member (we could arbitrarily choose the one that comes first in alphabetical order, `'HHHT'`). I will write a definition for `Belief` that returns a `frozenset`, just like before, but makes it a set of canonical coin sequences.\n", + "\n", + "Similarly, the four moves `[{3}, {2}, {1}, {0}]` are equivalent, in that they all say \"flip one of the coins, but since you're going to rotate the table first, it doesn't matter which one I specify.\" I will write a function `canonical_moves` that lists all the canonical rotationally invariant moves corresponding to a belief state." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Belief(coin_collection): \n", + " \"A set of all the coin sequences in this collection, canonicalized.\"\n", + " return frozenset(min(rotations(c)) for c in coin_collection)\n", + "\n", + "def canonical_moves(coin_collection):\n", + " \"All rotationally invariant moves for a sequence of N coins.\"\n", + " return [set(i for (i, coin) in enumerate(coins) if coin == 'H' and 'H')\n", + " for coins in sorted(coin_collection) if 'H' in coins]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({'HHHH', 'HHHT', 'HHTT', 'HTHT', 'HTTT', 'TTTT'})" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Belief(all_coins)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[{0, 1, 2, 3}, {0, 1, 2}, {0, 1}, {0, 2}, {0}]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "canonical_moves(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The starting belief set is down from 16 sequences to 6. Call these 4 heads, 3 heads, 2 adjacent heads, 2 opposite heads, 1 head, and no heads, respectively. Similarly, there are only 5 distinct moves, which we can call flip 4, flip 3, flip 2 adjacent, flip 2 opposite, and flip 1.\n", + "\n", + "I have to confess to a form of cheating here: I threw in the `sorted` in `canonical_moves` even though it was not necessary. By including it, I made sure that `{0, 1, 2, 3}` is the first of the possible moves, which makes `search` faster, because half the time `{0, 1, 2, 3}` is the right move to make.\n", + "\n", + "# Visualizing the Solution\n", + "\n", + "How does the solution work? One answer is \"it takes care of all possibilities.\" But it would be nice to gain more insight. I'll print a table showing the belief state after each move, using the newly-defined canonicalized `Belief` form, and lining them up neatly in columns." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def show(moves, belief=all_coins):\n", + " \"For each move, print the move number, move, and belief state.\"\n", + " show_line(0, 'start', belief)\n", + " for (i, move) in enumerate(moves, 1):\n", + " belief = update(belief, move)\n", + " show_line(i, move, belief)\n", + "\n", + "def show_line(i, move, belief, order=sorted(Belief(all_coins))):\n", + " \"Print the move number, move, and belief state.\"\n", + " ordered_belief = [(coins if coins in belief else ' ')\n", + " for coins in order]\n", + " print('{:2} | {:5} | {} | {}'\n", + " .format(i, join(move), join(ordered_belief, ' '), i))\n", + " \n", + "def join(items, sep='') -> str: return sep.join(map(str, items))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 | start | HHHH HHHT HHTT HTHT HTTT TTTT | 0\n", + " 1 | 0123 | HHHH HHHT HHTT HTHT HTTT | 1\n", + " 2 | 02 | HHHH HHHT HHTT HTTT TTTT | 2\n", + " 3 | 0123 | HHHH HHHT HHTT HTTT | 3\n", + " 4 | 01 | HHHH HHHT HTHT HTTT TTTT | 4\n", + " 5 | 0123 | HHHH HHHT HTHT HTTT | 5\n", + " 6 | 02 | HHHH HHHT HTTT TTTT | 6\n", + " 7 | 0123 | HHHH HHHT HTTT | 7\n", + " 8 | 0 | HHHH HHTT HTHT TTTT | 8\n", + " 9 | 0123 | HHHH HHTT HTHT | 9\n", + "10 | 02 | HHHH HHTT TTTT | 10\n", + "11 | 0123 | HHHH HHTT | 11\n", + "12 | 01 | HHHH HTHT TTTT | 12\n", + "13 | 0123 | HHHH HTHT | 13\n", + "14 | 02 | HHHH TTTT | 14\n", + "15 | 0123 | HHHH | 15\n" + ] + } + ], + "source": [ + "show(search())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that every odd-numbered move flips all four coins to eliminate the possibility of `TTTT`, flipping it to `HHHH`. We can also see that moves 2, 4, and 6 flip two coins and have the effect of eventually eliminating the two \"two heads\" sequences from the belief state, and then move 8 flips a single coin, thus eliminating the \"three heads\" and \"one heads\" sequences, and bringing back the \"two heads\" possibilities. Repeating moves 2, 4, and 6 in moves 10, 12, and 14 then re-eliminates the \"two heads\", and move 15 gets the belief state down to `{'HHHH'}`.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Different Numbers of Coins\n", + "\n", + "What if there are 3 coins on the table arranged in a triangle? Or 6 coins in a hexagon? To answer that, I'll generalize the two functions that have a \"4\" in them, `search`, and `rotations`. I'll also generalize `update`, which had `'HHHH'` in it. And I'll introduce the function `canonical_coins` to return a belief state of all canonical coin sequences of length `N`." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def search(N=4):\n", + " \"Breadth-first search from all_coins to all heads.\"\n", + " start = canonical_coins(N)\n", + " all_moves = canonical_moves(start)\n", + " goal = {'H' * N}\n", + " explored = set()\n", + " queue = deque([Node([], start)])\n", + " while queue:\n", + " (path, belief) = queue.popleft()\n", + " if belief == goal:\n", + " return path\n", + " for move in all_moves:\n", + " belief2 = update(belief, move)\n", + " if belief2 not in explored:\n", + " explored.add(belief2)\n", + " queue.append(Node(path + [move], belief2))\n", + "\n", + "def rotations(coins) -> [Coins]: \n", + " \"A list of all possible rotations of a coin sequence.\"\n", + " return [coins[r:] + coins[:r] for r in range(len(coins))]\n", + " \n", + "def update(belief, move) -> Belief:\n", + " \"Update belief: consider all possible rotations, then flip.\"\n", + " return Belief((flip(c, move) if 'T' in c else c)\n", + " for coins in belief\n", + " for c in rotations(coins))\n", + "\n", + "def canonical_coins(N) -> Belief: return Belief(map(Coins, product('HT', repeat=N)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First verify that we didn't break `search`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[{0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3}]" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "search(4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now test the new definitions:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['HHHHHT', 'HHHHTH', 'HHHTHH', 'HHTHHH', 'HTHHHH', 'THHHHH']" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rotations('HHHHHT')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({'HHHH', 'HHHT', 'HHTT', 'HTHT', 'HTTT', 'TTTT'})" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "canonical_coins(4)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({'HHHHH',\n", + " 'HHHHT',\n", + " 'HHHTT',\n", + " 'HHTHT',\n", + " 'HHTTT',\n", + " 'HTHTT',\n", + " 'HTTTT',\n", + " 'TTTTT'})" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "canonical_coins(5)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[{0, 1, 2, 3, 4}, {0, 1, 2, 3}, {0, 1, 2}, {0, 1, 3}, {0, 1}, {0, 2}, {0}]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "canonical_moves(_)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{1: 2, 2: 3, 3: 4, 4: 6, 5: 8, 6: 14, 7: 20, 8: 36, 9: 60, 10: 108}" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{N: len(canonical_coins(N))\n", + " for N in range(1, 11)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On the one hand this is encouraging; there are only 108 canonical coin sequences of length 10, far less than the 1024 non-canonical squences. On the other hand, it is discouraging; since we are searching over the belief states, that would be 2108 ≌ 1032 belief states, which is infeasible. However, we should be able to easily handle up to N=7, because 220 is only a million.\n", + "\n", + "# Solutions for 1 to 7 Coins" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{1: [{0}],\n", + " 2: [{0, 1}, {0}, {0, 1}],\n", + " 3: None,\n", + " 4: [{0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3},\n", + " {0, 1},\n", + " {0, 1, 2, 3},\n", + " {0, 2},\n", + " {0, 1, 2, 3}],\n", + " 5: None,\n", + " 6: None,\n", + " 7: None}" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{N: search(N) for N in range(1, 8)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Too bad; there are no solutions for N = 3, 5, 6, or 7. \n", + "\n", + "There are solutions for N = 1, 2, 4; of lengths 1, 3, 15. That suggests the conjecture: for every *N* that is a power of 2, there will be a solution of length 2*N* - 1. \n", + "\n", + "# Solution for 8 Coins\n", + "\n", + "Even though there are 236 = 68 billion belief states fo N = 8, I hope we can find a solution early in the search process. Let's try:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 47s, sys: 731 ms, total: 1min 48s\n", + "Wall time: 1min 50s\n" + ] + }, + { + "data": { + "text/plain": [ + "255" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time solution8 = search(8)\n", + "len(solution8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Eureka! That's evidence in favor of my conjecture, and it took less time than I thought it would. It is still not proof, and I'll need a more efficient/clever approach to test even for N=16. Can you come up with that approach? Can you prove the conjecture for all powers of 2? Here's the solution for N = 8 to help you discover a pattern:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[{0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 4, 5},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 2, 4, 5, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 4, 5},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 2, 3},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 4, 5},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 2, 4, 5, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 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6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 2, 3},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 4, 5},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 2, 4, 5, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 1, 4, 5},\n", + " {0, 1, 2, 3, 4, 5, 6, 7},\n", + " {0, 2, 4, 6},\n", + " {0, 1, 2, 3, 4, 5, 6, 7}]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution8" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Convex Hull.ipynb b/pytudes/ipynb/Convex Hull.ipynb new file mode 100644 index 0000000..de6c550 --- /dev/null +++ b/pytudes/ipynb/Convex Hull.ipynb @@ -0,0 +1,2039 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Convex Hull Problem" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Pound a bunch of nails into a board, then stretch a rubber band around them and let the rubber band snap taut, like this:\n", + "\n", + "\n", + "\n", + "The rubber band has traced out the *convex hull* of the set of nails. It turns out this is an important problem with applications in computer graphics, robot motion planning, geographical information systems, ethology, and other areas.\n", + "More formally, we say that:\n", + "\n", + "*Given a finite set, **P**, of points in a plane, the convex hull of **P** is a polygon, **H**, such that:*\n", + "\n", + "- *Every point in **P** lies either on or inside of **H**.*\n", + "- *Every vertex of **H** is a point in **P**.*\n", + "- **H** *is convex: a line segment joining any two vertexes of **H** either is an edge of **H** or lies inside **H**.*\n", + "\n", + "\n", + "In this notebook we develop an algorithm to find the convex hull (and show examples of how to use `matplotlib` plotting). The first thing to do is decide how we will represent the objects of interest:\n", + "\n", + "- **Point**: We'll define a class such that `Point(3, 4)` is a point where `p.x` is 3 and `p.y` is 4.\n", + "- **Set of Points**: We'll use a Python set: `{Point(0,0), Point(3,4), ...}`\n", + "- **Polygon**: We'll represent a polygon as an ordered list of vertex points.\n", + "\n", + "First, get the necessary imports done:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from __future__ import division, print_function\n", + "\n", + "%matplotlib inline \n", + "import matplotlib.pyplot as plt\n", + "import collections\n", + "import random\n", + "import math" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Points and Sets of Points\n", + "\n", + "I'll define the class `Point` as a named tuple of `x` and `y` coordinates, and `Points(n)` as a function that creates a set of *n* random points. \n", + "\n", + "There are two complications to the function `Points(n)`:\n", + "1. A second optional argument is used to set the random seed. This way, the same call to `Points` will return the same result each time. That makes it easier to reproduce tests. If you want different sets of points, just pass in different values for the seed.\n", + "2. Since `matplotlib` plots on a 3×2 rectangle by default, the points will be uniformly sampled from a 3×2 box (with a small border of 0.05 on each edge to prevent the points from bumping up against the edge of the box)." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "Point = collections.namedtuple('Point', 'x, y')\n", + "\n", + "def Points(n, seed=42):\n", + " \"Generate n random points within a 3 x 2 box.\"\n", + " random.seed((n, seed))\n", + " b = 0.05 # border\n", + " return {Point(random.uniform(b, 3-b), random.uniform(b, 2-b)) \n", + " for _ in range(n)}" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{Point(x=0.15172583449638682, y=1.6108693392839208),\n", + " Point(x=0.968326330695687, y=1.3139550880088586),\n", + " Point(x=1.3508070075242857, y=0.22290610532132638)}" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Points(3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Visualizing Points and Line Segments\n", + "\n", + "\n", + "Now let's see how to visualize points; I'll define a function `plot_points`. We will want to be able to see:\n", + "- The **points** themselves. \n", + "- Optionally, **line segments** between points. An optional `style` parameter allows you to specify whether you want lines or not, and what color they should be. This parameter uses the standard [style format](http://matplotlib.org/1.3.1/api/pyplot_api.html#matplotlib.pyplot.plot) defined by matplotlib; for example, `'r.'` means red colored dots with no lines, `'bs-'` means blue colored squares with lines between them, and `'go:'` means green colored circles with dotted lines between them. The lines go from point to point in order; if you want the lines to close\n", + "back from the last point to the first (to form a complete polygon), specify `closed=True`. (For that to work,\n", + "the collection of points must be a list; with `closed=False` the collection can be any collection.)\n", + "- Optionally, **labels** on the points that let us distinguish one from another. You get\n", + "labels (integers from 0 to *n*) if you specify `labels=True`." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def plot_points(points, style='r.', labels=False, closed=False): \n", + " \"\"\"Plot a collection of points. Optionally change the line style, label points with numbers, \n", + " and/or form a closed polygon by closing the line from the last point to the first.\"\"\"\n", + " if labels:\n", + " for (i, (x, y)) in enumerate(points):\n", + " plt.text(x, y, ' '+str(i))\n", + " if closed:\n", + " points = points + [points[0]]\n", + " plt.plot([p.x for p in points], [p.y for p in points], style, linewidth=2.5)\n", + " plt.axis('scaled'); plt.axis('off')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here's an example:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_points(Points(200))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Convexity\n", + "\n", + "\n", + "We want to make a *convex* hull, so we better have some way of determining whether a polygon is *convex*. Let's examine one that is:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "octagon = [Point(-10, 0), Point(-7, -7), Point(0, -10), Point(+7, -7), \n", + " Point(+10, 0), Point(+7, +7), Point(0, +10), Point(-7, 7)]\n", + "plot_points(octagon, 'bs-', labels=True, closed=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "If you start at point 0 at the left and proceed in order counterclockwise around the octagon, following edges from point to point, you can see that at every vertex you are making a **left** turn.\n", + "\n", + "Now let's consider a non-convex polygon:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pacman = octagon[:4] + [Point(0, 0)] + octagon[5:]\n", + "plot_points(pacman, 'ys-', labels=True, closed=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The `pacman` polygon is non-convex; you can see that a line from point 3 to point 5 passes *outside* the polygon. You can also see that as you move counterclockwise from 3 to 4 to 5 you turn **right** at 4. That leads to the idea: **a polygon is convex if there are no right turns** as we go around the polygon counterclockwise. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Turn Directions\n", + "\n", + "\n", + "Now how do we determine if a turn from point A to B to C is a left turn at B or a right turn (or straight)? Consider this diagram:\n", + "\n", + "\n", + "\n", + "It is a left turn at B if angle β is bigger than angle α; in other words, if β's opposite-over-adjacent ratio is bigger than α's: \n", + "\n", + " (C.y - B.y) / (C.x - B.x) > (B.y - A.y) / (B.x - A.x)\n", + " \n", + "But if we did that computation, we'd need special cases for when each denominator is zero. So multiply each side by the denominators:\n", + "\n", + " (B.x - A.x) * (C.y - B.y) > (B.y - A.y) * (C.x - B.x) \n", + " \n", + "(*Note:* This step should make you very nervous! In general, multiplying both sides of an inequality by a negative number reverses the inequality, and here the denominators might be negative. In this case it works out; basically because we are doing two multiplications so that negatives cancel out, but [the math proof](https://en.wikipedia.org/wiki/Cross_product) is tricky, involving some concepts in vector algebra, so I won't duplicate it here; instead I will provide good test coverage below.)\n", + " \n", + "That leads to the function definition: " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def turn(A, B, C):\n", + " \"Is the turn from A->B->C a 'right', 'left', or 'straight' turn?\"\n", + " diff = (B.x - A.x) * (C.y - B.y) - (B.y - A.y) * (C.x - B.x) \n", + " return ('right' if diff < 0 else\n", + " 'left' if diff > 0 else\n", + " 'straight')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Sketch of Convex Hull Algorithm\n", + "\n", + "\n", + "Now we have the first part of a strategy to find the convex hull:\n", + "\n", + "> *Travel a path along the points in some order. (It is not yet clear exactly what order.) Any point along the way that does not mark a left-hand turn is not part of the hull.*\n", + "\n", + "What's a good order? Let's see what happens if we start at the leftmost point and work our way to the rightmost. We can achieve that ordering by calling the built-in function `sorted` on the points (since points are tuples, `sorted` sorts them lexicographically: first by their first component, `x`, and if there are ties, next by their `y` component). We start with 11 random points, and I will define a function to help plot the partial hull as we go:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def plot_partial_hull(points, hull_indexes=()):\n", + " \"Plot the points, labeled, with a blue line for the points named by indexes.\"\n", + " plot_points(points, labels=True)\n", + " plot_points([points[i] for i in hull_indexes], 'bs-')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "Here are the points without any hull:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now I will start building up the hull by following the points in order from point 0 to 1 to 2 to 3:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 2, 3])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see that we made a valid left turn at point 1, but a right turn at 2. So we remove point 2 from the hull:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 3, 4, 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Point 4 is a right turn, so we remove it:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 3, 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "But now we see point 3 is also a right turn. The addition of one new point (5) can remove multiple points (4 and 3) from the hull. We remove 3 and move on to 6, 7, and 8:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 5, 6, 7, 8])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Point 7 is a right turn so we remove 7 and move on to 9:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 5, 6, 8, 9])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Point 8 is a right turn, so we remove 8. But then 6 and 5 are also right turns, so they too are removed. We proceed on to 10:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 9, 10])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now what do we do? We got all the way to the end of our set of 11 points, but we only got half the hull (the lower half). Well, if looking at all the points in left-to-right order gives us the lower half of the hull, maybe looking at all the points in right-to-left order will give us the upper half. Let's try. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [10, 8, 4, 2, 1 ,0])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Adding 0 makes, 1, and then 2 be right turns, so they are removed:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [10, 8, 4, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's bring back the lower hull and concatenate it with the upper hull:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_partial_hull(sorted(Points(11)), [0, 1, 9, 10] + [10, 8, 4, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "That's all there is to the basic idea of the algorithm, but there are a few edge cases to worry about: \n", + "\n", + "* **Degenerate polygons**: What happens when there are only 1 or 2 (or zero) points? Such a set of points should be considered convex because there is no way to draw a line segment that goes outside the points.\n", + "\n", + "* **Colinear points:** if three or more points are colinear, we should keep only the two \"outside\" ones. The rationale for not keeping them all is that we want the convex hull to be the minimal possible set of points. We need to keep the outside ones because they mark true corners in the hull. We can achieve this by rejecting a point when it is a \"straight\" turn as well as when it is a \"right\" turn.\n", + "\n", + "* **First and last points:** An astute reader might have noticed that our algorithm only rejects the middle point, point B, in the A->B->C turn. That means that the first and last point in sorted order will never be a candidate for rejection, and thus will always end up on the hull. Is that correct? Yes it is. The first point is the leftmost point, the one with lowest `x` value (and if there are ties, it is the lowest-leftmost point). That is an extreme corner, so it should always be on the hull. A similar argument holds for the last point in sorted order.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Implementation of Convex Hull Algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def convex_hull(points):\n", + " \"Find the convex hull of a set of points.\"\n", + " if len(points) <= 3:\n", + " return points\n", + " # Find the two half-hulls and append them, but don't repeat first and last points\n", + " upper = half_hull(sorted(points))\n", + " lower = half_hull(reversed(sorted(points)))\n", + " return upper + lower[1:-1]\n", + "\n", + "def half_hull(sorted_points):\n", + " \"Return the half-hull from following points in sorted order.\"\n", + " # Add each point C in order; remove previous point B if A->B-C is not a left turn.\n", + " hull = []\n", + " for C in sorted_points:\n", + " # if A->B->C is not a left turn ...\n", + " while len(hull) >= 2 and turn(hull[-2], hull[-1], C) != 'left':\n", + " hull.pop() # ... then remove B from hull.\n", + " hull.append(C)\n", + " return hull" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can try it out on our 11 random points, but it is not easy to tell at a glance whether the answer is correct:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[Point(x=0.3253748207631174, y=1.7900592822602743),\n", + " Point(x=1.3968712854329428, y=0.4086086096198411),\n", + " Point(x=2.7310024878562857, y=0.05565070635109892),\n", + " Point(x=2.835445111495586, y=1.375183795456248),\n", + " Point(x=2.7309330192147097, y=1.4818235191572668),\n", + " Point(x=1.8813296288048804, y=1.666404092312656)]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "convex_hull(Points(11))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "# Visualization of Results\n", + "\n", + "To visualize the results of the algorithm, I'll define a function to call `convex_hull` and plot the results: " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def plot_convex_hull(points):\n", + " \"Find the convex hull of these points, and show a plot.\"\n", + " hull = convex_hull(points)\n", + " plot_points(points)\n", + " plot_points(hull, 'bs-', closed=True)\n", + " print(len(hull), 'of', len(points), 'points on hull')" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "6 of 11 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_convex_hull(Points(11))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the octagon and pacman shapes:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 of 8 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_convex_hull(pacman)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "How about 100 random points?" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "15 of 100 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_convex_hull(Points(100))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Will 10,000 points be slow? " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 loops, best of 3: 48.3 ms per loop\n" + ] + } + ], + "source": [ + "P10K = Points(10000)\n", + "\n", + "%timeit convex_hull(P10K)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "No problem! Still well under a second! Here's what it looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "27 of 10000 points on hull\n" + ] + }, + { + "data": { + "image/png": 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1ygMYNOdMU9PLSwrwcs39jai1YmUmF2WsalJrZIfixlpmmhe1S66BMqLMSvFr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\nOzOCJhGrEGA0D+GqNXvmIoZNrGNnWJ1r6Iz0cIbtlpoy1iPj/bvRMk9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lsCNQJ6l5ueUx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\n1csnk1eC9037RNJ3Cp3d6MxF9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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_convex_hull(P10K)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "How about a non-random set? Here is a set of coordinates of 80 US cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "9 of 80 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P = Point\n", + "\n", + "USA = {\n", + " P(-621, 289), P(-614, 297), P(-613, 319), P(-613, 342), P(-612, 263), \n", + " P(-612, 332), P(-603, 247), P(-599, 277), P(-592, 238), P(-591, 323), \n", + " P(-586, 229), P(-581, 289), P(-581, 305), P(-576, 253), P(-568, 260), \n", + " P(-563, 322), P(-560, 234), P(-560, 285), P(-559, 292), P(-558, 246),\n", + " P(-557, 259), P(-555, 225), P(-549, 271), P(-543, 321), P(-535, 313), \n", + " P(-530, 249), P(-524, 278), P(-524, 288), P(-515, 308), P(-505, 206), \n", + " P(-504, 327), P(-492, 207), P(-488, 194), P(-488, 248), P(-487, 264), \n", + " P(-484, 305), P(-484, 328), P(-482, 297), P(-480, 289), P(-477, 210), \n", + " P(-470, 319), P(-468, 291), P(-462, 247), P(-461, 328), P(-452, 271), \n", + " P(-450, 210), P(-450, 226), P(-450, 245), P(-441, 311), P(-440, 301), \n", + " P(-438, 233), P(-438, 293), P(-431, 278), P(-425, 266), P(-423, 273),\n", + " P(-422, 213), P(-422, 236), P(-420, 251), P(-415, 297), P(-413, 196), \n", + " P(-409, 214), P(-409, 290), P(-401, 181), P(-401, 253), P(-400, 230), \n", + " P(-400, 282), P(-394, 251), P(-394, 301), P(-387, 263), P(-385, 272), \n", + " P(-371, 285), P(-370, 285), P(-369, 299), P(-363, 309), P(-357, 292), \n", + " P(-355, 297), P(-352, 306), P(-344, 314), P(-340, 328), P(-608, 270)\n", + " }\n", + "\n", + "plot_convex_hull(USA)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "A decidedly non-random set of points:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4 of 100 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "grid = {Point(x+0.5, y+0.5) \n", + " for x in range(10) for y in range(10)}\n", + "\n", + "plot_convex_hull(grid)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "A variant with some noise thrown in:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "13 of 100 points on hull\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def noisy(points, d=0.3, seed=42): \n", + " \"Add some uniform noise to each of the points.\"\n", + " random.seed(seed)\n", + " def noise(): return random.uniform(-d, +d)\n", + " return {Point(x + noise(), y + noise())\n", + " for (x, y) in points}\n", + "\n", + "plot_convex_hull(noisy(grid))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Circles and donuts:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "28 of 790 points on hull\n" + ] + }, + { + "data": { + "image/png": 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MGI9dfK4uVM7VMV7Oqo9OmmggX4wmuiHHMX3rp/qNLL/0yEy/rhKrzRlU+mCU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\ndXOi2/y3S1ggU1QajZLtOkv1r2qdI9D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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "square = {Point(random.uniform(-1, 1), random.uniform(-1, 1)) for _ in range(1000)}\n", + "circle = {p for p in square if p.x ** 2 + p.y ** 2 < 1}\n", + "plot_convex_hull(circle)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "28 of 628 points on hull\n" + ] + }, + { + "data": { + "image/png": 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d2eMFmXVNH02Ic4Evp5HMQfONwovxuiWmzeRtepEQCK8fs+ZyV6f78f48dQYc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\nf66na22ApqXYSCtdnH97vCby4RdAZu5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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "donut = {p for p in square if 0.2 < (p.x ** 2 + p.y ** 2) < 1}\n", + "plot_convex_hull(donut)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "19 of 720 points on hull\n" + ] + }, + { + "data": { + "image/png": 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8+MFmSvNMo7DSViSMrqMe0j0j0r7LFOACYFveBajHFcD37P+LgO/aJngNQ0N9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\n551TZT3Ntiaazkr0d3DFqq8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def rad(degrees): return degrees * math.pi / 180.0\n", + "\n", + "sine = {Point(rad(d), 5 * math.sin(rad(d))) for d in range(720)}\n", + "plot_convex_hull(noisy(sine))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "38 of 360 points on hull\n" + ] + }, + { + "data": { + "image/png": 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mNDerlZNtqWQOf73Dk8/m5pT3sRWt0/gZKMWJmBj3rMm8pd/kVJVl4tLqgWl4Kwf7d2y+\nyrDQufFPMa8Gvg/c1UjW6LGsbCxjVC6wBzhGa/aksKct0ilsBkoRA34LZIGu/wXfXZuF1hj/gtU0\nPxOQbGpREMBvYxoFFACjs4nn3MNNzjC8N3BDivrXajqFZqAUNwD32o8/1ahHMXPGmwirVZB4AHE5\nFvyYa2ISpm7DnRhB4K2KPSaOWtWFurpGYhOBA8Awrdmeqi63RMYLA6U4BvM0z8uicW05hVcPZst9\nuCcveY59QQjDDXEutktWYqo+G0O05+Gh0BMxtRgAHtaaazq8v60ko4cJ1uX4UWzVnRc4Vw1mywuY\nE+WEp05MXQ+FiFKMmW1Sto3EW/beM+WsNfNxhcG3lOLoVHS4NWS0MAC+go1FL2LjP87i5UL806kK\npzxXSBVfQUhCKUar9Nqdypu5fn5oX7sAt3RMFw+ejBUGStEPkwiTHOp23cNNP8GUQPOigeoWy30L\nghejAUwBTrPtTIydIPT60aiVR7LtDfvxMqUY1ZHdbS0ZKwyA+4D+AH/i673m8tencLUCjREMpZjU\n5hJ0JBwcZigwH63nY+IVwq8f+6B5jTNOUcTB5Mn8SYf3txVkpDBQilmYqETO4kV9MU9l4/cr3wB8\nCdd4KNOHwuHQ3PVTDIwdz0exL/PfTtGdeUqRpDBP6si42QSlyAM+AoYp4lVljNw+nPWDMCfpQkwk\nWiHBmQSZPhQOh2TXjzsEHbOCseuLKR0BKga8qDXnpKaz4WSiZvBjTBAJP+HWPcNZPxiTrcgpajKU\nsJkECToSDoew68f1RfgRMHscKz8H6nd27dlKpVe4c0ZpBkoxHngfiPVk76qd9Bseo9F1IzY2hBc8\nu5yD1i+moKtCppPoi1AKTFHonpjEKF2BN4AZJrwh9WSMZqAU2RiX4xjQWEj55TEag+O4apoK5diZ\nBEFoH4K+CKMxSVC2AL+020wDTk9N9xKJtGbgr5HYfxAcMdy83/mh1r+YkDCOc6X1aMzcsHgfCm2H\nP38ihGgGmKzK/eGOT6A+B2r3w3pPtabUJU+NeD6DZDUSL94H+OrmNX32xqmLIBDaisQCvFMxvgiO\nXaopZ4bW7FBq+yfwSCHQA7xFWFKXPDXiwiCcGA3JSm4nCghBaBsSfVVMqPv88M0/q8Aty5cWZIzN\nwEs+DRlT/06IDAfpq9LY2P5dOjiiLgxCNYBKYgc6uiNCJ6c1CXI98S9daezS0V1siYgLg/4Dw5Y2\nkNUogUdCh9Ocr4o//uXtSez6XEd3ryUiazMwgUgDh8BtQH1NNmuX9aQ2r5KcAzE+3oBUOxLSC69N\nYfRoyrOymEE9Md7iFA1ZCmr2QkVZynqY6iSMh9pA/9JJOPlV/nSLTUbpJC2dZd9rm6DycklkKi2l\nzSRNLbFJeOPaky31ZN563vNxWqr6GEk/A6U4FliOSW66/01Ozc1CZ2NsCHUY1+MHMFbdRowG5C+a\nKggdjVKzMLExXo1cv8oZF32BV58AcoHXteaMVHQvcjYDm73oISBLEde/4d9zs9DOn1uPseQuxRhz\nvo354yU0WUgH3sXMMjgVmeqB0jN57TWM9yzA6UqlJvtW5IQBcB4wE+BbPKqPpbQe8+eWYirhmKe/\n0QCexngaNmCq50pospA6/DMOwzDuyI4X7L24Zd1+GH6A9iVSwwSlyMXc0EP7sIu1jKAfu+qAq4Bn\nEoYArvuxUx1J3I+F1NCKqlxK8VvgcvtxvNZ81FHdg+hpBtdgQpC5kXu3WEGwCkcQJE4nFmPiEGKY\nbMgyTBA6ntan1bsHcBKg/KAjuuYlMsJAKQZi4sIBVpzKm8U4Dh5mg1kYLcD7h0sGIyEdaDmtnlL5\nGjWgC7XP2iVzlWJkx3UxzYcJ/qjEIaMh/0jzftVLWj99tt3IkbrjMPnlnBmF6Wi9RDIYCSnHk+0I\n81Dyz2p5gpzOYlLVy8zuZVZUboOKNeZ9+0czprnTUbKoxLne2INJuHUQNO6MgtECJDBJSDVmCDuV\n5A+lJs3hAHk9jSMdAEfZRkdEM0ZmmBCKkagPYjQCJ3/9dcBs0QKEtKL5tHpNw9kasqs6uGdNRFsY\nuAZChXEu6oJxNnpZYhKEtCQsZsYIiNnAdZvovjFVXYu6MPAaCDcCRyMORkK64p9VeB+lCjzLXwV+\nMYZ9xckP0L5EWxj4nTim4wqGctsEIZ3wziqMABZ6/A+cfIkpI80NiBVl8O3BMGCY+Vz2FjTU+yK7\nvAZCpWZjpG4RZqggsQhCOlGKKeQzwn4uxGiwTu3G4hF8TC2zat+jqLyBIbYMW/kHHRHNmNZTiwBK\ncS9wA1AL5JkAsKQbT8YIAzc9ukk9JQjpgRkaLMQt5DO1yWHOuCc/DBy9itHrxrJqjN3rKq15tL27\nFoVhwmD7+olPEIQnLxEnIyG90XorcCLBjEjmdRfW7jWSsmHZNDgZuzqkFFsUhMEg+7q5aUky987W\npJ4ShFSTfJpxk2112cRXASV2+XEd0a0oCYMtnmVB9855PoEgZdKEKODVbs31+zLG3lUOzG4k5tRT\nGG+LBLUraS0MbO6CMGHgHQ40Av9J8wEggpBeBLVb40nrPOAKbfvQbp0HDG/vLqW1MAD6YWrSgXeY\n4A4HJHmJEFWC2u0YjAet19613LN9u9sN0l0YDPK8dzUDd252AXaMhRgMhWgR1G4fsMtnYyNx1zK8\nO2gnpLnd7QbpLgwGe94bzcCvXpXgGWOJnUCIDOHa7ShMvo4ewKLhrH99GOud7EeiGXjeO5qBV73K\nwx1jnS02AyFSuKn5gvavhdhrfCJLc+zWohnYVw1ste+96lW1fY0DjwKLRSAIkSJcQyjEDn+HsX67\n3XKgUgxoz66kuzBwNIPtWttkkYlJJa/HGBljGK0hJZllBeGQSdQQVmHjbf7M167ybNmu2kFaxia4\nGY6KxkM3oLaHUusXBLK9KGA/5o8ThGgTngBla4VykpsARhj8q726kJbCICTDka1hP9eXIgojSWdj\nhg6jMVMzSzu6t4JwWHgzJ5sZsWKUslmUJ98Op9VDdg5U3qhUxblmp7ZPg5amwqBZgvOzhcAUJM+h\nEEX8D7fVdulonBqhXDQSfuoYEY+0jfZIgxZFYeAYEJ3kkiuQPIdCdPEVZMUMf2OkwIku3Q2IPmLE\nsxOCkQApvS5EmE2Yil9gphbXkCInukgJg97U+YORDK0pTiEI6UoRroYeA24iRVG3aTpMqCiDK/rB\noGKA43mfnlQykC1DUCrf8yeFFaeQ4YIQJUoxtoJiTJbvu0hRGcC0zXSkFFcAjwFspKihiPIYwexF\nLRWnEIQo4C/VXoeZIasGShUn35/FmMlxji4GGE1J9Tqy3m9gy6q2nk1IZ2HwI+CnAAfoVtKN6tEk\nr0YjMwlCdPE/1CqAGmAkxlA+VaHHYjXeQWy+aLMe/GyyQx0OaTpMAJqmUNjbjepT8d7wiRVtZWgg\nRBdzTTvJfI/BLRPoDH33OZtuYXC73bNpJwyUOnkVDCmArt1M9+L5igsroGKr1kvGJDgdSQZkITMo\nwjUmBssE9vZs125G8rQTBkYQ/LWXZ0EW0Asucj6L0VDIRLz+M2sxgXd/M1qDL+VZj/bqQKSmFi2S\nAVnIPFz/mdmYKNwHMUVWCjAxOA6dSTMIJxud3TSt6AZ0lAOTUArgXRkuCJHGXNvVGE/EpqpLGnWi\nQldj8neIMOhOQw+MY5FTdGIFsBgzbAAoRamUzM8KQhuyCaMZODhVl/bTzsIgMsMEW4TO66/trU+n\nMNJUEqIKUacI/31ZjhkKOw+5zqQZVGw1xsJYjplRgO5UchQbwUhMp6BqU306+3k1Yj8Qoog/hNlr\nSCzHONlVotpfGKSz09Fx2FTRTzGPeTwDJqBjasAD0clstFSGCELkSMzPMdWuafKrMcl+ps+F3F5Q\nvQc22noKbZvTIA01gybWO2/KGOlILP/sgbEdLMXVDgQhaiROlZuHnWe6fMhIuNuZbu+NCWSirXMa\npK3NQGv2Y5Og/pHLXgNOIxjAYaZd3keiFoXokjZT5emsGQCsAwo2MCwfref71pgbfyFurXtxQBKi\nhztVPpEmO7mfGPHshrAVbUzaagaWtfZ1RMi6Yozl1cGxugpCFHkAU3h1EUoVeAuyTmDP8R3RgXQX\nBuvs64Al6uTTmoYB5rUbbm26tThWV0GIHl67wTgCBVnr6dGtIzqR7sMERzMgRsPLwAob3fUybgLJ\n2chMghBtgglOhuJGLY6ppVsN3JYHmmzWvNNIvMbsVlHWlp2IjDBYz7DYSbw/BjgbV4qOAqpEEAiR\nxtgNrsVNcOJELTYCD2Txw0YYRzYNyxp07OT26ka6DxOaphfXMKoRYxdYQJpYXwWhDXkXcy3XYTSF\n64DYNo7MWcm4XIBGYi+3ZwfSWjPQmv1KsRUoWMG4AxiD4bOYoUEhRjh4Ck4IQkQJVFTKY+LD48mv\n20P/GNxmZxk+PlupVUe0dbozh7QWBpZ1QEEFQ/Jxx1FnAy/i2g4kyYkQfTxZu2rU3KHv8kz3wBYT\nYO7e9vr6dB8mgLUb2GFCaNlqUlBwQhAyjSgIg3UAu+gXW8ewGwgpW43YDgThsImCMGiaUfgSzy8n\npGw1TsZk46Qh1ZUE4RCIis0AgBUUD8REdfnKVgOJ0V9iQxCiRGLG7w4nUsIAGNFManRJlCpEExNw\ntxAzW7YSpaZ24fTP6rjNbrBzE2y3eTza1tHIS9oLA+/0IjC8mU0TqzMLQroTHnD39Vs56ZQfWmFw\nLCWXlujxi9u7K2kvDGxih26QC9Scr9SGIrMmkNghME8rQwQhIgQD7jTw4AJmxAAGU8H7nNhoHBLb\nl7QXBoHEDj1pLrG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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "donut2 = noisy({Point(5 * math.sin(rad(d)), 5 * math.cos(rad(d))) for d in range(360)})\n", + "\n", + "plot_convex_hull(donut2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tests\n", + "\n", + "So far, everything looks good! But I would gain even more confidence if we could pass a test suite:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'tests pass'" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " # Tests of `turn`\n", + " assert turn(octagon[0], octagon[1], octagon[2]) == 'left'\n", + " assert turn(octagon[2], octagon[3], octagon[4]) == 'left'\n", + " assert turn(octagon[1], octagon[0], octagon[7]) == 'right'\n", + " assert turn(octagon[5], octagon[6], octagon[7]) == 'left'\n", + " assert turn(octagon[2], octagon[1], octagon[0]) == 'right'\n", + " assert turn(pacman[1], pacman[2], pacman[3]) == 'left'\n", + " assert turn(pacman[3], pacman[4], pacman[5]) == 'right'\n", + " assert turn(Point(0, 0), Point(0, 1), Point(0, 2)) == 'straight'\n", + " assert turn(Point(2, 1), Point(3, 1), Point(4, 1)) == 'straight'\n", + " assert turn(Point(2, 1), Point(4, 1), Point(3, 1)) == 'straight'\n", + " assert turn(Point(0, 0), Point(1, 1), Point(2, 2)) == 'straight'\n", + " assert turn(Point(0, 0), Point(-1, -1), Point(2, 2)) == 'straight'\n", + " # More tests of `turn`, covering negative denominator\n", + " A, B = Point(-2, -2), Point(0, 0)\n", + " assert turn(A, B, Point(1, 3)) == 'left'\n", + " assert turn(A, B, Point(2, 2)) == 'straight'\n", + " assert turn(A, B, Point(3, 1)) == 'right'\n", + " assert turn(A, B, Point(-1, 1)) == 'left'\n", + " assert turn(A, B, Point(-1, -4)) == 'right'\n", + " assert turn(A, B, Point(-1, -1)) == 'straight'\n", + " assert turn(B, A, Point(-3, -4)) == 'left'\n", + " assert turn(B, A, Point(-4, -3)) == 'right'\n", + " assert turn(B, A, Point(-1, -1)) == 'straight'\n", + " assert turn(B, A, Point(-3, -3)) == 'straight'\n", + " \n", + " # Tests of convex_hull\n", + " assert convex_hull(octagon)== octagon\n", + " assert convex_hull(circle) == convex_hull(donut)\n", + " assert convex_hull(circle) == convex_hull(convex_hull(circle))\n", + " for n in (0, 1, 2, 3):\n", + " assert convex_hull(Points(n)) == Points(n)\n", + " collinear = {Point(x, 0) for x in range(100)}\n", + " assert convex_hull(collinear) == [min(collinear), max(collinear)]\n", + " P = Point(5, 5)\n", + " assert convex_hull(collinear | {P}) == [min(collinear), max(collinear), P]\n", + " grid1 = {Point(x, y) for x in range(10) for y in range(10)}\n", + " assert convex_hull(grid1) == [Point(0, 0), Point(9, 0), Point(9, 9), Point(0, 9)]\n", + "\n", + " return 'tests pass'\n", + " \n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "## How Many Points on the Hull?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The number of points on the hull for `Points(N)` seems to increase slowly as `N` increases. \n", + "How slowly? Let's try to find out. We'll average the number of points on the hull for `Points(N)` over, say, 60 random trials:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def average_hull_size(N, trials=60):\n", + " \"\"\"Compute the average hull size of N random points\n", + " (averaged over the given number of random trials).\"\"\"\n", + " return sum(len(convex_hull(Points(N, seed=trials+i)))\n", + " for i in range(trials)) / trials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll do this for several values of *N*, taken as powers of 2:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " N Hull Size\n", + " 1: 1.0\n", + " 2: 2.0\n", + " 4: 3.7\n", + " 8: 5.1\n", + " 16: 7.1\n", + " 32: 8.6\n", + " 64: 11.0\n", + " 128: 12.6\n", + " 256: 14.6\n", + " 512: 16.4\n", + "1024: 18.1\n", + "2048: 19.8\n", + "4096: 21.6\n", + "8192: 23.2\n" + ] + } + ], + "source": [ + "hull_sizes = [average_hull_size(2**e) \n", + " for e in range(14)]\n", + "\n", + "print(' N Hull Size')\n", + "for e in range(14): \n", + " print('{:4}: {:4.1f}'.format(2**e, hull_sizes[e]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we'll plot the results, with *N* on a log2 scale:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_hull_sizes(hull_sizes):\n", + " plt.plot(hull_sizes, 'bo-')\n", + " plt.ylabel('Hull size')\n", + " plt.xlabel('log_2(number of points)')\n", + "\n", + "plot_hull_sizes(hull_sizes)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That sure looks like a straight line! \n", + "\n", + "That means we can define `estimated_hull_size` by computing a slope and intercept of the line. (I won't bother doing linear regression; I'll just draw a straight line from the first to the last point in `hull_sizes`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def estimated_hull_size(N):\n", + " \"Estimated hull size for N random points, (inter/extra)polating from hull_sizes.\"\n", + " slope = (hull_sizes[-1] - hull_sizes[0]) / (len(hull_sizes) - 1)\n", + " return hull_sizes[0] + slope * math.log(N, 2)\n", + "\n", + "# Plot actual average hull sizes in blue, and estimated hull sizes in red\n", + "plot_hull_sizes(hull_sizes)\n", + "plt.plot([estimated_hull_size(2**e) \n", + " for e in range(len(hull_sizes))], \n", + " 'r--');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an estimate of the number of points on the hull of a quadrillion random points:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "86.15634904778565" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "estimated_hull_size(10**15)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Concluding Remarks and Further Reading\n", + "\n", + "The convex hull problem is an interesting exercise in algorithm design.\n", + "The algorithm covered here is called [Andrew's Monotone Chain](https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain).\n", + "It is a variant of the [Graham Scan](https://en.wikipedia.org/wiki/Graham_scan).\n", + "You can read more from [Tamassia](http://cs.brown.edu/courses/cs016/docs/old_lectures/ConvexHull-Notes.pdf) or [Wikipedia](https://en.wikipedia.org/wiki/Convex_hull)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Countdown.ipynb b/pytudes/ipynb/Countdown.ipynb new file mode 100644 index 0000000..bf97dd4 --- /dev/null +++ b/pytudes/ipynb/Countdown.ipynb @@ -0,0 +1,2867 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "
Peter Norvig
5 January 2016
\n", + "\n", + "# Countdown to 2016\n", + "\n", + "Alex Bellos [posed](http://www.theguardian.com/science/2016/jan/04/can-you-solve-it-complete-the-equation-10-9-8-7-6-5-4-3-2-1-2016) this New Year's puzzle:\n", + "\n", + "\n", + "> Fill in the blanks so that this equation makes arithmetical sense:\n", + "\n", + "> `10 _ 9 _ 8 _ 7 _ 6 _ 5 _ 4 _ 3 _ 2 _ 1 = 2016`\n", + "\n", + "> You are allowed to use *only* the four basic arithmetical operations: +, -, ×, ÷. But brackets (parentheses) can be used wherever needed. So, for example, the solution could begin\n", + "\n", + "> `(10 - 9) / (8` ...\n", + "\n", + "> or\n", + "\n", + "> `10 + (9 - 8)` ...\n", + "\n", + "Let's see if we can solve this puzzle, and some of the related ones from Alex's [first](http://www.theguardian.com/science/2016/jan/04/can-you-solve-it-complete-the-equation-10-9-8-7-6-5-4-3-2-1-2016) and [second](http://www.theguardian.com/science/2016/jan/04/did-you-solve-it-complete-the-equation-10-9-8-7-6-5-4-3-2-1-2016) post. We'll start with a simpler version of the puzzle." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Four Operators, No Brackets\n", + "\n", + "Suppose for the moment we are not allowed to use brackets. Then there are nine blanks, each of which can be filled by one of four operators, so the total number of possible expressions is:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "262144" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "4 ** 9" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The function `itertools.product` can enumerate all the ways of filling 9 blanks with one of the four operators:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "262144" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import itertools\n", + "\n", + "operators = ('+', '-', '*', '/')\n", + " \n", + "len(set(itertools.product(operators, repeat=9)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So we can fill in the equation with each possible sequence of operations, and evaluate each string to see if it equals 2016. But we need to catch errors such as dividing by zero, so we'll define a wrapper function, `evaluate`, to do the `eval`:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def evaluate(exp):\n", + " \"eval exp, or return None if there is an arithmetic error.\"\n", + " try:\n", + " return eval(exp)\n", + " except ArithmeticError:\n", + " return None\n", + "\n", + "def solve_no_brackets(operators, target=2016):\n", + " \"All solutions to the countdown puzzle (with no brackets).\"\n", + " exps = ('10{}9{}8{}7{}6{}5{}4{}3{}2{}1'.format(*ops)\n", + " for ops in itertools.product(operators, repeat=9))\n", + " return [exp for exp in exps if evaluate(exp) == target]\n", + "\n", + "solve_no_brackets(operators)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Too bad; we did all that work and didn't find a solution. What years *can* we find solutions for? Let's modify `solve_no_brackets` to take a collection of target years rather than a single one, and return a dict of the form `{year: 'expression'}` for each expression that evaluates to one of the target years:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{1979: '10*9*8+7*6*5*4*3/2-1',\n", + " 1980: '10*9*8+7*6*5*4*3/2/1',\n", + " 1981: '10*9*8+7*6*5*4*3/2+1',\n", + " 2013: '10*9*8*7/6/5*4*3-2-1',\n", + " 2014: '10*9*8*7/6/5*4*3-2/1',\n", + " 2015: '10*9*8*7/6/5*4*3-2+1',\n", + " 2017: '10*9*8*7/6/5*4*3+2-1',\n", + " 2018: '10*9*8*7/6/5*4*3+2/1',\n", + " 2019: '10*9*8*7/6/5*4*3+2+1'}" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def solve_no_brackets(operators, targets):\n", + " \"All solutions to the countdown puzzle (with no brackets).\"\n", + " exps = ('10{}9{}8{}7{}6{}5{}4{}3{}2{}1'.format(*ops)\n", + " for ops in itertools.product(operators, repeat=9))\n", + " return {int(evaluate(exp)): exp for exp in exps if evaluate(exp) in targets}\n", + "\n", + "solve_no_brackets(operators, range(1900, 2100))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Interesting: in the 20th and 21st centuries, there are only two \"golden eras\" where the countdown equation works: the three year period centered on 1980, and the seven year period that is centered on 2016, but omits 2016. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Four Operators, With Brackets\n", + "\n", + "Now let's return to the original puzzle, with the brackets. How many ways are there of bracketing an expression with 9 binary operators? I happen to remember that this is given by the [Catalan numbers](https://en.wikipedia.org/wiki/Catalan_number), and we can [look it up](http://www.wolframalpha.com/input/?i=9th+catalan+number) to find that there are 4862 diffferent bracketing. If we enumerated and evaluated all of them, it would take about 4862 times longer than doing a single `solve_no_brackets`, which took about 6 seconds, so the estimated time would be about 8 hours. I'm impatient, so I'd like a faster approach. \n", + "\n", + "I'll use the idea of [dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming): break the problem down into simpler subparts, and compute an answer for each subpart, and store intermediate results in a table so we don't need to re-compute them when we need them again.\n", + "\n", + "How do we break the problem into parts? In general, any expression must consist of an operator with two operands (which might in turn be complex subexpressions). For example, a complete countdown expression might be of the form\n", + "\n", + " (10 ... 8) + (7 ... 1)\n", + " \n", + "where `(10 ... 8)` means some expression that starts with 10 and ends with 8. Of course we need not use `'+'` as the operator, and we need not split after the 8; we could use any of the four operators and split anywhere. Let's start by defining `c10` as the tuple of integers forming the countdown from 10 to 1, and the function `splits` to split a tuple in all ways: " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "c10 = (10, 9, 8, 7, 6, 5, 4, 3, 2, 1)\n", + "\n", + "def splits(items):\n", + " \"Split sequence of items into two non-empty parts, in all ways.\"\n", + " return [(items[:i], items[i:]) \n", + " for i in range(1, len(items))]" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[((10,), (9, 8, 7, 6, 5, 4, 3, 2, 1)),\n", + " ((10, 9), (8, 7, 6, 5, 4, 3, 2, 1)),\n", + " ((10, 9, 8), (7, 6, 5, 4, 3, 2, 1)),\n", + " ((10, 9, 8, 7), (6, 5, 4, 3, 2, 1)),\n", + " ((10, 9, 8, 7, 6), (5, 4, 3, 2, 1)),\n", + " ((10, 9, 8, 7, 6, 5), (4, 3, 2, 1)),\n", + " ((10, 9, 8, 7, 6, 5, 4), (3, 2, 1)),\n", + " ((10, 9, 8, 7, 6, 5, 4, 3), (2, 1)),\n", + " ((10, 9, 8, 7, 6, 5, 4, 3, 2), (1,))]" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "splits(c10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now what I would like to do is build up a table that says, for every subsequence of the numbers, what are the expressions we can make with those numbers, and what do they evaluate to? We'll call the table `EXPS`. For example, with the subsequence `(10, 9, 8)`, we would have:\n", + "\n", + " EXPS[(10, 9, 8)] = {\n", + " 27: '((10+9)+8)',\n", + " 8: '((10-9)*8)', \n", + " -7: '(10-(9+8))', \n", + " ...}\n", + " \n", + "We'll do the same for every other subsequence, for example:\n", + "\n", + " EXPS[(7, 6, 5, 4, 3, 2, 1)] = {\n", + " 1: '((((7/((6/5)-4))+3)*2)*1)',\n", + " 2: '((((7/((6/5)-4))+3)*2)+1)',\n", + " 3.5: '((((7/((6/5)-4))+3)+2)+1)',\n", + " 4: '((7-((6/5)*((4/3)+2)))+1)',\n", + " ...}\n", + " \n", + "Once we have the tables for these two subsequences, we can put them together to get the table for the complete `countdown(10)` by considering all ways of taking a value from the first table, then one of the four operators, then a value from the second table. For example, taking the first entry from each table, and the operator `'+'`, we would have:\n", + "\n", + " EXPS[(10, 9, 8, 7, 6, 5, 4, 3, 2, 1)] = { \n", + " 28: '(((10+9)+8)+((((7/((6/5)-4))+3)*2)*1))',\n", + " ...}\n", + "\n", + "\n", + "I can implement `EXPS` as a defaultdict of dicts, and define `expressions(numbers)` to fill in `EXPS` entries for `numbers` and all sub-sequences of `numbers`. Within `fill_tables`, note that `Lnums` and `Rnums` are sequences of numbers, such as `(10, 9, 8)` and `(7, 6)`. `L` and `R` are values, such as `27` and `1`. And `Lexp` and `Rexp` are strings, such as `\"((10+9)+8)\"` and `\"(7-6)\"`. Rather than catching division-by-zero errors, we just avoid the division when the denominator is 0." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from collections import defaultdict, Counter\n", + "\n", + "EXPS = defaultdict(dict) # e.g., EXPS[(10, 9, 8)][27] == '((10+9)+8)'\n", + "\n", + "def expressions(numbers):\n", + " \"Fill EXPS table for numbers, and all sub-sequences of numbers. Return EXPS[numbers]\"\n", + " if numbers in EXPS: # Already did the work\n", + " pass\n", + " elif len(numbers) == 1: # Only one way to make an expression out of a single number\n", + " expr(numbers, numbers[0], str(numbers[0]))\n", + " else: # Split in all ways; fill tables for left and right; combine tables in all ways\n", + " for (Lnums, Rnums) in splits(numbers):\n", + " for (L, R) in itertools.product(expressions(Lnums), expressions(Rnums)):\n", + " Lexp, Rexp = '(' + EXPS[Lnums][L], EXPS[Rnums][R] + ')'\n", + " if R != 0: \n", + " expr(numbers, L / R, Lexp + '/' + Rexp)\n", + " expr(numbers, L * R, Lexp + '*' + Rexp)\n", + " expr(numbers, L - R, Lexp + '-' + Rexp)\n", + " expr(numbers, L + R, Lexp + '+' + Rexp)\n", + " return EXPS[numbers]\n", + "\n", + "def expr(numbers, value, exp): \n", + " \"Record exp as an expression with the given value, covering the sequence of numbers.\"\n", + " EXPS[numbers][value] = exp" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's give it a try:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{-62: '(10-(9*8))',\n", + " -7: '((10-9)-8)',\n", + " -6.888888888888889: '((10/9)-8)',\n", + " 0.125: '((10-9)/8)',\n", + " 0.1388888888888889: '((10/9)/8)',\n", + " 0.5882352941176471: '(10/(9+8))',\n", + " 2.375: '((10+9)/8)',\n", + " 8: '((10-9)*8)',\n", + " 8.875: '(10-(9/8))',\n", + " 8.88888888888889: '((10/9)*8)',\n", + " 9: '((10-9)+8)',\n", + " 9.11111111111111: '((10/9)+8)',\n", + " 10.0: '(10*(9-8))',\n", + " 11: '((10+9)-8)',\n", + " 11.125: '(10+(9/8))',\n", + " 11.25: '((10*9)/8)',\n", + " 27: '((10+9)+8)',\n", + " 82: '((10*9)-8)',\n", + " 98: '((10*9)+8)',\n", + " 152: '((10+9)*8)',\n", + " 170: '(10*(9+8))',\n", + " 720: '((10*9)*8)'}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "expressions((10, 9, 8))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'((10+9)+8)'" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "EXPS[(10, 9, 8)][27]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "That looks reasonable. Let's solve the whole puzzle.\n", + "\n", + "# Countdown to 2016: A Solution" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 29.1 s, sys: 713 ms, total: 29.8 s\n", + "Wall time: 29.8 s\n" + ] + }, + { + "data": { + "text/plain": [ + "'(((((((10+((9*8)*7))-6)-5)*4)+3)+2)-1)'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time expressions(c10)[2016]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We have an answer! And in a lot less than 8 hours, thanks to dynamic programming! \n", + "\n", + "Removing unnecessry brackets, this equation is equivalent to:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2016" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(10 + 9 * 8 * 7 - 6 - 5) * 4 + 3 + 2 - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Counting Solutions\n", + "\n", + "Alex Bellos had another challenge: \n", + "\n", + "> I was half hoping a computer scientist would let me know exactly how many solutions there are with only the four basic operations. Maybe someone will. \n", + "\n", + "As it stands, my program can't answer that question, because I only keep one expression for each value. \n", + "\n", + "Also, I'm not sure what it means to be a distinct solution. For example, are `((10+9)+8)` and `(10+(9+8))` different, or are they same, because they both are equivalent to `(10+9+8)`? Similarly, are `((3-2)-1)` and `(3-(2+1)` different, or the same because they both are equivalent to `(3 + -2 + -1)`? I think the notion of \"distinct solution\" is just inherently ambiguous, and each of these questions could reasonably be answered either way. My choice is to count each of these as distinct: every expression has exactly ten numbers, nine operators, and nine pairs of brackets, and if an expression differs in any character, it is different. But I won't argue with anyone who has a different definition of \"distinct solution.\"\n", + "\n", + "So how can I count expressions? One approach would be to go back to enumerating every equation (all 4862 × 49 = 1.2 bilion of them) and checking which ones equal 2016. That would take about 40 hours with my Python program, but I could get it under 40 minutes in a more efficient language.\n", + "\n", + "Another approach is to count subexpressions as the table is filled in. We won't enumerate all the expressions, just count them. I'll introduce a second table, `COUNTS`, such that\n", + "\n", + " COUNTS[(10, 9, 8)][27] == 2\n", + " \n", + "because there are 2 ways to make 27 with the numbers `(10, 9, 8)`, namely, `((10+9)+8)` and `(10+(9+8))`.\n", + "How do we compute the counts? By looking at every split and operator choice that can make the value, and summing up (over all of these) the product of the counts for the two sides. For example, there are 2 ways to make 27 with `(10 ... 8)`, and it turns out there are 3526 ways to make 1 with `(7 ... 1)`. So there are 2 × 3526 = 7052 ways to make 28 with this split by adding 27 and 1. \n", + "\n", + "I'll make `expr` handle `COUNTS` as well as `EXPS`. And I'll define `clear` to clear out the cache of `COUNTS` and `EXPS`, so that we can fill the tables with our new, improved entries." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "COUNTS = defaultdict(Counter) # e.g., COUNTS[(10, 9, 8)][27] == 2\n", + "\n", + "def expressions(numbers):\n", + " \"Fill EXPS table for numbers, and all sub-sequences of numbers. Return EXPS[numbers]\"\n", + " if numbers in EXPS: # Already did the work\n", + " pass\n", + " elif len(numbers) == 1: # Only one way to make an expression out of a single number\n", + " expr(numbers, numbers[0], str(numbers[0]), 1)\n", + " else: # Split in all ways; fill tables for left and right; combine tables in all ways\n", + " for (Lnums, Rnums) in splits(numbers):\n", + " for (L, R) in itertools.product(expressions(Lnums), expressions(Rnums)):\n", + " Lexp, Rexp = '(' + EXPS[Lnums][L], EXPS[Rnums][R] + ')'\n", + " count = COUNTS[Lnums][L] * COUNTS[Rnums][R]\n", + " if R != 0: \n", + " expr(numbers, L / R, Lexp + '/' + Rexp, count)\n", + " expr(numbers, L * R, Lexp + '*' + Rexp, count)\n", + " expr(numbers, L - R, Lexp + '-' + Rexp, count)\n", + " expr(numbers, L + R, Lexp + '+' + Rexp, count)\n", + " return EXPS[numbers]\n", + "\n", + "def expr(numbers, val, exp, count):\n", + " \"Fill EXPS[numbers][val] with exp, and increment COUNTS.\"\n", + " EXPS[numbers][val] = exp\n", + " COUNTS[numbers][val] += count\n", + " \n", + "def clear(): EXPS.clear(); COUNTS.clear()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{-62: '(10-(9*8))',\n", + " -7: '((10-9)-8)',\n", + " -6.888888888888889: '((10/9)-8)',\n", + " 0.125: '((10-9)/8)',\n", + " 0.1388888888888889: '((10/9)/8)',\n", + " 0.5882352941176471: '(10/(9+8))',\n", + " 2.375: '((10+9)/8)',\n", + " 8: '((10-9)*8)',\n", + " 8.875: '(10-(9/8))',\n", + " 8.88888888888889: '((10/9)*8)',\n", + " 9: '((10-9)+8)',\n", + " 9.11111111111111: '((10/9)+8)',\n", + " 10.0: '(10*(9-8))',\n", + " 11: '((10+9)-8)',\n", + " 11.125: '(10+(9/8))',\n", + " 11.25: '((10*9)/8)',\n", + " 27: '((10+9)+8)',\n", + " 82: '((10*9)-8)',\n", + " 98: '((10*9)+8)',\n", + " 152: '((10+9)*8)',\n", + " 170: '(10*(9+8))',\n", + " 720: '((10*9)*8)'}" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "expressions((10, 9, 8))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({-62: 1,\n", + " -7: 2,\n", + " -6.888888888888889: 1,\n", + " 0.125: 1,\n", + " 0.1388888888888889: 2,\n", + " 0.5882352941176471: 1,\n", + " 2.375: 1,\n", + " 8: 1,\n", + " 8.875: 1,\n", + " 8.88888888888889: 2,\n", + " 9: 2,\n", + " 9.11111111111111: 1,\n", + " 10.0: 2,\n", + " 11: 2,\n", + " 11.125: 1,\n", + " 11.25: 2,\n", + " 27: 2,\n", + " 82: 2,\n", + " 98: 1,\n", + " 152: 1,\n", + " 170: 1,\n", + " 720: 2})" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "COUNTS[(10, 9, 8)]" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "COUNTS[(10, 9, 8)][27]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Looks good to me. Now let's repeat the computation, this time keeping track of `COUNTS`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1min 4s, sys: 1.12 s, total: 1min 5s\n", + "Wall time: 1min 5s\n" + ] + }, + { + "data": { + "text/plain": [ + "'(((((((10+((9*8)*7))-6)-5)*4)+3)+2)-1)'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "\n", + "%time expressions(c10)[2016]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Answer (?)\n", + "\n", + "Now we can read off the answer:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "30066" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "COUNTS[c10][2016]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This says there are 30,066 distinct expressions for 2016. \n", + "\n", + "**But I don't believe it.**\n", + "\n", + "Why not? Because floating point division can have round-off errors. For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2015.9999999999998" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "2015 + 1/3 + 1/3 + 1/3" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "2015 + 1/3 + 1/3 + 1/3 == 2016" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Dealing with Round-off Errors\n", + "\n", + "So there might be perfectly good solutions that are hiding in the `EXPS` table under `2015.9999999999998` (or some similar number) when they should be exactly `2016`. Let's find all the values that are very near to `2016`:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2015.999999999997,\n", + " 2015.999999999999,\n", + " 2015.9999999999993,\n", + " 2015.9999999999995,\n", + " 2015.9999999999998,\n", + " 2016.0,\n", + " 2016.0000000000002,\n", + " 2016.0000000000005,\n", + " 2016.0000000000018,\n", + " 2016.000000000002,\n", + " 2016.0000000000023}" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{val for val in expressions(c10)\n", + " if abs(val - 2016) < 0.000001}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I suspect that all of these actually should be exactly 2016. \n", + "\n", + "To find out for sure, let's re-do all the calculations using exact rational arithmetic, as provided by the `fractions.Fraction` data type. From experience I know that this will be an order of magnitude slower, so we're looking at 10 minutes or more of computation.\n", + "\n", + "I'll replace the computation `L / R` with `divide(L, R)`, which calls `Fraction`. To mitigate the expense of this computation, I make two optimizations. First, `divide` replaces a whole fraction, such as `Fraction(6, 2)`, with an `int`, such as `3`. Second, I modify `expr` to *not* fill in `EXPS[c10]`, except for `EXPS[c10][2016]`. The rationale is that we don't need the other entries, and by not storing them, we save a lot of memory, and thus save garbage collection time." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from fractions import Fraction\n", + "\n", + "def expressions(numbers):\n", + " \"Fill EXPS table for numbers, and all sub-sequences of numbers. Return EXPS[numbers]\"\n", + " if numbers in EXPS: # Already did the work\n", + " pass\n", + " elif len(numbers) == 1: # Only one way to make an expression out of a single number\n", + " expr(numbers, numbers[0], str(numbers[0]), 1)\n", + " else: # Split in all ways; fill tables for left and right; combine tables in all ways\n", + " for (Lnums, Rnums) in splits(numbers):\n", + " for (L, R) in itertools.product(expressions(Lnums), expressions(Rnums)):\n", + " Lexp, Rexp = '(' + EXPS[Lnums][L], EXPS[Rnums][R] + ')'\n", + " count = COUNTS[Lnums][L] * COUNTS[Rnums][R]\n", + " if R != 0: \n", + " expr(numbers, divide(L, R), Lexp + '/' + Rexp, count)\n", + " expr(numbers, L * R, Lexp + '*' + Rexp, count)\n", + " expr(numbers, L - R, Lexp + '-' + Rexp, count)\n", + " expr(numbers, L + R, Lexp + '+' + Rexp, count)\n", + " return EXPS[numbers]\n", + "\n", + "def divide(L, R):\n", + " \"Exact rational division of L/R.\"\n", + " f = Fraction(L, R)\n", + " return (f.numerator if f.denominator == 1 else f)\n", + "\n", + "def expr(numbers, value, exp, count):\n", + " \"Fill EXPS[numbers][val] with exp, and increment COUNTS.\"\n", + " if numbers == c10 and value != 2016: \n", + " return\n", + " EXPS[numbers][value] = exp\n", + " COUNTS[numbers][value] += count" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Answer (!)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 12min 25s, sys: 1.44 s, total: 12min 26s\n", + "Wall time: 12min 27s\n" + ] + }, + { + "data": { + "text/plain": [ + "44499" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "\n", + "%time expressions(c10)[2016]\n", + "\n", + "COUNTS[c10][2016]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "That did indeed take about ten times longer, but we now have an answer that I have more confidence in (but I wouldn't accept it as definitive until it was independently verified and had an extensive test suite). And of course, if you have a different definition of \"distinct solution,\" you will get a different answer." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Dealing with the Exponentiation Operator\n", + "\n", + "Now let's turn to another of Alex's puzzles: making 2016 and other target values from a string of four or five `4`s, with exponentiation allowed. Exponentiation is tricky for five reasons:\n", + "\n", + "- **Division by zero**: `(0 ** -1)` is the same as `(1 / 0)`, and gives a `ZeroDivisionError`.\n", + "- **Irrationals**: `(3 ** (1 / 2))` is an irrational number; so we can't do exact rational arithmetic.\n", + "- **Imaginaries**: `(-1 ** (1 / 2))` is an imaginary number, but Python gives a `ValueError`.\n", + "- **Overflow**: `(10. ** (9. ** 8.))`, as a `float`, gives a `OverflowError`.\n", + "- **Finite memory**: [`(10 ** (9 ** (8 * 7)))`](http://www.wolframalpha.com/input/?i=10+%5E+9+%5E+56), as an `int`, gives an `OutOfMemoryError` (even if your memory was expanded to use every atom on Earth).\n", + "\n", + "How do we deal with this? We can't do exact rational arithmetic. We could try to do exact *algebra*, perhaps using [SymPy](http://www.sympy.org/en/index.html), but that seems difficult\n", + "and computationally expensive, so instead I will abandon the goal of exact computation, and do everything in the domain of floats (reluctantly accepting that there will be some round-off errors). We'll coerce numbers to floats when we first put them in the table, and all subsequent operations will be with floats. I define a new function, `expr2`, to call `expr`, catching arithmetic errors. Since we are making some rather arbitrary decisions about what expressions are allowed (e.g. imaginary numbers are not), I'll give up on trying to maintain `COUNTS`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from operator import add, sub, mul, truediv\n", + "\n", + "def expressions(numbers):\n", + " \"Fill EXPS table for numbers, and all sub-sequences of numbers. Return EXPS[numbers]\"\n", + " if numbers in EXPS: # Already did the work\n", + " pass\n", + " elif len(numbers) == 1: # Only one way to make an expression out of a single number\n", + " expr(numbers, float(numbers[0]), str(numbers[0]))\n", + " else: # Split in all ways; fill tables for left and right; combine tables in all ways\n", + " for (Lnums, Rnums) in splits(numbers):\n", + " for (L, R) in itertools.product(expressions(Lnums), expressions(Rnums)):\n", + " Lexp, Rexp = '(' + EXPS[Lnums][L], EXPS[Rnums][R] + ')'\n", + " expr2(numbers, L, pow, R, Lexp + '**' + Rexp)\n", + " expr2(numbers, L, truediv, R, Lexp + '/' + Rexp)\n", + " expr2(numbers, L, mul, R, Lexp + '*' + Rexp)\n", + " expr2(numbers, L, add, R, Lexp + '+' + Rexp)\n", + " expr2(numbers, L, sub, R, Lexp + '-' + Rexp)\n", + " return EXPS[numbers]\n", + "\n", + "def expr2(numbers, L, op, R, exp): \n", + " \"Fill table entries for op(L, R), catching errors.\"\n", + " try:\n", + " expr(numbers, op(L, R), exp)\n", + " except (ArithmeticError, ValueError):\n", + " pass\n", + " \n", + "def expr(numbers, value, exp): EXPS[numbers][value] = exp" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can solve the \"2016 with five fours\" puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'(((4**4)-4)*(4+4))'" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "\n", + "expressions((4, 4, 4, 4, 4))[2016]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I'll define a function to create a table of makeable integers:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def makeable(numbers):\n", + " \"A table of {i: expression} for all integers i from 0 up to first unmakeable.\"\n", + " return {i: expressions(numbers)[i]\n", + " for i in range(unmakeable(numbers))}\n", + "\n", + "def unmakeable(numbers):\n", + " \"Smallest positive integer than can't be made by numbers.\"\n", + " return next(i for i in itertools.count(1) if i not in expressions(numbers))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We'll use this to see if we can solve the \"0 to 9 with four fours\" puzzle:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: '(((4+4)-4)-4)',\n", + " 1: '(((4+4)-4)/4)',\n", + " 2: '((4/(4+4))*4)',\n", + " 3: '(((4+4)+4)/4)',\n", + " 4: '(((4-4)*4)+4)',\n", + " 5: '(((4*4)+4)/4)',\n", + " 6: '(((4+4)/4)+4)',\n", + " 7: '((4-(4/4))+4)',\n", + " 8: '(((4+4)-4)+4)',\n", + " 9: '(((4/4)+4)+4)'}" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "makeable((4, 4, 4, 4))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Yes: we can get 0 to 9 (but not 10).\n", + "\n", + "Now I'll see what integers we can make with five fives. Legend has it that you can get all the way up to 55:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: '((((5-5)*5)-5)+5)',\n", + " 1: '(((5-(5*5))/5)+5)',\n", + " 2: '((((5+5)/5)-5)+5)',\n", + " 3: '((((5*5)-5)-5)/5)',\n", + " 4: '((((5-5)-5)/5)+5)',\n", + " 5: '((5/((5**5)**5))+5)',\n", + " 6: '((((5/5)+5)*5)/5)',\n", + " 7: '(((5/5)+(5/5))+5)',\n", + " 8: '((((5+5)+5)/5)+5)',\n", + " 9: '((((5+5)*5)-5)/5)',\n", + " 10: '((((5*5)-5)-5)-5)',\n", + " 11: '((((5+5)*5)+5)/5)',\n", + " 12: '((((5+5)/5)+5)+5)'}" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ff = (5, 5, 5, 5, 5)\n", + "\n", + "makeable(ff)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We didn't get there. \n", + "\n", + "# More Operations\n", + "\n", + "With some research, I [see](http://www.infobarrel.com/Five_Fives_Problem_Recreational_Mathematics) that others who got up to 55 with five 5s used these three concepts:\n", + "\n", + "- **digit concatenation**: `55`\n", + "- **decimal point**: `.5`\n", + "- **unary operations**: `5!` and √ `5`\n", + "\n", + "\n", + "We'll refactor `expressions` to call these three new subfunctions:\n", + "\n", + "- `digit_expressions`: For every subsequence of numbers, we'll smush the digits together, and then make a table entry for those resulting digits as an integer, and with a decimal point in each possible position.\n", + "- `binary_expressions`: The code that previously was the main body of `expressions`.\n", + "- `unary_expressions`: Apply the unary operators to every entry in the table. (Because it applies to entries already in the table, make sure to call `unary_expressions` last.)\n", + "\n", + "We'll still do all computation in the domain of floats." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import sqrt, factorial\n", + "\n", + "def expressions(numbers):\n", + " \"Fill EXPS table for numbers, and all sub-sequences of numbers. Return EXPS[numbers]\"\n", + " if numbers not in EXPS: \n", + " digit_expressions(numbers)\n", + " binary_expressions(numbers)\n", + " unary_expressions(numbers)\n", + " return EXPS[numbers]\n", + "\n", + "def digit_expressions(numbers):\n", + " \"Fill tables with expressions made from the digits of numbers, and a decimal point.\"\n", + " exp = ''.join(str(n) for n in numbers)\n", + " expr(numbers, float(exp), exp)\n", + " for d in range(len(exp)):\n", + " decimal = exp[:d] + '.' + exp[d:]\n", + " expr(numbers, float(decimal), decimal)\n", + " \n", + "def binary_expressions(numbers):\n", + " \"Fill tables with all expressions formed by splitting numbers and combining with an op.\"\n", + " for (Lnums, Rnums) in splits(numbers):\n", + " for (L, R) in itertools.product(expressions(Lnums), expressions(Rnums)):\n", + " Lexp, Rexp = '(' + EXPS[Lnums][L], EXPS[Rnums][R] + ')'\n", + " if 1 <= R <= 10 and (L > 0 or int(R) == R):\n", + " expr2(numbers, L, pow, R, Lexp + '**' + Rexp)\n", + " expr2(numbers, L, truediv, R, Lexp + '/' + Rexp)\n", + " expr2(numbers, L, mul, R, Lexp + '*' + Rexp)\n", + " expr2(numbers, L, add, R, Lexp + '+' + Rexp)\n", + " expr2(numbers, L, sub, R, Lexp + '-' + Rexp)\n", + " \n", + "def unary_expressions(numbers):\n", + " for v in list(EXPS[numbers]):\n", + " exp = EXPS[numbers][v]\n", + " if v > 0: \n", + " expr(numbers, sqrt(v), '√' + exp)\n", + " if 2 <= v <= 6 and v == int(v):\n", + " expr(numbers, factorial(v), exp + '!')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now that we have more variety in the types of expressions formed, I want to choose a \"good\" expression to represent each value. I'll modify `expr` so that when there are multiple expressions for a value, it chooses the one with the least \"weight,\" where I define `weight` as the length of the string, plus a penalty of 1 for every square root sign (just because square root feels \"heavier\" than the other operations):" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def expr(numbers, value, exp): \n", + " if value not in EXPS[numbers] or weight(exp) < weight(EXPS[numbers][value]):\n", + " EXPS[numbers][value] = exp\n", + " \n", + "def weight(exp): return len(exp) + exp.count('√')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We'll try again:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 43.5 s, sys: 1.44 s, total: 45 s\n", + "Wall time: 45 s\n" + ] + }, + { + "data": { + "text/plain": [ + "{0: '(5*(55-55))',\n", + " 1: '((55/55)**5)',\n", + " 2: '(55/(.5*55))',\n", + " 3: '√(5!-(555/5))',\n", + " 4: '(5-(55/55))',\n", + " 5: '(5.55-.55)',\n", + " 6: '(5+(55/55))',\n", + " 7: '(((5+55)/5)-5)',\n", + " 8: '(.5*(5+(55/5)))',\n", + " 9: '(5!-(555/5))',\n", + " 10: '(5!-(55+55))',\n", + " 11: '(5.5/(5.5-5))',\n", + " 12: '(5!/(55/5.5))',\n", + " 13: '((5+(5+55))/5)',\n", + " 14: '((5*5)-(55/5))',\n", + " 15: '(5+(55/5.5))',\n", + " 16: '(5+(5.5+5.5))',\n", + " 17: '(5+((5+55)/5))',\n", + " 18: '(5+((5!-55)/5))',\n", + " 19: '((5*5)-(.5+5.5))',\n", + " 20: '(55/(5*.55))',\n", + " 21: '(5+(5+(55/5)))',\n", + " 22: '((55+55)/5)',\n", + " 23: '((5+(55/.5))/5)',\n", + " 24: '(5-(55/55))!',\n", + " 25: '(55-(5+(5*5)))',\n", + " 26: '(55-(5+(5!/5)))',\n", + " 27: '(.5*(55-(5/5)))',\n", + " 28: '(.5*(.5+55.5))',\n", + " 29: '(5+(5!/(5.5-.5)))',\n", + " 30: '(5*((55/5)-5))',\n", + " 31: '(55-(5-(5/5))!)',\n", + " 32: '(55-((5!-5)/5))',\n", + " 33: '(.55*(5+55))',\n", + " 34: '((5!+(55-5))/5)',\n", + " 35: '(5+(55-(5*5)))',\n", + " 36: '((5*5)+(55/5))',\n", + " 37: '((5!+(5!-55))/5)',\n", + " 38: '(5+(.5*(5!*.55)))',\n", + " 39: '(((5*5)-5.5)/.5)',\n", + " 40: '(55-(5+(5+5)))',\n", + " 41: '(5!-((5!/5)+55))',\n", + " 42: '((5+5.5)/(.5*.5))',\n", + " 43: '(55-(5!/(5+5)))',\n", + " 44: '(55-(55/5))',\n", + " 45: '((5*5!)-555)',\n", + " 46: '(55-((5-.5)/.5))',\n", + " 47: '((5!/5)+((5!-5)/5))',\n", + " 48: '(5!/(5*(5.5-5)))',\n", + " 49: '(55-(.5+5.5))',\n", + " 50: '(55.5-5.5)',\n", + " 51: '(.5+(55.5-5))',\n", + " 52: '(55-(.5+(.5*5)))',\n", + " 53: '(55.5-(.5*5))',\n", + " 54: '(((5*55)-5)/5)',\n", + " 55: '(.5*(55+55))',\n", + " 56: '((5+(5*55))/5)',\n", + " 57: '(55+((5+5)/5))',\n", + " 58: '((.5*5)+55.5)',\n", + " 59: '(5+(55-(5/5)))',\n", + " 60: '(5+(55.5-.5))',\n", + " 61: '(5.5+55.5)',\n", + " 62: '((55-(5!/5))/.5)',\n", + " 63: '(5.5+(.5*(5!-5)))',\n", + " 64: '(5!-(.5+55.5))',\n", + " 65: '(.5+(5!-55.5))',\n", + " 66: '(55+(55/5))',\n", + " 67: '(55+(5!/(5+5)))',\n", + " 68: '(5.5+(.5*(5+5!)))',\n", + " 69: '(5!-((.5+(5*5))/.5))',\n", + " 70: '(5+(5+(5+55)))',\n", + " 71: '((.5*5!)+(55/5))',\n", + " 72: '((.5+5.5)!/(5+5))',\n", + " 73: '((5*5)+(5!/(.5*5)))',\n", + " 74: '((5!/5)+(55-5))',\n", + " 75: '((5*5)+(55-5))',\n", + " 76: '(5+(5+(5!*.55)))',\n", + " 77: '(5+(.5*(5!+(5!/5))))',\n", + " 78: '(55+((5!-5)/5))',\n", + " 79: '(55+(5-(5/5))!)',\n", + " 80: '(5*(5+(55/5)))',\n", + " 81: '((√.5+(5!/√(5-.5)))/√.5)',\n", + " 82: '(5!-(((5!/5)-5)/.5))',\n", + " 83: '((.5*5!)+((5!-5)/5))',\n", + " 84: '(5+((5!/5)+55))',\n", + " 85: '(5+((5*5)+55))',\n", + " 86: '((55/.5)-(5!/5))',\n", + " 87: '((555-5!)/5)',\n", + " 88: '(.5+(.5*(5!+55)))',\n", + " 89: '(5!-(55-(5!/5)))',\n", + " 90: '(5!-(55-(5*5)))',\n", + " 91: '((5*5)+(5!*.55))',\n", + " 92: '(5!-(.5+(.5*55)))',\n", + " 93: '(.5+(5!-(.5*55)))',\n", + " 94: '(5!-((5/5)+(5*5)))',\n", + " 95: '(((55-5)/.5)-5)',\n", + " 96: '(5!-(5!/(5.5-.5)))',\n", + " 97: '(5!-((5!/5)-(5/5)))',\n", + " 98: '(5!-(55/(.5*5)))',\n", + " 99: '((55-5.5)/.5)',\n", + " 100: '((55/.5)-(5+5))',\n", + " 101: '((55.5-5)/.5)',\n", + " 102: '(5+(5!-((5!-5)/5)))',\n", + " 103: '(55+(5!/(.5*5)))',\n", + " 104: '(5!-(5+(55/5)))',\n", + " 105: '(55+(55-5))',\n", + " 106: '((555/5)-5)',\n", + " 107: '(5!-((5!-55)/5))',\n", + " 108: '(5!-((5+55)/5))',\n", + " 109: '(5!-(5.5+5.5))',\n", + " 110: '((555-5)/5)',\n", + " 111: '(555/√(5*5))',\n", + " 112: '((5+555)/5)',\n", + " 113: '(5!-(5+((5+5)/5)))',\n", + " 114: '(5+(5!-(55/5)))',\n", + " 115: '(5+(55+55))',\n", + " 116: '(5+(555/5))',\n", + " 117: '(5!-(5.5-(.5*5)))',\n", + " 118: '(5!-(5!/(5+55)))',\n", + " 119: '(5!-(55/55))',\n", + " 120: '(5.55-.55)!',\n", + " 121: '(5!+(55/55))',\n", + " 122: '(5!+(5!/(5+55)))',\n", + " 123: '(5!+(5.5-(.5*5)))',\n", + " 124: '(5!+√(5+(55/5)))',\n", + " 125: '(.5*(5*(55-5)))',\n", + " 126: '(5!+((55/5)-5))',\n", + " 127: '((5!/(5/5.5))-5)',\n", + " 128: '(5!+(5.5+(.5*5)))',\n", + " 129: '((5!-55.5)/.5)',\n", + " 130: '(5!+(55/5.5))',\n", + " 131: '(5!+(5.5+5.5))',\n", + " 132: '(5!*(.55+.55))',\n", + " 133: '(5!+((5!-55)/5))',\n", + " 134: '((5!/5)+(55/.5))',\n", + " 135: '((5!+555)/5)',\n", + " 136: '(5+(5!+(55/5)))',\n", + " 137: '(5+(5!/(5/5.5)))',\n", + " 138: '(.5+(.5*(5*55)))',\n", + " 139: '(((.5+5.5)!/5)-5)',\n", + " 140: '(.5*(5+(5*55)))',\n", + " 141: '(5!+((5+5.5)/.5))',\n", + " 142: '(5!+(55/(.5*5)))',\n", + " 143: '(((.5+5.5)!-5)/5)',\n", + " 144: '(((55/5)-5)!/5)',\n", + " 145: '(5!+(.5*(55-5)))',\n", + " 146: '(5!+((5/5)+(5*5)))',\n", + " 147: '(5!+((.5*55)-.5))',\n", + " 148: '(.5+(5!+(.5*55)))',\n", + " 149: '(5+((.5+5.5)!/5))',\n", + " 150: '(5*(55-(5*5)))',\n", + " 151: '(5!+(55-(5!/5)))',\n", + " 152: '(5!+(((5+5)/5)**5))',\n", + " 153: '(5!+(.5*(5!*.55)))',\n", + " 154: '(5+(5+(5!+(5!/5))))',\n", + " 155: '(5*(55-(5!/5)))',\n", + " 156: '((5!+(5!*5.5))/5)'}" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "\n", + "%time makeable(ff)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Wow! We almost tripled the 55 goal! I have to say, I would never have come up with the solution for 81 on my own. It works because (√(5 - .5) \\* √0.5) = √(4.5 \\* 0.5) = (√2.25) = 1.5." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Even More Operations \n", + "\n", + "At the risk of making the computation take even longer, I'm going to add two more operations:\n", + "\n", + "- **Floor**: ⌊*x*⌋ is the largest integer less than or equal to *x* (in other words, rounding down).\n", + "- **Ceiling**: ⌈*x*⌉ is the smallest integer greater than or equal to *x* (in other words, rounding up).\n", + "\n", + "These operations are useful because they produce integers, and our targets are the integers (from 0 up to whatever). \n", + "\n", + "In addition, I'll allow two consecutive applications of unary operators, thus allowing expressions such as\n", + "\n", + "- ⌊√5⌋ = 2\n", + "- ⌈5.5⌉! = 720\n", + "\n", + "But still not allowing three consecutive applications, such as\n", + "\n", + "- ⌈√5⌉! = 6\n", + "\n", + "To compensate for these new expressions, I'll be pickier about when I allow the square root function to apply." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import floor, ceil\n", + "\n", + "def unary_expressions(numbers):\n", + " for i in range(2):\n", + " for v in list(EXPS[numbers]):\n", + " exp = EXPS[numbers][v]\n", + " if 0 < v <= 100 and 4*v == round(4*v):\n", + " expr(numbers, sqrt(v), '√' + exp)\n", + " if 2 <= v <= 6 and v == round(v):\n", + " expr(numbers, factorial(v), exp + '!')\n", + " if v != round(v):\n", + " uexp = unbracket(exp)\n", + " expr(numbers, floor(v), '⌊' + uexp + '⌋')\n", + " expr(numbers, ceil(v), '⌈' + uexp + '⌉')\n", + " \n", + "def unbracket(exp):\n", + " \"Remove outer brackets from exp if they are there.\"\n", + " if exp.startswith('(') and exp.endswith(')'):\n", + " return exp[1:-1]\n", + " else:\n", + " return exp" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's try:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2min 25s, sys: 1.42 s, total: 2min 26s\n", + "Wall time: 2min 26s\n" + ] + }, + { + "data": { + "text/plain": [ + "{0: '⌊.55555⌋',\n", + " 1: '⌈.55555⌉',\n", + " 2: '⌊5*.5555⌋',\n", + " 3: '⌈5*.5555⌉',\n", + " 4: '⌊5-.5555⌋',\n", + " 5: '⌊5.5555⌋',\n", + " 6: '⌈5.5555⌉',\n", + " 7: '⌈.5+5.555⌉',\n", + " 8: '⌈√55+.555⌉',\n", + " 9: '⌊55/5.55⌋',\n", + " 10: '⌊555/55⌋',\n", + " 11: '⌈555/55⌉',\n", + " 12: '⌈55.55/5⌉',\n", + " 13: '⌈√5*5.555⌉',\n", + " 14: '⌈√55/.555⌉',\n", + " 15: 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'(55-⌈5*.55⌉)',\n", + " 53: '⌊55.55-√5⌋',\n", + " 54: '⌊55-.555⌋',\n", + " 55: '⌊55.555⌋',\n", + " 56: '⌈55.555⌉',\n", + " 57: '⌈.5+55.55⌉',\n", + " 58: '⌈√5+55.55⌉',\n", + " 59: '(5+⌊55-.55⌋)',\n", + " 60: '⌊5+55.55⌋',\n", + " 61: '⌈5+55.55⌉',\n", + " 62: '⌊√55+55.5⌋',\n", + " 63: '⌈√55+55.5⌉',\n", + " 64: '⌊5!-55.55⌋',\n", + " 65: '⌈5!-55.55⌉',\n", + " 66: '⌊5!*.5555⌋',\n", + " 67: '⌈5!*.5555⌉',\n", + " 68: '(5+⌈55+√55⌉)',\n", + " 69: '⌊555/⌈√55⌉⌋',\n", + " 70: '⌈555/⌈√55⌉⌉',\n", + " 71: '(5+⌊5!*.555⌋)',\n", + " 72: '(5+⌈5!*.555⌉)',\n", + " 73: '(5!-⌊55-√55⌋)',\n", + " 74: '⌊555/√55⌋',\n", + " 75: '⌈555/√55⌉',\n", + " 76: '(55+⌊5!/5.5⌋)',\n", + " 77: '(55+⌈5!/5.5⌉)',\n", + " 78: '⌊55.55/√.5⌋',\n", + " 79: '⌊555/⌊√55⌋⌋',\n", + " 80: '⌊(5*5)+55.5⌋',\n", + " 81: '⌈(5*5)+55.5⌉',\n", + " 82: '(55+⌊.5*55⌋)',\n", + " 83: '(55+⌈.5*55⌉)',\n", + " 84: '(5+((5!/5)+55))',\n", + " 85: '(5+(55+(5*5)))',\n", + " 86: '⌊⌈5+55.5⌉/√.5⌋',\n", + " 87: '((555-5!)/5)',\n", + " 88: '⌈√5**5.555⌉',\n", + " 89: '(5!-⌈.55*55⌉)',\n", + " 90: '⌊(55-5)/.55⌋',\n", + " 91: '⌈(55-5)/.55⌉',\n", + " 92: '⌊555/⌈5.5⌉⌋',\n", + " 93: '⌈555/⌈5.5⌉⌉',\n", + " 94: '(⌊55/.55⌋-5)',\n", + " 95: '(⌈55/.55⌉-5)',\n", + " 96: '⌊.55*(5!+55)⌋',\n", + " 97: '⌈.55*(5!+55)⌉',\n", + " 98: '(⌊55-5.5⌋/.5)',\n", + " 99: '⌊55/.555⌋',\n", + " 100: '⌊555/5.5⌋',\n", + " 101: '⌈555/5.5⌉',\n", + " 102: '⌈⌈55.5⌉/.55⌉',\n", + " 103: '⌊⌊√5+55⌋/.55⌋',\n", + " 104: '(5+⌊55/.55⌋)',\n", + " 105: '(55+(55-5))',\n", + " 106: '((555/5)-5)',\n", + " 107: '(55+⌊55-√5⌋)',\n", + " 108: '(5!-⌈55.5/5⌉)',\n", + " 109: '(55+⌊55-.5⌋)',\n", + " 110: '⌊55+55.5⌋',\n", + " 111: '⌈55+55.5⌉',\n", + " 112: '⌈555.5/5⌉',\n", + " 113: '(55+⌈√5+55⌉)',\n", + " 114: '⌊5!-5.555⌋',\n", + " 115: '⌈5!-5.555⌉',\n", + " 116: '(5+(555/5))',\n", + " 117: '(5!-⌈5*.555⌉)',\n", + " 118: '(5!-⌈5.55/5⌉)',\n", + " 119: '⌊5!-.5555⌋',\n", + " 120: '⌊5.5555⌋!',\n", + " 121: '⌈5!+.5555⌉',\n", + " 122: '(5!+⌈5.55/5⌉)',\n", + " 123: '⌊555/(5-.5)⌋',\n", + " 124: '⌊√5*55.55⌋',\n", + " 125: '⌊5!+5.555⌋',\n", + " 126: '⌈5!+5.555⌉',\n", + " 127: '⌊⌊5**5.5⌋/55⌋',\n", + " 128: '⌈⌊5**5.5⌋/55⌉',\n", + " 129: '(5!+⌊5/.555⌋)',\n", + " 130: '⌊√5.5*55.5⌋',\n", + " 131: '⌈√5.5*55.5⌉',\n", + " 132: '(5!+⌈55.5/5⌉)',\n", + " 133: '⌈55*(√55-5)⌉',\n", + " 134: '⌊55*√⌈5.55⌉⌋',\n", + " 135: '(5*⌊5*5.55⌋)',\n", + " 136: '⌈√⌈5.5⌉*55.5⌉',\n", + " 137: '⌊5.5*⌈55/√5⌉⌋',\n", + " 138: '⌊5*(5*5.55)⌋',\n", + " 139: '⌈5*(5*5.55)⌉',\n", + " 140: '(5*⌈5*5.55⌉)',\n", + " 141: '(5!+⌊5!/5.55⌋)',\n", + " 142: '(5!+⌈5!/5.55⌉)',\n", + " 143: '(5+⌈.5*(5*55)⌉)',\n", + " 144: '(⌈5.555⌉!/5)',\n", + " 145: '(5+(5*⌈.5*55⌉))',\n", + " 146: '⌊55*(5-√5.5)⌋',\n", + " 147: '(5!+⌊5*5.55⌋)',\n", + " 148: '(5!+⌈5*5.55⌉)',\n", + " 149: '⌈5.5*⌊.5*55⌋⌉',\n", + " 150: '(5*⌊.55*55⌋)',\n", + " 151: '⌊.55*(5*55)⌋',\n", + " 152: '⌈.55*(5*55)⌉',\n", + " 153: '⌊55*(√5+.55)⌋',\n", + " 154: '(5.5*⌈.5*55⌉)',\n", + " 155: '(5*⌈.55*55⌉)',\n", + " 156: '⌈(55+55)/√.5⌉',\n", + " 157: '(⌊.5*555⌋-5!)',\n", + " 158: '(⌈.5*555⌉-5!)',\n", + " 159: '(5!+⌊√.5*55.5⌋)',\n", + " 160: '(5*(5+⌊.5*55⌋))',\n", + " 161: '⌊(.5*5)**5.55⌋',\n", + " 162: '⌈(.5*5)**5.55⌉',\n", + " 163: '(⌊5!/.55⌋-55)',\n", + " 164: '(⌈5!/.55⌉-55)',\n", + " 165: '(55*⌈5*.55⌉)',\n", + " 166: '⌊⌈.5*5⌉*55.5⌋',\n", + " 167: '⌈⌈.5*5⌉*55.5⌉',\n", + " 168: '(5!+⌈55-√55⌉)',\n", + " 169: '(5!+⌊55-5.5⌋)',\n", + " 170: '(5!+⌊55.5-5⌋)',\n", + " 171: '(5!+⌈55.5-5⌉)',\n", + " 172: '⌈5.555**⌈√5⌉⌉',\n", + " 173: '⌊55*√⌊5+5.5⌋⌋',\n", + " 174: '(5!+⌊55-.55⌋)',\n", + " 175: '⌊5!+55.55⌋',\n", + " 176: '⌈5!+55.55⌉',\n", + " 177: '(55+⌊√5*55⌋)',\n", + " 178: '(55+⌈√5*55⌉)',\n", + " 179: '⌊55*(5.5-√5)⌋',\n", + " 180: '(5+⌊5!+55.5⌋)',\n", + " 181: '(5+⌈5!+55.5⌉)',\n", + " 182: '(⌊5.5*55⌋-5!)',\n", + " 183: '(⌈5.5*55⌉-5!)',\n", + " 184: '(5!+⌊5!-55.5⌋)',\n", + " 185: '(555/⌈.5*5⌉)',\n", + " 186: '⌈555.5/⌈√5⌉⌉',\n", + " 187: '(5!+⌈5!*.555⌉)',\n", + " 188: '((⌈.5*5⌉**5)-55)',\n", + " 189: '(⌊√55⌋*⌊.5*55⌋)',\n", + " 190: '(5*⌈5*√55.5⌉)',\n", + " 191: '⌈55*√⌊5+√55⌋⌉',\n", + " 192: '(⌈5.55⌉/(.5**5))',\n", + " 193: '⌊5!**(.55+.55)⌋',\n", + " 194: '⌊(555-5!)/√5⌋',\n", + " 195: '⌈(555-5!)/√5⌉',\n", + " 196: '(.5*⌊√.5*555⌋)',\n", + " 197: '⌈.5*⌈√.5*555⌉⌉',\n", + " 198: '(⌊55/.55⌋/.5)',\n", + " 199: '⌊55/(.5*.55)⌋',\n", + " 200: '(⌈55/.55⌉/.5)',\n", + " 201: '⌈555/(5-√5)⌉',\n", + " 202: '⌊555/(.5+√5)⌋',\n", + " 203: '⌊.5*⌊55*√55⌋⌋',\n", + " 204: '(.5*⌈55*√55⌉)',\n", + " 205: '(5*⌈5.5*√55⌉)',\n", + " 206: '⌈⌈5!-√55⌉/.55⌉',\n", + " 207: '⌊(5!-5)/.555⌋',\n", + " 208: '⌈(5!-5)/.555⌉',\n", + " 209: '(5.5*⌈5*√55⌉)',\n", + " 210: '⌈⌈5!-5.5⌉/.55⌉',\n", + " 211: '(⌊5!/.555⌋-5)',\n", + " 212: '(⌈5!/.555⌉-5)',\n", + " 213: '⌈⌊5!/.55⌋-5.5⌉',\n", + " 214: '⌈⌈5!/.55⌉-5.5⌉',\n", + " 215: '⌊⌊5!/.555⌋-.5⌋',\n", + " 216: '⌊5!/.5555⌋',\n", + " 217: '⌈5!/.5555⌉',\n", + " 218: '⌈.5*(555-5!)⌉',\n", + " 219: '(5!+⌊55/.55⌋)',\n", + " 220: '((5*55)-55)',\n", + " 221: '(5+⌊5!/.555⌋)',\n", + " 222: '(555/(.5*5))',\n", + " 223: '⌊5.5+⌊5!/.55⌋⌋',\n", + " 224: '⌊5.5+⌈5!/.55⌉⌋',\n", + " 225: '⌊(5+5!)/.555⌋',\n", + " 226: '⌈(5+5!)/.555⌉',\n", + " 227: '⌈555/√⌈5.5⌉⌉',\n", + " 228: '(⌊5!-5.55⌋/.5)',\n", + " 229: '⌈(5!-5.55)/.5⌉',\n", + " 230: '(5!+(55+55))',\n", + " 231: '(5!+(555/5))',\n", + " 232: '⌈(5!+√55)/.55⌉',\n", + " 233: '⌈⌈5!+√55⌉/.55⌉',\n", + " 234: '(5!+⌊5!-5.55⌋)',\n", + " 235: '(5*⌊55-√55⌋)',\n", + " 236: '⌊555/√5.5⌋',\n", + " 237: '⌈555/√5.5⌉',\n", + " 238: '⌈5*(55-√55)⌉',\n", + " 239: '(5!+⌊5!-.555⌋)',\n", + " 240: '(5*⌈55-√55⌉)',\n", + " 241: '(5!+⌈5!+.555⌉)',\n", + " 242: '(⌈5!+.555⌉/.5)',\n", + " 243: '(⌈5*.555⌉**5)',\n", + " 244: '⌊55*(5-.55)⌋',\n", + " 245: '(5*⌊55-5.5⌋)',\n", + " 246: '⌈(555-5)/√5⌉',\n", + " 247: '⌊5*(55-5.5)⌋',\n", + " 248: '⌊555.5/√5⌋',\n", + " 249: '⌈555.5/√5⌉',\n", + " 250: '(5*⌊55.5-5⌋)',\n", + " 251: '⌈(5+555)/√5⌉',\n", + " 252: '⌊5*(55.5-5)⌋',\n", + " 253: '⌈5*(55.5-5)⌉',\n", + " 254: '(5+⌈555/√5⌉)',\n", + " 255: '(5*⌈55.5-5⌉)',\n", + " 256: '(⌊55*√5.5⌋/.5)',\n", + " 257: '⌊55/(.5/√5.5)⌋',\n", + " 258: '(⌈55*√5.5⌉/.5)',\n", + " 259: '⌊5!/(55.5/5!)⌋',\n", + " 260: '(5*⌊55-√5.5⌋)',\n", + " 261: '⌈(5*.55)**5.5⌉',\n", + " 262: '⌈555/√(5-.5)⌉',\n", + " 263: '⌊5*(55-√5.5)⌋',\n", + " 264: '⌈5*(55-√5.5)⌉',\n", + " 265: '(5*⌈55-√5.5⌉)',\n", + " 266: '⌊5*(55.5-√5)⌋',\n", + " 267: '⌊(5*55)-√55⌋',\n", + " 268: '⌈(5*55)-√55⌉',\n", + " 269: '⌊(5*55)-5.5⌋',\n", + " 270: '(5*⌊55-.55⌋)',\n", + " 271: '(⌈.5-5⌉+(5*55))',\n", + " 272: '(⌊.5*555⌋-5)',\n", + " 273: '(⌈.5*555⌉-5)',\n", + " 274: '⌊(5*55)-.55⌋',\n", + " 275: '(5*⌊55.55⌋)',\n", + " 276: '⌈.55+(5*55)⌉',\n", + " 277: '⌊5*55.55⌋',\n", + " 278: '⌈5*55.55⌉',\n", + " 279: '⌈.5+⌈.5*555⌉⌉',\n", + " 280: '(5*⌈55.55⌉)',\n", + " 281: '⌈5.5+(5*55)⌉',\n", + " 282: '(5+⌊.5*555⌋)',\n", + " 283: '(5+⌈.5*555⌉)',\n", + " 284: '⌊5*((5**5)/55)⌋',\n", + " 285: '(5*⌊√5+55.5⌋)',\n", + " 286: '(5.5*⌊55-√5⌋)',\n", + " 287: '(555-⌊√5*5!⌋)',\n", + " 288: '(⌈55*√55⌉-5!)',\n", + " 289: '⌈55*√(.5*55)⌉',\n", + " 290: '(5*⌈√5+55.5⌉)',\n", + " 291: '⌊5.5*⌈55-√5⌉⌋',\n", + " 292: '⌈5.5*⌈55-√5⌉⌉',\n", + " 293: '⌊5!*√⌈5.555⌉⌋',\n", + " 294: '⌈5!*√⌈5.555⌉⌉',\n", + " 295: '(5!+⌊5!+55.5⌋)',\n", + " 296: '(5!+⌈5!+55.5⌉)',\n", + " 297: '(⌊5.5*55⌋-5)',\n", + " 298: '(⌈5.5*55⌉-5)',\n", + " 299: '⌊5.5*(55-.5)⌋',\n", + " 300: '(5*⌊5+55.5⌋)',\n", + " 301: '⌊⌊5.5*55⌋-.5⌋',\n", + " 302: '⌊5*(5+55.5)⌋',\n", + " 303: '⌈5*(5+55.5)⌉',\n", + " 304: '⌈.5+⌈5.5*55⌉⌉',\n", + " 305: '⌊.55*555⌋',\n", + " 306: '⌈.55*555⌉',\n", + " 307: '(5+⌊5.5*55⌋)',\n", + " 308: '(5+⌈5.5*55⌉)',\n", + " 309: '(⌈(√.5+5)*55⌉-5)',\n", + " 310: '(5*⌊55+√55⌋)',\n", + " 311: '⌈(√5**5)*5.55⌉',\n", + " 312: '⌊5*(55+√55)⌋',\n", + " 313: '⌈5*(55+√55)⌉',\n", + " 314: '⌈5.5*⌊√5+55⌋⌉',\n", + " 315: '(5*⌈55+√55⌉)',\n", + " 316: '⌊√(55/5.5)**5⌋',\n", + " 317: '⌈√(55/5.5)**5⌉',\n", + " 318: '⌊(5!+55)/.55⌋',\n", + " 319: '⌈(5!+55)/.55⌉',\n", + " 320: '(5*⌊5!-55.5⌋)',\n", + " 321: '⌊⌈5.555⌉!/√5⌋',\n", + " 322: '⌊5*(5!-55.5)⌋',\n", + " 323: '⌈5*(5!-55.5)⌉',\n", + " 324: '(⌈5.5⌉*⌊55-.5⌋)',\n", + " 325: '(5*⌈5!-55.5⌉)',\n", + " 326: '⌈(5!/55)**√55⌉',\n", + " 327: '(⌈5.5⌉*(55-.5))',\n", + " 328: '⌈.5*(55+(5*5!))⌉',\n", + " 329: '⌊(55*⌈5.5⌉)-.5⌋',\n", + " 330: '(55*⌈5.55⌉)',\n", + " 331: '⌈.5+(55*⌈5.5⌉)⌉',\n", + " 332: '⌊.55*(5+(5*5!))⌋',\n", + " 333: '(⌈5.5⌉*55.5)',\n", + " 334: '⌈5*(5!*.555)⌉',\n", + " 335: '(5*⌈5!*.555⌉)',\n", + " 336: '(5!+⌊5!/.555⌋)',\n", + " 337: '⌊.5*(5!+555)⌋',\n", + " 338: '⌈.5*(5!+555)⌉',\n", + " 339: '⌊55*√⌈5*√55⌉⌋',\n", + " 340: '⌈55*√⌈5*√55⌉⌉',\n", + " 341: '⌊55*(√.5+5.5)⌋',\n", + " 342: '⌈55*(√.5+5.5)⌉',\n", + " 343: '⌊5*(.55*(5+5!))⌋',\n", + " 344: '⌈5*(.55*(5+5!))⌉',\n", + " 345: '(5*⌈.55*(5+5!)⌉)',\n", + " 346: '(⌊55*√(5+5)⌋/.5)',\n", + " 347: '⌊5!*(.55+√5.5)⌋',\n", + " 348: '(⌈5.5⌉*⌈√5+55⌉)',\n", + " 349: '(⌊(5-.55)**5⌋/5)',\n", + " 350: '(⌊5!+55.5⌋/.5)',\n", + " 351: '((5!+55.5)/.5)',\n", + " 352: '(⌈5!+55.5⌉/.5)',\n", + " 353: '⌈⌈555/√5⌉/√.5⌉',\n", + " 354: '⌊(.5*⌈5.5⌉!)-5.5⌋',\n", + " 355: '(5*(5+(5!*.55)))',\n", + " 356: '⌈(55/5)**√⌈5.5⌉⌉',\n", + " 357: '⌊5.5*(5!-55)⌋',\n", + " 358: '⌈5.5*(5!-55)⌉',\n", + " 359: '⌊.5*⌊⌈5.55⌉!-.5⌋⌋',\n", + " 360: '(.5*⌈5.555⌉!)',\n", + " 361: '⌊(√5+5)*(55-5)⌋',\n", + " 362: '⌊.5*(5+⌈5.55⌉!)⌋',\n", + " 363: '(5.5*(5!*.55))',\n", + " 364: '⌈5!*(.55*5.5)⌉',\n", + " 365: '(5+(.5*⌈5.55⌉!))',\n", + " 366: '(5!*(.55+(.5*5)))',\n", + " 367: '(5!+⌊55*(5-.5)⌋)',\n", + " 368: '(5!+⌊555/√5⌋)',\n", + " 369: '(5!+⌈555/√5⌉)',\n", + " 370: '⌊√55*(55-5)⌋',\n", + " 371: '⌈√55*(55-5)⌉',\n", + " 372: '(55+⌈√(5+5)**5⌉)',\n", + " 373: '⌊55*√⌈5.5**√5⌉⌋',\n", + " 374: '⌈55*√⌈5.5**√5⌉⌉',\n", + " 375: '(5*⌈(5+5)*√55⌉)',\n", + " 376: '(55+⌊⌈5.5⌉!/√5⌋)',\n", + " 377: '(55+⌈⌈5.5⌉!/√5⌉)',\n", + " 378: '(⌊√55⌋*⌊55-.5⌋)',\n", + " 379: '⌊5!*√(55/5.5)⌋',\n", + " 380: '⌊55*(√55-.5)⌋',\n", + " 381: '⌈55*(√55-.5)⌉',\n", + " 382: '⌈55**(√55/5)⌉',\n", + " 383: '(5!+⌊5*(55-√5)⌋)',\n", + " 384: '⌊(55*⌊√55⌋)-.5⌋',\n", + " 385: '(55*⌊√55.5⌋)',\n", + " 386: '(555-⌊5!/√.5⌋)',\n", + " 387: '(⌊√.5*555⌋-5)',\n", + " 388: '⌊⌊√55⌋*55.5⌋',\n", + " 389: '⌈⌊√55⌋*55.5⌉',\n", + " 390: '(5*⌊55.5/√.5⌋)',\n", + " 391: '⌊⌊√.5*555⌋-.5⌋',\n", + " 392: '⌊√.5*555.5⌋',\n", + " 393: '⌈√.5*555.5⌉',\n", + " 394: '⌈√.5*⌈555.5⌉⌉',\n", + " 395: '⌊√.5*(5+555)⌋',\n", + " 396: '⌊.55*⌈5.55⌉!⌋',\n", + " 397: '(5!+⌊.5*555⌋)',\n", + " 398: '(5!+⌈.5*555⌉)',\n", + " 399: '⌊⌈5.5⌉!*.555⌋',\n", + " 400: '⌈⌈5.5⌉!*.555⌉',\n", + " 401: '⌊(√5+5)*55.5⌋',\n", + " 402: '(⌊55*√55⌋-5)',\n", + " 403: '(⌈55*√55⌉-5)',\n", + " 404: '⌊√55*(55-.5)⌋',\n", + " 405: '⌈√55*(55-.5)⌉',\n", + " 406: '⌊⌊55*√55⌋-.5⌋',\n", + " 407: '⌊55*√⌊55.5⌋⌋',\n", + " 408: '⌈55*√⌊55.5⌋⌉',\n", + " 409: '⌊55*√55.5⌋',\n", + " 410: '⌈55*√55.5⌉',\n", + " 411: '⌊√55*55.5⌋',\n", + " 412: '⌈√55*55.5⌉',\n", + " 413: '(5+⌈55*√55⌉)',\n", + " 414: '⌈√55.5**⌈.5*5⌉⌉',\n", + " 415: '⌊√55*⌈55.5⌉⌋',\n", + " 416: '⌈√55*⌈55.5⌉⌉',\n", + " 417: '⌊5*(5**(5*.55))⌋',\n", + " 418: '⌊55*√⌈√5+55⌉⌋',\n", + " 419: '⌊(5**5)/√55.5⌋',\n", + " 420: '⌊⌈5*.55⌉**5.5⌋',\n", + " 421: '⌈⌈5*.55⌉**5.5⌉',\n", + " 422: '(5!+⌊5.5*55⌋)',\n", + " 423: '(5!+⌈5.5*55⌉)',\n", + " 424: '⌈5.5*⌊55/√.5⌋⌉',\n", + " 425: '⌊55*(√5+5.5)⌋',\n", + " 426: '⌊55*√(5+55)⌋',\n", + " 427: '⌈55*√(5+55)⌉',\n", + " 428: '⌊⌈5.5*55⌉/√.5⌋',\n", + " 429: '(5.5*⌈55/√.5⌉)',\n", + " 430: '(555-(5+5!))',\n", + " 431: '⌈√55*⌈√5+55⌉⌉',\n", + " 432: '(555-⌈√5+5!⌉)',\n", + " 433: '(555-⌊√5+5!⌋)',\n", + " 434: '(555-⌈.5+5!⌉)',\n", + " 435: '⌊555.5-5!⌋',\n", + " 436: '⌈555.5-5!⌉',\n", + " 437: '(⌊√5-5!⌋+555)',\n", + " 438: '(⌈√5-5!⌉+555)',\n", + " 439: '⌊(⌈√55⌉*55)-.5⌋',\n", + " 440: '(5+(555-5!))',\n", + " 441: '⌈.5+(⌈√55⌉*55)⌉',\n", + " 442: '(5+⌈5!/(.5*.55)⌉)',\n", + " 443: '⌊55*√(5!-55)⌋',\n", + " 444: '(⌈√55⌉*55.5)',\n", + " 445: '⌈√55*(5+55)⌉',\n", + " 446: '⌊55*√(5!*.55)⌋',\n", + " 447: '⌊⌈√5⌉**5.555⌋',\n", + " 448: '⌈⌈√5⌉**5.555⌉',\n", + " 449: '⌈55*(5+√(5+5))⌉',\n", + " 450: '(5!+(55*⌈5.5⌉))',\n", + " 451: '⌊5!*(⌈5.55⌉-√5)⌋',\n", + " 452: '⌊55*(√5+⌈5.5⌉)⌋',\n", + " 453: '⌈55*(√5+⌈5.5⌉)⌉',\n", + " 454: '(⌊(5+5!)/.55⌋/.5)',\n", + " 455: '(⌊√55⌋*(5!-55))',\n", + " 456: '⌊5.5*⌊√5**5.5⌋⌋',\n", + " 457: '⌈5.5*⌊√5**5.5⌋⌉',\n", + " 458: '(⌊5-.5⌋*(5!-5.5))',\n", + " 459: '⌊555/(.5+√.5)⌋',\n", + " 460: '⌈555/(.5+√.5)⌉',\n", + " 461: '⌈55*√⌊√5.5**5⌋⌉',\n", + " 462: '(5.5*⌈√5**5.5⌉)',\n", + " 463: '⌈5*(5!-(.5*55))⌉',\n", + " 464: '(⌈√55⌉*⌈√5+55⌉)',\n", + " 465: '(5*(5!-⌊.5*55⌋))',\n", + " 466: '⌊⌊√.5*5!⌋*5.55⌋',\n", + " 467: '⌊55*(.5+⌈√55⌉)⌋',\n", + " 468: '(5!*(5-(5.5/5)))',\n", + " 469: '⌊55*(5+(√.5*5))⌋',\n", + " 470: '(555-⌈√.5*5!⌉)',\n", + " 471: '(555-⌊√.5*5!⌋)',\n", + " 472: '⌈⌈√.5*5!⌉*5.55⌉',\n", + " 473: '(5.5*⌈5**(5-√5)⌉)',\n", + " 474: '(5!*(5-(.5+.55)))',\n", + " 475: '((5!*⌊5-.55⌋)-5)',\n", + " 476: '(55+⌈⌈√5⌉**5.5⌉)',\n", + " 477: '⌊√.5*(5!+555)⌋',\n", + " 478: '⌈√.5*(5!+555)⌉',\n", + " 479: '((5*5!)-⌈5!+.55⌉)',\n", + " 480: '(5!*⌊5-.555⌋)',\n", + " 481: '((5*5!)-⌊5!-.55⌋)',\n", + " 482: '⌊√55*(5!-55)⌋',\n", + " 483: '⌈√55*(5!-55)⌉',\n", + " 484: '⌈(√5*5!)/.555⌉',\n", + " 485: '⌊√5*⌈5!/.555⌉⌋',\n", + " 486: '⌈√5*⌈5!/.555⌉⌉',\n", + " 487: '⌊5!/(.55**√5.5)⌋',\n", + " 488: '⌊.55*⌊5!*√55⌋⌋',\n", + " 489: '⌊.55*⌈5!*√55⌉⌋',\n", + " 490: '⌈.55*⌈5!*√55⌉⌉',\n", + " 491: '⌈5!*((5/.55)-5)⌉',\n", + " 492: '(⌊5-.5⌋*⌈√5*55⌉)',\n", + " 493: '⌈(⌊5/.55⌋**5)/5!⌉',\n", + " 494: '(⌊55*(5-.5)⌋/.5)',\n", + " 495: '(5*⌊55/.55⌋)',\n", + " 496: '(⌊555/√5⌋/.5)',\n", + " 497: '⌈555/(.5*√5)⌉',\n", + " 498: '(⌈555/√5⌉/.5)',\n", + " 499: '⌊5*(55/.55)⌋',\n", + " 500: '(555-55)',\n", + " 501: '(555-⌈5!/√5⌉)',\n", + " 502: '(555-⌊5!/√5⌋)',\n", + " 503: '⌊⌊5.5**5⌋/(5+5)⌋',\n", + " 504: '⌈⌊5.5**5⌋/(5+5)⌉',\n", + " 505: '(5!+(55*⌊√55⌋))',\n", + " 506: '⌊(5-.5)*(5!-√55)⌋',\n", + " 507: '(⌊5*(5!+5.5)⌋-5!)',\n", + " 508: '(⌈5*(5!+5.5)⌉-5!)',\n", + " 509: '⌊√.5*⌈5.555⌉!⌋',\n", + " 510: '⌈√.5*⌈5.555⌉!⌉',\n", + " 511: '⌈⌊5!*√5.5⌋/.55⌉',\n", + " 512: '(5!+⌊√.5*555⌋)',\n", + " 513: '(5!+⌈√.5*555⌉)',\n", + " 514: '⌈√5.5*⌈5!/.55⌉⌉',\n", + " 515: '(5!+(5!+(5*55)))',\n", + " 516: '(5!+⌊.55*⌈5.5⌉!⌋)',\n", + " 517: '(5!+⌈.55*⌈5.5⌉!⌉)',\n", + " 518: '(555-⌈5**√5⌉)',\n", + " 519: '(555-⌊5**√5⌋)',\n", + " 520: '((5*(5!-5))-55)',\n", + " 521: '⌈(5**5)/⌈5.55⌉⌉',\n", + " 522: '⌊55*(5+(5-.5))⌋',\n", + " 523: '⌈55*(5+(5-.5))⌉',\n", + " 524: '(⌈5!*(5!/55)⌉/.5)',\n", + " 525: '(5*((55/.5)-5))',\n", + " 526: '(⌊5*(55-√5)⌋/.5)',\n", + " 527: '(5!+⌊55*√55⌋)',\n", + " 528: '(5!+⌈55*√55⌉)',\n", + " 529: '((5!*(5-.55))-5)',\n", + " 530: '(555-(5*5))',\n", + " 531: '(555-(5!/5))',\n", + " 532: '⌊5**(5-(5.5/5))⌋',\n", + " 533: '⌊5!*(5-.555)⌋',\n", + " 534: '⌈5!*(5-.555)⌉',\n", + " 535: '(55+(5!*⌊5-.5⌋))',\n", + " 536: '⌈(5-.5)*⌊5!-.55⌋⌉',\n", + " 537: '⌊5.5*((.5*5)**5)⌋',\n", + " 538: '⌈5.5*((.5*5)**5)⌉',\n", + " 539: '(5+(5!*(5-.55)))',\n", + " 540: '((5+5)*⌊55-.5⌋)',\n", + " 541: '⌈.55+(5!*(5-.5))⌉',\n", + " 542: '(⌊5*(5!-.5)⌋-55)',\n", + " 543: '(555-⌈√5*5⌉)',\n", + " 544: '(555-⌊√5*5⌋)',\n", + " 545: '(555-(5+5))',\n", + " 546: '((5!*5.55)-5!)',\n", + " 547: '⌊555-√55⌋',\n", + " 548: '⌈555-√55⌉',\n", + " 549: '⌊555-5.5⌋',\n", + " 550: '⌈555-5.5⌉',\n", + " 551: '⌈555.5-5⌉',\n", + " 552: '⌊555-√5.5⌋',\n", + " 553: '⌊555.5-√5⌋',\n", + " 554: '⌊555-.55⌋',\n", + " 555: '⌊555.55⌋',\n", + " 556: '⌈555.55⌉',\n", + " 557: '⌊√5+555.5⌋',\n", + " 558: '⌈√5+555.5⌉',\n", + " 559: '(5+⌊555-.5⌋)',\n", + " 560: '⌊5+555.5⌋',\n", + " 561: '⌈5+555.5⌉',\n", + " 562: '⌊√55+555⌋',\n", + " 563: '⌈√55+555⌉',\n", + " 564: '⌈(5**5)/5.55⌉',\n", + " 565: '(5+(5+555))',\n", + " 566: '(⌊√5*5⌋+555)',\n", + " 567: '(⌈√5*5⌉+555)',\n", + " 568: '(⌈5*(5!-5.5)⌉-5)',\n", + " 569: '⌊(5*(5!-5))-5.5⌋',\n", + " 570: '(5*⌊5!-5.55⌋)',\n", + " 571: '⌊√55*⌊55/√.5⌋⌋',\n", + " 572: '⌊5*(5!-5.55)⌋',\n", + " 573: '⌈5*(5!-5.55)⌉',\n", + " 574: '(5+⌈(5**5)/5.5⌉)',\n", + " 575: '(5*⌈5!-5.55⌉)',\n", + " 576: '⌈.55+(5*(5!-5))⌉',\n", + " 577: '⌊55*(5+5.5)⌋',\n", + " 578: '⌈55*(5+5.5)⌉',\n", + " 579: '((5!/5)+555)',\n", + " 580: '((5*5)+555)',\n", + " 581: '⌈5.5+(5*(5!-5))⌉',\n", + " 582: '⌈5!*(5.55-√.5)⌉',\n", + " 583: '(55/(5/⌊5!/√5⌋))',\n", + " 584: '⌈5*(5!-√(55/5))⌉',\n", + " 585: '(5*(5!-⌈5*.55⌉))',\n", + " 586: '⌊5*(5!-(5*.55))⌋',\n", + " 587: '((⌊√5⌋**5)+555)',\n", + " 588: '⌈5!*√⌊5-.555⌋!⌉',\n", + " 589: '((5*5!)-(55/5))',\n", + " 590: '⌈5!*(5-(5/55))⌉',\n", + " 591: '(⌊5**√5⌋+555)',\n", + " 592: '(⌈5**√5⌉+555)',\n", + " 593: '⌈(5*5!)-√55.5⌉',\n", + " 594: '⌊(5*5!)-5.55⌋',\n", + " 595: '(5*⌊5!-.555⌋)',\n", + " 596: '⌈√(5+5)**5.55⌉',\n", + " 597: '⌊5*(5!-.555)⌋',\n", + " 598: '⌈5*(5!-.555)⌉',\n", + " 599: '⌊(5*5!)-.555⌋',\n", + " 600: '(5*⌊5.555⌋!)',\n", + " 601: '⌈(5*5!)+.555⌉',\n", + " 602: '⌊5*(5!+.555)⌋',\n", + " 603: '⌈5*(5!+.555)⌉',\n", + " 604: '(⌊5.5*55⌋/.5)',\n", + " 605: '(55*(55/5))',\n", + " 606: '(⌈5.5*55⌉/.5)',\n", + " 607: '⌊(5*5!)+√55.5⌋',\n", + " 608: '(⌊5!/√5⌋+555)',\n", + " 609: '(⌈5!/√5⌉+555)',\n", + " 610: '(55+555)',\n", + " 611: '(⌈√5**5⌉+555)',\n", + " 612: '(5+⌊(5*5!)+√55⌋)',\n", + " 613: '⌊5*(5!+(5*.55))⌋',\n", + " 614: '(((5**5)-55)/5)',\n", + " 615: '((.5*5!)+555)',\n", + " 616: '(5.5*⌊5!-√55⌋)',\n", + " 617: '⌊5*(.5+⌈√5*55⌉)⌋',\n", + " 618: '⌈5*(.5+⌈√5*55⌉)⌉',\n", + " 619: '⌊√5*⌊.5*555⌋⌋',\n", + " 620: '(5*⌊√5*55.5⌋)',\n", + " 621: '(.5*⌈√5*555⌉)',\n", + " 622: '⌈√5*⌈.5*555⌉⌉',\n", + " 623: '⌊5!*√⌊5*5.55⌋⌋',\n", + " 624: '⌈5!*√⌊5*5.55⌋⌉',\n", + " 625: '(5**⌊5-.555⌋)',\n", + " 626: '(⌊5.5+(5**5)⌋/5)',\n", + " 627: '⌊5*(5!+5.55)⌋',\n", + " 628: '⌈5*(5!+5.55)⌉',\n", + " 629: '⌊5.5*(5!-5.5)⌋',\n", + " 630: '(5*⌈5!+5.55⌉)',\n", + " 631: '⌈5.5+(5*(5+5!))⌉',\n", + " 632: '⌊5.5*⌈5!-5.5⌉⌋',\n", + " 633: '⌈5.5*⌈5!-5.5⌉⌉',\n", + " 634: '⌊5!*√⌈5*5.55⌉⌋',\n", + " 635: '(5*⌊5!+√55.5⌋)',\n", + " 636: '(((5**5)+55)/5)',\n", + " 637: '⌊5*(5!+√55.5)⌋',\n", + " 638: '⌊(5!-5)*5.55⌋',\n", + " 639: '⌈(5!-5)*5.55⌉',\n", + " 640: '(5*⌊55*√5.5⌋)',\n", + " 641: '⌈.5+(5*⌈5!+√55⌉)⌉',\n", + " 642: '(5+⌊5*(5!+√55)⌋)',\n", + " 643: '⌊5.5*⌊5!-√5.5⌋⌋',\n", + " 644: '⌊5*(55*√5.5)⌋',\n", + " 645: '(5*⌈55*√5.5⌉)',\n", + " 646: '⌈5*(5!+(5/.55))⌉',\n", + " 647: '⌊5.5*(5!-√5.5)⌋',\n", + " 648: '(5!*(⌊.5*55⌋/5))',\n", + " 649: '⌊⌊5!-√5⌋*5.55⌋',\n", + " 650: '((5+5)*(5!-55))',\n", + " 651: '(⌈√5⌉*⌈5!/.555⌉)',\n", + " 652: '⌊(5!*5.5)-√55⌋',\n", + " 653: '⌊(5!-√5)*5.55⌋',\n", + " 654: '⌊5.5*⌊5!-.55⌋⌋',\n", + " 655: '⌊(5*5!)+55.5⌋',\n", + " 656: '⌈(5*5!)+55.5⌉',\n", + " 657: '⌈5.5*(5!-.55)⌉',\n", + " 658: '⌈5!*√⌊.55*55⌋⌉',\n", + " 659: '⌊(5!*5.5)-.55⌋',\n", + " 660: '(5.5*⌊5.55⌋!)',\n", + " 661: '((5!*5.55)-5)',\n", + " 662: '⌊(5!-√.5)*5.55⌋',\n", + " 663: '⌊5.5*(5!+.55)⌋',\n", + " 664: '⌊⌈5.5⌉!-55.5⌋',\n", + " 665: '(⌈5.55⌉!-55)',\n", + " 666: '⌊5!*5.555⌋',\n", + " 667: '⌈5!*5.555⌉',\n", + " 668: '⌊(.5+5!)*5.55⌋',\n", + " 669: '⌈(.5+5!)*5.55⌉',\n", + " 670: '(5!+(555-5))',\n", + " 671: '(5+(5!*5.55))',\n", + " 672: '(5!+⌊555-√5⌋)',\n", + " 673: '(5!+⌈555-√5⌉)',\n", + " 674: '(5!+⌊555-.5⌋)',\n", + " 675: '⌊5!+555.5⌋',\n", + " 676: '⌈5!+555.5⌉',\n", + " 677: '(5!+⌊√5+555⌋)',\n", + " 678: '(5!+⌈√5+555⌉)',\n", + " 679: '⌈(5.5**5)/√55⌉',\n", + " 680: '(5+(5!+555))',\n", + " 681: '⌈5!*(5+(5/√55))⌉',\n", + " 682: '⌊55*(5+√55)⌋',\n", + " 683: '⌈55*(5+√55)⌉',\n", + " 684: '(⌈5.5⌉*⌊5!-5.5⌋)',\n", + " 685: '(5*⌊.5*(5*55)⌋)',\n", + " 686: '⌊(√5-⌈.5⌉)*555⌋',\n", + " 687: '⌊5.5*⌊5!+5.5⌋⌋',\n", + " 688: '⌈5.5*⌊5!+5.5⌋⌉',\n", + " 689: '(5!+⌈(5**5)/5.5⌉)',\n", + " 690: '⌊5.5*(5!+5.5)⌋',\n", + " 691: '⌈5.5*(5!+5.5)⌉',\n", + " 692: '(5+⌊5.5*(5+5!)⌋)',\n", + " 693: '⌊(5+5!)*5.55⌋',\n", + " 694: '⌈(5+5!)*5.55⌉',\n", + " 695: '(⌈5.55⌉!-(5*5))',\n", + " 696: '(⌈5.55⌉!-(5!/5))',\n", + " 697: '(⌈(.5*√55)**5⌉-5)',\n", + " 698: '⌊5.5*⌊5!+√55⌋⌋',\n", + " 699: '⌈5.5*⌊5!+√55⌋⌉',\n", + " 700: '(5*(5*⌈.5*55⌉))',\n", + " 701: '⌈5.5*(5!+√55)⌉',\n", + " 702: '⌊(5**5)/(5-.55)⌋',\n", + " 703: '⌈(5**5)/(5-.55)⌉',\n", + " 704: '(5.5*⌈5!+√55⌉)',\n", + " 705: '(5*(5!+⌊5!/5.5⌋))',\n", + " 706: '⌊(5!-√5)*⌈5.55⌉⌋',\n", + " 707: '(⌈5.5⌉!-⌈5+√55⌉)',\n", + " 708: '(⌈5!-√5⌉*⌈5.55⌉)',\n", + " 709: '(⌈5.5⌉!-(55/5))',\n", + " 710: '(⌈5.55⌉!-(5+5))',\n", + " 711: '(⌈5.5⌉!-⌊5/.55⌋)',\n", + " 712: '⌊⌈5.55⌉!-√55⌋',\n", + " 713: '⌈⌈5.55⌉!-√55⌉',\n", + " 714: '⌊⌈5.55⌉!-5.5⌋',\n", + " 715: '(⌈5.555⌉!-5)',\n", + " 716: '(⌈5.5⌉!-⌊5-.55⌋)',\n", + " 717: '⌊⌈5.555⌉!-√5⌋',\n", + " 718: '⌈⌈5.555⌉!-√5⌉',\n", + " 719: '⌊⌈5.555⌉!-.5⌋',\n", + " 720: '⌈5.5555⌉!',\n", + " 721: '⌈.5+⌈5.555⌉!⌉',\n", + " 722: '⌊√5+⌈5.555⌉!⌋',\n", + " 723: '⌈√5+⌈5.555⌉!⌉',\n", + " 724: '(⌊5!/√.5⌋+555)',\n", + " 725: '(5+⌈5.555⌉!)',\n", + " 726: '⌈5.5+⌈5.55⌉!⌉',\n", + " 727: '⌊√55+⌈5.55⌉!⌋',\n", + " 728: '⌈√55+⌈5.55⌉!⌉',\n", + " 729: '(⌈√5⌉**⌈5.555⌉)',\n", + " 730: '(5+(5+⌈5.55⌉!))',\n", + " 731: '(⌈5.5⌉!+(55/5))',\n", + " 732: '(5!*(5+(5.5/5)))',\n", + " 733: '(5+⌈⌈5.5⌉!+√55⌉)',\n", + " 734: '(5!+⌊√5*(5*55)⌋)',\n", + " 735: '(5*(5!+⌊.5*55⌋))',\n", + " 736: '⌊√5.5**√(5+55)⌋',\n", + " 737: '⌊5*(5!+(.5*55))⌋',\n", + " 738: '(⌈5.5⌉*⌈√5*55⌉)',\n", + " 739: '⌊5!*√⌈5*√55.5⌉⌋',\n", + " 740: '(5*(5!+⌈.5*55⌉))',\n", + " 741: '(⌈5.5⌉!+⌊5!/5.5⌋)',\n", + " 742: '(⌈5.5⌉!+⌈5!/5.5⌉)',\n", + " 743: '⌊⌊5!**√5⌋/(5+55)⌋',\n", + " 744: '((5!/5)+⌈5.55⌉!)',\n", + " 745: '((5*5)+⌈5.55⌉!)',\n", + " 746: '(5!+((5+(5**5))/5))',\n", + " 747: '(⌈5.5⌉!+⌊.5*55⌋)',\n", + " 748: '(⌈5.5⌉!+⌈.5*55⌉)',\n", + " 749: '⌈5!*(√5+⌊5-.55⌋)⌉',\n", + " 750: '((5+5!)*⌈5.55⌉)',\n", + " 751: '⌈5!*(√.5+5.55)⌉',\n", + " 752: '(5!+⌊5.5*(5!-5)⌋)',\n", + " 753: '(⌈5.5⌉*(5!+5.5))',\n", + " 754: '(5!+⌊5!*√⌈.5*55⌉⌋)',\n", + " 755: '((5*(5!+55))-5!)',\n", + " 756: '(⌈5.5⌉*⌈5!+5.5⌉)',\n", + " 757: '(⌈5.5⌉!+⌊5*√55⌋)',\n", + " 758: '(⌈5.5⌉!+⌈5*√55⌉)',\n", + " 759: '⌈5!*√⌊5.5*√55⌋⌉',\n", + " 760: '(5*⌊55*(5-√5)⌋)',\n", + " 761: '⌈5*(55*(5-√5))⌉',\n", + " 762: '(⌈5.5⌉*⌊5!+√55⌋)',\n", + " 763: '⌈5*(5!**(.5+.55))⌉',\n", + " 764: '⌊⌈5.5⌉*(5!+√55)⌋',\n", + " 765: '(5*⌈55*(5-√5)⌉)',\n", + " 766: '⌈(⌈√5⌉**5.5)/.55⌉',\n", + " 767: '⌈((5*5)-5.5)**√5⌉',\n", + " 768: '⌊√⌈5.55⌉**√55⌋',\n", + " 769: '⌊55**√(5*.55)⌋',\n", + " 770: '(55*⌊√55/.5⌋)',\n", + " 771: '⌈(5*5.55)**⌊√5⌋⌉',\n", + " 772: '(55+⌊⌈5.5⌉!-√5⌋)',\n", + " 773: '(⌊5!*√55.5⌋-5!)',\n", + " 774: '(55+⌊⌈5.5⌉!-.5⌋)',\n", + " 775: '(55+⌈5.55⌉!)',\n", + " 776: '⌈⌈5.5⌉!+55.5⌉',\n", + " 777: '⌊(555-5)/√.5⌋',\n", + " 778: '⌈(555-5)/√.5⌉',\n", + " 779: '(⌊555/√.5⌋-5)',\n", + " 780: '(⌈555/√.5⌉-5)',\n", + " 781: '⌊(5**5)/⌊5-.55⌋⌋',\n", + " 782: '⌈(5**5)/⌊5-.55⌋⌉',\n", + " 783: '⌊⌊555/√.5⌋-.5⌋',\n", + " 784: '⌊√⌊.5*5⌋*555⌋',\n", + " 785: '⌊555.5/√.5⌋',\n", + " 786: '⌈555.5/√.5⌉',\n", + " 787: '⌈⌈555.5⌉/√.5⌉',\n", + " 788: '⌈(5-.5)*(5!+55)⌉',\n", + " 789: '(5+⌊555/√.5⌋)',\n", + " 790: '(5+⌈555/√.5⌉)',\n", + " 791: '⌊(5+555)/√.5⌋',\n", + " 792: '⌈(5+555)/√.5⌉',\n", + " 793: '⌈⌈5.5⌉!*(5.5/5)⌉',\n", + " 794: '(⌈.55*⌈5.5⌉!⌉/.5)',\n", + " 795: '(5!+(5!+555))',\n", + " 796: '⌈55**(5/⌈.5*5⌉)⌉',\n", + " 797: '⌊5.5*(5!+(5*5))⌋',\n", + " 798: '((⌈√5⌉**5)+555)',\n", + " 799: '⌈5!*(5+√(5*.55))⌉',\n", + " 800: '(5*((⌈√5⌉*55)-5))',\n", + " 801: '⌊⌊√55⌋*(5!-5.5)⌋',\n", + " 802: '⌈⌊√55⌋*(5!-5.5)⌉',\n", + " 803: '⌊⌊5!**√5⌋/55.5⌋',\n", + " 804: '⌈⌊5!**√5⌋/55.5⌉',\n", + " 805: '((5!-5)*⌊√55.5⌋)',\n", + " 806: '⌊(5-.5)**(5-.55)⌋',\n", + " 807: '(5!+⌊5.5*(5+5!)⌋)',\n", + " 808: '(5!+⌈5.5*(5+5!)⌉)',\n", + " 809: '(⌊5!*√(5+55)⌋-5!)',\n", + " 810: '(⌈√5⌉*((5*55)-5))',\n", + " 811: '⌈(5+(5!**√5))/55⌉',\n", + " 812: '⌈(5*⌊5-.55⌋)**√5⌉',\n", + " 813: '(⌊5!*(√5+5)⌋-55)',\n", + " 814: '(⌊55*√55⌋/.5)',\n", + " 815: '⌊55/(.5/√55)⌋',\n", + " 816: '(⌈55*√55⌉/.5)',\n", + " 817: '⌊5**(5/(⌈5.5⌉/5))⌋',\n", + " 818: '((5*5!)+⌊5!/.55⌋)',\n", + " 819: '((5*5!)+⌈5!/.55⌉)',\n", + " 820: '((⌈√5⌉*(5*55))-5)',\n", + " 821: '⌊5!/(√.5**5.55)⌋',\n", + " 822: '⌊5!*√⌊55-√55⌋⌋',\n", + " 823: '(⌊√5*5!⌋+555)',\n", + " 824: '(⌈√5*5!⌉+555)',\n", + " 825: '(55*(5+(5+5)))',\n", + " 826: '⌊(5*5!)**(.5+.55)⌋',\n", + " 827: '⌊(5-.55)**(5-.5)⌋',\n", + " 828: '⌈(5-.55)**(5-.5)⌉',\n", + " 829: '⌈(√5+5)*(5!-5.5)⌉',\n", + " 830: '(5*⌊⌈√5⌉*55.5⌋)',\n", + " 831: '(⌈√5⌉*⌊.5*555⌋)',\n", + " 832: '⌊(.5+⌈.5⌉)*555⌋',\n", + " 833: '⌈(.5+⌈.5⌉)*555⌉',\n", + " 834: '(⌊5!*√55⌋-55)',\n", + " 835: '(⌈5!*√55⌉-55)',\n", + " 836: '⌊⌊√55⌋*(5!-.55)⌋',\n", + " 837: '⌈⌊√55⌋*(5!-.55)⌉',\n", + " 838: '⌊(5.5**5)/⌈5.5⌉⌋',\n", + " 839: '⌈(5.5**5)/⌈5.5⌉⌉',\n", + " 840: '(5!+⌈5.555⌉!)',\n", + " 841: '(5!+⌈.5+⌈5.55⌉!⌉)',\n", + " 842: '(⌈5.5⌉!+⌊√5*55⌋)',\n", + " 843: '(⌈5.5⌉!+⌈√5*55⌉)',\n", + " 844: '⌊5!*√(55-5.5)⌋',\n", + " 845: '⌊√55*⌊5!-5.5⌋⌋',\n", + " 846: '⌈√55*⌊5!-5.5⌋⌉',\n", + " 847: '(⌊√55⌋*⌈5!+.55⌉)',\n", + " 848: '⌊5!*√⌊55.5-5⌋⌋',\n", + " 849: '⌊√55*(5!-5.5)⌋',\n", + " 850: '(5*(5!+(55-5)))',\n", + " 851: '⌊⌊(5!-5)*√55⌋-.5⌋',\n", + " 852: '⌊5!*√(55.5-5)⌋',\n", + " 853: '⌈5!*√(55.5-5)⌉',\n", + " 854: '(5+⌈5!*√(55-5)⌉)',\n", + " 855: '(5*⌈5.55**⌈√5⌉⌉)',\n", + " 856: '⌊(5!-5)*√55.5⌋',\n", + " 857: '⌈(5!-5)*√55.5⌉',\n", + " 858: '(5+⌈(5!-5)*√55⌉)',\n", + " 859: '⌊55**(√5-.55)⌋',\n", + " 860: '⌈55**(√5-.55)⌉',\n", + " 861: '⌊5!*(5+(5!/55))⌋',\n", + " 862: '⌈5!*(5+(5!/55))⌉',\n", + " 863: '⌈5**(⌊5!/5.5⌋/5)⌉',\n", + " 864: '(⌊.5*55⌋/(.5**5))',\n", + " 865: '(5*⌊55*√(5+5)⌋)',\n", + " 866: '⌈5!*√⌊55-√5.5⌋⌉',\n", + " 867: '⌊√55*⌊5!-√5.5⌋⌋',\n", + " 868: '⌈√55*⌊5!-√5.5⌋⌉',\n", + " 869: '⌊5*(55*√(5+5))⌋',\n", + " 870: '((555-5!)/.5)',\n", + " 871: '⌊5!**√⌈5.55/5⌉⌋',\n", + " 872: '⌊5*(5!+(55-.5))⌋',\n", + " 873: '⌈5*(5!+(55-.5))⌉',\n", + " 874: '⌊(5*(5!+55))-.5⌋',\n", + " 875: '(5*⌊5!+55.5⌋)',\n", + " 876: '⌈.5+(5*(5!+55))⌉',\n", + " 877: '⌊5*(5!+55.5)⌋',\n", + " 878: '⌈5*(5!+55.5)⌉',\n", + " 879: '⌈√5*⌈√.5*555⌉⌉',\n", + " 880: '(5*⌈5!+55.5⌉)',\n", + " 881: '⌊5!*√⌊55-.55⌋⌋',\n", + " 882: '⌊√55*⌊5!-.55⌋⌋',\n", + " 883: '⌊⌊5!*√55⌋-5.5⌋',\n", + " 884: '⌊⌈5!*√55⌉-5.5⌋',\n", + " 885: '⌈⌈5!*√55⌉-5.5⌉',\n", + " 886: '⌈√55*(5!-.55)⌉',\n", + " 887: '⌈⌊5!-.5⌋*√55.5⌉',\n", + " 888: '(⌊5!*√55.5⌋-5)',\n", + " 889: '⌊5!*(55/√55)⌋',\n", + " 890: '⌈5!*(55/√55)⌉',\n", + " 891: '⌈.55+(5!*√55)⌉',\n", + " 892: '⌊⌊5!*√55.5⌋-.5⌋',\n", + " 893: '⌊⌊5.5⌋!*√55.5⌋',\n", + " 894: '⌊5.5+⌊5!*√55⌋⌋',\n", + " 895: '⌈5.5+⌊5!*√55⌋⌉',\n", + " 896: '⌈5.5+⌈5!*√55⌉⌉',\n", + " 897: '⌊5!*√⌈55.55⌉⌋',\n", + " 898: '⌈5!*√⌈55.55⌉⌉',\n", + " 899: '(5+⌈5!*√55.5⌉)',\n", + " 900: '(5*(5+(5!+55)))',\n", + " 901: '⌊⌈.5+5!⌉*√55.5⌋',\n", + " 902: '⌊(5-(5.5/5))**5⌋',\n", + " 903: '⌈(5-(5.5/5))**5⌉',\n", + " 904: '(5!+⌊555/√.5⌋)',\n", + " 905: '(5!+⌈555/√.5⌉)',\n", + " 906: '(⌈√5⌉*⌊5.5*55⌋)',\n", + " 907: '⌊⌈√5⌉*(5.5*55)⌋',\n", + " 908: '⌈⌈√5⌉*(5.5*55)⌉',\n", + " 909: '(⌈√5⌉*⌈5.5*55⌉)',\n", + " 910: '⌊√5*⌊55*√55⌋⌋',\n", + " 911: '⌈√5*⌊55*√55⌋⌉',\n", + " 912: '⌊√5*⌈55*√55⌉⌋',\n", + " 913: '⌈√5*⌈55*√55⌉⌉',\n", + " 914: '⌊⌊5.5**5⌋/5.5⌋',\n", + " 915: '⌊5.5**⌊5-.55⌋⌋',\n", + " 916: '⌈5.5**⌊5-.55⌋⌉',\n", + " 917: '⌈⌈√5+5!⌉*√55.5⌉',\n", + " 918: '⌊5.5*⌈5.5**⌈√5⌉⌉⌋',\n", + " 919: '⌈5.5*⌈5.5**⌈√5⌉⌉⌉',\n", + " 920: '(5+⌊5.5**⌊5-.5⌋⌋)',\n", + " 921: '⌊(.5*5)**√55.5⌋',\n", + " 922: '⌈(.5*5)**√55.5⌉',\n", + " 923: '(55+⌊5!*(√5+5)⌋)',\n", + " 924: '(55+⌈5!*(√5+5)⌉)',\n", + " 925: '(5*(555/⌈√5⌉))',\n", + " 926: '⌊⌊(5+5!)*√55⌋-.5⌋',\n", + " 927: '⌊√55*⌊5!+5.5⌋⌋',\n", + " 928: '⌈√55*⌊5!+5.5⌋⌉',\n", + " 929: '⌊5!*√⌊5+55.5⌋⌋',\n", + " 930: '⌈5!*√⌊5+55.5⌋⌉',\n", + " 931: '⌊(5+5!)*√55.5⌋',\n", + " 932: '⌈(5+5!)*√55.5⌉',\n", + " 933: '⌊5!*√(5+55.5)⌋',\n", + " 934: '⌈5!*√(5+55.5)⌉',\n", + " 935: '(55*⌈5!/√55⌉)',\n", + " 936: '⌈(5+5!)*√⌈55.5⌉⌉',\n", + " 937: '⌊5!*√⌈5+55.5⌉⌋',\n", + " 938: '⌈5!*√⌈5+55.5⌉⌉',\n", + " 939: '⌊5.5/(.5**√55)⌋',\n", + " 940: '⌈5.5/(.5**√55)⌉',\n", + " 941: '⌊√55*⌊5!+√55⌋⌋',\n", + " 942: '⌊⌊5**5.5⌋/√55⌋',\n", + " 943: '⌈⌊5**5.5⌋/√55⌉',\n", + " 944: '(55+⌊5!*√55⌋)',\n", + " 945: '(55+⌈5!*√55⌉)',\n", + " 946: '(5.5*⌊(5+5)**√5⌋)',\n", + " 947: '⌊(√.5+⌈.5⌉)*555⌋',\n", + " 948: '⌊5.55**⌊5-.5⌋⌋',\n", + " 949: '⌈5.55**⌊5-.5⌋⌉',\n", + " 950: '(5*(5*⌈5*√55⌉))',\n", + " 951: '⌊5.5*⌈(5+5)**√5⌉⌋',\n", + " 952: '⌊5!*√⌈55+√55⌉⌋',\n", + " 953: '⌈5!*√⌈55+√55⌉⌉',\n", + " 954: '⌊(5!+555)/√.5⌋',\n", + " 955: '⌊5!*(.55+√55)⌋',\n", + " 956: '⌈5!*(.55+√55)⌉',\n", + " 957: '⌊5!*(.5+√⌈55.5⌉)⌋',\n", + " 958: '⌈5!*(.5+√⌈55.5⌉)⌉',\n", + " 959: '⌊(5!*⌈√55⌉)-.55⌋',\n", + " 960: '(5!*⌈55/√55⌉)',\n", + " 961: '⌊√⌈.5*5⌉*555⌋',\n", + " 962: '⌊5.5*(5!+55)⌋',\n", + " 963: '⌈5.5*(5!+55)⌉',\n", + " 964: '⌈(√5-.5)*555⌉',\n", + " 965: '⌊(5!/5.55)**√5⌋',\n", + " 966: '⌈(5!/5.55)**√5⌉',\n", + " 967: '⌊5!*√⌈5!-55.5⌉⌋',\n", + " 968: '⌈5!*√⌈5!-55.5⌉⌉',\n", + " 969: '((⌊5-.5⌋**5)-55)',\n", + " 970: '(5*⌈5!**(5.5/5)⌉)',\n", + " 971: '(⌈5*(5!/.55)⌉-5!)',\n", + " 972: '⌊√5*(555-5!)⌋',\n", + " 973: '⌈√5*(555-5!)⌉',\n", + " 974: '⌊5!*√⌊5!*.555⌋⌋',\n", + " 975: '⌈5!*√⌊5!*.555⌋⌉',\n", + " 976: '(⌈√55⌉*⌊√5*55⌋)',\n", + " 977: '⌈(5+5)*((.5*5)**5)⌉',\n", + " 978: '⌊5!*(√.5+√55.5)⌋',\n", + " 979: '⌊5!*(5+√⌊5+5.5⌋)⌋',\n", + " 980: '⌈5!*(5+√⌊5+5.5⌋)⌉',\n", + " 981: '((5-.5)*⌊5!/.55⌋)',\n", + " 982: '⌊5!*√⌈5!*.555⌉⌋',\n", + " 983: '⌈5!*√⌈5!*.555⌉⌉',\n", + " 984: '(⌈√55⌉*⌈√5*55⌉)',\n", + " 985: '⌊(5-.5)*⌈5!/.55⌉⌋',\n", + " 986: '⌈(5-.5)*⌈5!/.55⌉⌉',\n", + " 987: '⌊√⌈√5*5⌉**5.55⌋',\n", + " 988: '⌊5!*(√5+⌈5.55⌉)⌋',\n", + " 989: '⌈5!*(√5+⌈5.55⌉)⌉',\n", + " 990: '((555/.5)-5!)',\n", + " 991: '⌊5!*(5-(√5-5.5))⌋',\n", + " 992: '⌈5!*(5-(√5-5.5))⌉',\n", + " 993: '⌈√5*⌊⌈√5⌉**5.55⌋⌉',\n", + " 994: '⌊5!*(5*√(5*.55))⌋',\n", + " 995: '(⌈5.5⌉!+(5*55))',\n", + " 996: '⌊⌈5**(5-√.5)⌉-5.5⌋',\n", + " 997: '⌊5!*(5+√(55/5))⌋',\n", + " 998: '⌊⌊5**5.5⌋/⌊√55⌋⌋',\n", + " 999: '⌈⌊5**5.5⌋/⌊√55⌋⌉',\n", + " ...}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "clear()\n", + "\n", + "%time makeable(ff)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The output got truncated by Jupyter Notebook after 1000 entries. Let's see what the first unmakeable integer actually is:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "23308" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "unmakeable(ff)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I think we've conquered the five 5s problem.\n", + "\n", + "# Conclusion\n", + "\n", + "We were able to solve the puzzles, and we now have some tools to explore new puzzles. What can you discover?" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Differentiation.ipynb b/pytudes/ipynb/Differentiation.ipynb new file mode 100644 index 0000000..318e0f1 --- /dev/null +++ b/pytudes/ipynb/Differentiation.ipynb @@ -0,0 +1,1392 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Symbolic Math: Differentiation Program\n", + "\n", + "This notebook describes how to write a program that will manipulate mathematical expressions, with an emphasis on differentiation. The program can compute $\\frac{d}{dx} x^2 + \\sin(x)$ to get the result $2x + \\cos(x)$. Usually in a programming language, when we say `sin(x)` we are computing with *numbers*, not *symbolic expressions*. That is, programming languages have built-in functions like `sin` and numbers like 0 so that we can ask for the value of `sin(0)` and get back 0. But now we want to do something different: treat $\\sin(x)$ as a *symbolic expression* that represents any value of $x$. That facility is not built-in to most programming languages, so we need a way to represent and manipulate these symbolic expressions. Python has a large system called `sympy` to do just that, but we will develop a smaller, simpler system from scratch.\n", + "\n", + "# Representing Symbolic Expressions as Tuples\n", + "\n", + "Here is one simple way to represent symbolic expressions: We will represent numbers as themselves, because they are already built-in to Python. We will represent math variable (such as $x$) and constants (such as $\\pi$) as Python strings (such as `'x'` and `'pi'`). And we will represent compound expressions (such as $x + 1$) as Python tuples, such as `('x', '+', 1)`. \n", + "\n", + "We will use the notion of [arity](http://en.wikipedia.org/wiki/Arity) of an expression. An expression can be: \n", + "\n", + "* Binary (arity = 2): $(x + y)$ is a binary expression because it has two sub-expressions, $x$ and $y$.\n", + "* Unary (arity = 1): $-x$ and $\\sin(x)$ are both unary expressions, because they each have one sub-expression, $x$.\n", + "* Nullary (arity = 0): $x$ and $3$ are both nullary, or *atomic* expressions, because they have no sub-expressions,\n", + "\n", + "We can define this as a Python function:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def arity(expr):\n", + " \"The number of sub-expressions in this expression.\"\n", + " if isinstance(expr, tuple):\n", + " return len(expr) - 1\n", + " else:\n", + " return 0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "exp = ('x', '+', 1)\n", + "arity(exp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This table summarizes the kinds of expressions and how we will represent them:\n", + "\n", + "\n", + "
Math
Expression		Math TypeArityPython
Representation		Python
Type\n", + "
$3$Integer03int\n", + "
$3.14$Number03.14float\n", + "
$x$Variable0'x'str\n", + "
$\\pi$Constant0'pi'str\n", + "
$-x$Unary op1('-', 'x')tuple\n", + "
$\\sin(x)$Unary func1('sin', 'x')tuple\n", + "
$x+1$Binary op2('x', '+', 1)tuple\n", + "
$3x - y/2$Nested
Binary op		2((3, '*', 'x'), '-',
 ('y', '/', 2))		tuple\n", + "\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Differentiation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In Calculus, *differentiation* is the process of computing the *derivative* of a function: the rate of change of the function with respect to a variable. We denote the dirivative of $y$ with respect to the variable $x$ as $\\frac{dy}{dx}$. \n", + "\n", + "We can compute the derrivative by consulting a [table of differentiation rules](http://myhandbook.info/form_diff.html). Here are the rules for variables, constants, unary negation, and the four basic binary arithmetic operations: " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\frac{d}{dx} (x) = 1$\n", + "\n", + "$\\frac{d}{dx} (c) = 0$\n", + "\n", + "$\\frac{d}{dx} (-u) = - \\frac{du}{dx}$\n", + "\n", + "$\\frac{d}{dx} (u + v) = \\frac{du}{dx} + \\frac{dv}{dx}$\n", + "\n", + "$\\frac{d}{dx} (u - v) = \\frac{du}{dx} - \\frac{dv}{dx}$\n", + "\n", + "$\\frac{d}{dx} (u \\times v) = v \\frac{du}{dx} + u \\frac{dv}{dx}$\n", + "\n", + "$\\frac{d}{dx} (u \\; / \\; v) = (v \\frac{du}{dx} - u \\frac{dv}{dx}) \\; / \\; v^2$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Defining `D(y, x)`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will define the Python function `D(y, x)` to compute the symbolic derivative of the expression `y` with respect to the variable `x`. We can handle each of the seven rules, one by one. If the input is of a form that does not match one of the rules, we will raise a `ValueError`." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def D(y, x='x'):\n", + " \"\"\"Return the symbolic derivative, dy/dx.\n", + " Handles binary operators +, -, *, /, and unary -, over variables and constants.\"\"\"\n", + " if y == x: \n", + " return 1 # d/dx (x) = 1\n", + " if arity(y) == 0:\n", + " return 0 # d/dx (c) = 0\n", + " if arity(y) == 1:\n", + " (op, u) = y # y is a compund expression of the form (op, u)\n", + " if op == '-': return ('-', D(u, x)) # d/dx (-u) = - du/dx \n", + " if arity(y) == 2: \n", + " (u, op, v) = y # y is a compound expression of the form (u, op, v)\n", + " if op == '+': return D(u, x), '+', D(v, x)\n", + " if op == '-': return D(u, x), '-', D(v, x)\n", + " if op == '*': return (v, '*', D(u, x)), '+', (u, '*', D(v, x))\n", + " if op == '/': return ((v, '*', D(u, x)), '-', (u, '*', D(v, x))), '/', (v, '*', v)\n", + " raise ValueError(\"D can't handle this: \" + str(y))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what `D` can do:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, '+', 0)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(('x', '+', 1), 'x')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((('x', '*', 0), '+', (3, '*', 1)), '+', 0)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(((3, '*', 'x'), '+', 'c'), 'x')" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(('y', '*', 1), '+', ('y', '*', 1))" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(('y', '*', 'y'), 'y')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These answers are all mathematically *correct*, but they are not *simplified*—better answers would be `1`, `3`, and `(2, '*', 'y')`, respectively. So we have solved the basic problem, but there are enhancements we could make in several directions:\n", + "\n", + "* *Simplify*: Return `1` instead of `(1, '+', 0)`.\n", + "* *Diversify*: Handle more types of expressions, like $x^2$, and $\\sin(x)$.\n", + "* *Refactor*: Maker the code cleaner by introducing a better representation for expressions.\n", + "\n", + "I choose to refactor first (because that will make the other two tasks easier). \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Representing Symbolic Expressions as Class Objects" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will refactor the representation of expressions, replacing tuples with a user-defined class, `Expression`. Why do that? Three reasons:\n", + "\n", + "* **Hygiene**: The code is cleaner with a separate type. A tuple can be used for a lot of things; when I have an expression I want to know for sure it is an expression. \n", + "* **Ease of Coding**: I will be able to form a new expression with the simple code `x + 1` rather than the more verbose `(x, '+', 1)`.\n", + "* **Prettier Output**: We can see the prettier `(x + 1)` form on output, rather than the uglier `('x', '+', 1)`.\n", + "\n", + "Here's what I have in mind:\n", + "\n", + "\n", + "\n", + "
Math
Expression		Math
Type		ArityPython
Representation		Python
Type\n", + "
$3$Integer03int\n", + "
$3.14$Number03.14float\n", + "
$x$Variable0Expression('x')Expression\n", + "
$\\pi$Constant0Expression('pi')Expression\n", + "
$-x$Unary op1Expression('-', 'x')Expression\n", + "
$\\sin(x)$Unary func1Expression('sin', 'x')Expression\n", + "
$x+1$Binary op2Expression('+', x, 1) (given def for `x`)Expression\n", + "
$3x - y/2$Nested
Binary op		23 * x - y / 2   (given defs for `x`, `y`)Expression\n", + "
\n", + "\n", + "Note that not every math expression is an instance of the new class `Expression`; we still use good old Python `int` and `float` for numbers. But variables, constants (like $\\pi$ or $c$), and unary and binary expressions are all instances of `Expression`. Note also that I considered having separate subclasses of `Expression` for each of these, but I decided the complication was not worth it.\n", + "\n", + "To understand the implementation of `Expression`, you need to understand Python's [special method names](https://docs.python.org/3/reference/datamodel.html#special-method-names), the method names that begin and end with double underscores, like `__init__` and `__add__`. If you're not familiar with the concept, glance at [the documentation](https://docs.python.org/3/reference/datamodel.html#special-method-names), but here is a quick summary:\n", + "\n", + "* `__init__(self, ...)` *The constructor that defines what happens when a new object is created.*\n", + "* `__add__(self, other)` *The method called when the code asks for `self + other`. Similar for `__sub__`, etc.*\n", + "* `__radd__(self, other)` *'r' for reverse. Called when the code asks for, say, `1 + self`, where `1` is not an `Expression`. Similar for `__rsub__`, etc.*\n", + "* `__neg__(self)` *The method called when the code says `(- self)`. Similar for `__pos__`.*\n", + "* `__hash__(self)` *Computes a hash value, an integer, used as a key into a hash table (`dict`).*\n", + "* `__eq__(self, other)` *Called to check whether `self == other`.*" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from __future__ import division\n", + "\n", + "class Expression(object): \n", + " \"A mathematical expression (other than a number).\"\n", + " def __init__(self, op, *args): self.op, self.args = op, args\n", + " \n", + " def __add__(self, other): return Expression('+', self, other)\n", + " def __sub__(self, other): return Expression('-', self, other)\n", + " def __mul__(self, other): return Expression('*', self, other)\n", + " def __truediv__(self, other): return Expression('/', self, other)\n", + " def __pow__(self, other): return Expression('**', self, other)\n", + " \n", + " def __radd__(self, other): return Expression('+', other, self)\n", + " def __rsub__(self, other): return Expression('-', other, self)\n", + " def __rmul__(self, other): return Expression('*', other, self)\n", + " def __rtruediv__(self, other): return Expression('/', other, self)\n", + " def __rpow__(self, other): return Expression('**', other, self)\n", + " \n", + " def __neg__(self): return Expression('-', self)\n", + " def __pos__(self): return self\n", + " \n", + " def __hash__(self): return hash(self.op) ^ hash(self.args)\n", + " def __ne__(self, other): return not (self == other)\n", + " def __eq__(self, other): return (isinstance(other, Expression) \n", + " and self.op == other.op \n", + " and self.args == other.args)\n", + " def __repr__(self):\n", + " \"A string representation of the Expression.\"\n", + " op, args = self.op, self.args\n", + " n = arity(self)\n", + " if n == 0: \n", + " return op\n", + " if n == 2: \n", + " return '({} {} {})'.format(args[0], op, args[1])\n", + " if n == 1:\n", + " arg = str(args[0])\n", + " if arg.startswith('(') or op in {'+', '-'}:\n", + " return '{}{}'.format(op, arg)\n", + " else:\n", + " return '{}({})'.format(op, arg)\n", + "\n", + "def arity(expr):\n", + " \"The number of sub-expressions in this expression.\"\n", + " if isinstance(expr, Expression):\n", + " return len(expr.args)\n", + " else:\n", + " return 0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's first define some symbols:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "a, b, c, d, u, v, w, x, y, z, pi , e = map(Expression, [\n", + "'a', 'b', 'c', 'd', 'u', 'v', 'w', 'x', 'y', 'z', 'pi', 'e'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, for example, `a` is now an object of type `Expression` such that `a.op` is the string `'a'` and `a.args` is the empty tuple, and `arity(a)` is 0. The Python expression `a + 1` is equivalent to `a.__add__(1)`, which invokes the `Expression.__add__` method to create a new object of type `Expression`:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(a + 1)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a + 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Python expression `1 + a` is equivalent to `1.__add__(a)`. But since the integer `1` doesn't know how to add a `Symbol`, Python instead calls `a.__radd__(1)`, where `radd` stands for \"reversed add\":" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1 + a)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1 + a" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try something more interesting:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((-b + ((b ** 2) - ((4 * a) * c))) / (2 * a))" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(-b + (b**2 - 4*a*c)) / (2 * a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rewriting `D(y, x)` with the Expression Class\n", + "===\n", + "\n", + "We can now rewrite `D`; notice that the code is a bit neater, since we don't have to create tuples, we can just use operators like `+`. " + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def D(y, x=x):\n", + " \"\"\"Return the symbolic derivative, dy/dx.\n", + " Handles binary operators +, -, *, /, and unary -, over variables and constants.\"\"\"\n", + " if y == x: \n", + " return 1 # d/dx (x) = 1\n", + " if arity(y) == 0:\n", + " return 0 # d/dx (c) = 0\n", + " op = y.op\n", + " if arity(y) == 1:\n", + " u = y.args[0]\n", + " if op == '-': return -D(u, x) # d/dx (-u) = - du/dx\n", + " if arity(y) == 2: \n", + " (u, v) = y.args\n", + " if op == '+': return D(u, x) + D(v, x)\n", + " if op == '-': return D(u, x) - D(v, x)\n", + " if op == '*': return D(u, x) * v + D(v, x) * u\n", + " if op == '/': return (v * D(u, x) - u * D(v, x)) / v ** 2\n", + " raise ValueError(\"D can't handle this: \" + str(y))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(x + 2, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(((0 * x) + 3) + 0)" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(3 * x + c, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((1 * y) + (1 * y))" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(y * y, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((0 * x) + (1 * -c))" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(- c * x, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Representing Functions\n", + "===\n", + "\n", + "Let's represent expressions like $\\sin(x)$. We'll need to be clear of the difference between the function `sin` and the functional expression `sin(x)`. I choose to do that by making `sin` be an object of type `Function`, which is a subtype of `Expression`, and making `sin(x)` be an `Expression` whose `op` is `sin`:\n", + "\n", + "\n", + "
ExpressionTypeArityopargs\n", + "
`sin``Function`0`'sin'``()`\n", + "
`sin(x)``Expression`1`sin``(x,)`\n", + "
\n", + " \n", + "\n", + "What operations does `Function` need to support? We need to be able to create a new one, with an op and no args; it can inherit the `__init__` method from `Expression` to do this. Once we create a new one, it needs to be able to create a functional expression, like `sin(x)`. We can do that with the `__call__` method of `Function`:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Function(Expression):\n", + " \"A mathematical function of one argument, like sin or ln.\"\n", + " def __call__(self, x): return Expression(self, x)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "sin, cos, tan, cot, sec, csc, ln, sqrt = map(Function, [\n", + "'sin', 'cos', 'tan', 'cot', 'sec', 'csc', 'ln', 'sqrt'])" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "sin" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sin" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'args': (), 'op': 'sin'}" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vars(sin)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "sin(x)" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sin(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'args': (x,), 'op': sin}" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "vars(sin(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((-b + sqrt((b ** 2) - ((4 * a) * c))) / (2 * a))" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(-b + sqrt(b**2 - 4*a*c)) / (2 * a)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((sin(x) ** 2) + (cos(x) ** 2))" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sin(x)**2 + cos(x)**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "Extending `D(y, x)` to handle Exponentiation and Functions\n", + "====\n", + "\n", + "In this section, we extend `D(y, x)` to handle:\n", + "\n", + "* The binary exponentiation operator, $u^v$, denoted with `u ** v`.\n", + "* The six trigonometric functions sin, cos, tan, cot, csc, sec, and the natural logarithm functions, ln.\n", + "* The chain rule for nested functions.\n", + "\n", + "Here are the rules:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\\frac{d}{dx} (x^n) = n x^{(n-1)}$ *if n is an integer*\n", + "\n", + "$\\frac{d}{dx} (u^v) = v u^{(v-1)} * \\frac{du}{dx} + u^v * \\ln(u) * \\frac{dv}{dx}$\n", + "\n", + "$\\frac{d}{dx} \\sin(x) = \\cos(x)$\n", + "\n", + "$\\frac{d}{dx} \\cos(x) = -\\sin(x)$\n", + "\n", + "$\\frac{d}{dx} \\tan(x) = \\sec(x)^2$\n", + "\n", + "$\\frac{d}{dx} \\cot(x) = -\\csc(x)^2$\n", + "\n", + "$\\frac{d}{dx} \\sec(x) = \\sec(x) \\tan(x)$\n", + "\n", + "$\\frac{d}{dx} \\csc(x) = - \\csc(x) \\cot(x)$\n", + "\n", + "$\\frac{d}{dx} \\ln(x) = 1 / x$\n", + "\n", + "$\\frac{dy}{dx} = \\frac{dy}{du} \\frac{du}{dx}$\n", + "\n", + "We can add these rules to the ones we had before, giving us:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def D(y, x=x):\n", + " \"\"\"Return the symbolic derivative, dy/dx.\n", + " Handles binary operators +, -, *, /, and unary -, as well as\n", + " transcendental trig and log functions over variables and constants.\"\"\"\n", + " if y == x: \n", + " return 1 # d/dx (x) = 1\n", + " if arity(y) == 0:\n", + " return 0 # d/dx (c) = 0\n", + " if arity(y) == 1:\n", + " op, (u,) = y.op, y.args\n", + " if op == '+': return D(u, x)\n", + " if op == '-': return -D(u, x)\n", + " if u != x: return D(y, u) * D(u, x) ## CHAIN RULE\n", + " if op == sin: return cos(x)\n", + " if op == cos: return -sin(x)\n", + " if op == tan: return sec(x) ** 2\n", + " if op == cot: return -csc(x) ** 2\n", + " if op == sec: return sec(x) * tan(x)\n", + " if op == csc: return -csc(x) * cot(x)\n", + " if op == ln: return 1 / x \n", + " if arity(y) == 2: \n", + " op, (u, v) = y.op, y.args\n", + " if op == '+': return D(u, x) + D(v, x)\n", + " if op == '-': return D(u, x) - D(v, x)\n", + " if op == '*': return D(u, x) * v + D(v, x) * u\n", + " if op == '/': return (v * D(u, x) - u * D(v, x)) / v ** 2\n", + " if op == '**': return (v * u**(v-1) if u == x and isinstance(v, int) else\n", + " v * u**(v-1) * D(u, x) + u**v * ln(u) * D(v, x))\n", + " raise ValueError(\"D can't handle this: \" + str(y))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chain Rule\n", + "---\n", + "\n", + "The trickiest part is the chain rule. Consider $\\frac{d}{dx} \\sin(\\ln(x))$. Let:\n", + "\n", + "$y = \\sin(\\ln(x))$\n", + "\n", + "$u = \\ln(x)$\n", + "\n", + "According to the chain rule, \n", + "\n", + "$\\frac{dy}{dx} = \\frac{dy}{du} \\frac{du}{dx}$. \n", + "\n", + "So we have:\n", + "\n", + "$\\frac{dy}{du} = \\frac{d}{du} \\sin(u) = \\cos(u) = \\cos(\\ln(x))$\n", + "\n", + "$\\frac{du}{dx} = \\frac{d}{dx} \\ln(x) = \\frac{1}{x}$\n", + "\n", + "Finally, we can multiply them together to get:\n", + "\n", + "$\\frac{dy}{dx} = \\frac{dy}{du} \\;\\frac{du}{dx} = \\cos(\\ln(x)) \\; \\frac{1}{x} = \\cos(\\ln(x)) / x$.\n", + "\n", + "\n", + "Now let's do the same thing in Python. Let:" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Y = sin(ln(x))\n", + "U = ln(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So let's go on with the computation of the derivative, `D(y, x) = D(y, u) * D(u, x)`. We'll look at the two terms on the right:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "cos(ln(x))" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(Y, U)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1 / x)" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(U, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And multiply the two terms together:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(cos(ln(x)) * (1 / x))" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(Y, U) * D(U, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can do the same computation all in one step:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(cos(ln(x)) * (1 / x))" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(Y, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More Examples of Differentiation\n", + "===\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First an example where all is well:" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3 * (x ** 2))" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(x ** 3, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But most of the time, `D` gives an answer that is technically correct, but not in simplified form. The example below should yield `2*a*x + b`:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((((0 * (x ** 2)) + ((2 * (x ** 1)) * a)) + ((0 * x) + (1 * b))) + 0)" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(a*x**2 + b*x + c, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next example should give `50 * (5*x - 2)**9`:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(((10 * (((5 * x) - 2) ** 9)) * (((0 * x) + 5) - 0)) + (((((5 * x) - 2) ** 10) * ln((5 * x) - 2)) * 0))" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D((5*x - 2)**10, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for the next example, we should get $\\frac{d}{dx} \\sin(\\ln(x^2)) = 2 \\cos(\\ln(x^2)) / x$." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(cos(ln(x ** 2)) * ((1 / (x ** 2)) * (2 * (x ** 1))))" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D(sin(ln(x**2)), x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In each case, the answer is correct, but not simplified." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Simplification: `simp(y)`\n", + "------\n", + "\n", + "\n", + "Now let's work on simplification. We'll define `simp(y)` to return an expression that is equivalent to the expression $y$, but simpler. We should say that the notion of *simpler* is not at all precise. Which is simpler, $x^2 -x -12$ or $(x + 3)(x - 4)$? It depends on what you want to do next. But we can all agree that $x$ is simpler than $(2 - 1)x + 0$. Our version of `simp` will just do the easiest of simplifications. There's lots we could add to make it better.\n", + "\n", + "Another difficult issue is dealing with indeterminate results like dividing by 0. We would like to be able to simplify $x/x$ to 1. But that is only true if $x$ is not 0. We'll ignore that problem and go ahead and simplify $x/x$ to 1, but we'll feel a little uneasy about it. We'll also simplify 0/0 to `undefined` and 1/0 to `infinity`." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def simp(y):\n", + " \"Simplify an expression.\"\n", + " if arity(y) == 0:\n", + " return y \n", + " y = Expression(y.op, *map(simp, y.args)) ## Simplify the sub-expressions first\n", + " op = y.op\n", + " if arity(y) == 1:\n", + " (u,) = y.args\n", + " if y in simp_table:\n", + " return simp_table[y]\n", + " if op == '+':\n", + " return u # + u = u\n", + " if op == '-':\n", + " if arity(u) == 1 and u.op == '-':\n", + " return u.args[0] # - - w = w\n", + " if arity(y) == 2:\n", + " (u, v) = y.args\n", + " if evaluable(u, op, v): # for example, (3 + 4) simplifies to 7\n", + " return eval(str(u) + op + str(v), {})\n", + " if op == '+':\n", + " if u == 0: return v # 0 + v = v\n", + " if v == 0: return u # u + 0 = u\n", + " if u == v: return 2 * u # u + u = 2 * u\n", + " if op == '-':\n", + " if u == v: return 0 # u - v = 0\n", + " if v == 0: return u # u - 0 = u\n", + " if u == 0: return -v # 0 - v = -v\n", + " if op == '*':\n", + " if u == 0 or v == 0: return 0 # 0 * v = u * 0 = 0\n", + " if u == 1: return v # 1 * v = v\n", + " if v == 1: return u # u * 1 = u\n", + " if u == v: return u ** 2 # u * u = u^2\n", + " if op == '/':\n", + " if u == 0 and v == 0: return undefined # 0 / 0 = undefined\n", + " if u == v: return 1 # u / u = 1\n", + " if v == 1: return u # u / 1 = u\n", + " if u == 0: return 0 # 0 / v = 0\n", + " if v == 0: return infinity # u / 0 = infinity\n", + " if op == '**':\n", + " if v == 1: return u # u ** 1 = u\n", + " if u == v == 0: return undefined # 0 ** 0 = undefined\n", + " if v == 0: return 1 # u ** 0 = 1 \n", + "\n", + " # If no rules apply, return y unchanged.\n", + " return y\n", + "\n", + "from numbers import Number\n", + "\n", + "# Deal with infinity and with undefined numbers (like infinity minus infinity)\n", + "infinity = float('inf') \n", + "undefined = nan = (infinity - infinity)\n", + "\n", + "# Table of known exact values for certain functions.\n", + "# Use this, for example, to simplify sin(pi) to 0 or ln(e) to 1.\n", + "\n", + "simp_table = {\n", + " sin(0): 0, sin(pi): 0, sin(pi/2): 1, sin(2*pi): 0,\n", + " cos(0): 1, cos(pi): -1, cos(pi/2): 1, cos(2*pi): 1,\n", + " tan(0): 0, tan(pi): 0, tan(pi/2): infinity, tan(2*pi): 0, tan(pi/4): 1,\n", + " ln(1): 0, ln(e): 1, ln(0): -infinity}\n", + "\n", + "def evaluable(u, op, v):\n", + " \"Can we evaluate (u op v) to a number? True if u and v are numbers, and not a special case like 0^0.\"\n", + " return (isinstance(u, Number) and isinstance(v, Number)\n", + " and not (op == '/' and (v == 0 or u % v != 0))\n", + " and not (op == '^' and (u == v == 0)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try it out. First an easy one; $1x + 0$ should be $x$: Simplifying " + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "x" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp(x*(y/y) + 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Similarly, $(2 - 1)x^{\\cos(y-y)} + \\tan(\\pi)$ should be just $x$:" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "x" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp((2 - 1) * x ** cos(y-y) + tan(pi))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are two examples where `simp` helps, but does not do all the simplifications it could:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(cos(ln(x ** 2)) * ((1 / (x ** 2)) * (2 * x)))" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp(D(sin(ln(x**2)), x))" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((10 * (((5 * x) - 2) ** 9)) * 5)" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp(D((5 * x - 2)**10, x))" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp(cos(pi - pi))" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simp(D(3 * x + c, x))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Economics.ipynb b/pytudes/ipynb/Economics.ipynb new file mode 100644 index 0000000..84ef6a5 --- /dev/null +++ b/pytudes/ipynb/Economics.ipynb @@ -0,0 +1,1500 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Economics Simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a simulation of an economic marketplace in which there is a *population* of actors, each of which has a level of wealth. On each time step two actors (chosen by an *interaction function*) engage in a transaction that exchanges wealth between them (according to a *transaction function*). The idea is to understand the evolution of the population's wealth over time. I heard about the problem when I visited the Bard College Computer Science Department in 2008. *Update:* In 2017, a version posed by Uri Wilensky [became popular](http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/). We cover his version [below](#Uri-Wilensky-Version).\n", + "\n", + "![](money.png)\n", + "\n", + "Why is this interesting? \n", + "- It is an example of using simulation to model the world. The model is simple but captures some aspects of a complex world.\n", + "- Many students will have preconceptions about how economies work that will be challenged by the results shown here.\n", + "- It reveals subtle differences between computational thinking, mathematical thinking, and statistical thinking." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Population Distributions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will model a population as a list of `N` numbers, each number being one actor's wealth. We'll start with a Gaussian distribution (also known as a *normal* distribution or *bell-shaped curve*), with a mean wealth of 100 [simoleons](http://en.wiktionary.org/wiki/simoleon) and a standard deviation of 1/5 the mean:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import random\n", + "\n", + "N = 5000 # Default size of the population\n", + "MU = 100. # Default mean of the population\n", + "\n", + "population = [random.gauss(mu=MU, sigma=MU/5) for actor in range(N)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Population Statistics and Visualization\n", + "\n", + "How evenly is the wealth in a population distributed? The traditional measure is the [Gini coefficient](http://en.wikipedia.org/wiki/Gini_coefficient), which Wikipedia says is computed by this formula (which assumes the *y* values are sorted):\n", + "\n", + "![Gini](https://upload.wikimedia.org/math/b/b/5/bb50601acc135c45a24bb0493f7555b4.png)\n", + "\n", + "A Gini index of 0 means total equality (everyone has the same amount), and values closer to 1 mean more inequality (most of the money in the hands of a few individuals). Here's a table of Gini coefficients for several countries:\n", + "\n", + "\n", + "
Sweden 0.250\n", + "
Canada 0.326\n", + "
Switzerland 0.337\n", + "
United States 0.408\n", + "
Chile 0.521\n", + "
South Africe 0.631\n", + "
\n", + "\n", + "\n", + "The Gini coefficient is traditionally computed over *income*, but we will be dealing with *wealth*. Here is the computation:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gini(y):\n", + " \"Compute the Gini coefficient (a measure of equality/inequality) in a population, y.\"\n", + " y = sorted(y)\n", + " n = len(y)\n", + " numer = 2 * sum((i+1) * y[i] for i in range(n))\n", + " denom = n * sum(y)\n", + " return (numer / denom) - (n + 1) / n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.11285526402866708" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "gini(population)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll define the function `hist` to plot a histogram of a population. Our `hist` wraps `plt.hist`, but with some specific keyword values:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def hist(population, label='pop', **kwargs):\n", + " \"A custom version of `hist` with better defaults.\"\n", + " label = label + ': G=' + str(round(gini(population), 2))\n", + " h = plt.hist(list(population), bins=30, alpha=0.5, label=label, **kwargs)\n", + " plt.xlabel('wealth'); plt.ylabel('count'); plt.grid(True)\n", + " plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vh04tqQJF6WtG6RMrZ74i5IyQEeK817PSFoaIhDDQRZZ2XK58p+bfVahgFGik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\nq0OMAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist(population)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Transactions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a transaction, two actors come together and exchange some of their wealth. For now we will use a wealth-conserving transaction function in which all the wealth from both actors is put into a pot, which is then split randomly and uniformly between the two actors:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def random_split(A, B):\n", + " \"Take all the money uin the pot and divide it randomly between the two actors.\"\n", + " pot = A + B\n", + " share = random.uniform(0, pot)\n", + " return share, pot - share" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(39.32170492026867, 160.67829507973133)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random_split(100, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Interactions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How do we decide which parties interact with each other? We will define an interaction function that, given the size of the population, randomly selects any two actors in the populations (denoted by their index numbers in the list). We'll call this function `anyone`, meaning that any actor can interact with any other actor:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def anyone(N): return random.sample(range(N), 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1593, 1439]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "anyone(N)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `simulate` takes an initial population, calls an interaction function to select two actors, and a transaction function to split their wealth, and repeats this T times. After each transaction, we yield the population, so `simulate` yields the complete history of the simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def step(population, transaction=random_split, interaction=anyone):\n", + " \"Modify the population by doing one transaction.\"\n", + " i, j = interaction(len(population))\n", + " population[i], population[j] = transaction(population[i], population[j]) \n", + " return population\n", + " \n", + "def simulate(population, T, step=step, transaction=random_split, interaction=anyone):\n", + " \"Run simulation on population for T transactions; yield population at each time step.\"\n", + " population = population.copy()\n", + " yield population\n", + " for t in range(T):\n", + " yield step(population, transaction, interaction)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a simple example of simulating a population of 4 actors for 8 time steps:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[100, 100, 100, 100]\n", + "[100, 100, 166.07034848304477, 33.92965151695522]\n", + "[100, 129.37411310873642, 166.07034848304477, 4.555538408218797]\n", + "[100, 21.916292438917807, 166.07034848304477, 112.01335907803742]\n", + "[100, 21.916292438917807, 89.32137618847126, 188.7623313726109]\n", + "[88.88749715846127, 33.028795280456535, 89.32137618847126, 188.7623313726109]\n", + "[88.88749715846127, 0.008026672184755057, 122.34214479674304, 188.7623313726109]\n", + "[88.88749715846127, 0.008026672184755057, 147.86216819550745, 163.24230797384647]\n", + "[88.88749715846127, 54.73884147345122, 147.86216819550745, 108.51149317257999]\n" + ] + } + ], + "source": [ + "for pop in simulate([100] * 4, 8):\n", + " print(pop)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SImulation Visualization\n", + "\n", + "If we want to do larger simulations we'll need a better way to visualize the results.\n", + "The function `show` does that:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import statistics\n", + "\n", + "def show(population, k=40, percentiles=(1, 10, 50, 90, 99), **kwargs):\n", + " \"Run a simulation for k*N steps, printing statistics and displaying a plot and histogram.\"\n", + " N = len(population)\n", + " start = list(population)\n", + " results = [(t, sorted(pop)) # Sort results so that percentiles work\n", + " for (t, pop) in enumerate(simulate(population, T=k * N, **kwargs))\n", + " if t % (N / 10) == 0]\n", + " # Printout:\n", + " print(' t Gini stdev' + (' {:3d}%' * len(percentiles)).format(*percentiles))\n", + " print('------- ---- -----' + ' ----' * len(percentiles))\n", + " fmt = '{:7,d} {:.2f} {:5.1f}' + ' {:4.0f}' * len(percentiles)\n", + " for (t, pop) in results:\n", + " if t % (k * N // 10) == 0: # Print 11 report lines (initial plus 10 as t varies)\n", + " data = [percent(pct, pop) for pct in percentiles]\n", + " print(fmt.format(t, gini(pop), statistics.stdev(pop), *data))\n", + "\n", + " plt.title('/'.join(map(str, percentiles)) + ' Percentile Plots')\n", + " times = [t for (t, pop) in results]\n", + " plt.hold(True); plt.xlabel('wealth'); plt.ylabel('time'); plt.grid(True)\n", + " for pct in percentiles:\n", + " line = [percent(pct, pop) for (t, pop) in results]\n", + " plt.plot(line, times)\n", + " plt.show()\n", + " \n", + " plt.title('Histograms') \n", + " R = (min(pop+start), max(pop+start))\n", + " hist(start, 'start', range=R)\n", + " hist(pop, 'end', range=R)\n", + " plt.show()\n", + "\n", + " plt.title('Ordered Curves')\n", + " order = list(range(len(pop)))\n", + " start.sort()\n", + " pop.sort()\n", + " plt.plot(sorted(start), order, label='start')\n", + " plt.plot(sorted(pop), order, label='end')\n", + " plt.xlabel('wealth'); plt.ylabel('order'); plt.grid(True)\n", + " plt.legend()\n", + "\n", + " \n", + "def percent(pct, items):\n", + " \"The item that is pct percent through the sorted list of items.\"\n", + " return items[min(len(items)-1, len(items) * pct // 100)]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.50 99.4 1 11 71 231 454\n", + " 40,000 0.49 98.0 1 11 71 231 452\n", + " 60,000 0.50 99.1 1 10 69 233 441\n", + " 80,000 0.49 96.6 1 11 71 230 442\n", + "100,000 0.50 100.4 1 11 69 230 465\n", + "120,000 0.50 101.1 1 10 69 230 468\n", + "140,000 0.50 101.8 1 10 69 230 466\n", + "160,000 0.50 102.7 1 11 68 227 477\n", + "180,000 0.49 98.4 1 11 72 229 450\n", + "200,000 0.49 99.0 1 11 70 231 464\n" + ] + }, + { + "data": { + "image/png": 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orFgBt90Wbyk0/ZBps/GN/Hz+tWcPi1pb+UpubrxF0nzB2H7XdjrXdoYKBFzD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\n2ABpUQ2vPUGabDMwYwZ0dsLatbBwYdJum0nePWPNWOhCSsk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zP8bT/wH8985uVEREdi1J72cyheiijKvixznu/kAhg+1K1DNJJsRMEGYuZUpG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\nfjx/BdFfA1kFy2lmexIVkgf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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are four parts to this output:\n", + "\n", + "**The printout:** For the starting population and for every 20,000 transactions along the way, we \n", + "print the Gini coefficient and standard deviation of the population, and the wealths at five percentile points in the population: the 1%, 10%, 50% (median), 90% and 99% marks.\n", + "\n", + "**The plots:** This shows the same information as the printout (except for the Gini index), but with more data points along the way. The leftmost (blue) line is the 1% mark, the rightmost (purple) is the 99% mark, and the inner lines are the 10%, 50% and 90% marks, respectively. For the plot, time goes from bottom to top rather than top to bottom. So, the 99% (purple) line starts at around 150, and over time increases to over 400, indicating that the richest 1% are getting richer. The fact that the lines are going more or less straight up after about 50,000 transactions suggests that the system has converged.\n", + "\n", + "**The histograms:** The starting and ending populations are plotted as histograms. \n", + "\n", + "**The ordered curves:** Here the initial (blue) and final (green) populations are sorted, and the curves show wealth versus ordinal number. The poorest actor (ordinal number 0) has wealth 0 in both the initial and final populations. The 2000th poorest actor (a bit below the median; at the 40th percentile) has wealth of almost 100 in the initial population, but only about 50 in the final population.\n", + "\n", + "The results show that income inequality is increasing over time. How can you tell? Because the Gini coefficient is increasing over time, the standard deviation is increasing, and the 1% and 10% marks are decreasing (the blue and olive lines are moving left as time increases) while the 90% and 99% marks are increasing (the aqua and purple lines are moving right as time increases).\n", + "\n", + "\n", + "\n", + "Would the population continue to change if we let the simulation run longer? It looks like only the 1% line is changing, the other lines remain pretty much in one place from about T=15,000 to T=25,000. This suggests that running the simulation longer would not have too much effect." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Effect of Starting Population\n", + "\n", + "What happens to the final result if we vary the starting population? I'll introduce the function `samples` to sample from a distribution function `n` times, normalizing the result to have the specified mean:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def samples(distribution, *args, n=N, mu=MU):\n", + " \"Sample from the distribution n times, then normalize results to have mean mu.\"\n", + " numbers = [distribution(*args) for _ in range(N)]\n", + " return normalize(numbers, mu)\n", + "\n", + "def normalize(numbers, mu):\n", + " \"Make the numbers non-negative, and scale them so they have mean mu.\"\n", + " numbers = [max(0, n) for n in numbers]\n", + " factor = len(numbers) * mu / sum(numbers)\n", + " return [x * factor for x in numbers]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can easily make an initial population from a distribution function. I'll start with a uniform distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.33 57.9 2 19 102 181 200\n", + " 20,000 0.49 97.1 1 11 72 224 447\n", + " 40,000 0.50 102.7 1 10 69 229 486\n", + " 60,000 0.50 101.1 1 11 68 233 460\n", + " 80,000 0.50 101.0 1 10 69 229 490\n", + "100,000 0.51 101.7 1 10 67 234 465\n", + "120,000 0.50 99.7 1 10 70 229 462\n", + "140,000 0.50 99.5 1 11 71 229 444\n", + "160,000 0.51 102.6 1 10 66 235 469\n", + "180,000 0.50 102.3 1 10 68 229 455\n", + "200,000 0.51 102.3 1 10 70 232 472\n" + ] + }, + { + "data": { + "image/png": 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8o333j3O6gkG+tncvYzwe7pg4EWeMH82tiR4JzgSSS5LJOT+Hwv8pZNxN45jw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\nxcVw112gszfHhaWNjaxuaWF7W5sWoARBdSj8B/xHxKXrs/+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LSxkzZgz//d//zc6dOzn++OO5+OKLGTlyZL1vSV9cXMydd97J8uXL6dWrF48//njF7Viq\nGj58OM8//zxHHnlkxTNctm/fXnHTzG9/+9u8+eabrFy5kieffJLbb7/9kPexqKiIgoICAPLz8w95\nPdWJ/JYuZnYyMN3dz0qqGwbcBVzq7vuCupGAu/vEoDwTGAusBua6e8+g/mbgEncfUcP2dEsXkRRU\nd2uPYT8YRv61+ZFtM1YYo+DhgsjWX5Phw4dz0kkn8cADdSe1LVu2cO6559KvXz9+/vOfk5+fz44d\nO3jllVfYtWsX3/ve91Le7v79+zn11FO59957GTFiBL///e/5zW9+w9///ndatfr87/q6+vnoo49y\nxhlncP/99/Pv//7vh5RYsuWWLha84gWzq4EfAYMSSSXwKnCzmR1hZt2AHsAidy8FtptZ32Ay/3Yg\ncw9zFpEGsX79em644QaOP/54TjnlFKZMmVKxbPz48XzjG99g6NChtGvXjjPPPJMPPvigYvnixYv5\n0pe+RPv27bn55pvZu3dvytv97W9/S/v27XnmmWcqfsm3a9eOoUOH1iupQPyo4MCBA9xzzz20bt2a\nu+++G3dnzpw59VpPwogRI/jqV7/KkUceeUifbyhRn278PLCA+JlcJWY2HJgCHAP8j5l9YGaPALj7\nMuBFYBnxeZfvephWvwdMBVYAK919ZpT9zhbNcSy9JopFqCnEwt0ZOHAgZ599NuvXr+evf/0rkydP\n5n/+538q2kyfPp0hQ4awfft2Bg4cWPGlv3//fq677jqGDh3Kli1buPHGG3nppZcqrb9Dhw4sWLCg\n2m3/9a9/5brrrquzjx06dODYY4+lQ4cOld4fe+yxTJo0CYClS5dy1llnVfrcF7/4RZYuXVrjeh95\n5BGOO+44zjvvvIzfpfhQRTrH4u5Dqql+spb2E4AJ1dS/D5yZxq6JSCP27rvvsmnTJn7yk58A8TmA\nO++8kxdeeIErrrgCiD/75Kqr4lce3HbbbUyePBmAhQsXUl5ezj333APA9ddfz3nnnVdp/bU9PnjT\npk2VHkE8ffp0br/9dg4cOMAFF1zAzJkz61xHQn0fQfz973+/4ohp1qxZfOMb3+CEE07g/PPPr3Nb\njYmex5LFdL1CSLEINYVYrF69mnXr1nHssccC8SOYgwcPcvHFF1e0Sf7yP+qoo9i7dy8HDx5k/fr1\ndO5c+cTRk08+OeVtd+zYsdIjiAcOHMjWrVuZOnUqzz33XL32o76PIO7Tp0/F+wEDBnDLLbfw8ssv\nN7nEkunTjUVEPuekk06ie/fubNmyhS1btrB161a2b9/O9OnT6/zsCSecwLp16yrVlZSkfqbbZZdd\nRmFhYZ3tansEceJBYL1792bJkiWVPrdkyRJ69+6dUl+a6jNzlFiyWFMYS28oikWoKcSib9++tG3b\nlkmTJrF3714OHDjA0qVLee+992r8TOIL+Pzzz6dVq1ZMmTKF8vJyXn75ZRYtWpTytu+99162bt3K\nbbfdxj/+8Q8Adu7cSXFxcaV2tT2CeOTIkUD86LBly5ZMmTKFsrIy/vM//5MWLVpw6aWXVrvtl156\nid27d+PuzJ49m+eee67S0zD379/P3r17cXfKysrYt29fo0w8GgoTkQpdc7sSK4xFuv5UtGjRgtde\ne417772Xbt26UVZWxumnn84vfvGLGj+TuNajdevWvPzyy9x555389Kc/5ZprruH66ytfWtC2bVtm\nzpxZ8Qz6ZB07duTtt9/mZz/7GRdeeCG7du0iNzeXCy+8kEcffbQeexvvS2FhIXfccQcjR46kZ8+e\nTJs2reJU4+eff54JEybwt7/9DYDJkydz55134u5069aNxx9/nIsuuqhifVdeeSVvvvkmZsbChQv5\n9re/zdy5cysNETYGejSxSDPVVIdZ5PBky3UsIiLSjCixZLGmMJbeUBSLkGIhUVNiERGRtFJiyWJN\n4XqFhqJYhBQLiZoSi4iIpJUSSxbTWHpIsQgpFhI1Xcci0kydfPLJFdd+SPNRn9vbHColliymsfSQ\nYhFKxCIWi2W0H5K9NBQmIiJppcSSxTSWHlIsQopFSLGIhhKLiIiklRJLFtO8QkixCCkWIcUiGkos\nIiKSVkosWUzjxyHFIqRYhBSLaCixiIhIWimxZDGNH4cUi5BiEVIsoqHEIiIiaaXEksU0fhxSLEKK\nRUixiEakicXMpprZBjNbklTXwcxmm9knZjbLzNonLRtlZivNbLmZXZlUf46ZLTGzFWb2cJR9FhGR\nwxP1EcuTwFVV6kYCb7j76cAcYBSAmfUCbgJ6AgOARyy8Q96jwB3ufhpwmplVXadUQ+PHIcUipFiE\nFItoRJpY3H0esLVK9WDgqeD9U8C1wftBwAvuXu7uMWAl0NfM8oC27v5u0O7ppM+IiEgjk4k5luPd\nfQOAu5cCxwf1nYE1Se3WBXWdgbVJ9WuDOqmDxo9DikVIsQgpFtFoDLfN93SvsPDBQnLycgBoc0wb\n8nrkkd8nH4BYcYyNJRshL9428Q8rcUiscnaWExpLfzJZLi4ublT9yWS5uLi4UfWnIctFRUUUFBQA\nkJ+fTzqZe9q/1ytvwOxkYLq7nxWUlwP93X1DMMw11917mtlIwN19YtBuJjAWWJ1oE9TfDFzi7iNq\n2J6PnTu21j6t+3gdV+ddzfXXXp+mvRQRadrMDHdPy5PfGmIozIJXwqvAsOD9UGBaUv3NZnaEmXUD\negCLguGy7WbWN5jMvz3pMyIi0shEfbrx88AC4mdylZjZcOBB4Aoz+wS4LCjj7suAF4FlwOvAdz08\nnPoeMBVYAax095lR9jtbVB0Gas4Ui5BiEVIsohHpHIu7D6lh0eU1tJ8ATKim/n3gzDR2TUREIhL5\nHEtDS3WOZdvCbRzd4eg619c1tysPjHogXd0TEWmU0jnH0hjOCsuIjTs30nt47zrbxQpj0XdGRCSL\n6F5hWUzjxyHFIqRYhBSLaCixiIhIWimxZLHERVGiWCRTLEKKRTSUWEREJK2UWLKYxo9DikVIsQgp\nFtFQYhERkbRSYsliGj8OKRYhxSKkWERDiUVERNJKiSWLafw4pFiEFIuQYhENJRYREUkrJZYspvHj\nkGIRUixCikU0lFhERCStlFiymMaPQ4pFSLEIKRbRUGIREZG0UmLJYho/DikWIcUipFhEQ4lFRETS\nSokli2n8OKRYhBSLkGIRDSUWERFJKyWWLKbx45BiEVIsQopFNJRYREQkrZRYspjGj0OKRUixCCkW\n0chYYjGz/zCzj8xsiZk9Z2ZHmFkHM5ttZp+Y2Swza5/UfpSZrTSz5WZ2Zab6LSIitctIYjGzE4G7\ngXPc/SygFfBNYCTwhrufDswBRgXtewE3AT2BAcAjZmaZ6HtTovHjkGIRUixCikU0WmVw2y2Bo83s\nIPAFYB3xRHJJsPwpoIh4shkEvODu5UDMzFYCfYF3GrrTtRkz5mFKSrbV2a5r1xweeOAHDdAjEZGG\nl5HE4u6fmtlvgBJgDzDb3d8ws1x33xC0KTWz44OPdAYWJq1iXVDXqJSUbCM/f1yd7WKxutukQ1FR\nkX6RBRSLkGIRUiyikZHEYmY5wGDgZGA78GczuwXwKk2rllNS+GAhOXk5ALQ5pg15PfLI75MPQKw4\nxsaSjRVtY8UxgErLk8ula0sr/eNLTPbVVI7F4uX8/JrLpaWxiu3XtT6V01NOaCz9yWS5uLi4UfUn\nk+Xi4uJG1Z+GLBcVFVFQUABAfn4+6WTuh/TdfXgbNbsBuMrd7wrKtwFfAS4F+rv7BjPLA+a6e08z\nGwm4u08M2s8Exrr754bCzMzHzh1b6/bXfbyOlbNX0v+e/nX2NVYYo+DhgpT2a9iwcSkfsRQU1N1O\nRKShmBnunpa560zNsZQAXzGzNsA+4DLgXWAXMAyYCAwFpgXtXwWeM7OHiA+B9QAWNXCf02bx4g8Z\nNmxcSm01HyMiTU2m5lgWmdlfgMXA/uC/jwFtgRfN7FvAauJnguHuy8zsRWBZ0P67Xsuh1sxZC2rd\n/q712zlie3k6duWQ7N7tKR3ZwOHNxxRp/LiCYhFSLEKKRTQydlaYu48Hxlep3gJcXkP7CcCEVNbd\nqtWXal1etu8jvCyWyqpERKSeUkosZvZXd7+srrrGolXLI2tdbi1a8q9/baGwsKjOdfniPWnqVcPT\nL7GQYhFSLEKKRTRqTSzBHMhRwHFm1gFITOy0oxGe7lsf+8sOkJPTv852a3cXRt8ZEZEsUteV998G\n3gfOCP6beE0D/ivarsnhqnqqbXOmWIQUi5BiEY1aj1jcfTIw2czudvcpDdSnRmXz5i0pn8G1ePEy\n0nw6uIhIk5PSHIu7TzGzC4D85M+4+9MR9avRKC8n5TO45s27NtrO1JPGj0OKRUixCCkW0Uh18v4Z\n4BSgGDgQVDuQ9YlFRETqJ9XTjc8FetV27Ui22le2ncKiYSm13bxnebSdqSedox9SLEKKRUixiEaq\nieUjIA9YH2FfGqWDrcrJ6Z+fUttVq+akffupXqWvK/RFpLFINbEcBywzs0XEb8ECgLsPiqRXUiHV\nq/Sru0Jfv8RCikVIsQgpFtFINbGMi7ITIiKSPVJ6gqS7v1ndK+rOyeHROfohxSKkWIQUi2ikelbY\nTsJnoxwBtAZ2u3u7qDomIiJNU6rXsbRNvA+eNT+Y+PNTpBHT+HFIsQgpFiHFIhopDYUl87hC4KoI\n+iMiIk1cSonFzP4t6XWDmT0I7I24b3KYNH4cUixCikVIsYhGqmeFDUx6Xw7EiA+HiYiIVJLqHMvw\nqDsi6afx45BiEVIsQopFNFIdCutiZq+Y2b+C10tm1iXqzomISNOT6uT9k8CrwInBa3pQJ42Yxo9D\nikVIsQgpFtFINbF0cvcn3b08eBUAnSLsl4iINFGpJpbNZnarmbUMXrcCm6PsmBw+jR+HFIuQYhFS\nLKKRamL5FnATUEr8Dsc3AMMi6pOIiDRhqSaWB4Ch7t7J3Y8nnmjGR9ctSQeNH4cUi5BiEVIsopFq\nYjnL3bcmCu6+BTj7cDZsZu3N7M9mttzMlprZl82sg5nNNrNPzGyWmbVPaj/KzFYG7a88nG2LiEh0\nUk0sLcysQ6JgZseS+sWVNZkMvO7uPYEvAh8DI4E33P10YA4wKtheL+JDcT2BAcAjwT3LpBYaPw4p\nFiHFIqRYRCPV5PAbYKGZ/Tko3wj88lA3ambtgIvcfRiAu5cD281sMHBJ0OwpoIh4shkEvBC0i5nZ\nSqAv8M6h9kFERKKR6vNYngb+DdgQvP7N3Z85jO12AzaZ2ZNm9oGZPWZmRwG57r4h2GYpcHzQvjOw\nJunz64I6qYXGj0OKRUixCCkW0Uh5OMvdlwHL0rjdc4Dvuft7ZvYQ8SMTr9KuajklHxcW0iYnJ76h\nNm04Ji+PnPx8ALbFYuzZsKmi7bZYDKDS8uSy7zvAtlisxuVVy7FYEQD5+f1rLH/2Wbj9utp/9tkm\nYrGiWteXLPGHkjjEVzleTmgs/clkubi4uFH1J5Pl4uLiRtWfhiwXFRVRUFAAQH7w/ZUu5n5I392H\nt1GzXGChu3cPyhcSTyynAP3dfYOZ5QFz3b2nmY0kfsf+iUH7mcBYd//cUJiZ+SVjx9a6/fUri9mw\n4G36DP1OnX2d94dfc+FdP0ppv96f+gT33VFSZ7tnn72WW28tTGmdqbaNxcZRUDAupXWKiFRlZrh7\nWuau6/08lnQIhrvWmNlpQdVlwFLit40ZFtQNBaYF718FbjazI8ysG9ADWNRwPRYRkVRlJLEE7gGe\nM7Ni4meF/QqYCFxhZp8QTzYPQsUw3IvEh+JeB77rmTjUamKqDgM1Z4pFSLEIKRbRONxThg+Zu38I\nnFfNostraD8BmBBpp0RE5LBl8ohFIpaYsBPFIpliEVIsoqHEIiIiaaXEksU0fhxSLEKKRUixiIYS\ni4iIpJUSSxbT+HFIsQgpFiHFIhoZOyssG+0r205h0bA6223eszz6zoiIZIgSSxodbFVOTv/8Otut\nWjUn+s4QHz/WL7I4xSKkWIQUi2hoKExERNJKiSWL6ZdYSLEIKRYhxSIaSiwiIpJWSixZTOfohxSL\nkGIRUiyiocQiIiJppcSSxTR+HFIsQopFSLGIhhKLiIiklRJLFtP4cUixCCkWIcUiGkosIiKSVkos\nWUzjxyGdJJO/AAAOVUlEQVTFIqRYhBSLaCixiIhIWimxZDGNH4cUi5BiEVIsoqHEIiIiaaXEksU0\nfhxSLEKKRUixiIYSi4iIpJUSSxbT+HFIsQgpFiHFIhoZTSxm1sLMPjCzV4NyBzObbWafmNksM2uf\n1HaUma00s+VmdmXmei0iIrXJ9BHL94FlSeWRwBvufjowBxgFYGa9gJuAnsAA4BEzswbua5Oj8eOQ\nYhFSLEKKRTQylljMrAtwDfB4UvVg4Kng/VPAtcH7QcAL7l7u7jFgJdC3gboqIiL1kMkjloeAHwGe\nVJfr7hsA3L0UOD6o7wysSWq3LqiTWmj8OKRYhBSLkGIRjVaZ2KiZfQ3Y4O7FZta/lqZey7IafVxY\nSJucHABatWnDMXl55OTnA7AtFmPPhk0VbbfFYgCVlieXfd8BtsViNS4/lHL53r0V24/FigDIz+9f\nbfmzzzYRixXVuDxRTkj8oSQO8VWOlxMaS38yWS4uLm5U/clkubi4uFH1pyHLRUVFFBQUAJAffD+l\ni7kf0nf34W3U7FfArUA58AWgLfAKcC7Q3903mFkeMNfde5rZSMDdfWLw+ZnAWHd/p5p1+yVjx9a6\n/fUri9mw4G36DP1OnX2d94dfc+FdP0ppv1Jt+/7UJ7jvjpKU1vnss9dy662FdbaLxcZRUDAupXWK\niFRlZrh7WuauM3LE4u6jgdEAZnYJcJ+732Zmk4BhwERgKDAt+MirwHNm9hDxIbAewKKG7ne67Cvb\nTmHRsJTabt6zPNrOiIikWUYSSy0eBF40s28Bq4mfCYa7LzOzF4mfQbYf+K5n4lArTQ62Kienf35K\nbVetmnPI2ykqKqo4BG7uFIuQYhFSLKKR8cTi7m8CbwbvtwCX19BuAjChAbvWpCxe/CHDho2rVFda\nGqOgoKhSXdeuOTzwwA8armMi0uxkPLFIeuze7eTnj6tUV918XCw27vOVzYB+lYYUi5BiEY1MXyAp\nIiJZRokli1U9Fbk5q3racXOmWIQUi2gosYiISFopsWSxxEWUorH0ZIpFSLGIhhKLiIiklRJLFtMc\nS0hj6SHFIqRYREOJRURE0kqJJYtpjiWksfSQYhFSLKKhxCIiImmlxJLFNMcS0lh6SLEIKRbRUGIR\nEZG0UmLJYppjCWksPaRYhBSLaCixiIhIWunuxo1cqg8Fq+6BYMmPNG7u9NyNkGIRUiyiocTSyKX6\nULDDeSCYiEg6aSgsi+loJaRfpSHFIqRYREOJRURE0kqJJYvpOpaQrlcIKRYhxSIaSiwiIpJWSixZ\nTHMsIY2lhxSLkGIRDSUWERFJKyWWLKY5lpDG0kOKRUixiEZGEouZdTGzOWa21Mz+Zmb3BPUdzGy2\nmX1iZrPMrH3SZ0aZ2UozW25mV2ai3yIiUrdMHbGUA/e6e2/gfOB7ZnYGMBJ4w91PB+YAowDMrBdw\nE9ATGAA8YmaWkZ43IZpjCWksPaRYhBSLaGQksbh7qbsXB+93AcuBLsBg4Kmg2VPAtcH7QcAL7l7u\n7jFgJdC3QTstIiIpyfgci5nlA32At4Fcd98A8eQDHB806wysSfrYuqBOaqE5lpDG0kOKRUixiEZG\n7xVmZscAfwG+7+67zMyrNKlaTsnHhYW0yckBoFWbNhyTl0dOfj4A22Ix9mzYVNF2WywGUGl5ctn3\nHWBbLFbj8kMp+74Dad9+QiKZJIbBqpZLS2OVbryX+MPK9nJCY+lPJsvFxcWNqj+ZLBcXFzeq/jRk\nuaioiIKCAgDyg++TdDH3Q/ruPvwNm7UCXgNmuPvkoG450N/dN5hZHjDX3Xua2UjA3X1i0G4mMNbd\n36lmvX7J2LG1bnv9ymI2LHibPkO/U2c/5/3h11x4149S2qdU20axzvenPsF9d5TU2S4WG0dBwbiU\nti0izYeZ4e5pmbvO5FDYE8CyRFIJvAoMC94PBaYl1d9sZkeYWTegB7CooToqIiKpy8hQmJn1A24B\n/mZmi4kPeY0GJgIvmtm3gNXEzwTD3ZeZ2YvAMmA/8F3P1KFWI1Xdc1t2bSvlmJy8SnW+95/AuAbr\nV2NRpOduVFAsQopFNDKSWNx9PtCyhsWX1/CZCcCEyDrVxFX73JZYOBeTsPa14obqkog0Uxk/K0yi\nUzWpNGf6VRpSLEKKRTSUWEREJK2UWLJY1VORm7Oqpx03Z4pFSLGIhhKLiIiklRJLFtMcS0hj6SHF\nIqRYREOJRURE0iqjt3SRaCXfCiZh85ZShv1gWEqf75rblQdGPZD+jmWArlcIKRYhxSIaSizNTLmV\nkX9tfkptY4WxSPsiItlJQ2FZTHMsIf0qDSkWIcUiGjpikRotLl6c0rBZNg2ZicjhU2LJYtXNsdTH\n7rLdKQ2bNYUhM42lhxSLkGIRDQ2FiYhIWimxZDHNsYT0qzSkWIQUi2gosYiISFppjiWLHe4cS6qa\nwiS/xtJDikVIsYiGEosctmya5BeRw6ehsCymOZaQfpWGFIuQYhENHbFIg0l1yAx0bYxIU6bEksUa\nao4lVakOmUH6h800lh5SLEKKRTSUWKRRagonBIhI9ZRYslhjOlqpr3SfEKBfpSHFIqRYREOT9yIi\nklZN6ojFzK4GHiaeEKe6+8QMd6lRa2xzLFFIdcisdG0pfb/UV8NmaF4hmWIRjSaTWMysBfBfwGXA\np8C7ZjbN3T/ObM8ar12lpVmfWFIdMiv9SynTZk2jZENJnW3/sfIfdD+1e53tmur8TnFxsb5MA4pF\nNJpMYgH6AivdfTWAmb0ADAaUWGpQvndvprvQaOzdtTflJDRv9DwuvfbSOts11Qs+t23blukuNBqK\nRTSaUmLpDKxJKq8lnmxEMqI+1+Vk+1GQSLKmlFhS9unbRbUu37d7F5g1TGcyaK9+jVXYVpr+WNTn\nupxUj4JeGfdKWofrqms7b/Y8Yttin2sXRVIbM2FMSvuTqYQai8UafJvNgbl7pvuQEjP7CjDO3a8O\nyiMBrzqBb2ZNY4dERBoZd0/LL+6mlFhaAp8Qn7xfDywCvunuyzPaMRERqaTJDIW5+wEz+3dgNuHp\nxkoqIiKNTJM5YhERkaYha668N7OrzexjM1thZvdnuj9RM7MuZjbHzJaa2d/M7J6gvoOZzTazT8xs\nlpm1T/rMKDNbaWbLzezKzPU+/cyshZl9YGavBuVmGQcAM2tvZn8O9m+pmX25ucbDzP7DzD4ysyVm\n9pyZHdFcYmFmU81sg5ktSaqr976b2TlB/FaY2cMpbdzdm/yLeIL8O3Ay0BooBs7IdL8i3uc8oE/w\n/hji809nABOBHwf19wMPBu97AYuJD3/mB/GyTO9HGuPxH8CzwKtBuVnGIdjHAmB48L4V0L45xgM4\nEfgHcERQ/hMwtLnEArgQ6AMsSaqr974D7wDnBe9fB66qa9vZcsRScfGku+8HEhdPZi13L3X34uD9\nLmA50IX4fj8VNHsKuDZ4Pwh4wd3L3T0GrCRLrgMysy7ANcDjSdXNLg4AZtYOuMjdnwQI9nM7zTQe\nQEvgaDNrBXwBWEcziYW7zwO2Vqmu176bWR7Q1t3fDdo9nfSZGmVLYqnu4snOGepLgzOzfOK/TN4G\nct19A8STD3B80KxqjNaRPTF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(samples(random.uniform, 0, 200))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And try a constant distribution, where everyone starts out the same:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.00 0.0 100 100 100 100 100\n", + " 20,000 0.48 94.0 1 11 72 226 424\n", + " 40,000 0.49 97.3 1 11 71 235 446\n", + " 60,000 0.50 98.1 1 11 68 233 443\n", + " 80,000 0.50 99.1 1 11 69 227 472\n", + "100,000 0.50 99.2 1 11 68 229 452\n", + "120,000 0.50 100.9 1 11 67 235 444\n", + "140,000 0.50 100.9 1 11 70 228 472\n", + "160,000 0.50 101.3 1 10 70 229 474\n", + "180,000 0.50 100.4 1 11 70 226 455\n", + "200,000 0.51 101.6 1 9 68 233 471\n" + ] + }, + { + "data": { + "image/png": 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HwgHcDpsnpbOyoD36snWJHgYYqX5L0tN5ra0t7p2Ptt/okDwtmeRpyaQvTsdT5KFrQxet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\nI0Xyxzsc8NRTRmieT38azj3XaolSnlgiwd9aWrjv0CE+O2k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GTh3I5xs+5w9X/6FM6+teYSKSiVJ5r7DjHrG4u5vZaHc/G3g3FR+aSd5b+h73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\n9md+kC+Lez9SmI+HgDeAEcF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def constant(mu=MU): return mu\n", + "\n", + "show(samples(constant))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The resulting histogram looks different, but only because the starting distribution is so narrow and tall; the end distribution has a Gini coefficient of about 1/2 and standard deviation of about 100, just like we get from the other starting distributions.\n", + "\n", + "Here is one that statisticians call the [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) (with carefully chosen parameters):" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.50 97.5 1 9 71 230 442\n", + " 20,000 0.50 101.2 1 10 68 237 474\n", + " 40,000 0.50 98.8 1 11 70 230 451\n", + " 60,000 0.50 100.6 1 11 68 232 460\n", + " 80,000 0.50 98.3 1 10 71 229 444\n", + "100,000 0.50 99.1 1 11 71 228 457\n", + "120,000 0.50 99.3 1 11 70 232 450\n", + "140,000 0.51 100.7 1 10 68 232 465\n", + "160,000 0.49 98.2 1 11 70 232 445\n", + "180,000 0.51 101.7 1 10 69 233 480\n", + "200,000 0.51 103.2 1 10 67 233 494\n" + ] + }, + { + "data": { + "image/png": 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wTkpP56ysLBauX8++JUvsFkdjEa3vtVL3XB0dmzvwbfYR9odx57px5R4MufX+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\nPNop+EIYtXFAIpIpIgHz2A98DqgC1gDfMi/7JrD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Z2ctm9jszaw90c/e18T7XAPvH7XsAKzLevype1yyE2EeqTMmFmEuZklGm9CTu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\nZw84H/h9xvJPgR8BbzRVrpb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def beta(): return random.betavariate(0.9, 12)\n", + " \n", + "show(samples(beta))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Surprise:** We can confirm that the starting population doesn't matter much. I thought it would make a real difference, but we showed that three very different starting populations—Gaussian, uniform, and beta—all ended up with very similar final populations; all with G around 1/2 and standard deviation around 100. The final distribution in all three cases looks similar to the normalized beta(0.9, 12) distribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Effect of Transaction Function\n", + "\n", + "Does the transaction function have an effect on the outcome? So far we've only used the `random_split` transaction function; we'll now compare that to the `winner_take_all` function, in which the wealth from both actors is thrown into a pot, and one of them takes all of it:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def winner_take_all(A, B): return random.choice(([A + B, 0], [0, A + B]))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.89 287.7 0 0 0 364 1448\n", + " 40,000 0.94 398.9 0 0 0 111 2135\n", + " 60,000 0.96 475.2 0 0 0 0 2576\n", + " 80,000 0.97 560.1 0 0 0 0 3066\n", + "100,000 0.97 629.9 0 0 0 0 3346\n", + "120,000 0.98 683.4 0 0 0 0 3569\n", + "140,000 0.98 729.2 0 0 0 0 3843\n", + "160,000 0.98 800.1 0 0 0 0 4144\n", + "180,000 0.99 859.6 0 0 0 0 4140\n", + "200,000 0.99 902.2 0 0 0 0 4140\n" + ] + }, + { + "data": { + "image/png": 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YEmZUY4wxHgqnZvR3YDqwnGNrRiec2h0PrGZkTPxRVV5NeJWFutDrKH2WFzWj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\nPWOl5d0WGt5uoL6wnn137WP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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population, transaction=winner_take_all)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the results look **very** different: most of the wealth goes to the 99th percentile (purple line on the far right of the plot), with everybody else getting wiped out (although the 90th percentile holds out until around 50,000 transactions). The Gini coefficient is all the way up to 0.99 and the standard deviation is over 800, and still rising.\n", + "\n", + "That makes sense: any time two actors with non-zero wealth interact, one of them will end up with zero—the number of actors with zero wealth increases monotonically until all the wealth is with one actor, and from then on the wealth just gets swapped around.\n", + "\n", + "At the other end of the spectrum, let's try a transaction function, `redistribute`, that taxes both parties 31% (the average income tax rate in the US) and splits that tax revenue evenly among the two parties; the non-taxed part is split with `random_split`:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def redistribute(A, B, rate=0.31):\n", + " \"Tax both parties at rate; split the tax revenue evenly, and randomly split the rest.\"\n", + " tax = rate * (A + B)\n", + " Arand, Brand = random_split(A + B - tax, 0)\n", + " return tax / 2 + Arand, tax / 2 + Brand" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.32 59.8 18 36 88 183 285\n", + " 40,000 0.33 62.1 16 34 86 187 289\n", + " 60,000 0.33 61.9 18 35 85 185 297\n", + " 80,000 0.33 60.8 17 35 87 181 287\n", + "100,000 0.33 61.7 17 34 87 183 297\n", + "120,000 0.33 61.2 18 35 88 183 291\n", + "140,000 0.33 61.1 16 35 87 185 291\n", + "160,000 0.33 61.6 17 35 86 186 294\n", + "180,000 0.33 61.6 17 35 86 183 301\n", + "200,000 0.33 61.3 17 34 87 187 295\n" + ] + }, + { + "data": { + "image/png": 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33yyEuLAzPl9ysrYNjhkHFOuOZW3xWlbvXR04YVaQnKxtivT001Yr6TH4pGRr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\nlBVSyq2hdCOwBxhI9LR/e/qzQk9Hyz1wh5KxaD/Okuhp//a0QwTbvjc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MvhQkp7OAlcAzQHnQZiKxy7YQ1I8zswPM7CjgGGBpCvsXEZE0Svaqwd9OeFxo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\n6sKYuXgRzWgOzCsWCnP3bPc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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population, transaction=redistribute)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Another surprise:** This transaction function does indeed lead to less inequality than `split_randomly` or `winner_take_all`, but surprisingly (to me) it still increases inequality compared to the initial (Gaussian) population.\n", + "\n", + "Here's one more interaction function, `status_quo`, in which both actors keep half of their wealth out of the transaction, and the other half is randomly split using a triangular distribution in such a way that the most likely outcome is that each actor keeps what they started with, but from there probability falls off on either side, making larger and larger deviations from the status quo less and less likely:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def status_quo(A, B):\n", + " \"A transaction that is most likely to leave things unchanged, but could move any amount of wealth around.\"\n", + " a = random.triangular(0, (A + B) / 2, A / 2)\n", + " return (A / 2 + a), (A + B) - (A / 2 + a)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.21 38.5 34 56 95 152 210\n", + " 40,000 0.22 40.5 31 53 95 155 222\n", + " 60,000 0.22 40.3 31 53 95 155 217\n", + " 80,000 0.23 41.3 31 52 95 154 222\n", + "100,000 0.23 41.8 32 52 94 158 224\n", + "120,000 0.23 41.0 32 53 95 157 223\n", + "140,000 0.23 40.9 31 53 94 155 216\n", + "160,000 0.23 41.2 31 53 94 156 223\n", + "180,000 0.23 40.9 31 52 95 156 219\n", + "200,000 0.22 40.6 31 53 95 155 219\n" + ] + }, + { + "data": { + "image/png": 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KqdUi8hnwuFLqSxG5ChillLpaRM4HzlZKXSAiccAaYDxaEfO1wHil1M9Wcfly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\n+ee8vOflwHdAFRUwcKBWVkI5oK8pbm1lSWkpuXFxquKBm7Z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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population, transaction=status_quo)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `status_quo` transaction increases inequality from the initial population, but not as much as the other transaction functions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Effect of Interaction Function" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have been using `anyone` as our interaction function: anyone can enter into a transaction with anyone else. Suppose that transactions are constrained to be *local*—that you can only do business with your close neighbors. Will that make income more equitable, because there will be no large, global conglomorates? " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def neighborhood(n, width=5): \n", + " \"Choose two agents in the same neighborhood\"\n", + " i = random.randrange(n - width)\n", + " return random.sample(range(i, i + width + 1), 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.48 94.6 1 12 73 223 431\n", + " 40,000 0.49 96.2 1 11 71 232 428\n", + " 60,000 0.49 95.4 1 11 73 226 426\n", + " 80,000 0.50 98.6 1 11 69 234 449\n", + "100,000 0.49 98.4 1 11 71 228 465\n", + "120,000 0.49 96.7 1 11 72 233 445\n", + "140,000 0.50 99.3 1 10 70 229 460\n", + "160,000 0.49 97.8 1 11 70 231 442\n", + "180,000 0.50 98.3 1 11 70 233 461\n", + "200,000 0.49 96.4 1 11 72 226 437\n" + ] + }, + { + "data": { + "image/png": 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Q3D/2/oOzxpyVemWGigiMHWskI1iErvmVYDhsISL8eOJE7qqp4YING9gbCFj+\nHcOB7hcJUm0LcQruEjeB6gDuYjejvzKailsqGPXZUaioInggSPhQGBXPzEjWsDogEXlIRJpEZFO/\ntrtEpE5E3jZfl/Y7doeIVIvIdhG5uF/76SKySUR2icj9/do9IvKkec1bIjK237EbzPN3isj1g+l5\n8ODxbbtbdzO7bPY7v/nh5vHHobbWGAlpbI9SiureXvaZ2zIsbW/niaamdKulyQDmvDyHszvOZsJ9\nE3AXu40MuL8eZv+P9rPtI9tYUbqCDedtSLea74hhnQMSkbOBbuBRpdRss+0uoEsp9dNjzp0GPAEs\nACqAfwCTlFJKRFYBX1ZKrRGRF4GfK6VeEZGbgVlKqS+KyEeADyilPioihcBa4HRAgHXA6Uqp4xKu\nRUR99rOK3/3u6Pbfrv0tq+tX89DVD1loEQuJRIw9gR58EM4+O93aaAYhphTZr79OnsvFxYWFnFtQ\nwLn5+UzJyuy9XDTp59BfDrH1A1sp+0QZ0x5L7SJn288BKaWWi0hlkkPJlL4aeFIpFQVqRKQaOENE\naoFcpdQa87xHgWuAV8xr7jLbnwEeMN9fArza53BE5FXgUuCpZHr6ktQbnVE6g99v+P0J7zFtuN0w\nYQI023S7CA0AoXgc3+uvU+7xsPOMM8hxZW68XmMPVEyx/979ND7cSLDGKPfkG2/TosknIF1zQF8W\nkQ0i8j8i0rcv8WjgQL9z6s220UBdv/Y6s+2oa5RSMaBDRIoGkZUUs2TXUVTkVXCwK0lszi7U18Oq\nVTBxomUidaw/gVW28DocfLWigoZwmEczNOSm+0UCO9ii460Oau6uYdr/TuOcwDksUUsYf/f4dKv1\njkjH49ivgbvN0NoPgJ8An7VI9jsaDr744o1897vjACgoKGDu3LmMnDkSn8t3pMP1LT6zzeeyMsjO\nZllrK/RbHGcb/TL8cx9WyLtCKV7JziaqlG3u72Q+b9iwwVb6pPPzhg0b0q5PtDuKW9yEakO83f12\nyr5/2bJlPPzwwwCMGzcOKxj2dUBmCO6FvjmggY6JyO2AUkr92Dz2MkZ4rRb4l1Jqmtn+UeA8pdTN\nfecopVaJiBNoUEqVmucsUUp9wbzmQVPGcSE4EVFXXql4/vmj23vCPYz4zxH0fLMHh9gwWTAWgylT\n4OGH9RyQzakJBFj09tvUL16MU8/5aE6Rnm09rJmxhim/n0Lu/FyypmbhcGdmLbhUaC30G5mISP9F\nK9cCW8ww/ylwAAAgAElEQVT3zwMfNTPbxgNVwGqlVCNGaO0MMWZsrwee63fNDeb7DwFLzfevABeJ\nSL6ZkHCR2ZaUZGH5LHcWLoeLtkDbydxr6nA6Ye5c+OUvoasr3dpoBqAxFOK7NTVcUFionY/GErKn\nZzPrb7M4cN8B1s5eyxs5b1D3y7oTX2hDhjsN+wlgBTBZRPaLyKeA+8yU6g3AecD/A1BKbQOeBrYB\nLwJfVInh2ZeAh4BdQLVSqq8GzUPACDNh4TbgdlNWG/B9jEy4VcD3lFLtA+kZSlLsIBKPoJRCYeP8\n+m99C556ytie2wKODT+9l7HCFv9v925Gv/UWDhEemDTp1JVKE7pfJLCLLVz5Lnp39JJ/Tj4z/zST\nUZ+y6caZJ2C4s+CuS9L8h0HOvwe4J0n7OmBWkvYQ8OEBZD0MPDwUPZNVw/Y4Pcwrn8equlVcPvny\noYhJPWvXwnXXwWwbr1d6D/Px0lK29vTw97Y29gWDFLnd6VZJ8y4hZ24OE+6bQN39dez83E7G3jGW\niq9UpFutk0bXghNRlZWKmprjj33zn9+kN9LL/Zfef/xBO3DZZXD99fCxj6VbE80A/LWlhSu3bGHb\nggVMy85OtzqaDCcejVNzVw1dq7vo3tQNcSi6rIjyL5STvzj/xAIsxPbrgDIFxwCBSEEo9henVpmh\nEgrB8uVGEoLGtlxSVMRNo0Zx2aZNbFqwgDy9DkhzCrQvbaf+F/XEumMAzFs7j9x5uWnW6p1jw/Su\n1DNQZKS6tZqROTYt9OlwQHb2wLvpvQPsEt+2A1bZwu1w8LOqKmpDIbpiMUtkphrdLxKkyxbxSJzt\nN2yn+kvVjL19LDNfmMmi/Ysy2vmAHgEByYtJx1Wc53Y+x4NXPJh6hYaC222kX//f/xnJCBpbEojF\n+OKuXTgBt86C07xDutZ00bmyk/kb5+PMevds5aFHQEBBkl1sHeJgfMF4tjRvOf6gXaiosHRX1L7F\nZxrrbPGr+npeOHyY1rPPptSTeTtWgu4X/UmXLbyjvUQOR9h5004aH2mkd3dvxlbA7o8eAQElJce3\nRWIRmnqa7BuCa22FZ5+Fp59OtyaaQajwemmNRvlnWxsfSNbRNJoh4Kv0sbB6IU2PN3H4pcPsu3Mf\n4eYw3govvkofvkof2bOyKb+5HKcvc0ZIegQElJUd3/bnHX9m7si5TC6enHqFhkJ1NeTlwZlnWiZS\nx/oTWGWLLHOEOjsnxxJ56UD3iwTptIW70E3FVyqY8eQMztx/Jme3ns2sv85i7DfGkrcoj47XO1g5\nZiUbL9nIzi/spH35gEsfbYMeAWHsbHAs5bnl7GuzZoHnsNDQAIWF6dZCcwJGuN2McLv586FDfHXM\nGBx6HkhjEc4sJ9lTs8meaqT3l99UTvBAkO6N3Wy5cgsNv22g8tuVZE3PovD8Qjxl9gsB63VAIurL\nX1Y88MDR7Wvq13Dt09ey/7b99tyzZc4c+PrX4ROfSLcmmhOwPxjkqs2bCcTj/GPOHMYk2/9Do7GQ\nwN4AXWu66FjeQfOTzURaIsxdNpeC85JMeL9D9Dogi0iWHRuIBhiVM8qezgegsVEXIc0Qxvp8rJ8/\nn7ErVxJ+jz/waYaHeDTOjut3EO2IEmmOEG4ME24K48x14hvvY+RnRpI9234LofUcEMmX0kwqmsSW\n5i3YdoR4ySXw0kuWitSx/gRW2+LxpiZC8TiVXq+lclOB7hcJ7GoLcQqtr7TS+mIr0c4oE/9rIud0\nncPZh89m/tr5TLx3Iu5C+5WC0iMgjOmUYwnHwuR6c+07ArrsMnjiCbj55nRrohkCB8NhZmZn4xqo\n7IZGcxJ0rOyg9ge1OP1OHD4HKqbInZdLx4oOArsCdLzVQelHStOt5gnRc0Ai6qyzFMuXH92+r20f\n73vkfdTcVpMWvU5IezuMGQN79ybPI9fYiqVtbVywcSNvnnYai/NTW7NLk1nEI3E6V3YS64wR6zFe\n8d648b43RrwnzoH/OpD02mlPTCNvUR7eCu+w7xGk54AsYlSSSuaN3Y32XQMEkJ8PRUWwZQu8733p\n1kZzAmabhUj/88AB/qwdkGYAgnVBVo5ZmfSYu8yNZ6QHz0gPZTeU4RnpwV/lxzvKi4oqVFwx4uoR\niMOmUZskaAdE8iSEjlAHuV4b11nasQOCQci1Tsdl/bb2fq9jtS0KXC4qvF6KXC72B4OMzaBMON0v\nEgy3Ldwj3Ez+78mIS4h1xYh2Rol1xY5737Olh84VnYQOhnBmO/FP8pM1KYvA7gDZs7LJmZWDp9xj\n3ykEE+2AgMOHj2+bO3Iuaw+upTfSS5Y7K/VKnYilS+GKK2D+/HRrohkCLoeDLQsW8MPaWk5bu5bL\ni4t5YNIk8nV1bE0/nD4n5Z8rH/L5SinCjWECuwL07uqlc0Un+761DxVRTHt8GmUfT7LK3kbo3k/y\nLLhifzHhWJhoPJp6hYaKxU83+ik3wXDYIt/l4r6JE7mgsJBLN23iyuJiPlRq/4li3S8S2M0WIoJ3\nlBfvKC+1P6yl7e9tZM/KJv+sfIouLUq3eidEOyCSFxToCnfhcXrI8+alXqGhUFYGLS3p1kJzkvzk\nwAG+vmcPD1RVca1OHtEkQSlF5HCEUG2IaHuUWLeZjNCd5NWvvXdnL94KLzP/MhP/BH+6b2NIaAcE\nJCvT1dDVQEmWjX8g/vEPOOMMS0XqWH+C4bLFh0pK+MmBA1T6fDhtHp/vQ/eLBMNli8CeANuv3064\nKUy4MYzD48BX6cNV5MKZ7cSZc/TLPcKNr9J3XHvOvJyMKkaqHRDGvm7HEo1H8bpsvGiwuBh27063\nFpqT4O+trdy5bx9ZDgcX6Tp+mn60v9ZO54rOI58dbgeRlgjxUBxnrhNnjxNnr/FyBVxkTcmy/fzO\nUNAOiOQjoKaeJvK9Nk6X/bd/gxtvtFSkfspNYLUtIvE4127dyjUjRrB8ypSMWpCq+0WC4bLFqE+P\nYtSnjfUg8XCc4P4gXWu76F7XTfsb7bS/1g5xyJqaRe6CXJz5mTPKGQztgEi+JbdTnASigdQrM1T2\n7IFQCJSyPBlBYz0uET47ahT319XxvoICPp1s8ZnmPU+wNsi6BeuIHDJK9DtznRReWMjoh0ZT9P4i\nPCX2q2h9KmTOY9gwEo8f3zazdCZ1nXWpV2aoXHwx7NoFAeucpF3rXKUDq20RVYr76+q4dfRoPpYB\nmW/90f0iwXDbwlfpY87SOUx7YhpjvzmWwgsKCdWH2HfnPt6qeIvlRctZPWM1m67YxJ6v76Hl+cxO\nRNIjICDZmsBsTzbd4e7UKzNUXnsNpk2DLBuuUdIch9vhYJzPx6aeHnpiMfwWbqWueXeRMzOHnJk5\nxHpjBHYHCNYECe4LEtgboPvtbjpWdNC7rZfWv7Vy4L8OcG7wXBzezBxL6FpwIurDH1Y89dTR7ZFY\nhJx7cui8vdOeyQjXXw+nnw633ZZuTTRD5E+HDvFvW7cyPSuLrRZnMGoym0hb5Mhi0t5tvbS/3k73\nxm5843z4x/vxjfMZr/G+I+9dha60VjrQteAsorf3+Da3002eN4+OUAelLhuGTG64AT7+cTjrLFiw\nIN3aaIbAJL+fYpeLf8yZk25VNDZi99d2U/fTOnLm5ZA1OYusKVmMv3s8eYvzcPrf3SPlzBy3WUyy\naRSlFOFYGKfYtANccAH84hfGSMgidKw/wXDY4oYdO1icn8+oDNsTSPeLBFbbIrAnQN3P65j62FRm\nPTeLaY9NY9xd4yi8oPBd73xAOyAgeRZcb6SXUDREkd/G5Syuugrq6uDNN9OtiWYIzM3JIZQs40Xz\nnsU33kflHZXUP1DPuvnreD3rdVaOX8nbi98muD+YbvWGHT0HJKIuu0zx4ovHH6v4aQVLb1jK5OLJ\nqVdsqEyfbuwL9Mor6dZEMwiReBzP669zVXExz82alW51NDYlHooTqgux64u7aF/WjivfhX+yUena\nP9lP1mTjr3+SP+0VD/QckEUMtKOB3+2nsbvR3g4oGITvfCfdWmhOwO/MbXe/NHp0mjXR2BmH14F/\nop85r8wxpgGaEpWuA7sCND3eRO+uXiKHIlR+u5LyL5Tj8GRuICtzNbcQzwBru84YfQY17TUp1eWk\nUMpwQOVDL98+GDrWn8BqW2zv7eVjpaVcXGTjkO4A6H6RIJW2EBG8I70UnFtA+WfLmXjfRGb+eSaT\nfzuZ7NnZ7L51N3v/Y2/K9BkOtANi4EICEwom8MoeG4e2XnoJSkth3Lh0a6I5AcUuF16Hg/d6yFtz\n6vRu7aVncw8AvgmZs7FhMnQIbhBcDhdl2TYu+Fdfb2xIZ9FaAF3zK4HVtvjkyJEsfvttzlq/nhWn\nn26p7OFG94sEVtlCKUXvjl6iHeZ2C10DbLfQrz3cHCZcHybcFMZV4MJd6kbFMvuBRjsgBv79FhHa\ngm2pVeZkCAYHjh9qbENcKV5ubSUOLMyz6f5SmpQSrA2y+crNhBvDxHuSZ0a6il3GItQJPrKmZ1Hy\noRJyTssha1JWxlY+OBbtgAZhQfkCltUsS7caA7N9O0yaZJk4ve9LAitt8VJrK1+urubFWbO4rLjY\nEpmpRPeLBFbZwj/Oz6LdiwCIBWJEDkWIHIoQbg4n3h8KE2k23rcva+fAjw8AcE7gnFP+frugHRAD\nj4DWNaxjXMG4lOpyUgQC0NOTbi00J+D9RUXcOHIkqzo7M9IBaYYXp9+Jc6wT39jB53Pqf13Pvjv3\nsWb6GtylbjylnsTfkmM+l7pxj3DjcNt7pKTXAYmoG29U/OEPxx+b9qtpPPaBx5hfPj/1ip2IeNzY\nlvuNN2Dq1HRrozkB12zezJSsLH48cWK6VdFkMLFAjFB9yBglNZsjpubEyCncHKZ3ay/hxvBR152+\n6nTyzrA2/KvXAQ0jh3sPc7DrIKeNPC3dqiSnpwe6u+Gpp+DOOyGDNjh7L9EaifC/zc08d/gwU3p7\ntQPSnBJOv5OsqiyoGvicxscb2fHJHUe17f7qbibcO4GCswuGWcOTQ/9qkTwE1xpopSSrBKfDpvWY\ncnNh71549ll45hlLROr1HgmssMXP6+qYtGoVyzs6+Pvs2WzP0ArYul8kyARbqPDRUa3xPxpP+efL\nyZpqv61b9AiI5A6oyF9EQ3dD6pU5GUaNgsWLYe1a+PCH062NxqQhFOLW3btZ3dnJmnnzmOD3p1sl\nzXuIUZ8eRenHSmlf2s6OT++g8o7KdKs0IHoENACdoU5KskrSrcbg7NwJjzwCH/qQJeJ0plOCU7HF\nd2pqiCjFlgUL3hXOR/eLBJliC6ffSd7iPCLNEZqfak63OgOiHRAQix3fFogGcDuTlMm2E9/5Dtx6\nq7EYVWMbzi8o4C8tLdxVU5NuVTTvYVwFRoBr20e3sfebeznwswPEQ/aqxq5DcCTfD2h/x37G5I1J\nvTInw9SphvIWVULQ6z0SnIotPlZWRmM4zAuHDxNTCmcad620At0vEtjBFvFQnMjhCJHWCNH2qPFq\nix73PtISOXLN/nv2A5B/Tj558+2zGPqEDkhEJgO/AcqUUjNFZDZwlVLqB8OuXYoIhY5vq8yvpK6z\nLvXKnAyHDsGUKenWQpOE68rKeOHwYcpXrOBjpaX8tKoKR4Y7Ik1qqf9NPZ0rOw1ncyhCpMX4Gw/G\ncRe7cRW5cBW4cBWafwtcuAvdeEd7yZ6RjavIxbjvjrPF9t0DccJ1QCLyGvB14LdKqdPMti1KqZkp\n0G/YERF1ySWKl18+ur36cDWLHlrE4W8cTo9iQ+HLXzYc0Fe+km5NNAOwq7eXKatX033OOWQ7bZpR\nqbEV8VCc3p29rJ2zlpIPllB2fRnuEmNhqafEgzPPaQtnkqp1QFlKqdXH3HD0VL7UbiTzwavqV3HB\n+AtSr8zJ8PbbcOml6dZCMwgFLuO/2MrOTi4oLEyzNhq7s+tLuzj464MAOPwOSq8rpfiKYls4nOFg\nKEkILSIyEVAAIvJBwOb5ySdHsgfTsflj7R+CGzECenstE5cJaxxShVW2+HtbG4vz8jg3P98SeelA\n94sEw22L8d8fz9SHp1J2QxnZM7PZ+bmdvOZ4jWWyjO4t3cP63elgKA7oS8BvgakiUg/cBtw8FOEi\n8pCINInIpn5thSLyqojsFJFXRCS/37E7RKRaRLaLyMX92k8XkU0isktE7u/X7hGRJ81r3hKRsf2O\n3WCev1NErh9Mz66u49uK/cUc6j00lNtMH/F48hQ+jW04Oz+fzT09XLppEwH9b6U5Ae4iNyNvGMm0\nh6cxb/U8ii9P1A7s3tBNx8oOwk3hQSRkFid0QEqpvUqpC4ESYKpS6mylVM0Q5f8BuOSYttuBfyil\npgBLgTsARGQ68GFgGnAZ8GtJjDt/A3xGKTUZmCwifTI/A7QqpSYB9wP3mbIKge8AC4CFwF39Hd2x\nxJNkJrqdbiKxyPEH7EZHh2Wi0p3dYyesskVjOExXLMblxcX4MrRcku4XCVJti/IvlDPu7nFU3FZB\ny59b2H3Lbt4a8xaR1gz4bRoCQ8mCKwCuB8YBrj6foJS65UTXKqWWi8ixy3CvBs4z3z8CLMNwSlcB\nTyqlokCNiFQDZ4hILZCrlFpjXvMocA3wiinrLrP9GeAB8/0lwKtKqQ7zHl4FLgWeSqZnsi1aPE4P\nwWgQpZR9469ZWcaeQBrbUun1ku90Mi831779SGNb8s/MJ//Mo5+dV01ZxaqqVbjyXTjznLjyzL/H\nfCYOY74xBqfPvskvQ3kkexHD+WwG1vV7vVNKlVJNAEqpRqDUbB8NHOh3Xr3ZNhroPxlTZ7YddY1S\nKgZ0iEjRILKSkuzBdFzBOLI92Wxv2T7U+0o9NTUw07pkRB3rT2CVLZa2t+N1OJjoy9ytk3W/SGAH\nWyzYsoCF1QuZs3QO0x6dxvgfjWf0F0dTfGUxWZOziPXEqLmzhpq7ao6rC2c3hpIF51NKfXUYdbDS\nQu/oEXPbthv57nfHAVBQUMDcuXNZsmQJWe4slr++nObi5iND774OaIvPJSUsW7ECXC576PMu+tzH\nqcrzbNxIaOdOwuY23Ha5v5P5vGHDBlvpk87PGzZssI0+4hb+9M0/0f12N7NDs4k0R1gfXY+r0MX8\nqvkg8Prq13G4HJZ837Jly3j44YcBGDduHJaglBr0Bfw/4HPAKKCo73Wi6/pdXwls6vd5O8aiVoCR\nwHbz/e3Af/Q772WM+Zsj55jtHwV+0/8c870TaO53zoP9rnkQ+MgA+qnbb1fHEYlFlOf7HtUV6jr+\noB0IBpXKzVXq0KF0a6IZhNpAQPGvf6nf1derSCyWbnU07yKan21W/+JfquGRBtW7p1dFuiIqHo+n\n7PsN9zE0PzDQayghuDDwn8BbJMJva0/CxwlHj0yeB240398APNev/aNmZtt4jB0vVisjTNchImeY\nSQnXH3PNDeb7D2EkNYAxP3SRiOSbCQkXmW3JbzBJUslrNa8xqWgS2e7sk7jVFOJ2g98PLS3p1kQz\nCMVuN9+urORndXV8a9++dKujeRcQaY+w9rS17PzMTgC8o734J/hx5diz2sFgDMUBfQ2oUkqNU0qN\nN18ThiJcRJ4AVmBkru0XkU8B92I4h53ABeZnlFLbgKeBbRjzTl80vSwYqeAPAbuAaqVUX92Ch4AR\nZsLCbRijKJRSbcD3MRzlKuB7Sqn2gfSsS7LcZ1bZLOo66+z7D+pwwPXXG5vRWcSx4af3MlbZItvp\n5NuVlVR4vbjs2pdOgO4XCdJti2hXlIO/Okj3hm6i7VGm/M8UCi/I3AXOQ5kD2g28o9WOSqnrBjh0\n4QDn3wPck6R9HTArSXsII3U7mayHgYeHomc0SV2HkqwSYipGW6CNQr9N/4G7usCcW9DYk5hS/O7g\nQV5ta+OTZWXpVkeT4SzPW37kff7Z+QT2Bqh7oA53iRvvKC++CT68o72IIzMedobigHqADSLyL+BI\n2U41hDTsTKGt7fg2EWF22Ww2NW3ivHHnHX+CHZg6FbZts0xc38Sjxjpb1ASDfGX3bmZkZTEmQzPh\ndL9IkG5bLNq/iODeIOFDYSLNRnHS3p29dPyug56tPRAH8Qi+8T6Kryim6r8G2bvbBgzFAf3FfL1r\nGWjPMI/TQyCaZK8Gu7Bvn+GENLZlot/PCzNncuvu3SzZsIHWs86i0G3zfaY0tsU3xodvzNEPMkop\nXnO8duSzp8xD3sI8Cs8vtPc6RoZWCeGRZK9UKJcqSpJsfLqvbR+bmzZz9tizU6/QUKmrg4oKy8Sl\nO75tJ6y0RYXXy95gkM+MHJmRzkf3iwR2tIWIcF70PGb/fTbjfzCewgsKCewJsPnyzey6eRfB/fZd\nrD7gCEhEnlZKfVhENnP8Wh2llJozvKqljoKC49s2N29mfvl8cjw5qVdoqPh8yVP4NLZBKcXS9nZK\n3G7OSFZyQ6OxAHEKRRcWUXRh0ZG21n+0cvDXB1lZuRKAxU2L8ZR60qViUgYLwd1q/t2OsR9QH4JZ\nc+3dQrIkhNlls9nQuMHeQ9h4PPl2ru+QdMe37YQVtlBK8akdO1jb1cXq009n3ECxXpuj+0WCTLJF\nvCdO++uJ5N/I4YjtHNCAITilVN+WC1VKqdp+rxrgXTXx4PUe31aZX4mIUNtRm3qFhkJDA7zyClx1\nVbo10QxAdyzGn1tauHv8+Ix1PprMJf+cfMo+UXbkV96ZY7+acAM6IBG52Qy/TTG3Quh77QM2DXRd\nJpJsP6BwLExXqIsif9HxB+1AJGKsBbIwtdeO8e10YYUtcl0ufjh+PP+2dSs1Fo5UU43uFwkyyRYH\nHzxI699aqbitgun/Nx3v6CRP2mlmsCSEJ4ArMaoNXNnvNU8p9YkU6JYyQqHj2+o668hyZ9l3DuhX\nv9Kjnwzg2pISKrxexq9aRUeyWK9GM0w4c51EWiIEdgcI7ArQ/HQzHW91EDoYQsXtUaR0wDkgZWxl\n0AF8LHXqpIdk8/gTCicQiAZoC7RRnFV8/AnpJh43suB6eiDbmnJBmRTfHm6sssVtu3fTEonwpxkz\nyHcNZdWD/dD9IkEm2aLiKxWMuGYEjb9vpO4XdUSaEnsIiVuY/NvJjPrUqDRqOLR1QO96VJKHge0t\n2ynJKrFvCO6734XSUsMJTZmSbm00A1Dp83FdaSkfSJbrr9EME6GDIWrurqHl2RacOU4KlhTgn+DH\nV+nDW+nFN9aHf1L65yUzc4tGi0k2gAhEAhT4CuybAbdyJcyYYanzyaT49nBjlS0+VFLCI42N9GTw\ndty6XyTIBFt0b+xm9fTVOP1O5q2fx6J9i5jx5Awm/GgC5Z8vp/jSYrKnZ+Nwp//nP/0a2IBkIbjW\nQCsFviQLhOxAMAj33gvXDVRqT2MXZmVnc25BATft3Eko2d7vGo3FqJgi1hEjVBeid1svvbt6iQXt\n+QCkHRDGdMqxdIQ6yPflH3/ADtx9t5G6d/PNlorNpPj2cGOVLfxOJ3+dNYtgPM77NmzgtfZ2ohnm\niHS/SGB3WyiliIfjiEc49MwhNl2yidVTVvPWqLeI9drPCek5IMCTZG1WMBrE7bBp2ZSdO+Gaa5Iv\nYNLYjiynk/+bMYNf1tdza3U1G3t66D7nHLKT5f9rNKfAitIVRFoilH6slJy5Ofgn+8malIVvog+n\nz379TY+ASJ6GvaNlB1OKbTq5//73wxNPWF6GJxPi26nCals4RLilooIHJk2iwuvNKOej+0UCu9hC\nKUVgb4DWV1ppeLiB2ntqqf5KNc58o19NfWQqY78xlpJrSsiekW1L5wN6BARAd/fxbQ1dDUwZYVMH\ndN118MtfwrPPwsfe9Vny7xoCsRgf3baNi4tsmlmpsS2xnhgdKzroXNVJ16ouOld1Ih4ha2oW3nIv\nnnIP/io/E+6ZgH+i3xYJBkNBVLIc5PcQIqKuuUbx5z8f3b6ybiUfe/Zj7LllDw6x4T/mT38Kr74K\nL7984nM1tuDX9fV8qbqax6dN4+N6czrNSVB9azX1v6jHN9HHuO+Oo2BJAb6K9O4vJSIopU4pTdiG\nv6ypJxI5vm1RxSLiKs7etr2pV2gorF8P116bbi00J8HN5eV8euRIGpLFfDWaQaj6aRVTH5mKr9LH\nvm/uw11s0/npk0Q7IGDs2OTt+d58usNJ4nN2YOdOmDzZUpF2iW/bgeGwRVgpumMxohkWddD9IkE6\nbBGPxul4s4PgviAqpnD4HMaeBO8C9BwQxrY6yegKd5HntekeLgsXwvPPg83TQjUGr7W3c9XmzZyZ\nl8dN5eXpVkdjU1RcEToYondrL13ruuha10X7snZ8lT4KLypk7NfHkn9evm2TCk4W7YCAgweTtwej\nQXyu9MZZB6W01FJxdl/jkEqstsXjTU3cUlHB98ePt1RuKtD9IsFw2CJUH6L6lmoCuwIE9gSIh+Lk\nL84nd2EuJR8soernVWmf7xkutAPC2NXgWOIqTjQepTfSm3qFhkJtLZx7brq10AyBQCzGCy0tnJds\n613Nex5XgYvCCwvxjvHiHeuld2cvXeu7UEpBDMKNYTxlHjxlHtxlbuNvsRtxZH4cTjsgoKsreXu+\nN5/WQGtqlRkqV18N998PH/wgWFSvbtmyZfpp18QqWyilyHrjDYCMdUC6XyQYDls4s52Mvnn0UW3R\nzihda7voWttFsCZI56pOIk0Rwk1hQnUhYl0x5r4+l4JzMrNP9aEdEJCXZJrHIQ4mFE6wrwO68Ua4\n804jG+7009OtjWYARISLCgspcrn44ujRJ75AowFceS4Kzy+k8PzCo9qjnVGW5y8HoOGhBoL7ghRf\nUYy7KDOz4rQDAtxJ/u1i8Rg7D++kMr8y9QoNBacTsrIsrYagn3ITWGmLDd3d/H3OHMvkpRrdLxKk\n2xZ7vr7nyPvWl1rp3dGLd4yXwvcVDnKVfdFp2CTPglt7cC1+l9++1RAALrzQWIyqsTWVPh/PHjqU\nbjU07wJCdYk1ZM5sJw63g4b/bmD/f+6nc20nmVZYQDsgIBA4vi2mYhT4CuxZBaGPggJLR0B6vUcC\nKyRF34gAACAASURBVG3RGolQ5fcTz7Afhz50v0iQKlsopYi0Reit7qVjRQctz7fQ8FADBecWUPG1\nCko+XIJ4hI7lHTQ/2czeb+zl7QVv0/5ae0r0swodggOi0ePb1jesp6qoKvXKDJWuLnjqKaMoqcbW\nPDptGl+uruZf7e38YerUdKujsTkHf3uQXV/aBYPsnjD+B+Mp+0QZ7hI37hFuPCUenHlO+26gOQDa\nAZE8Dbssp4zG7sbUKzNUtm83YodnnmmZyHTHt+2ElbZwAuN9Ppotrl6eKnS/SJAKW4z67CiKrywm\n0hoh2hql/fV2au6sOeqcokuLyJ2XO+y6DDfaAZE8CeGC8RfwkWc+glLKnk8V5eXGCtq//MXYG0hj\nW27bvZtVXV3sXbgw3apoMgBxCs5cJ7Xfr6X9tXYCu405gpnPzWTEVSPSrJ212HiCI3XkJnmQWFW/\nioWjF9rT+QBUVMDSpXDTTUYqtgXoWH8Cq2yxubsbnznEXtXZaYnMVKP7RYJU2aLlTy0cfPAgvdt7\nURGFZ6SHvXfsZf0569l89Wa237id2ntr6VzdSTyaWTvs9kePgIC6uuPb5o6cy87DO6nvrGd0nk3X\nb8ybB2PGgM6wsi3fralBATWLFlE5UNFBjeYYRt4wkpE3jAQgFogRbYsSOhii++1uo0bc2i6aHmli\nH/sY/8PxVH7TpstFToDeD0hEXXWV4rnnjj925f9eybljz+XrZ3099YoNlVGjYPlymDgx3ZpokvDP\ntjYu3LgRgNfnzuWcDK2GoEkvqyavIlBthOIKLy7EN95HzpwcCi8oxD/Jn5ZIjd4PyCKSbVDZFeri\nn3v/yY1zb0y5PifFJz8J3/teurXQDEBTOEyJ281zM2eyOD8/3epoMpTyLxgV1MUrFF5QSNaULMo+\nUUbW5Cz7ThMMAe2AAI/n+LZsTzbReJQcT07qFToZbrkFXnrJElE61p/AKlt8fPt2/nvyZK4aMQJn\nhv5Q6H6RIF22GPXZUYy7exwqpNj7H3vZ89U9dK7MzDnF/mgHRPIsOIc4yHJn2XdDuj7uvRf02hLb\nkud0cndtbcYmIGjSi1KKSGuEYE2QWFdiYdCcf8yh6KIkoZsMQychkHwEBEYiwobGDVw08aLUKjRU\n4nF4/HFYtcoScXq9RwKrbNFy1lk81dzMFZs3871x4zKyIKnuFwlSbYvmJ5rZ/ontR7V5x3hxl2Rm\n8dFj0SMgkjsgpRStgVY8zgG8kx3YuBHKyizfmltjHW6Hg4hS+BwO9geD6VZHk2GUfbyM01cdXe1+\n+pPTyZlt86mBIaIdEJDsd6Gxu5H6rnr+f3tnHiVXVS38366qW1VdPc+dHtKZ58RAEiAJkUFABCXg\nA0V5IPBEUfChn0w+RJCFPvH5FBXXCzJIFBVEfQgfAYIfxjAEQobOnE7SmUg6PaTn6urums73x63u\n6iRdIZ2urlvddX5r3VXn7rp9e9+9Tt19z7777HPu2HMTr9CpEg5HtzigY/1R4mGLzV4v39y9m6/s\n2sVzM2bwoxGaqaj7RZThtEWoK0TP4R68W700v9HMh49+SPUt1ez55h6wgVFkkHNBDjbX6Llt6xAc\nA88DcjvcBEIBvH4v2e4kzV6aOxeys80khE9/2mptNMfxuW3bqPP72ThvHrMyRscTq2botP6zlarz\nq/r2nSVOAi0BAIxcA0eeA2exE88MDxlnZlB8fTGeGR6cBUkcjTlN9Dygk8wDuulvNzE+ZzzfO+97\niVfsVPnv/4Zdu+Dxx63WRNOPTV4vl2zaxPk5OTw/c6bV6miSiJ7aHnZctwPfLh/+Wj/ps9Ip+kIR\nnuke3OPcuMe5ceQ4kj69Oh7zgPQICEhPH1ie6cxM7ndAAJdcAr/+tdVaaI7jgX37aAgEODsri0A4\njDFQxVtNSuIqdTH3H3MBCPvD1D1TR81dNYTao1luE340gbH3jLVKxYShfxWYxQQGYvWB1SwZuySx\nygyWjAzw+eJyKh3rjzJUWzw/cyavzp7N7+vruWfv3vgoZRG6X0SJty1sThtjvjyGkptKyFqY1SfP\nvXhkrnA6WLQDwlxaZyAm5k1kX+u+xCozWCorweGA9eut1kTTD5fNxqX5+VS63Uz3eKxWR5OkhHvM\nEZB3vRdftQ97ph2ArpoBVskchegQHANnwQG0dbfR3NWcWGUGi80GkybBvn1mcdIhoOd7RImHLVoD\nAVY2N3N3RcXQFbIQ3S+ixNMWrW+3sv1z2wn7w0z+5WRyL8zFKDKS/t1PPNEjIKCzc2D5wbaDXDDu\ngsQqM1ieeQb27IFFi6zWRHMcGXY7nysq4upt21jX3j5il+TWDA9pE9PIvyKfYFOQgz88iLPYmVLO\nB7QDAiAUY+lbX8CHy+FKrDKDZfVqMxGhtHTIp9Kx/ijxsIXDZuMXkybx+aIibti5k4o1a/jhgQOE\nRpgj0v0iSjxt0frPVo48fgSAzq2d7Lx5J3vv28vhZYfx7YrPe91kxzIHJCL7RWSTiGwUkbURWa6I\nrBSRahF5XUSy+x3/HRHZLSI7ROSSfvIzRWSziOwSkUf7yZ0i8lzkb9aISMyUkra2geWG3cAmSe6j\n162DL33Jai00MchwOPjvSZOomj+fqwoKuG/fPtbHeumoSSmKPl/EorpFzNs4j9mvzCZ7cTY2t42O\ntR2sn7eeNZVr8G71EmgOMFqny1g2D0hE9gLzlFIt/WSPAE1KqR+LyD1ArlLqXhGZAfweWACUA38H\nJiullIi8D9yulPpARFYAP1dKvS4iXwNmK6W+LiKfB65SSl07gB6qvFzx4Ycn6jh32VyevOJJ5pfO\nj78B4sWCBfCTn8B551mtiSYGrYEAX66upiEQ4J6xY/lUXh62FAu1aAZHT10PW6/cSqg9RE9tD+Hu\nMK5SF85SJ+6x7r75Qu7xbjLPzMTIT3xtuJE+D0g4cQS2FOi9ky4HVgH3AlcAzymlgsB+EdkNnCUi\nB4BMpdQHkb/5LXAl8HrkXA9E5H8GHoulSKwkhDnFc1ixe0VyO6DsbOjpsVoLzUl4+MABqrxeNi9Y\ngMdut1odzQjAVeJi3nvRpKJQZ4iumi42nL2B9neildWNIoOy28sYd/84C7QcOlbGlxTwhoh8ICJf\njsiKlVL1AEqpOqAoIi8D+o9RDkdkZUD/QjqHIrJj/kYpFQJaRWTA+uUDLUgHcNeiu1i2btngriqR\ndHfDqlVQXh6X0+lYf5R42MIbDPJ4bS3L6+v51ZQpI9b56H4RxSpb2NPteKZ7CAfCFFxZwFm7z2JJ\n1xIW1y8esc4HrB0BLVZKHRGRQmCliFRjOqX+xDM+GHOoePTojTz44DgAcnJymDt3Lueffz7pznS6\n93Tz5j/e5MILLgSiHbA3HdPSfRFWTZ4MjzzC+cuXW6/PKNrv5XT/ftzZZzP+/fdZtHcvD5eU8MnI\nU06yXN9g9quqqpJKHyv3q6qqrPv/Yai/pZ6qZVVcc9E1lN1WltD/v2rVKp555hkAxo0bRzxIilpw\nIvIA4AW+DJyvlKoXkRLgH0qp6SJyL6CUUo9Ejn8NM7x2oPeYiPxa4Dyl1Nd6j1FKvS8iduCIUqpo\ngP+t8vIUTU0n6tUd7CbnRzm03tuK2+EelmsfMv/1X3DkCPz0p1Zroolwd00NPz90iJvHjOF/9FIZ\nmjjQ+GIj267aRtY5WRRdV0TpLaWWV8WOxzsgS65ARDwikhFppwOXAFuAl4AbI4d9CegtEfoScG0k\ns208MAlYGwnTtYnIWWIm0N9w3N/0poddA7wZSx9njHJvWxu2MiV/SvI6HzCTEF55BQIBqzXRRHi1\nuZm7Kiq089EMGqUU/qN+OjZ20PRaE3XL6zj444PmkgwANii/vdxy5xMvrArBFQP/KyIqosPvlVIr\nRWQd8CcRuRlzdPM5AKXUdhH5E7AdCABfV9Gh223AM4AbWKGUei0ifwr4XSRhoQk4IQOul4GW5Abo\nCfbgsCV5sYjzzoOiInjuObj++iGdatWqVX1D71TndG0RCIc5Ggiwq6sLpdSomFio+0WU4bBF+wft\nbDhrAwDiFOweO66xLpwlTpxFToxig7LbyrBn2EmfFaNy8gjFkrurUmofMHcAeTNwUYy/+U/gPweQ\nrwdmDyDvIeLAPoqSkoHlaw+vZWH5wlM5hXWIQE1N7JLemoRi2GzsWLCAj1dVcUt1NT+YMIHiWENs\njQZw5EZvw8qvmPP2HJzFTowiA7t7ZCaunCqjYxw3RGItVHmw7SDjc8cnVpnB0tICbjfk5w/5VPop\nN8pQbJFjGLx9xhlk2O3MWLuW5XV18VPMAnS/iDIctnCPc5N3aR6e6R6yl2Sz5bItvFf5Hm+lvcUq\nWUX3odG7lHuSx5cSgyOGFYLhYPKH4H7wAzMMpyeiJhVZDgePTp7MV0pLOWfDBs7OzGSaHqVqBmC1\nsfqYfWeJk4wzMnDkOXDkOLBnjN5RUJLfXRNDODyw3LAbdAeT/OljxQp4LOYc20GhY/1R4mWL8W43\nZ2Rk8NNDh/j11KlDV8wCdL+IMhhb+Kp9dB/spudwD/5af99noDlAsDlIoMX8PJ65q+bimZoaS3ho\nB0Ts1yfVTdXMLjrh9VJyceGF5mTUCy+0WhPNALza3MzqtjbmZ2biD4dx2nTUOxWo+20dNXfWkD4r\nHVeZC2eZE880D7kX5uLId2DkGThyHThyHdjT7aMiWeV00A4Is5rNQGxv3M6Uc5M8lfaf/4QnnojL\nqfRTbpR42eKzhYWsPfNMFm3cSKbdzoPjk/yd4gDofhHlVG1h5BsE24J0bunEX+fHOGhgFBo4C50Y\nhQb5V+Tjrkji6R0JQjsgYofg0o10/CF/YpUZDGvWQGsrnHGG1ZpoTsLktDSCSuEQIaQU9hR92k0l\n8i/PZ0nnEoJNQfyNfgKNAQJHAwQaA3Qf6Gbr0q1MfXIqaZPScI91j5p5PYMlNa/6OGIlKbV2t1KS\nESNHOxl4+WW48kpwxWfNouPL0KQy8bRFjmHwxJQp3L9/P75Yi08lMbpfRBmMLWwOG85iJxmzMsi9\nIJeia4oo+3oZEx+ZyPiHxvPhTz5k8yc3s9q9mlWyil237xo+xZMU7YCIvSDdFVOv4C87/pJYZQbD\nzTfD8uWwfr3Vmmg+gr+3tHBxbi6ZsVIuNSmBUoqmV5toeKGBQEOAYEsQcZgjYrGn3shY/xqIXYqn\nKL0oubPglDLLOFRWxuV0OtYfJd62+EppKV/auZPtnZ3MGGHp2LpfRDldWxz88UGaVzbTuakTBCb9\nfBLpM9Jxlbtw5DlSNglBj4CIPQJq7mom152bWGUGg8tlTmIqKLBaE81HcGFuLg9UVvKZLVusVkVj\nAc4Sp5kNV+ok5A1Ru6yWln+0YOQbKet8QDsgADo7B5ZXN1UndyWE116DuSdUNDptdKw/SrxtEVKK\nLIeDvd3dVI2wJbl1v4hyurYouaGE6cunc8Y7ZzDl8Sl4N3mpubMmvsqNQHQIjtgL0oVVGMOW+KVu\nT5krroDvfQ+2boVZs6zWRjMA3aEQy2preezwYfIMgz/PnMmcjAyr1dJYwKFfHmLv3XuxZ9gZ98A4\nir9YbLVKlqMdEJCZObC8uauZfM/Qa6wNGwUF5izaxsa4nE7H+qPEyxarWlv5Vk0N/zN5Ml8tLR2R\n4RbdL6IMxRYFVxYQag9x9OWj7PvuPhr/1Ej67HScY5xm5esxTlxjzEmr7vLUmCOkHRCxs5jLMsvY\n17KPRRWLEqvQqRIMmjnk9fVWa6IZgLBS3LN3L9cXF3NNUdGIdD6a+OGucFN5XyWV91US8oVoX9uO\nb6cPf50fb5UX/6t+OjZ04D/sZ8HWBaTPHFnJKqeDfgcEdMdIdCvwFNDhT+J4vdsNv/89PP10XE6n\nY/1RhmKLQDjME7W1XLRpE7V+P8unTSM/1qJTIwDdL6LEyxZ2j53c83Mpu7WM8Q+OZ+rjU5n90myC\nrUEy5mUgTiEciDFDfhShR0CAzzewPNedS2NnfMJbw8auXVBaarUWmn58ZssWXm9pYYbHw68mTyag\nFE49+tGcAhXfrqB9TTubP7mZ7n3d2NJsnNt2LjZjdI4VtAMCuroGlnf4O0gz0hKrzGDYuRN++EN4\n5524nE7H+qMMxRa/nT6dt9vaWNfRwc8PHeK23bt5cdYsFscqOpjk6H4RJV62CPeEzXBbvZ9AQ+CY\nz1BniEBTAKPAIH1WOmIbvQ8v2gEROwRX01LDZ6Z8JrHKDIbycrOSakuL1Zpo+lHkdPLZwkI+W1jI\nXTU1dIXDTE1L4gcZTcKpf7ae6i9X45nhIWthFs5iJ2mT08hanIVrjAvPTA/OgtG/ku7oHNcNkljz\ngKbmT2Vj3cbEKjMYMjLgk58007DjgI71RxmqLR7av5/KNWt4pamJNz/2MQpG8LLcul9EiZctCq4s\noPS2UnzbfdQ9VcfBHx5kzx17sKfZyTkvJyWcD2gHBMR+B+S0O7FLkq9GeNZZ8NJLVmuh6YdSij/U\n1+Ox29m6YAE5IzgBQTM8eDd5qf1Vbd++I9+BzW3rqwuXKohSymodLEVE1FVXKf761xO/e3rj0/xh\nyx/4+w1/T7xip8qOHeaE1N27rdZEg+l8erPfXpw1i6me1FjZUnNqeLd4aXurjc6tnTT8sYFga5CJ\nP51IxbcqrFZt0IgISqkheUz9DgiznNpAXD/ner7x6jdo7W4lx52TWKVOleJiaGiwWgtNBAXU+v0c\n6ulhRVOTdkCaY9j2L9vo2t2FI99B/tJ8iq4pInN+JkqplJwnpkNwgD1GlM2wG0wvmM7OozsTq9Bg\n6OkBm82clDpEdKw/yunaQoCfTJyIx2Zj1gireh0L3S+iDNUWM/88kylPTKH0q6Uov+LAwwdYO30t\n7xa9S9UFVez+xm5qH6+l7Z02gm1D/00nO3oERGwHFFZhWrpbSOowZUkJzJ4Nzz4LN95otTYpTUgp\nrtm2jZ0+H7+dPp2LYxUZ1KQsGXMyyJgTrQUYaAlw6NFDeDd4af1nK62rWvu+c09wc07NOVaomTC0\nA+LkDqitu43yrPLEKjQYRMww3MsvD9kB6fkeUU7HFkop3DYbrcHgqAot6H4RJd628G70Uv9sPRV3\nVVBycwnOYidGkYGz2Ik9I8kToOKAdkDEXg/IJjZCKoRNkvx20tMT+0WWJmE4bDb+MGMGZe++yxst\nLXoEpImJd6uX5lebaXqpiewl2ZTdWma1SpaQ5HfWxOD1xv7OF/Ald0VsgHAYLrtsyKfRsf4oQ7HF\nOVlZ2EfRC2XdL6LEwxZHnjrCutnr2Hv3XjzTPYy9eywqlMR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sOGbPnh3vCOViOb1lOb0Vlpzu784K/773+8ykFTDWHTepBnyoqpNFZCHwkYgM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\nbHddG2BzxPrN7roKm5s5lz7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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population, interaction=neighborhood)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Surprise:** The `neighborhood` interaction is not too different from the `anyone` interaction. \n", + "\n", + "Let's get even more local, allowing trade only with your immediate neighbor (to either side):" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.11 20.1 54 75 100 126 148\n", + " 20,000 0.45 85.3 1 13 79 218 373\n", + " 40,000 0.47 90.1 1 11 76 224 407\n", + " 60,000 0.48 92.0 1 12 73 228 404\n", + " 80,000 0.48 92.5 1 12 73 231 406\n", + "100,000 0.48 94.3 1 12 71 227 421\n", + "120,000 0.48 94.1 1 12 73 226 437\n", + "140,000 0.49 95.7 1 12 71 236 421\n", + "160,000 0.49 97.5 1 11 71 231 454\n", + "180,000 0.48 95.0 1 12 72 227 434\n", + "200,000 0.50 97.8 1 11 70 235 442\n" + ] + }, + { + "data": { + "image/png": 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0LWzC3eyOtjhhZ6BnQI8Cpwdp/71Sarp5vAUgIhXAJUAFcCbwZ/EHtj8EfFsp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\ny22dYSmKlT/JlimlGkWkBFgrIrsxRCmWRKYOjvv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A7l5pZj3isQcAc/LeuyKet1OsXr2WqVPLmxy3sfpDOp9UVtAy/77giYLGzZv3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\n", 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VtSLyDrAWOAb8wv2QAPdx6qXBn/ic3RNZB7N4beVrrL9v/fffC3g3lzHGFJfN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\njDFRs2JijDEmav8fUiIRclxMBf8AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def adjacent(n): return neighborhood(n, 1)\n", + " \n", + "show(population, interaction=adjacent)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is still surprising that we still have no efect from restricting trade." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# United States Distribution\n", + "\n", + "We've drawn from mathematical distributions; let's look at the actual distribution of family income in the United States. Each row in the following table is a tuple giving the lower bound and upper bound (in thousands of dollars of income), followed by the cumulative percentage of families in the row or a previous row. The table I got this from actually had \"\\$250,000 or above\" as the final row; I had to cut it off somewhere, and arbitrarily chose \\$300,000." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "USA_table = [ \n", + " (0, 10, 7.63),\n", + " (10, 20, 19.20),\n", + " (20, 30, 30.50),\n", + " (30, 40, 41.08),\n", + " (40, 50, 49.95),\n", + " (50, 60, 57.73),\n", + " (60, 70, 64.56),\n", + " (70, 80, 70.39),\n", + " (80, 90, 75.02),\n", + " (90, 100, 79.02),\n", + " (100, 110, 82.57),\n", + " (110, 120, 85.29),\n", + " (120, 130, 87.60),\n", + " (130, 140, 89.36),\n", + " (140, 150, 90.95),\n", + " (150, 160, 92.52),\n", + " (160, 170, 93.60),\n", + " (170, 180, 94.55),\n", + " (180, 190, 95.23),\n", + " (190, 200, 95.80),\n", + " (200, 250, 97.70),\n", + " (250, 300, 100.0)]\n", + "\n", + "def USA():\n", + " \"Sample from the USA distribution.\"\n", + " p = random.uniform(0, 100)\n", + " for (lo, hi, cum_pct) in USA_table:\n", + " if p <= cum_pct:\n", + " return random.uniform(lo, hi) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what it looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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ZdLQnkp9F3EN6e9Mfuvxi2tCQZfjwTJvt0lAkS4kKhogAvWvupGUxbf+LRG8q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\nVDBERCQWFQwREYnl/wP9xzRf/8enkwAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist(samples(USA), label='USA')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hey—that looks like the beta distribution. Let's compare:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist(samples(beta), label='beta')\n", + "hist(samples(USA), label='USA')" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.45 88.3 2 18 75 217 420\n", + " 20,000 0.50 100.3 1 10 69 228 451\n", + " 40,000 0.50 102.5 1 11 69 229 468\n", + " 60,000 0.50 101.6 1 11 69 231 481\n", + " 80,000 0.50 100.6 1 10 71 223 480\n", + "100,000 0.50 100.5 1 11 69 229 457\n", + "120,000 0.50 99.0 1 11 70 228 465\n", + "140,000 0.50 99.2 1 10 71 225 462\n", + "160,000 0.50 101.5 1 10 67 232 461\n", + "180,000 0.50 100.1 1 10 70 237 448\n", + "200,000 0.49 98.1 1 12 71 228 455\n" + ] + }, + { + "data": { + "image/png": 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K+HX4NfBppdRqEXlGRN6rlHoO+DTQopSaKiIfAe4ALheRPOC7wEJAgLUi8oRS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\niw0NPLxvH8syMqIXyGK0/c6OvsN9VF5XyZEnj6D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dvTx8FANdc5hLRESakKjFZLWZXW5mLcPH5cDqXAbbkyTxuHJlii6JuZQpGmWK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\nd7KZrTKzeRltnc1supl9bGY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UdNNTp5MU35Iy1a2QGGMKH+vmipCRS0cSt6YXt9/+68eC2EdqmcIXxFyWKTyW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\nWCbvFJr/zbfu30qZYmWoVqY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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(samples(USA))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The USA distribution is indeed similar to the beta(0.9, 12) distribution, and to the stationary ending distribution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Uri Wilensky Version\n", + "\n", + "[Another version](http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/) of this simulation made the rounds in 2017. This version has these rules:\n", + "\n", + ">Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, every person with money gives a dollar to one randomly chosen other person. After some time progresses, how will the money be distributed?\n", + "\n", + "To implement this all-at-once transactions rather than one-at-a-time transactions, I'll define a new `step` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.00 0.0 100 100 100 100 100\n", + " 2,000 0.24 43.4 16 48 93 165 208\n", + " 4,000 0.33 58.7 3 27 96 185 247\n", + " 6,000 0.37 66.1 2 15 99 188 326\n", + " 8,000 0.38 68.2 6 13 91 178 368\n", + " 10,000 0.40 72.5 2 15 85 200 321\n", + " 12,000 0.42 75.7 1 12 92 210 351\n", + " 14,000 0.41 74.2 3 15 79 230 295\n", + " 16,000 0.43 78.9 2 18 83 220 354\n", + " 18,000 0.45 84.9 5 16 78 227 424\n", + " 20,000 0.50 93.7 2 7 70 230 395\n" + ] + }, + { + "data": { + "image/png": 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JNBGbkZk1C556Cqqs5YS/6Hyn+Mn0T7gx+UbfC/QEiqJmZT58GO6807n+yBF1\n/raOT7hjzx7ez8lxKjcJgRGo1v7vjYuI4JnERM7v3NmprU77ZselO8j/Nt91pYvtT8OTwwmID2DQ\n/EEExvpHJgg9JtNMnnkGfv0VwgLDkLMk9596v0O9Lzcq87hf2GBQUxnccYe6JXN9V5nF4ntNHsIf\ndTWm6b1TTkGmpKBMnsyJiRNZM3Ik58bEYJGy1sAArC8tZW5e42sZPKGpLehImsq2lrHn9j3svmk3\nO6/a6dbATCyYSIolhRTp+Ch7s4wRS0f4jYHxBB1yXP7ww3VpZW5IvoHZ62bX1gUZ2/GU0R9+gBkz\nXNdFRoLu4/c5VimZnZVFdnU1AhgWFsavWoZme3roU5XbHVKRag4wuzUrh5495NawxM6IZeh3Q32s\nsu3pcO6ynj3VtDKJiWr5w789zKur69bDeCvjstepqVFX+xcUOJZv3w5DO94X2184YTYTu2pVk9uf\nGxPD0hEjvKhIpzEspRYKlhaABEOgAWulFWup+tj/0P66hgJEoHBat2LONxPcO5jqI3ULHIP7BjN6\n/WhMke3vvl6PyTQR+8D/66875pO84fsbmLd1Xu3x2X3P5rfrfvO1xNbx/feOWzCDmhFAx6/49vhx\nLnWz4h/g8V69+Fffvj5UpFOfrLey2HffPpd1IQPUdSt9XuhDeHK4387o8iR6TKYFfPut47G9gQH4\nbuZ3PtHhMb/wo486Gpi5c1tsYPzRfw7+qaslmmbExrJo2DDOi3GcHTQmIoI948a12sCcLNfJ29hr\nslZZMReYqc6ppmxbGQW/FpD4XCIx5znP4Or7Ul+G/zKciJERXjEw/nitWkv7G7t5gFWrICgIqqvV\n40sGXcK3u+osT5fXulBhrgDayfbLzz6rzipLS1OPb7hBfZx6quob1Pcr8QvSy8tJLy/nyp07qf+t\n2lhayinr13No/Hh627Zs1fEoG0dtpGxLGQBppDXY1pxvJnZ6LLHTYzFFm2rdXJ3O7+R1nScbHdJd\ndtVVcPbZcPPNrtuWVJcQ9ZK6yvq9qe9x+5jbfSWz5VRUQFiYc/nu3Wp2Zp02RzRyl7pl9GiS9fT+\nXmPvnXs5+t5Rt/WJzyWS+GSi7wS1E/SYTBOxNzIffgjTp0N0tHOS4tEfjGZzzmaHspyHckgIT/CV\n1JahKOomZdu3w+rVsE/zKZ9/vrpLWwfwHbcH8mtqeGj/fioVBYE6++ybfMfZSH/t2pUP9RsDj1Cx\np4KqzCrI9WIIAAAgAElEQVSEUaDUKGy/YHuD7SeemEhAJz1zuT26kWki9Vf8g5rDLCOjXrtnnK/l\nxls3MrrbaI9r8tqeFvUNyogRda60ttLUSvxRlyc0FZrNvHbkCC9kZtaWTYiMZFULt84+Wa+TPeYC\nM3v+ugdLiQVplpRtLaPrLV3VNPiVCtYKK0qFglKpULCkwGUfaaSRTHLtsb+MYvzx89P3k2kh/fqp\n62Ua4+kznvaKgfEqGzbAv/6lzjgD2LoVPvgAbrutbXV1MPZWVLDg2DEkahqRPZWVBAhBjaJglpIq\nRWFxvSnnhRMnEq3vAeQWa4WVVZ2dp4RnvZFFv9f7YQw3YggxYAxV//Z8pGftc0OIup9KSL8QWI7f\n/ZifrHTokQw4TsLanreddze+y7sbHfN8RQRGkP1gNhFB7cRf7so1VlICur/fp9yXkcFb2dkNthkY\nGso/evbk7JgYeukBf5fsuXUPOf9xTs8DMGrdKAJiAzCGGQnsok9w8Qa6u6yJCCHkKadIhxT/9d+6\nK1cZwLSkaXx1+VcEm9rRj0B1NYwZAzt2OJZ3kM/bXzArCnk1NTx64ADzjx1zqn+tXz8e6tmzDZS1\nD4pXFbNl0ha39WfUnIEhoEOuxPAZ+jqZZmBvYFyNlJWnFWYOmelU/tPen8ivcJPkrhV4bU78iy/C\n+PHOBubTTxs91V/n6fujLleapJQcq6lhXUkJC/LyCFy+nJ5r17o0MMrkyR43MO3lOjVGdW41hb8X\ncvyb4w22Wx64nGNfO19bb2jyBf6qqzV4NSYjhPgIuBDIk1IO18pmAbcCtm/G41LKJVrdY8DNgAW4\nT0r5q1Y+CvgUCAYWSynv18oDgXnAaCAfmCmlrIugNsC8ec5lQgjmzpjLwvSFTnVRQU3fOKrN2bPH\nMdD/1lvQqZM6xfnjj+HSS6EZG2HpNE6ZxULEypUOZf1DQri+SxeGh4cTaTQSIAQKEGY0cnlcXIdY\nLd5SNp+6merM6kbbhY8KJyBWj2H5M151lwkhJgFlwLx6RqZUSvlGvbaDgC+AsUAP4H/AACmlFEKs\nA+6RUm4QQiwG5kgplwoh7gSGSSnvEkLMBC6WUl7pRkttTObjj+Gmm5zbWBQLWSVZ9JnTx6F83ox5\nXDfCu7tkepyKCliyBJ57znlm2TffqFuE6ngMq5Q8dfAgL2qzxM6IimJ5sfNmUwsGDybMYCCnpoYR\n4eEMCwsj2GDQDY4LLGUWDj52EGuFmg8/dFAowiiwlls59NQhh7a9n+pN1BlRhPQNIbh3MMKoX09P\n4fcxGSFEb+CnekamTEr5er12jwJSSvmydvwL8E/gMPCHlHKwVn4lMFlKeacQYgkwS0q5TghhBHKl\nlHFudNQamS1bIDnZsf7rnV9z+X+dd5G8fsT1zJ0xt6Vv37coCpSVqWtkcnNh5kz1uH4b/QfNJ6wt\nLmZ2VhZLCgootlobbCv1mU5NpmRjCZvHbm6wTYpM8Y2YDkB7jcncI4RIE0L8Rwhh89t0B+z3os3W\nyroDWXblWVqZwzlSSitQJIRoNO/D6687l1066FLuGXuPQ9nzf3neqwbGo/7XoiIwGlU32OjRMHWq\namBuvx3uvx8eeUTdHbMRA+OvPmF/1NWYpvFRUSwYMoSi009n/qBBRBqNxAcEMDA0lOh6u1+K1NTa\nx6L8lsf/2uN1ai7hw8Lp/1Z/+r7SV3283JfgRMdJOakilVSRyoqIFT7R5Cn8VVdraIt1Mv8GntXc\nYM8DrwN/9VDfjVjbG4FEunWD2bOjSU5Orp0rv2zZMhKLEuuaHoQnDz7Jk38+SXxYPJ+O+JSQgJDa\n9rYvQ2uO09LSWt+fyQSnn06qJjtF+5sKkJhIynvvOba31bvpj0bq2+o4TXP5+Yue5n5+3Xbt4gcg\n5fTTHeoTTz2VPuvW1bk0k5OZtmMHjxcUMCw8nKlnnkmEydRkfTb84fp469gQZGDfsH21xweeOMDa\nQ2sBahdY2nKTJZclsyxwGScePUFMSgx/OfMvar0ffp/saUs9qampfKpNEkq07YnSCnzuLnNX58Jd\ntgSYheou+1NKOUgrb8hdliOljHejo9ZdNmuWun/XtGnOab0mfDSBNVlrnM6fNXkWsybP8j/f+dat\njr6/f/9bHcV06aImxvQ3vTpOZFVV0XPt2gbbnJg4kU4ddJGmlJJd1+3i2HwXs8hcbGHsjvGZ4wnu\n2Y6WIfgJ7SEmk4hqSIZpxwlSylzt+QPAWCnl1UKIwcB84FRUN9hv1AX+1wL3AhuAn4G3pJRLhBB3\nAUO1wP+VwIymBP5tXHCBmtbLHV+lf8XMr52nNIOfZWf+4APVLeaKESPUIJRubPyaR/bv55UjRxps\n01HjNkqNwvKg5S06d+yOsYQNcZE4VqfJ+HVMRgjxBbAaSBJCZAohbgJeEUJsE0KkAZOBBwCklDuB\nr4CdwGLgLllnAe8GPgL2Ahm2Kc9aWawQIgO4H3i0Ofp++UX97c1xvZjYwcAEGYN46/y3WHXzKg7d\nd6g5L+OW+kPkFnPbbeoiy8pKmDMH/vnPurqtWyHe5eDOu5o8jD/qaq2mcquVXmvWIFJT3RqY5/v0\noV9wMK80cZ+Zk/E6GQINpMgUh0fic4lNOrd+rMZTmryFv+pqDV6NyUgpr3ZR/EkD7V8EXnRRvgkY\n5qK8GriiNRqTk9VszK54dOKjvLTqJQCqrdWEB4Yzuutogkx+uh97cLC6APPDDx3LjUZIT4chQ9pG\nl45Lfi0o4Ei141qQgokTiannFnuid29fymoXdLmqC+Y8M5YiC3mf57lttyJcDfyPyxhHaP9QX8nT\nsaNDpZVxlbtsxw73v71ZJVn0e6sfNdaa2rLBcYNJv8v99rltzkMPqSn/6/Prr3DOOb7Xo9Mo3xw/\nzmV2WzJ3NLeYlBJruRVrqRVLgYXMlzOJOSuGmtwazPlmrBVWrOVWlHKF419rGQCMYIowqQkxQw0Y\ngg0YAg1ghNJ1pU6vMWzxMDpf0NnH7+zkQM/C3AomTnRtYBSpkFmcSdLbSZgVs0PdY5Me85G6FnLV\nVa6NzIEDvtei0yhD1q9nZ0WFQ5lITeWvXbtyT/fujAgPbyNlrcNcaCbrzSwC4gIoTy8n5/0cos+M\nBolqUMqsdX9LrQiDwBRtoiZXvaEr/L2QTud1whBsIHRwKMZQI8YwI1GToghODKbT1E4YTB0qK1a7\npUONZCIiJKXONzkcOAB97Bb5f7H9C6759hqHNnvu2UNS5ySPakr15N4Rw4erG5bZM3MmzJ+vusva\nQpMH8UddntBUoyiUW63cu28fn+c5u32aO6rxh+tkLbfWuqnAce+WuJlxmKJNRJ0WRdTkKIxhRozh\nRowhTf+OegJ/uE6u8Edd+kimGdQ3MPv3q9nv4+rlCLh62NWkH0vnhZUv1Jad8n+n+NeMsvo88QRc\nWW9i3cSJzTIwOt5jXm4ut+/diwF1MVegwYBJCI6bzW7POXjqqT7T11yKVhSx74F9JFyfgDRLKg9W\ncvQd91sb2zi+UHV35byfo6/K7yB0qJEMSB5+WM1blpDgPuC/7NAyUuamOJXfNeYu3pn6jneFtpSa\nGkhMrJsqd+GF8NNPbSpJp465ubncuHt3k9renJDARwMHellR60gVqW7rYs6LofPUzgR0DsAUbSJi\nTAQBnQP0fGLtFL9fJ+Mv2Af+X38dHnzQTbt6e8r0jOzJ/EvmE2wKpl+nfnQKaTRrTdtQXq5mW378\n8bqyH39UV5zq+AWdVq6k0GJptF3/kBAmREYSbDAQbTLxVO/ehJv8y+lQebCSvPl5BPUIQpgESqWC\nUqVueVy2pQxrpZWqg1WUbyt3ef5pR08jqKufztLUcUB3l7UAd2ve7A1u94juvHnemwyNH8rA2IFe\nWenvUf+rqwDxRRfBxo1qLrO20ORB/FFXczUVTJpU+zy3upqua5wzSwDsq6xkX2Vl7fHlcXGMiYz0\niqaWEtInhMQnE11rqDfKsY/J1KJ4R1dT8cfvE/ivrtbQIadnzJ7tnJwYVIu95fYt3Jh8IzllOVzx\n9RUM/vdgHlj6gO9FNhdFcRzF2BgzRt8N0w9xZWCuiY/nr127cle3bszp3x/r5MnIlJQmGxh/Yfyh\n8Y222XHJDk4sOeEDNTptTYd0l4H7G3xXWzBXPVHlvwsw16+H+gHimBh4+2245hrX5+i0OU8dPMgn\nOTlk19Q02O7dAQO4pWtXAgzt534w1ZTapHxiic8mkvhUorfl6LQSPSbTROyNTFAQHD+uziyrT2Zx\nJr1n162wrnyikmCTHyfVkxI+/xyuv149njpVzWXWubP6RnX8nmpFYWd5OdWKwtTt2ymoF7d5qW9f\nHunVq43UNY9d1+1yWoEfc3YMIkioCyaD6h4OZSEGyneUIwyC7nd3x1JkIWRACCF9Q9ronejY8Ovc\nZf5KdTVERsKjj6quM/v/0/YGZlrSNK8aGI/kKRLC0R3288/QvbuaYmbZsma7yvw1d5I/6vKUJiPw\nR1ERn+XlORkYgBu6dPG5ppaS9GESp+4/ldFbRjNyzUiSU5M5fO5hut3ejfiZ8XS6oBNRE6MIGxZG\ncK9gTFEmlAqFkjUlHJt/jLzP8tg8fjPbzt/Gun7raveFsZY3MdVyE2nr6+QOf9XVGjpk4N/Gyy+r\nfy+5BAzRWVz5teM6k+zS7DZQ1QKuv75uJFNVBSHa3V9KijqNztUubTp+Q1Z1NX/fv9+h7LouXTg1\nMpJLYmNJaEcjUmOw0Wn0ESkjiU2JdWprLjSzYdgGarIdXYbhyeGUpdUFTUeuHIkxTF/v1V7pkO6y\n7Gzo1q2urqCygM6vOOY1Kn+8nNCAdppQ74474P33644rK9WRjY5f8VtBAedu2+ayzlWizJON/B/z\n2TF9R5Panl5+OsZQ3dC0Bbq7rJncf79qYP694d9M+3IaMxbMIO5VxyX/B+872H4NjKLAU085lvnZ\nGgsdlWFhYUS6yciw0VX+o5OM2ItiSZEpjNs7rsF2Xa7tgiG4w/1UnTR0uE9u8mT17webPmDR3kX8\nsOcHFFk3af8/0/5DYnSiT7R4xf96553Qo4djWVycGrtpwnoZf/UJ+6OulmgqsVh4JTOTxw8coOua\nNZRYnWMNsQEBnBUT4zNN3qYxTcLk/iY5RaYw6LNBCINn16n543UC/9XVGjrcLe7ixTBjBqTdkVZb\nZj9teUDnAW0hy3Pcd586u8yeoiIwGJq1KFPHO6wuLuaRehmx/xIdzfdDhxJhNPrf9t4+ILBrIMH9\ngqnaX+VQHtQrCHOBGWOEEUNAh7sfPmnocDEZRXHeiTjl0xSWHV5We+zXiTAbY84c1SdoIykJ9u5V\nn8+bB9dd1za6dGp58fBhHj94kLOio6lQFNaUlLhsd1V8PF8MHuxjdW1D/qJ8dkxrWnxmxP9GYIox\nYQwzYggzqFmcw4166n8voa+TaSI2I/P00/DMM/Xq6i3AbNdGBiA3F44eVZNmnnaac/3KlWqGZh2/\nILWwkL9s3epUfne3brw9YECHHN3YOPHLCbZPcdzCInJiJCWrnA3zZGVyh75W3kIP/DeTZ59VvUlv\nvw27dsHFCy92qF9982qfafGa/zUhAUaNgvHj1XUyGRmwaFFd/aRJ6nDO9sjN9b6mVuKPulqqKaOi\ngneys1l47BgLjx3jQFUVyS5yz71z9CjXNzFzc2s1eZPWaOp8QWdSZIrDI+k9532dxu4a2ywD44/X\nCfxXV2vocDEZgNtvV/9OnQrz/vsRt4y8hWlfqtmKJ3w8AYAfr/yRaae08wzGR47ARx85Dt06d4YT\ndjmjHnnE/Z4HOh5FNPID8nLfvkyIjKRzQABRJhNRJhOh7SidjC/Yee1Ojs0/5lCW+GwixnAjlmIL\nxnCjvqWAn9Hh3GU2Fi6EK65Qn9dYawh63nHBm+UpC0ZDO5+X//DD8OqrjmWBgaobDWDKFHWEo7sY\nfEJDRubyuDi+crUXuI4Dh186zMEnDmIMMxLYJZDKfZUNtg+IDWDicd013Br0mEwTqW9kDh5U9/gC\nSMtNY+T7I2vrjv/jOLGhziuU2z35+c7bgNo47zxYssS3ejoIipRsLy8neeNGl/WP9urFTQkJJIW2\n07VZbYSrjdM6X9QZU7RJHc0INXtAj7/1cD5Zp8noMZkWYruZf/KPJx0MDEDcq3GszFzJ0dLGt5Nt\nDT73v0ZGwt13u66bPx/wX5+wP+pyp0lKyQ/5+Xx49Cif5OTQa82aWgMzITKSMRERhGobkp0WGcmT\nvXt7zMC0p+vUVJRqpTaHmf2jPon/TKTbHd3oektXut7alaT3k9waGH+8TuC/ulpDh4zJJCWBLant\nWX3OYlveNowGI5XmSo6WHmX7se2c/snpwEniNrNRXg7v1Ns+Oi5OnQjQubPrc3SazQmzmRk7nKfj\nnhISwqpRo9pAUftGBAoGLxxM1eEqkKrRUaoUlGoFWS3Vv2ZJ+Y5yStaWULCkoPbcbnd2oyi1CGmW\nIKDvi32Ju9TNaF7HK3RYd9mhQ9C7t2MbKSXnfX4evx34zaH856t/ZsqAKT5Q6WVqatQ4zZw5znW/\n/w5nnul7TScZ1+3axed5eS7rugUGcsxsZsOoUSS72mdCxyNYq6wcefUIAXEBVGdWk/lipkO9CBLI\nate/exMLJhIQc3LnjGsuekymidQ3MllZakZ8e6SUDP73YHbn100bLXqkiMigyJNz/v3y5XV5dkDf\nQdMDlFos7K6oYF9lJZnV1WRUVPCR3RRxgPSxYxkcFtZGCjsuUkqkWWIts7Kq8yqXbfq/3Z+4S+MI\n6tp+Ml97G93INJH6Rqa0VLLheCpVliqmfKGOUvpE9+Fg0UEA7hl7D29Pedurmnyyn/eOHepU5uxs\nSE9XN9ABdcc2WxLGv/0NnnwS4uP9do9xf9Rlr6nQbObujAy+POY4vbZvcDAHqurSpTyXmMiTthkn\nXtbkL7SlJlexG4A00kgm2e15SR8kgUDNmSYgYmwE4UOd1zJ5Gn/8/FprZDpcTMY2dTm3LI8z5zm6\nh87uezbJCcl0CulETHAMUsr2P4JJTgYXSRgpLVUvxMKFvtd0EtJples744GhoZwVE8OziYntal+Y\nk4Vxu8dRnVONIdCAVNSRjFKtULyxmEH9B1GdVY0534w530zuR3Ujzr237XXqa+BnA0m4NsGX8k8K\nOuRIZsMGGDNGLb/+u+v5bNtnLs/JeSiHhPCT4EulKFBcDHl5MGiQY10H+fy9xZbSUkZt2tRou0XD\nhjFVn1zRJkgpkVaJrNGMTI1C+Y5ytp7pnMoHIGRACIYQA4ZAdYtoW5bo/m/0J2JUx4ul6SOZFvDn\nn3VGZniX4U71h+47RK+oXu1/FGPDYICYGNVtVp+ffoJp7TyzQRtySmgoz/fpw5MHDzrVfZCUxK32\nu+PpeI2M+zLIfst5J1sRKNSZZYAhyIAIFBgCDZjzzQ7tBn05CGEShA0NI2ygHi/zJB1ynczDD8Mt\nt6jP/z7h78hZkpfPfrm2PnFOIvO2zvO6Dp/Pie/b17ls6FCHQ3+dp++PulJTUwk1Gnmid28Ojx/P\nt/VW7N+2dy/vZGfzaU4OFa5cll7S5G94S5NSo2AuNFOdXU35jnKXbWSNJGxoGClKCmdUnsHpxaer\nGQD+xCEfWpcruxB/WXybGxh//PxaS4ccyQD8/LPj8S0jb+GR/z1Se3zbotu4dvi1J88aGVDTx4wZ\nA/Yrz/v2hXffVbds1mkxvYKD6RUczPpRoxi3eXNt+T0ZGQCEGI3MjI9vK3ntAimluv6lUn1YK60o\nVepamE1jHF2SNheWIdSAMcyIMcxI2PAwyrc5GhtjpJFR6/S1SW1Jh4zJ/Pijaw/R97u/d8jKvPjq\nxYzqOor4sPiTx3UGapZmV2s5XC0e0mkSt+zezcf1pioD7Bk3Tk8Xg3PKflOMCVMnU61BUSrVxZUi\nUGAMMaoxkRADhiADGKAivaL23OB+wYzbOQ5DYId0xPgcPSbTAtwltp0xcAYGYajdjtk2tfnB8Q/y\n+nmv+0qe98nNVQP+Q4fCzp115WvW6EamhdQ3MBtGjWJMZGQbqfE/SteXOhxbCi1IRWItrnMjJtyc\nQNK7SbrxOMnokJ+mqQHTan3aipwlHTYue2PtG2zI3kClueGMr83FZ/7XsjI13f+dd6ous8sug4su\ncjQwAOvX+61P2B91NaRp7ObNiNRULk9PZ9bBgzx18CDfHD/eppraitTUVBJnJTrEQE7ddyojfh2B\nCKi7Qc79OJflQctrc5NtHOM6oainNPkj/qqrNXTIkcz558OWLeoSkoY4r995LN2/FIBx/xlXW17w\ncAExITHelOg5Cgqc85Jt2wa33QZXXgnh4RAcDJWV6oVZu7ZtdLZzZEoKipRUKgrlVitpZWWct20b\nX7swLPqKfwjpF0JIvxAm10xWYzGVCivCVji0KdtUxvrB6+u2WQ4zYgg0kP99PiH9QwjqFUS/V/oh\nLZKIcREnl0v7JKJDxmRsNPTWFakQ83IMJdWO27xuv3M7Q+OHujnLD6mqgpdect5zGvQ1Mj7gQGUl\n/datcyh7qEcPXuvfv40U+TdSUQ2Otdxa+1DKteNSK2Xbyzj01CG354/eOJqI0R1vLYs30WMyLUSb\n9OOW5PeSnQwMgFXxzVRUjxES4rr84499q6ODYZWS+zIyeOeo83YRr2dl8XpWFpfExvLN0HZ0w+ID\nhEHUzhYDOPj0QQ4/d9ipnSHMQFC3IEIHhyItkqr9VVTur0Ra9Rsnf6NDxmSEqNuwzKnuGYF4RrD9\n2HanuqXXLmVEwgiP6fCJ/1VKdcW/tl9MLTffrF4I28OXmlqAP+pqSNOfhYUuDYw9r/Xr52FF7e86\nNYbN2NRHKVeozKhk8JeDGb5oOON2jWNyzWQixzVtsoU/XifwX12toUOOZKSEw4eh/v9x8YzjiHDz\nbZsZ2dVxQ7N2iRCqodHxGcPCnZMpRhmNDAsPR5GSlOho+rgbZerU0uuRXpRsKCH/m3wAArsGYgw3\nEnlqJHmf57EidAVjd44lqEeQuqI/QOixGT+jQ8dkPvwQ/vrXumNXeczsZ5m1ez74AG6/3bFs4kR4\n8EG45JK20XQSUWaxkFNTw/9lZ/NWtmOKE/MZZ2ByN3dep1Fq8muwlqgxmvId5SjVCntu2lNbbwgz\nIKvVHGX2/82jU6IJTw7HGGHEGG4k7tI4gvsG64aoGegxmVZQfz1i/YD+ltu3+FCNl3n/fedV/du3\nO6WV0WkZ07ZvZ9GJE07lSSEh7B43Tv9RayWBsYEQqz4PH6aOErve2NWpnbSqCTBzP86lOrua4D7B\nWEutWMusnFh8gqw5WZiPmTFGGbGcsDicOzZ9LGGDO/asP2/QYW+t1q+HJ55wLOse4biL2fFy765r\n8In/deVKGDbMddoYFzPO/NUn7I+6bJosisKwsDBiA5x3VNxbWYlh2TJ+KyhwqvOmJn/Cl5qEUc0Y\n0P3u7vR9oS/dbu1G93u7E39VPP1e6cfATwZyysenkDU9i8iJjvGbDUM2qFs8tyH++Pm1lkZHMkKI\nJOBdoIuUcqgQYjhwkZTyea+r8xLdusGAAc7l1wy/hmu/u7b2+P6l95N+V7oPlXmB0093XT5yJHz1\nlW+1nISsKi5m0pbGR7w5NTWsKCoiMTiYnsHBPlDWsVCqFVZ3X+00OrFhCDYQNjRMTWcTbaKmsoao\nSVHETo8loHOA+ugSQFBPfc8fT9NoTEYIsQz4B/C+lHKkVrZDStmu/CxNXSdTP/j/8tkvk1Oawyvn\nvEKAsR3u/b1ypbqBzoMPOtcpisPMMp2WUaMolFmtlFqtlFosFFks/HDiBD/l57On0jlLhPSznQ/9\nCSklFTsrkFKy+4bdhA4K5dj8Yy7bGqOMYAVpURNr1if24lh6PdqLsKFhGENPokS3PsYXMZlQKeX6\nej5l17cLJwE/X/0zizMWExcax5qsNbWZmS8fcjkTek5oY3XN5Ikn4IUXXNeFh+sGxkNsLi3lnowM\nLFJSaLFQaLFglpLugYEAJIeHM71zZwINBmbExraxWv+gOrsa8wkzlmILlkILRz84SsHPzi7F8vRy\nOk/rTOnmUkyRJgyhBgwBBvq+3JewYWEIk0AYRe1fDOjxLz+jKUYmXwjRD20YIIS4DMjxqiofMW6c\nGpuxZ8qAKYQFhJEyN6W2LDkhmcFxgz3++l7fz/uOOyAiAh57zLmu/roZX2lqIf6oy6Yps7qaTWVl\nTvV5ZjOz+/fnvh49fK7JX6jOrua3//7G+H7jsZZZQaqr+ndft9vtOQPnDST+yngMAd4LGfvbdbLh\nr7paQ1OMzN3AB8BAIUQ2cBC4tuFTVIQQHwEXAnlSyuFaWQywEOgNHAKukFIWa3WPATejjpTuk1L+\nqpWPAj4FgoHFUsr7tfJAYB4wGsgHZkopM5uiDdRNIZ0013OXLbxsIVcMuaKpXfoXPXvCI49AXBw8\n+yxk2l2a6dP1tDItQErJ8uJiMquqSD9xgp3Z2VRYrZwdE8P/Cgsd2pZZrdy/b59PjYy/sabHGvax\nj3Cc1w3ZEzk+ktCBoSS9r2dhPtlo8joZIUQYYJBSljbauO6cSUAZMM/OyLwMnJBSviKEeASIkVI+\nKoQYDMwHxgI9gP8BA6SUUgixDrhHSrlBCLEYmCOlXCqEuBMYJqW8SwgxE7hYSnmlGy21MZkFC2Dm\nzLo6s9XMc8uf41j5Md7f9L7DebeOupUPpn3Q1Lfsf1RUqJlAXeXR0Y1MsymzWIhYudJt/TXx8RiE\n4PK4OKbprjGXSKuszUVWnV1Nxd4KDj9zmMp9rrOcj/h9BDFntpOEtCchrY3JNCXwHw1cDyRiN/KR\nUt7bRIG9gZ/sjMxuYLKUMk8IkQCkSikHCiEeVbuVL2vtfgH+CRwG/pBSDtbKr9TOv1MIsQSYJaVc\nJ4QwArlSyjg3OmqNzPXXw9y5dXV5ZXkkvJ7g0H5CzwmsvGll+/fvlpRAVJRjWWQkHDjgnJ1Zp8lU\nK0mKwCwAACAASURBVArBy5c7ld+UkMDI8HDu6d69/X93fEzWnCwOPH4ApcJ9doqBnw0k4doEt/U6\nnqe1RqYp49LFqAZmO7DJ7tFS4qWUeQBSylzAtidtd+CIXbtsraw7kGVXnqWVOZwjpbQCRUKITo0J\nOPdcx+Mu4V04cO8Bh7Kx3cZ6/UfCJ3Pi6608p3t3df620fVsG3+dp+8vuqSUVCsK527dCmlpTvWf\n5OZy7759baBMxV+ukz1N1dTjvh6cUX4GKTKF08tdT70P6h5ExZ4KqjKrqDleg2JuWbokf7xO4L+6\nWkNTYjLBUkoX8189hid9No1YhRt58MFEMjJg9uxokpOTSUlJwWw1M/mfk6EY6KO2nLNgDmeKM7no\nvIuAug/fFpTzxHFaWppH+3N5rG2ak6pdgZTsbMjOJnXZMoiKcmpvw2t6Wnicpv2gt6WeT3JymNdV\nW2Welgb79tVtSmQzOMnJnB4VRWpqKkIIn+u10dafV2uPl69dTuY5mQw6OojALoFsyN+AUqMQdl8Y\nSpXCxsKNKNUKwyqGYQwxssWyBaVKIRn188i+IhsRKJiQNAFDkIF1mesgAIbkDcEUZWLp1qWU31DO\n1Nun+sX79afPLzU1lU8//RSARHeZhJtBU9xlD6DGVRYB1bZyKWWTljC7cJftAlLs3GV/SikHuXCX\nLQFmobrL/pRSDtLKG3KX5Ugp451VOLrLHnoIXnmlbhvmjUc3MvbDsS71f3TRR9w88uamvFX/YuvW\nhndlKyiAGN3P3RysUlJoNnPFzp38WVRUWx5q+yJpnBUTww9Dh+ruMh8gFYm11Iq50MyeW/ZQvq2c\nkKQQYqfHolQrKNUKslpy5LUjLs/v/XRvjOHq1gI1uTVU7Kqg91O9CR/e8ESFjoQv1snUAK8CT1A3\n6pBA3ya+hsBxhPEjcCPwMnAD8INd+XwhxJuobrD+wHot8F8shBgHbECND71ld84NwDrgcuCPpgh6\n/XWYMKEuJ+SYbmP4/frfOWveWU5tCyp9kw7EoxQXOxuYZ56BW26B2FgI0lc1twSjEBiEcDAwADcm\nJPBOUlIbqerYCIPAFGXCFGUi+Xf3N1U9HupB2ZYyRICg6I8iStaX0On8TpRvL6fozyKkWVKTWwPA\n8a+P039Of3rc23FnBXqSpsRkHgL6SykTpZR9tEeTDIwQ4gtgNZAkhMgUQtwEvAScI4TYA5ylHSOl\n3Al8BexEjQPdJeuGWXcDHwF7gQwp5RKt/CMgVgiRAdwPPNqQnk520ZpLL3Vci3hmnzORsySfTP/E\n4Zx//PaPprzVFlF/iNxqdu9W31R0tGP5qlXw9NNqPKYRA+NxTR6irXXtKi9HpKbSedWqukLNRfb1\n8eN8kpODP2Q0b+vr5Ap/0BSUEETM2TEULC6gfEc5Ww1bqTpQRd68PKqPVNcaGBv77ttHqkhl/8P7\nfarTH66Vp2nKSGYfUNGSzqWUV7upOttN+xeBF12UbwKGuSivBpq8iKV+jsJzzoE//oC//EX9bb75\nh5v5JO0Tp/MKKwuJDIrEaPDz1BSxsZCSAvZf1Pnz1WGbTqvoExzMC336YJGSUKORGkVhQ1YW3wHH\nzGZu3rOH7/PzyaisZFdFhb7rpR9Sk1dD1pvqHKJCCjn6m+Omcr2f7E3k+Ej1ZkFRXXHRZ0S76kqn\nGTQlJvMdMAT4E8eYTJOmMPsLQghZUiKJdLFx3v790LcvbDq6iYXpCxEIXln9ilO7K4deyZeXfukD\ntS3EYoGFC9WA07ZtdeVWa10ASsdj1CgKUStXUuVmQzg9R1nbUrS8iKMfHMUYakRa1b1mjv/3uNsp\n0oO+GESXq7r4WKX/44t1Mje4KpdSznVV7q8IIWRiouTQIee6b75xvWdXjbWGhNcSKKxyXMmd+1Au\nXcL98Mu4Zk3dqOWyy+Af/4D+/R39hDotJq+mhipFocJqpUZKkjdudGrzVv/+bCsv54YuXZhU322p\n41MOv3iYg48fdFsfOiSUinRHJ03cZXEM+nIQBpN+U2bD60bmZMFVFmaA4GA4etT9RKsfdv/AjIUz\nnMrfOPcNHjjtgVZpSvV0niJ7IwPw3HPw+OPNGsV4XJOHaEtd523dyq/1UsYAakzGboLF+MhIPkxK\nYqiLrZd9hT9+fv6kSUqJNEuWLljKhKQJZNyZQVmac945G4YwA5FjIxn+63Cv5lKz4U/XyobXFmMK\nIb7S/m4XQmyr99ja0hf0J/6/vfMOb6s6G/jvSLK8R2LHK4mz93D2TmMSRqAllD1CA4RSyigpI4yP\nAgmr7L3LhjJK2RASoGASRvYiZDqOE2fHseNtWdI93x9XtiVLshXbGrbO73n0WPe950qvjmS9Ou95\nh5RQXd10JO8pfU/hy4u+JCPOtQvf27++7WftWsDYsfDNNzDDESV3xx160qUQ+m2r96KECu/ckpXF\nvK5dmx23vKyMPA+l/RWhgxACg9lAdFY0iRMSGbNuDDkyh/4veo4O1Co1juUeY9ftuyh8vJAjHx6h\nbFUZlv0Wj+MV7nhdyQghMqSUBxzGxjnESgAPSSnbVdVIbysZ0Cus9Orl4ZqF7sZ7TvYcrp9wPSPS\nm8hBCTa7dumbTM58/jn84Q/B0aeD8NqBA8zdts3juc4mEw/36cPcDPeWwIr2gVarUXuwFusRvQVB\n6bJSChYUeB2fNieNhIkJGKONGKIN9bf64xgDMQNi2n2+lN/yZKSUdeX8+0opdzd60oEtfcJQxJvH\n8JPzP3FzlU3sNjG0DQxAjx7w7rtw4YUNstNP16uCvvde8PRqJ5TabByureWw1cpbBw/y4gH9X6F7\nZCRmIaht9IGJMxopnDiRGC+lehTtA4PZQFRWFFFZeufSpGlJxAyMQbNoWIus7LxxJ93nd8cQbUCz\naNiO2dhxlYfCs42YZpum97oJU5payVwFXI2edOkcLB4P/CSl9Kncf6jgbSXz7rtwgce6zbCndA89\nnuhRf5x7SS7ju40nytQ27XP97n/dvh0+/hg2b4Y339Rld94JWVn6i46NDbxOLSQQeq0sK+OsTZvY\nV6vnTExMSOBAbS0FNTV0Npn4aOhQBsbE0NlkIsJgCMm5Ujr5RlvoZK+2s3rkaqq3Ne8iNWeaMZgN\niAhB9Y6G8QkTE8j+XzbGaGOb6dXW+DPj/x3gK/S8Feckx3JfS8qEMr/8AtnZEB3tfUxarGsEWV0j\ns0M3HSI11mP1mtCif3+9nwzAa6/pgQALF+pLtz//WU8UevVVCON+J/8rKeGl/fvpEx3NP5367Tzc\nuzc3ZWUFUTNFqGOMNjJ+6/hmx9UW1aLVaEirRNZKVg5s6JRY9ksZy2KWAWCINrA5YTMcarg2qmcU\nI38aSWRm+63SEZbRZZ99pnuPmqOwtJCsJ9y/aK4YdQXXjb+OoakhnmxXVqa/UA8l6etZuhSmeq54\nGw6IRhnWY+PjeapvX8YlJGBo5750RWCRdom92o5Wo6FVO241GsWLi8m/Jb/5B/CEASbkTyCqR9t4\nT1qCCmH2EU/usuZeeo2thrt/uJt//uhWhACAozcfpXN0COegXHMNPPecu/z66+Hhh72W+w8Xymw2\nLt26lY+LitzOfZedzQmqgKgCsBy0YD1kRavVsFfa0So1tv91O5a9DRFmwiSQdqlv+Ec5BQBEGbCV\n27Dsdo1GG/7NcMyp5vrj6D7RGGND8/8xEAUyOyQTJzY/JsoU1eQm/76yfa0yMn73vz77LDzzjB5Z\ndsYZDfLHH4crroBBgwKvUwvxh14/lpZ6NDCnde7MRE+lIQKgU2tROvmGN500q8b+F/eDBFOiCWmX\nbJvrOaKwjuzvs0mclIiIEK2OJAvFuWotYWtkfvlFX8k095mY2XcmozNGs+aAe5+2Sa9O4sj8I20W\nCOA3GjcuAzzW1wkzTktORubkoEnJGwcPUmixcFdBAYuKi4lepvvJpyclccRqpcJuJ8pg4NvsbDJV\nFesOS/WOavL+5lvTuUmHJrmsRhSeCWt3GegRveef3/S1X27/kj+8655j0q9zP367+jcijBFtpWbb\nk5end8J0Jkze8+Ol2Grl6+JiLtyyxeuYvPHj6dNUtIiiw2Ars1GzpwZrkRVrkZW9j+2l9kAtNQU1\nbmNjh8UyZsOYdp8T4wnlLmshN98MmZkwebL3MVJKau21vLzuZY/nF81eFNoG5h//gPvuc5fv2uU5\n+zSM2FtTw5aqKh4uLKR3VFR9LgxAz6goCmr0L5In+vZlXhhH34UbUkqkTbL3sb3k35qPMdFIwoQE\nrEesVKz1Xn4mYUJChzQwbUHYrmT27IHu3d3HLd29lGmvT3ORRRgiSItLIz0unYy4DD7f/jlx5ji2\nXrOVrgnNlxvxht/9rwUF8NJLehOzxgEA/frBiy/qfQ4CqVMLaWu9GkeVOfNsv37MTU8nqpnAiFCc\nK6WTb+Tm5jI2dSxrJ67FXmZvdnzfJ/oS0SUCY6wRQ6wBY6yxfqM+ZmAMBnPb1DULxblSK5kWMHs2\nJCd7Pjc8bbib7IU/vNA+WzD37An336/ff/ZZ13IzO3bA9Ol675lp07w9QodF5uRgl5K/bNvGqwcP\nupy7ZscOBsfEkKOiyzo0tjIb9jI7wiyQtZ5/bHe7sRt9H+kbYM06FmG5khkyRM/0H9aoDdqJb57I\n/3b9z+3a/5zzH84dcm4g1PQ/n38Os2a5yjSt+QiIDsBRq5UU586WToyKi+P9wYNJjogg0WRSOTJh\ngmbTWBrRKI/MCDgtbga/N5jE3yViTjeHpUtM5cn4iBBCfvyxZM4cKC/XZddco0f41jHo2UFsLXKt\nVBxtiubXq36lT+c+AdTWz8ycCUuWNBzv2KH3neng1GoaZ27axCKnFqnRBgMVU6cqoxLGWA5YsB61\nYq/Qc2DsFXa2XrYVW4kNAHNXM9IqsZfbieoRRVSvKKJ6RmHqbGoohunIjTFEGTDGGDF1Mum3JBOm\nRBPGeGO7NVDKyPhI4z2Zs8/WK6vMnNkwxmq3sjhvMbPem0VSVBJlljI02dBFT97VtnMVNP+rzQY/\n/aS3aq5j4UIYPpzcxERyGu3ThAJtNVfX7djB004h3WPi4/ll5EhMLegcGor+c6WTb7REJ3ulnZqC\nGqp3VVOzqwZbqQ2tSsOyz4Jlj4Wa3TXU7KlxWQU1JvOaTPo/47mtQEv18jdqT6aF/POf7pG9EcYI\nTh9wer0xcS71/+IfXgykev7FZNL3YfbuhVGj4PBhuOsu/dzdd7sFA3QkHunTh79kZLCrpoZZmzax\nuryciEZldx7q3Zv5qm6ZwsHKwSup2tLQQbPTiZ2wV9qpPVRLTX4Npk4mIlIjiOwWSdyoOCJSIjDF\nm1wCBAyRBhCQODUxiK8kOITlSubmm/V+Xk01MJRSYrjb9ddtW69kgsq+fZ4LY372mR4Q4KFCc0dE\nSonhhx9cZI/26cO0pCTMQtA3OproMC+/E47k/yOfPfft8XhuwCsDiOwWWW9YzCkdOyFTuct8RAgh\nn35asnQpfPCB67kDByA9vdH4Rg3LLP+wYDZ2kA9TYaHeAmDePM/n//AHPUAgTGgqnPnitDTe8lB+\nR9Gx2f3P3RQsLABNL3yJ1uwlLuTIHH+oFRT81n65I3L22e4GJjbWc4WVC4de6HIceW8kYqHg58Kf\n20yf3Ca+3PyGzQZXXuluYB55BCoryf3++5A0MP6cq2NTpniUj4uPb9LABOX9awalk280p1OP23ow\nrWYa02qnkWPPIUfqt5SzUrxeY0oy0XNhTwa/P9hverVHwsrIZGY23J8/H44c0SPNYmJcx2lS48mZ\nT1J4faFbOf/Jr06mtKY0ANr6gc2bISICvvqqQfb443qZmRtvdJ+IMKHMZvMoXzTcPWdKEZ6UrSwj\nV+RS9JF7QdU6sm7PouedPUk9rx30mgogYeUuq9uTaS5i9+kVT3Pd4us8npuTPYfXzngNg2iH9vng\nQWjcg/7XX2FoiPfF8RObKioYtnq1m/z05GTeGjSIRFPYxsUoGiE1yYYTN3Ds+2Nex8SNimPMmjEB\n1CowqD0ZH2kcwtw4R8YZTWoY73bf7DUbzRTNLyI+Mt5favqfyy6D11/X77/7Lpx7btj2lfmtspKh\nq1a5yMxCYAnDCggK39BqNZZGem4CaO5qJjIjkqhejqrsjq+bzKsy6TS9/VaPUHsyLeTZZ/UkdyH0\n71lnDMLA2YPOrj9+YMYDyLskln9Y2tTABMX/+sorDfsxt9yihzPXTcTSpSHrE/aHXkNiYzkrxdXH\nXislV2zbxrXbtxO3dCk35eVh0zzv+obiXCmdfKOlOhnMBqZp05h0ZBIT905k3PZxjNkwhpG/jEQY\nBeWryznywRH99l/9tmHGBmqP1PpVr1AmLP0BJhPY7Q0V7529IusPrmfkiyNdxod098vjxWCAJ57Q\nb6BHmtXlhEybBp06QWIijB8Pb74J5g4SUeeFD4cO5afSUubv3EledTVHrFZedqrI/OjevZyeksK0\npKQgaqkIJYQQbmHLhY8XYko0YcHi8ZqfU10Dhibun0hkRnj0JQo7d9lf/wrPP+99XHF1MckPuVbP\n/OLCL/h9/9/7WcMg0a+f3nOmMRERepJmGHy5bqmsZHAjt1ljPhg8mHNS1YZuOCDtEtsxG/YKO7Zy\nG/Zyu952uUZDWiSaRau/1R3n35Lv9fGGfj4UQ6QBadXHGuOMdDqxU7spM6P2ZHzEeU/G20v2lID5\n8EkPc1q/0+gc3ZmUmBRMhg6y+DvpJPj2W3f5vn2uYXhhxq7qarJXr6bc7lobJNlkoshLqLOi41Cx\nsYLV2e7BIHUkTErAnGbGmKBn8dfdpE0SPzZer1WWZMKYYMQUb8LU2YQpvn1/Zygj4yPORqaoyHup\n/zu+u4OK2gqeXvk0dun6RXPekPN4/5z320ynoNUp2rxZL0XtTHY2LFpE7vbtIVc7CQIzV3/asoW3\nDx3yeO7gpEmkNXIdhmKdKaWTbzSlU/G3xWw8aaP3iwXkaJ6v9adewULVLmsBKSlwzjnw/vv6FoUz\n90y/B4BxXcdx0UcX1cs3/HWDx14z7ZKnn3aXbdgAXR0N2MLkh0djTk9OdjMyt2VlMb97dzpFhHAH\nVEWbYi/3XuGyx509SD4tmer8ar2JWVz7ra4cKMJyJQMwZQosXeq9jYpds2O6x9UGd6jaZQCrV8PY\nsa6ydetgxIjg6BNkxq9Zw8q6PhBOTE1M5JvsbCJbUKlZ0X6xV9rJvy1fL/lvBGmT2I7aqD1Si/WI\nFcuehk3+zL9mYow3Yj1ixRhnpNe9vTAmdAwDpNxlPtLYyHiqVwawv3w/XR9zb6n88ukvc/moy/2p\nov+prIQ5c2DxYn3VkpUF/3Nq0nbDDXp5mQ7wj9FS9lssjFy9msNWq4v8LxkZJEdEEGMwsKi4mGM2\nG6d07syjffqoXjRhyrKEZU2ueiK7R5I+N50u53QhbmgT1XhDHJUn00L2eC6wSnJ0MoKG+bw7527k\nXdIvBibgMfEFBfDRR1BVpZc9cDYwmzfDo4+S26gicagQqLnKjIzk0OTJ7JkwgU+HDuXlAQO4r1cv\nIg0GdlZX89nRo/xSVsaWqiqe+OILjD/8gMjNZVVZWUD0a45QzLPoiDodeu9QkwYGwFJoYffC3V6r\nOftDr1AkLPdk3n4bxo1zlUkpWfjDQhb+sNBFfse0OwKomZ/p0sX7uQcegDfeCJwuIciR2lq2VVVh\nFII9FgsXbN7sNmZSQgLndemC2WBge3w8yZ07MzkxkYFhWvctHClbXcaWC7c0OSaqVxQT8icESKPQ\nJizdZeefD++913Bu+9Ht3LDkBr7c8WW97Ns/fcsJvU5onzXKvCElfPihe4kD0EtRDxumt2UOk14y\nznjqK9OYRcOGcaq3sERFu0azachaiVar/63Or2bdxHXH/TgD3xhI2sVpCEPHcaGq6LIW4Gxgftzz\nI1Nfm+pyfvu12+mX3KhtZkdACO+VlsvKYPt2vRVAGHFDXh6P793r09gVZWXKyLQD7JV2KjZUoFVr\naDWOxMkap1u1huWARU+utEmKPi7Ceth1Dw4PX6lxI+MYvng4xlgjwiwQJtEhNvb9TdgZmVdecT1e\ntGOR2xjnHtwfn/8xfxz4R7/oEpSY+NGj4f/+T9+XkRI0rSGk+cgRcq+/npzp0yE6Gs46K2SCAPw1\nV6d27sz7hw9jFIJCi3tJkMvS03l14MCA6tQalE6wLG6Zmyz1glQMUYb625qqNUweNhlhEsSPjOfQ\nu4eI6h6F1CTdb+hO/OjgFMENxfevtYSdkbn8cpg7t+H4/hn3c/+M+wEoqS6h80OudcoOVXhOzmu3\npKXBffe5yqZO1SuG/vADvPaafgO9rExT+zjtmHKbjZt27mR/bS05SUl8d8xzCffXDh5kTloaOZ3a\nbxXdjsTGP2yk+Mvi+uOoXlGYEk0NqxSLezHT3g/1Jmt+lotsb+5euuU0tB/PvDJ8q1z4m7Dbk7nz\nTli40Pu4BbkL3Db/V/x5BeO6jvNyRTtn61ZYvhzWrnVP0ty5E3r3Do5efmZvTQ3dly/3eG5wTAzP\n9+9PgtFIrZSMiY9XYcohwv4X97P9r9vd5MO+GEbMoJiG1UqkAREpMJg60J5qkFB5Mj7ivPH/6qt6\nWxVPFBwroNeTvVxkE7tN5LtLviPKFOVvNQOHlHrOzNtvN8hSU/VSCGvX6oansrJDd8u8bscOnt63\nz01eMXUqsWHaYydUqNhUQenSUqQm2fPPPdTur0WYBXEj4ihfXQ6NFixTyqdgigs7x0xAUEbGRxon\nYwLcfz/cdpv7WIvNwktrXuLTbZ+SX5LPrmO7AHjv7PeosdUwNHUoozNHt1qnoPpf9+9vKCPjRG5s\nLDmvvgrnnRcEpbzjj7n6vKiIWZs2eT1/bMqUJrtjhqL/vL3qpNk0dt2+i/3P7Sd+bLzHDpQZV2aQ\nfmk6xjgjxlhj/V9DtOG4N+BDcZ4gNPVS0WWtwJubPdIUyZSsKW4tmC/48AIAEiITKL211N/q+ZfM\nTH0107hYZmWlHuM9Y4b3KqIdAOEl6e2StDQ0IN1sJkaVkQkINXtrWN69wXVZZ2BGrRxFdL9oIpJU\n3bj2TFivZOpeutVu5cavb+S3I79hNprZWbyTHcU76sf1T+7PJdmXcOuUWztW3kwdGRlw8KBes2z9\nes9jOpjr7H8lJZy4YYObfHpSEhlmMwkmE4dra8mIjEQAtZrG37p1Y0gY5hD5g9pDtVRuqmTn/J1U\nrKvwOi5H5gROKYVHlLvMR5yNzFVXwXPP6fIz3z+TT7Z+4jL2xok3MjBlIEZh5KQ+J9EtoVvjh+tY\nHDsGH3wAf/mL5/NjxsCyZRDVgfaknNhnsXCotpYym41Su50ym41im42/e2jmdnZKCnnV1aSZzTzT\nrx/9OpDhbQlSSqRNujTwqrtZdluwHLBQu78W2zEbWrWGvVpv/nX434fdHqvPY31ImZWCIcaAIdqA\nMcaIwdwBf9S1M5SR8RFvTcuKqoq46eubeGOD55Iqc7Ln8MYf/VNuJWT8r07+7FwgZ9MmiI+HuDi9\nEkAT+xKBIphztb68nA2VleyzWLh91y6nE+spvfZaEkJgfupoq3kq+V8JRZ8UISIFwigofKiQ6L7R\nVOdVAxDZLRJrsRWtWgMDLg28RKSo7wQZOySWjfEbmTpiKoZoR+SX468x2lh/jIT48fEBiwYLmf+9\nRoSiXu12T0YIUQCUoseJWKWU44QQnYD3gR5AAXCelLLUMf42YC5gA+ZJKb92yEcBrwNRwCIp5d+b\ne+41a/ScRICUmBS+3vm1x3HWO6wdpxOmNzz1lhk6tOH+JZfA668HTJ1QJDsujg+Lirh39263c4k/\n/gjAb2PHMrgDudIKHyukeFGxi6zOwABY9lpAgKmTSd98jzLovVUiBOWrykHC6DWjiR8Vz9Hco2Tl\nZDV+CkWYELSVjBAiHxgtpSxxkj0IHJVSPiSEuAXoJKW8VQgxGPg3MBboBnwL9JNSSiHECuBaKeUq\nIcQi4Ekp5RIPz1e/krnoIvj3vz3r9fyq57l60dUusvOGnMc7Z72D0dABw1qbi8o5ckTv8hbGfFNc\nzMkbvXdKjDcaOTJ5crvpN7PvuX3svn83Xa/uCgZ0N5ejZpdm0Vzue5JpNRr2Cjv2Mju2MhtalXsC\nJMDotaOJHxmczHlF29Fu3WVCiF3AGCnlUSfZVmCalPKQECIdyJVSDhRC3ApIKeWDjnFfAQuA3cB3\nUsrBDvkFjuuv8vB8bhv/deTnQy9HaoynPBmAV2a9wtyRc93k7Za6zX5nBgyAp54CoxEsFn1SBg0K\njn5BZtmxY/zOSxBETlIS/+jRA6umYZWSaUlJIeUy88baSWsp+8V7S4Ks27MwdzHr7i6zw/VlFg1/\nfZAZogxqH6WD0W7dZejf+N8IIezAi1LKl4E0KeUhACnlQSFEqmNsV+AXp2v3OWQ2wLm64V6H3Cfe\neQc6d4aePRtkPRJ78MQpT/D3Ja5et8s/u5xqazXXjLvG14dvlqD6X99+Gx57DBY51W4rKyNXSnJm\nzAiOTk0Q6Lm6artrVvm8rl15op9r0dTc3FxmBtl/LjWJrcSGrczGzht3silhExP7TcReZcdeaUer\n0ur/NmVgAJJPTSZxcmKb6xiK+wyhqBOErl6tIZhGZrKU8oAQogvwtRBiG+5LjTZeZl0K9HTcT+Kn\nn0bwzDM5QEOzoJycHOZNmEdWSRZnvX8WOBY1I6pHYM+3g6O6jPP4lh6vX7++Vde36thohPnzyfny\nS0hJIffoUb1d6MyZ8MAD5I4fH1h9mjle71hVBOr5WL9eLyLqaEX95Jdf8mlkJAWOld1pe/ZwbOtW\nRnftSmeTiUn5+ZiNRr/qp9k0po6ailajkftDLtU7q0m6I0lXF31+DLEG7PPsrDy4EkOUgSljpmCI\nMbB813LERMHM2TMxJhpZtmoZQgiXx19nXUcOgZnfYB8H+vPk63EdwdQnNzeX1x37sD2df4G3BCpZ\ngAAAIABJREFUkJCILhNC3AVUAH8GcpzcZd9LKQd5cJctBu5Cd5d9L6Uc5JA36S7r00eyc6f78zu7\nywA0qTHyxZFsPKT74Vf+eSVju45ty5ccOixeDKee6ir76ivd2IQxD+3Zwy35+S6yGIOBKs3z/sPm\nsWMZ1MYb/1JKSr4pQavVqFhXQcGdBS7nTckmzGlmqjZXAZD9XTadTlCFPBVtS7t0lwkhYgCDlLJC\nCBELnAwsBD5DX248CFwCfOq45DPg30KIx9HdYX2BlY6N/1IhxDhgFTAHeMrb8zY2MIMGwRNPuLrL\nfj30KyNeHIEmG75MOuSGfx2eikSmpen9qZOTw7KBGcCumho3WZ2B+T47m3SzGbPBQJeICOL9tB9z\n5D9H2HyBe3fOOmxHbdiO2sj+PptOOcq4KEKTYO3QpQE/CiHWAcuBzx0hyQ8CJzlcZzOABwCklJuB\n/wCbgUXA1bJhCXYN8AqwHdghpVzsiwLbtukVVU4+2TXAavgLw10MzB2/u4NRGaNa81q90niJHBQW\nLHA5zAUYNQp69NDzZEKEQM/VT6XeywaNiY9nYGwse1as8JuBAehybhd6P9B8FewNJ2wgV+Qi7TI0\nPlONUDr5Tqjq1RqCspKRUu4CRniQFwMnernmn8A/PcjXAMOOV4cBA/R8mVGN7MfGv25k+AvD64/v\nWXoP5w85n7S4NJKikjpO3szOndC3b9NjLr44MLqECLfu3MmDhYVez8s23pC1llixldjYOHMj1Tv0\nHJTOp3WmeFExEWkRSKvEVuzeqTTr/7IQBqFn2lv17o4xA2OC95NRoWiCkNiTCQRCCFldLTn1VHD+\nsXDppXqJmejoBtm6A+sY9ZL76mVGrxl8O+dbv+saEIqLPRfAjIjQky8vuijgKgWTWk3jyu3beb1x\nWLeDn0eOZGJi20Re5Ypcr+e639yd/S/sp99T/YjqGYVlrwUpJXHD44gbHjorS0X40G7zZAJNU3ky\nBw5Aerq7fP3B9Yx8caSLbP6k+Vw+8nJizbHERsQSZ44jwtiOq8Ta7e5lYx55BG68MTj6BIgqu51n\n9+3j5kab+wAzkpJYUV5Ohd0OQFezmfwJEzAb2mapkH97Pnvu3+P1vCoKqQgllJHxESGETEmRFBW5\nyn19+ZsOb2LY8569cvKuls1hbrBj4qWEsjLYsQPG6tFzuaAHsf70E0y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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def give_dollar(population, transaction, interaction):\n", + " \"Everyone with at least a dollar gives a dollar to a random person.\"\n", + " N = len(population)\n", + " for i in range(N):\n", + " if population[i] >= 1:\n", + " population[i] -= 1\n", + " population[random.randrange(N)] += 1\n", + " return population\n", + "\n", + "show([100] * 100, k=200, step=give_dollar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So we see that inequality rises from a Gini of 0 to about 1/2 over 20,000 time steps. Let's try again starting from the first 100 actors from our initial (Gaussian) population:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t Gini stdev 1% 10% 50% 90% 99%\n", + "------- ---- ----- ---- ---- ---- ---- ----\n", + " 0 0.12 19.4 58 71 95 119 151\n", + " 2,000 0.29 48.1 10 35 91 169 205\n", + " 4,000 0.39 66.5 3 13 88 187 329\n", + " 6,000 0.40 67.7 5 11 97 194 283\n", + " 8,000 0.39 65.8 3 13 87 179 274\n", + " 10,000 0.38 64.5 3 21 84 187 294\n", + " 12,000 0.40 71.8 5 27 78 187 376\n", + " 14,000 0.44 80.8 2 13 70 201 460\n", + " 16,000 0.47 84.3 2 11 80 193 443\n", + " 18,000 0.45 81.7 5 13 79 202 421\n", + " 20,000 0.45 80.6 0 10 79 204 400\n" + ] + }, + { + "data": { + "image/png": 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v/dfs2AFA/ZQpmDSTmEaAkFJNNWORSjZnq/N9yXcloIeMlzPYedNOpFWxZpQu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\nHJybl4ddSnqYzZTYbIe87pj4eFaNGXPIfp09F5pdoyKngnXTXKu0hOM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D4HP06vePFrONyWShI2Qlhu0ZQ0ZQztBiyZkrFQYREcmgwhBALP2OGmMIJ4aM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\n9hhERCSDCoOIiGRQYRARkQw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9Bb/+CjfeGB05CxIt7VkQy+keP2QE/+T06x4GwN3AByJSGtgIDAZKAp+IyBBg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\nth7Yypxtc+hwUgevo5zg6FE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(population[:100], k=200, step=give_dollar)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Mathematician, a Statistician, and a Programmer walk into a problem ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In 2013, mathematician George Andrew's editorial *[Drowning in the Data Deluge](http://www.ams.org/notices/201207/rtx120700933p.pdf)* complains of an \"overblown enthusiasm for data analysis.\" The tone was that this new fad for \"big data\" was taking away from traditional mathematics.\n", + "\n", + "Two Stanford professors, mathematician Persi Diaconis and \n", + "statistician Susan Holmes, were more accepting of new ideas. The three of us got to discussing Andrew's editorial and the differences between mathematical, statistical, and computational thinking. At the time, I had just heard about the economics problem covered in this notebook, and I suggested the three of us work on it, and compare approaches and results.\n", + "In the end, all three of us found similar results, in that we all identified the shape of the final distribution. But there were differences in how we got there:\n", + "\n", + "**Mathematical thinking** (Persi):\n", + "\n", + "- **Tool:** Paper and pencil.\n", + "- **Notes:** The process can be modeled by a Markov chain, using the same techniques as in [this paper](http://statweb.stanford.edu/~cgates/PERSI/papers/kac10.pdf). In the limit, there is a difference between the continuous case (where money is a real number, and the distribution is stationary), and the discrete case (where money comes in integer amounts and the distribution is not ergodic as there is an absorbing state). \n", + "\n", + "**Statistical thinking** (Susan):\n", + "\n", + "- **Tool:** Simulation in `R`, with N=10 actors for T=1,000 transactions.\n", + "- **Notes**: this is extremely similar to what happens for random genetic drift in generations, that also gives clumping (and extinction of some of the alleles).\n", + "\n", + "**Computational thinking** (Peter):\n", + "\n", + "- **Tool:** Simulation in `IPython`, with N=5000 actors for T=200,000 transactions.\n", + "- **Notes**: Results are very similar to Susan's, but with more variations explored and more pretty pictures." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Fred Buns.ipynb b/pytudes/ipynb/Fred Buns.ipynb new file mode 100644 index 0000000..72e4948 --- /dev/null +++ b/pytudes/ipynb/Fred Buns.ipynb @@ -0,0 +1,1475 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Peter Norvig, 15 June 2015
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Let's Code About Bike Locks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [June 15, 2015 post on Bike Snob NYC](http://bikesnobnyc.blogspot.com/2015/06/lets-get-this-show-on-road-once-we-all.html) leads with \"*Let's talk about bike locks.*\" Here's what I want to talk about: in my local bike shop, I saw a combination lock called *WordLock®*,\n", + "which replaces digits with letters. I classified this as a Fred lock,\n", + "\"[Fred](http://bikesnobnyc.blogspot.com/2014/06/a-fred-too-far.html)\" being the term for an amateurish cyclist with the wrong equipment.\n", + "I tried the combination \"FRED,\" and was amused with the result:\n", + "\n", + "![](http://norvig.com/ipython/fredbuns.jpg)\n", + "\n", + "FRED BUNS! Naturally I set all the other locks on the rack to FRED BUNS as well. But my curiosity was raised ... \n", + "\n", + "# Questions\n", + "\n", + "1. How many words can the WordLock® make?\n", + "3. Can a lock with different letters on the tumblers make more words? \n", + "4. How many words can be made simultaneously? For example, with the tumbler set to \"FRED\", the lock\n", + "above also makes \"BUNS\" in the next line, but with \"SOMN\", fails to make a word in the third line.\n", + "Could different letters make words in every horizontal line?\n", + "5. Is it a coincidence that the phrase \"FRED BUNS\" appears, or was it planted there by mischievous WordLock® designers? \n", + "\n", + "Vocabulary\n", + "===\n", + "\n", + "Before we can answer the questions, we'll need to be clear about the vocabulary of the problem and how to represent concepts in code:\n", + "\n", + "* **Lock**: For our purposes a lock can be modeled as a `list` of 4 **tumblers**. \n", + "* **Tumbler:** Each tumbler has 10 distinct letters. I will represent a tumbler as a `str` of 10 letters.\n", + "* **Combination**: Choosing a letter from each tumbler gives a combination, such as \"FRED\" or \"BUNS\". There are 104 = 10,000 combinations.\n", + "* **Word**: Some combinations (such as \"BUNS\") are *words*; others (such as \"SOMN\") are not words. We'll need a collection of dictionary words.\n", + "\n", + "Now on to the code! First the imports I will need and the vocabulary concepts:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from __future__ import division, print_function # To work in Python 2.x or 3.x\n", + "from collections import Counter, defaultdict\n", + "import itertools\n", + "import random \n", + "\n", + "Lock = list # A Lock is a list of tumblers\n", + "Tumbler = ''.join # A Tumbler is 10 characters joined into a str\n", + "Word = ''.join # A word is 4 letters joined into a str" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The only remaining vocabulary concept is `combinations`. I will define `fredbuns` to be a lock with four tumblers, but with each tumbler consisting of not all ten letters, but only the two letters that spell \"FRED BUNS\": " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "fredbuns = ['FB', 'RU', 'EN', 'DS'] # A lock with two letters on each of four tumblers" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We need a way to get the combinations that can be made from this lock. It turns out that the built-in function `itertools.product` does most of the job; it generates the product of all 2 × 2 × 2 × 2 = 16 combinations of letters:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('F', 'R', 'E', 'D'),\n", + " ('F', 'R', 'E', 'S'),\n", + " ('F', 'R', 'N', 'D'),\n", + " ('F', 'R', 'N', 'S'),\n", + " ('F', 'U', 'E', 'D'),\n", + " ('F', 'U', 'E', 'S'),\n", + " ('F', 'U', 'N', 'D'),\n", + " ('F', 'U', 'N', 'S'),\n", + " ('B', 'R', 'E', 'D'),\n", + " ('B', 'R', 'E', 'S'),\n", + " ('B', 'R', 'N', 'D'),\n", + " ('B', 'R', 'N', 'S'),\n", + " ('B', 'U', 'E', 'D'),\n", + " ('B', 'U', 'E', 'S'),\n", + " ('B', 'U', 'N', 'D'),\n", + " ('B', 'U', 'N', 'S')]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(itertools.product(*fredbuns))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I would prefer to deal with the string `'BUNS'` rather than the tuple `('B', 'U', 'N', 'S')`, so I will define a function, `combinations`, that takes a lock as input and returns a list of strings representing the combinations:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def combinations(lock):\n", + " \"Return a list of all combinations that can be made by this lock.\"\n", + " return [Word(combo) for combo in itertools.product(*lock)]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['FRED',\n", + " 'FRES',\n", + " 'FRND',\n", + " 'FRNS',\n", + " 'FUED',\n", + " 'FUES',\n", + " 'FUND',\n", + " 'FUNS',\n", + " 'BRED',\n", + " 'BRES',\n", + " 'BRND',\n", + " 'BRNS',\n", + " 'BUED',\n", + " 'BUES',\n", + " 'BUND',\n", + " 'BUNS']" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "combinations(fredbuns)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dictionary Words\n", + "===\n", + "\n", + "I happen to have handy a file of four-letter words (no, not *[that](http://en.wikipedia.org/wiki/Four-letter_word)* kind of four-letter word). It is the union of an official Scrabble® word list and a list of proper names. The following shell command tests if the file has already been downloaded to our local directory and if not, fetches it from the web:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "! [ -e words4.txt ] || curl -O http://norvig.com/ngrams/words4.txt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the first few lines of the file:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AADI\r\n", + "AAHS\r\n", + "AALS\r\n", + "ABAS\r\n", + "ABBA\r\n", + "ABBE\r\n", + "ABBY\r\n", + "ABED\r\n", + "ABEL\r\n", + "ABET\r\n" + ] + } + ], + "source": [ + "! head words4.txt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python can make a set of words:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "WORDS = set(open('words4.txt').read().split())" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4360" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(WORDS)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So that means that no lock could ever make more than 4,360 words. Let's define `words_from(lock)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def words_from(lock): \n", + " \"A list of words that can be made by lock.\"\n", + " return [c for c in combinations(lock) if c in WORDS]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['FRED', 'FUND', 'FUNS', 'BRED', 'BUND', 'BUNS']" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "words_from(fredbuns)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Note*: An alternative is to represent a collection of words as a `set`; then `words_from` could do `return combinations(lock) & WORDS`. \n", + "\n", + "I will also introduce the function `show` to print out a lock and its words:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def show(lock):\n", + " \"Show a lock and the words it makes.\"\n", + " words = words_from(lock)\n", + " print('Lock: {}\\nCount: {}\\nWords: {}'\n", + " .format(space(lock), len(words), space(sorted(words))))\n", + " \n", + "space = ' '.join # Function to concatenate strings with a space between each one." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: FB RU EN DS\n", + "Count: 6\n", + "Words: BRED BUND BUNS FRED FUND FUNS\n" + ] + } + ], + "source": [ + "show(fredbuns)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this tiny lock with just two letters on each tumbler, we find that 6 out of the 16 possible combinations are words. We're now ready to answer the real questions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 1: How Many Words?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is the answer:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "wordlock = ['SPHMTWDLFB', 'LEYHNRUOAI', 'ENMLRTAOSK', 'DSNMPYLKTE']" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: SPHMTWDLFB LEYHNRUOAI ENMLRTAOSK DSNMPYLKTE\n", + "Count: 1118\n", + "Words: BAAL BAAS BAKE BALD BALE BALK BALL BALM BALS BAMS BAND BANE BANK BANS BARD BARE BARK BARM BARN BARS BASE BASK BASS BAST BATE BATS BATT BEAD BEAK BEAM BEAN BEAT BEEN BEEP BEES BEET BELL BELS BELT BEND BENE BENS BENT BERK BERM BEST BETS BIAS BIKE BILE BILK BILL BIND BINE BINS BINT BIOS BIRD BIRK BIRL BISE BISK BITE BITS BITT BLAE BLAM BLAT BLED BLET BLOT BOAS BOAT BOLD BOLE BOLL BOLT BOND BONE BONK BONY BOOK BOOM BOON BOOS BOOT BORE BORK BORN BORT BOSK BOSS BOTS BOTT BRAD BRAE BRAN BRAS BRAT BRAY BRED BREE BREN BROS BULK BULL BUMP BUMS BUND BUNK BUNN BUNS BUNT BUOY BURD BURL BURN BURP BURS BURY BUSK BUSS BUST BUSY BUTE BUTS BUTT BYES BYRE BYRL BYTE DAKS DALE DALS DAME DAMN DAMP DAMS DANE DANK DANS DARE DARK DARN DART DATE DEAD DEAL DEAN DEED DEEM DEEP DEES DEET DEKE DELE DELL DELS DELT DEME DEMY DENE DENS DENT DENY DEON DERE DERM DESK DHAK DHAL DIAL DIED DIEL DIES DIET DIKE DILL DIME DIMS DINE DINK DINS DINT DIOL DION DIRE DIRK DIRL DIRT DISK DISS DITE DITS DOAT DOES DOLE DOLL DOLS DOLT DOME DOMS DONE DONS DOOM DORE DORK DORM DORP DORS DORY DOSE DOSS DOST DOTE DOTS DOTY DRAM DRAT DRAY DREE DREK DROP DUAD DUAL DUEL DUES DUET DUKE DULL DULY DUMP DUNE DUNK DUNS DUNT DUOS DURE DURN DUSK DUST DUTY DYAD DYED DYES DYKE DYNE FAKE FALL FAME FANE FANS FARD FARE FARL FARM FART FAST FATE FATS FEAL FEAT FEED FEEL FEES FEET FELL FELT FEME FEMS FEND FENS FEOD FERE FERN FESS FEST FETE FETS FIAT FILE FILL FILM FILS FIND FINE FINK FINN FINS FIRE FIRM FIRN FIRS FIST FITS FLAK FLAM FLAN FLAP FLAT FLAY FLED FLEE FLEY FLOE FLOP FOAL FOAM FOES FOLD FOLK FOND FONS FONT FOOD FOOL FOOT FORD FORE FORK FORM FORT FOSS FRAE FRAP FRAT FRAY FRED FREE FRET FROE FROM FUEL FULL FUME FUMY FUND FUNK FUNS FURL FURS FURY FUSE FUSS FYKE HAED HAEM HAEN HAES HAET HAKE HALE HALL HALM HALT HAME HAMS HAND HANK HANS HANT HARD HARE HARK HARL HARM HARP HART HASP HAST HATE HATS HEAD HEAL HEAP HEAT HEED HEEL HELD HELL HELM HELP HEME HEMP HEMS HENS HENT HERD HERE HERL HERM HERN HERS HEST HETS HIED HIES HIKE HILL HILT HIMS HIND HINS HINT HIRE HISN HISS HIST HITS HOED HOES HOKE HOLD HOLE HOLK HOLM HOLP HOLS HOLT HOLY HOME HOMY HONE HONK HONS HOOD HOOK HOOP HOOT HORN HOSE HOST HOTS HUED HUES HULK HULL HUMP HUMS HUNK HUNS HUNT HURL HURT HUSK HUTS HYMN HYTE LAKE LAKY LALL LAME LAMP LAMS LAND LANE LANK LARD LARK LARS LASE LASS LAST LATE LATS LEAD LEAK LEAL LEAN LEAP LEAS LEEK LEES LEET LEKE LEKS LEND LENS LENT LEON LESS LEST LETS LIAM LIAN LIED LIEN LIES LIKE LILT LILY LIME LIMN LIMP LIMY LINE LINK LINN LINS LINT LINY LION LIRE LISP LIST LITE LITS LOAD LOAM LOAN LOLL LONE LOOK LOOM LOON LOOP LOOS LOOT LORD LORE LORN LORY LOSE LOSS LOST LOTS LUES LUKE LULL LUMP LUMS LUNE LUNK LUNT LUNY LURE LURK LUST LUTE LYAM LYES LYLE LYRE LYSE MAES MAKE MALE MALL MALM MALT MANE MANS MANY MARE MARK MARL MARS MART MARY MASK MASS MAST MATE MATS MATT MEAD MEAL MEAN MEAT MEED MEEK MEET MELD MELL MELS MELT MEME MEMS MEND MERE MERK MERL MESS METE MHOS MIEN MIKE MILD MILE MILK MILL MILS MILT MIME MIND MINE MINK MINT MIRE MIRK MIRS MIRY MISE MISS MIST MITE MITT MITY MOAN MOAS MOAT MOKE MOLD MOLE MOLL MOLS MOLT MOLY MOME MOMS MONK MONS MONY MOOD MOOL MOON MOOS MOOT MORE MORN MORS MORT MOSK MOSS MOST MOTE MOTS MOTT MULE MULL MUMM MUMP MUMS MUNS MUON MURE MURK MUSE MUSK MUSS MUST MUTE MUTS MUTT PALE PALL PALM PALP PALS PALY PAMS PANE PANS PANT PARD PARE PARK PARS PART PASE PASS PAST PATE PATS PATY PEAK PEAL PEAN PEAS PEAT PEED PEEK PEEL PEEN PEEP PEES PEKE PELE PELT PEND PENS PENT PEON PERE PERK PERM PERP PERT PEST PETS PHAT PHON PHOT PIAL PIAN PIAS PIED PIES PIKE PILE PILL PILY PIMP PINE PINK PINS PINT PINY PION PIRN PISS PITS PITY PLAN PLAT PLAY PLED PLOD PLOP PLOT PLOY POEM POET POKE POKY POLE POLL POLS POLY POME POMP POMS POND PONE PONS PONY POOD POOL POON POOP POOS PORE PORK PORN PORT POSE POST POSY POTS PRAM PRAT PRAY PREE PREP PREY PROD PROM PROP PROS PUKE PULE PULL PULP PULS PUMP PUNK PUNS PUNT PUNY PURE PURL PURS PUSS PUTS PUTT PYAS PYES PYRE SAAD SAKE SALE SALL SALP SALS SALT SAME SAMP SAND SANE SANK SANS SARD SARK SASS SATE SEAL SEAM SEAN SEAS SEAT SEED SEEK SEEL SEEM SEEN SEEP SEES SELL SELS SEME SEND SENE SENT SERE SERS SETS SETT SHAD SHAE SHAM SHAT SHAY SHED SHES SHOD SHOE SHOP SHOT SIAL SIKE SILD SILK SILL SILT SIMP SIMS SINE SINK SINS SIRE SIRS SITE SITS SLAM SLAP SLAT SLAY SLED SLOE SLOP SLOT SNAP SNED SNOT SOAK SOAP SOKE SOLD SOLE SOLS SOME SOMS SONE SONS SOOK SOON SOOT SORD SORE SORN SORT SOTS SUED SUES SUET SUKS SULK SUMP SUMS SUNK SUNN SUNS SURD SURE SUSS SYED SYKE SYNE TAEL TAKE TALE TALK TALL TAME TAMP TAMS TANK TANS TAOS TARE TARN TARP TARS TART TASK TASS TATE TATS TEAK TEAL TEAM TEAS TEAT TEED TEEL TEEM TEEN TEES TELE TELL TELS TEMP TEND TENS TENT TERM TERN TESS TEST TETS THAE THAN THAT THEE THEM THEN THEY TIED TIES TIKE TILE TILL TILS TILT TIME TINE TINS TINT TINY TIRE TIRL TITS TOAD TOED TOES TOKE TOLD TOLE TOLL TOME TOMS TONE TONS TONY TOOK TOOL TOOM TOON TOOT TORE TORN TORS TORT TORY TOSS TOST TOTE TOTS TRAD TRAE TRAM TRAP TRAY TREE TREK TRES TRET TREY TROD TROP TROT TROY TULE TUMP TUNE TUNS TURD TURK TURN TUSK TUTS TYEE TYES TYKE TYNE TYRE WAES WAKE WALE WALK WALL WALY WAME WAND WANE WANK WANS WANT WANY WARD WARE WARK WARM WARN WARP WARS WART WARY WASP WAST WATS WATT WEAK WEAL WEAN WEED WEEK WEEL WEEN WEEP WEES WEET WELD WELL WELT WEND WENS WENT WERE WERT WEST WETS WHAM WHAP WHAT WHEE WHEN WHET WHEY WHOM WHOP WILD WILE WILL WILT WILY WIMP WIND WINE WINK WINS WINY WIRE WIRY WISE WISP WISS WIST WITE WITS WOAD WOES WOKE WOKS WOLD WONK WONS WONT WOOD WOOL WOOS WORD WORE WORK WORM WORN WORT WOST WOTS WRAP WREN WUSS WYES WYLE WYND WYNN WYNS WYTE\n" + ] + } + ], + "source": [ + "show(wordlock)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# How Secure is WordLock?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The lock makes 1118 words (according to my word list). You might say that an attacker who knows the combination is a word would find this lock to be only 11.18% as secure as a 4-digit lock with 10,000 combinations. But in reality, every cable lock is [vulnerable](https://www.sfbike.org/news/video-how-to-lock-your-bike/) to an attacker with wire cutters, or with a knowledge of lock-picking, so security is equally poor for WordLock® and for an equivalent lock with numbers. (You should use a hardened steel U-lock instead.)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Random Locks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 2 asks if a different lock can make more words. As a baseline, before we get to improved locks, I will start with completely random locks, as produced by the function `random_lock`. I use `t=4` to say that by default there are 4 tumblers, and `c=10` to indicate 10 letters on each tumbler (\"c\" for \"circumference\"). I give `random_lock` an argument to seed the random number generator; that makes calls repeatable if desired." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def random_lock(t=4, c=10, seed='seed'):\n", + " \"Make a lock by sampling randomly and uniformly from the alphabet.\"\n", + " random.seed(seed)\n", + " return Lock(Tumbler(random.sample(alphabet, c))\n", + " for i in range(t))\n", + "\n", + "alphabet = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: EBHLJPYKQR VNSYPCWBGR BJOHSCFMRP XCSLUNMQJI\n", + "Count: 15\n", + "Words: BROS BYRL EBBS EBON ECRU EGOS ENOL EPOS EROS ERRS HYMN HYPS KNOX PROM PROS\n" + ] + } + ], + "source": [ + "show(random_lock())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wow, that's not very many words. Let's repeat 100 times and take the best one, with \"best\" determined by the function `word_count`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def word_count(lock): return len(words_from(lock))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: IDQPSFOJCW MQYGODAINT NLRZPXWFBI STGWCOLJEH\n", + "Count: 259\n", + "Words: CABS CAFE CALE CALL CALO CANE CANS CANT CAPE CAPH CAPO CAPS CARE CARL CARS CART CAWS CINE CIRE COBS COFT COIL COLE COLS COLT CONE CONS COPE COPS CORE CORS COWL COWS DABS DAFT DAIS DALE DALS DANE DANG DANS DAPS DARE DART DAWS DAWT DAZE DIBS DIFS DILL DINE DING DINO DINS DINT DIPS DIPT DIRE DIRL DIRT DOIT DOLE DOLL DOLS DOLT DONE DONG DONS DOPE DORE DORS DOWS DOZE DYNE FABS FAIL FALL FANE FANG FANO FANS FARE FARL FARO FART FAZE FIBS FIFE FILE FILL FILO FILS FINE FINO FINS FIRE FIRS FIXT FOBS FOIL FONS FONT FOPS FORE FORT FOWL IDLE IMPS INFO INNS INRO IONS JABS JAIL JANE JAPE JARL JARS JAWS JIBE JIBS JILL JILT JINS JOBS JOLE JOLT JOWL JOWS OAFS OARS ODIC OGLE OGRE OILS OMIT OOPS OOZE OTIC OTIS PAIL PALE PALL PALS PANE PANG PANS PANT PAPS PARE PARS PART PAWL PAWS PILE PILL PINE PING PINS PINT PIPE PIPS POIS POLE POLL POLO POLS PONE PONG PONS POPE POPS PORE PORT POWS PYIC PYRE PYRO QOPH SABE SABS SAFE SAIL SALE SALL SALS SALT SANE SANG SANS SAPS SAWS SIBS SIFT SILL SILO SILT SINE SING SINH SINS SIPE SIPS SIRE SIRS SIZE SMIT SNIT SOBS SOFT SOIL SOLE SOLO SOLS SONE SONG SONS SOPH SOPS SORE SORT SOWS SYBO SYNC SYNE SYPH WABS WAFT WAIL WAIT WALE WALL WANE WANS WANT WAPS WARE WARS WART WAWL WAWS WIFE WILE WILL WILT WINE WING WINO WINS WIPE WIRE WONS WONT WOPS WORE WORT WOWS WYLE WYNS\n" + ] + } + ], + "source": [ + "random_locks = [random_lock(seed=i) for i in range(100)]\n", + "\n", + "show(max(random_locks, key=word_count))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Still not very good. We will need a more systematic approach." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 2: More Words (via Greedy Locks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "My first idea for a lock with more words is this: consider each tumbler, one at a time, and fill the tumbler with the letters that make the most words. How do I determine what letters make the most words? A `Counter` does most of the work; we feed it a list of the first letter of each word, and then ask it for the ten most common letters (and their counts): " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('S', 373),\n", + " ('T', 268),\n", + " ('P', 268),\n", + " ('B', 267),\n", + " ('D', 251),\n", + " ('C', 248),\n", + " ('L', 246),\n", + " ('M', 239),\n", + " ('A', 236),\n", + " ('R', 203)]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "first_letters = [w[0] for w in WORDS]\n", + "\n", + "Counter(first_letters).most_common(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In other words, the letters SPTBDCLMAR are the most common ways to start a word. Let's add up those counts:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2599" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def n_most_common(counter, n): return sum(n for (_, n) in counter.most_common(n))\n", + "\n", + "n_most_common(Counter(first_letters), 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that SPTBDCLMAR covers 2,599 words. We don't know for sure that these are the best 10 letters to put on the first tumbler, but we do know that whatever letters are best, they can't form more than 2,599 words, so we have an upper bound on the number of words in a lock (and the 1,118 from `wordlock` is a lower bound).\n", + "\n", + "What letters should we put on the second tumbler? We will do the same thing, but this time don't consider *all* the words in the dictionary; just consider the 2,599 words that start with one of the ten letters on the first tumbler. Continue this way until we fill in all four tumblers. This is called a *greedy* approach, because when we consider each tumbler, we pick the solution that looks best right then, for that tumbler, without consideration for future tumblers." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def greedy_lock(t=4, c=10, words=WORDS):\n", + " \"Make a lock with t tumblers, each consisting of the c letters that cover the most words at that position.\"\n", + " lock = Lock()\n", + " for i in range(t):\n", + " # Make a tumbler of c letters, such that the tumbler covers the most words.\n", + " # Then update words to only include the ones that can be made with this tumbler\n", + " counter = Counter(word[i] for word in words)\n", + " tumbler = Tumbler(L for (L, _) in counter.most_common(c))\n", + " words = [w for w in words if w[i] in tumbler]\n", + " lock.append(tumbler)\n", + " return lock" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: STPBDCLMAR OAIEURLHYN RNALEOTISM SETADNLKPY\n", + "Count: 1177\n", + "Words: AALS AEON AERY AHED AHIS AHOY AILA AILS AIMS AINS AIRN AIRS AIRT AIRY AITS ALAE ALAN ALAS ALEA ALEE ALEK ALES ALIA ALIT ALLS ALLY ALMA ALME ALMS ALOE ALTS ANAL ANAS ANAY ANES ANIL ANIS ANNA ANNE ANOA ANON ANSA ANTA ANTE ANTS ARAK AREA ARES ARIA ARID ARIE ARIL ARMS ARMY ARON ARSE ARTS ARTY AULD AUNT AURA AYAN AYES AYIN AYLA BAAL BAAS BAIL BAIT BALD BALE BALK BALL BALS BAMS BAND BANE BANK BANS BARD BARE BARK BARN BARS BASE BASK BASS BAST BATE BATS BATT BEAD BEAK BEAN BEAT BEEN BEEP BEES BEET BELL BELS BELT BEMA BEND BENE BENS BENT BERK BEST BETA BETS BIAS BILE BILK BILL BIMA BIND BINE BINS BINT BIOS BIRD BIRK BIRL BISE BISK BITE BITS BITT BLAE BLAT BLED BLET BLIN BLIP BLOT BOAS BOAT BOIL BOLA BOLD BOLE BOLL BOLT BOND BONE BONK BONY BOOK BOON BOOS BOOT BORA BORE BORK BORN BORT BOSK BOSS BOTA BOTS BOTT BRAD BRAE BRAN BRAS BRAT BRAY BREA BRED BREE BREN BRIA BRIE BRIN BRIS BRIT BROS BULK BULL BUMP BUMS BUNA BUND BUNK BUNN BUNS BUNT BUOY BURA BURD BURL BURN BURP BURS BURY BUSK BUSS BUST BUSY BUTE BUTS BUTT BYES BYRE BYRL BYTE CAEL CAID CAIN CALE CALK CALL CAME CAMP CAMS CANE CANS CANT CARA CARD CARE CARK CARL CARN CARP CARS CART CASA CASE CASK CAST CATE CATS CEES CEIL CELL CELS CELT CENT CERE CESS CETE CHAD CHAP CHAT CHAY CHIA CHID CHIN CHIP CHIS CHIT CHON CHOP CIAN CINE CION CIRE CIST CITE CITY CLAD CLAN CLAP CLAY CLIP CLOD CLON CLOP CLOT CLOY COAL COAT COED COEN COIL COIN COLA COLD COLE COLS COLT COLY COMA COME COMP CONE CONK CONN CONS CONY COOK COOL COON COOP COOS COOT CORA CORD CORE CORK CORN CORS CORY COSS COST COSY COTE COTS CRAP CRED CRIS CRIT CROP CUED CUES CULL CULT CUNT CURD CURE CURL CURN CURS CURT CUSK CUSP CUSS CUTE CUTS CYAN CYMA CYME CYST DAIS DALE DALS DAME DAMN DAMP DAMS DANA DANE DANK DANS DARE DARK DARN DART DATA DATE DEAD DEAL DEAN DEED DEEP DEES DEET DEIL DELE DELL DELS DELT DEME DEMY DENE DENS DENT DENY DEON DERE DESK DHAK DHAL DIAL DIED DIEL DIES DIET DILL DIME DIMS DINA DINE DINK DINS DINT DIOL DION DIRE DIRK DIRL DIRT DISK DISS DITA DITE DITS DOAT DOES DOIT DOLE DOLL DOLS DOLT DOME DOMS DONA DONE DONS DORE DORK DORP DORS DORY DOSE DOSS DOST DOTE DOTS DOTY DRAT DRAY DREE DREK DRIP DROP DUAD DUAL DUEL DUES DUET DUIT DULL DULY DUMA DUMP DUNE DUNK DUNS DUNT DUOS DURA DURE DURN DUSK DUST DUTY DYAD DYED DYES DYNE LAID LAIN LALL LAMA LAME LAMP LAMS LANA LAND LANE LANK LARA LARD LARK LARS LASE LASS LAST LATE LATS LEAD LEAK LEAL LEAN LEAP LEAS LEEK LEES LEET LEIA LEIS LELA LENA LEND LENS LENT LEON LESS LEST LETS LIAN LIED LIEN LIES LILA LILT LILY LIMA LIME LIMN LIMP LIMY LINA LINE LINK LINN LINS LINT LINY LION LIRA LIRE LISA LISP LIST LITE LITS LOAD LOAN LOID LOIN LOLA LOLL LONE LOOK LOON LOOP LOOS LOOT LORD LORE LORN LORY LOSE LOSS LOST LOTA LOTS LUES LUIS LULL LUMA LUMP LUMS LUNA LUNE LUNK LUNT LUNY LURE LURK LUST LUTE LYES LYLA LYLE LYRA LYRE LYSE MAES MAIA MAID MAIL MAIN MALE MALL MALT MAMA MANA MANE MANS MANY MARA MARE MARK MARL MARS MART MARY MASA MASK MASS MAST MATE MATS MATT MEAD MEAL MEAN MEAT MEED MEEK MEET MELD MELL MELS MELT MEME MEMS MEND MERE MERK MERL MESA MESS META METE MHOS MIEN MILA MILD MILE MILK MILL MILS MILT MIME MINA MIND MINE MINK MINT MIRA MIRE MIRK MIRS MIRY MISE MISS MIST MITE MITT MITY MOAN MOAS MOAT MOIL MOLA MOLD MOLE MOLL MOLS MOLT MOLY MOME MOMS MONA MONK MONS MONY MOOD MOOL MOON MOOS MOOT MORA MORE MORN MORS MORT MOSK MOSS MOST MOTE MOTS MOTT MULE MULL MUMP MUMS MUNS MUON MURA MURE MURK MUSA MUSE MUSK MUSS MUST MUTE MUTS MUTT MYLA MYNA MYRA PAID PAIK PAIL PAIN PALE PALL PALP PALS PALY PAMS PANE PANS PANT PARA PARD PARE PARK PARS PART PASE PASS PAST PATE PATS PATY PEAK PEAL PEAN PEAS PEAT PEED PEEK PEEL PEEN PEEP PEES PEIN PELE PELT PEND PENS PENT PEON PERE PERK PERP PERT PEST PETS PHAT PHIS PHON PHOT PIAL PIAN PIAS PIED PIES PILE PILL PILY PIMA PIMP PINA PINE PINK PINS PINT PINY PION PIRN PISS PITA PITS PITY PLAN PLAT PLAY PLEA PLED PLIE PLOD PLOP PLOT PLOY POET POIS POLE POLL POLS POLY POME POMP POMS POND PONE PONS PONY POOD POOL POON POOP POOS PORE PORK PORN PORT POSE POST POSY POTS PRAT PRAY PREE PREP PREY PROA PROD PROP PROS PULA PULE PULL PULP PULS PUMA PUMP PUNA PUNK PUNS PUNT PUNY PURE PURL PURS PUSS PUTS PUTT PYAS PYES PYIN PYRE RAIA RAID RAIL RAIN RAIS RALE RAMP RAMS RAND RANK RANT RARE RASE RASP RATE RATS READ REAL REAP REED REEK REEL REES REID REIN REIS RELY REMS REMY REND RENE RENT REST RETE RETS RHEA RHOS RIAL RIAN RIAS RIEL RILE RILL RIME RIMS RIMY RIND RINK RINS RIOT RISE RISK RITA RITE ROAD ROAN ROES ROIL ROLE ROLL ROME ROMP ROMS ROOD ROOK ROOT RORY ROSA ROSE ROSS ROSY ROTA ROTE ROTL ROTS RUED RUES RUIN RULE RULY RUMP RUMS RUNE RUNS RUNT RUSE RUSK RUST RUTS RYAN RYAS RYES RYND RYOT SAAD SAID SAIL SAIN SALE SALL SALP SALS SALT SAME SAMP SANA SAND SANE SANK SANS SARA SARD SARK SASS SATE SEAL SEAN SEAS SEAT SEED SEEK SEEL SEEN SEEP SEES SEIS SELL SELS SEME SEND SENE SENT SERA SERE SERS SETA SETS SETT SHAD SHAE SHAT SHAY SHEA SHED SHES SHIN SHIP SHIT SHOD SHOE SHOP SHOT SIAL SILD SILK SILL SILT SIMA SIMP SIMS SINE SINK SINS SIRE SIRS SITE SITS SLAP SLAT SLAY SLED SLID SLIP SLIT SLOE SLOP SLOT SNAP SNED SNIP SNIT SNOT SOAK SOAP SOIL SOLA SOLD SOLE SOLS SOMA SOME SOMS SONE SONS SOOK SOON SOOT SORA SORD SORE SORN SORT SOTS SRIS SUED SUES SUET SUIT SULK SUMP SUMS SUNK SUNN SUNS SURA SURD SURE SUSS SYED SYNE TAEL TAIL TAIN TALA TALE TALK TALL TAME TAMP TAMS TANK TANS TAOS TARA TARE TARN TARP TARS TART TASK TASS TATE TATS TEAK TEAL TEAS TEAT TEED TEEL TEEN TEES TELA TELE TELL TELS TEMP TEND TENS TENT TERN TESS TEST TETS THAE THAN THAT THEA THEE THEN THEY THIN THIS TIED TIES TILE TILL TILS TILT TIME TINA TINE TINS TINT TINY TIRE TIRL TITS TOAD TOEA TOED TOES TOIL TOIT TOLA TOLD TOLE TOLL TOME TOMS TONE TONS TONY TOOK TOOL TOON TOOT TORA TORE TORN TORS TORT TORY TOSS TOST TOTE TOTS TRAD TRAE TRAP TRAY TREE TREK TRES TRET TREY TRIP TROD TROP TROT TROY TUIS TULE TUMP TUNA TUNE TUNS TURD TURK TURN TUSK TUTS TYEE TYES TYIN TYNE TYRE\n" + ] + } + ], + "source": [ + "show(greedy_lock())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember that the `wordlock` gave 1118 words, so the greedy lock with 1177 is better, but only by 5%. Is it possible to do better still? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 2: More Words (via Improved Locks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's another idea to get more words from a lock:\n", + "\n", + "1. Start with some lock.\n", + "2. Pick, at random, one letter on one tumbler and change it to a new letter.\n", + "3. If the change yields more words, keep the change; otherwise discard the change.\n", + "4. Repeat.\n", + "\n", + "We can implement this strategy with the function `improved_lock`, which calls `changed_lock` to make a random change:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def improved_lock(lock, steps=3000):\n", + " \"Randomly change letters in lock, keeping changes that improve the score.\"\n", + " score = word_count(lock)\n", + " for i in range(steps):\n", + " lock2 = changed_lock(lock)\n", + " score2 = word_count(lock2)\n", + " if score2 >= score: \n", + " lock, score = lock2, score2\n", + " return lock\n", + "\n", + "def changed_lock(lock): \n", + " \"Change one letter in one tumbler.\"\n", + " lock2 = Lock(lock)\n", + " i = random.randrange(len(lock))\n", + " old = random.choice(lock[i])\n", + " new = random.choice([L for L in alphabet if L not in lock[i]])\n", + " lock2[i] = lock2[i].replace(old, new)\n", + " return lock2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see how this does to improve the best lock we've seen so far, the greedy lock:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: STPBDCLMWF OAIEURLHYP RNALEOTISC SETADNLKHY\n", + "Count: 1240\n", + "Words: BAAL BAAS BACH BACK BAIL BAIT BALD BALE BALK BALL BALS BAND BANE BANK BANS BARD BARE BARK BARN BARS BASE BASH BASK BASS BAST BATE BATH BATS BATT BEAD BEAK BEAN BEAT BECK BEEN BEES BEET BELL BELS BELT BEND BENE BENS BENT BERK BEST BETA BETH BETS BIAS BICE BILE BILK BILL BIND BINE BINS BINT BIOS BIRD BIRK BIRL BISE BISK BITE BITS BITT BLAE BLAH BLAT BLED BLET BLIN BLOT BOAS BOAT BOCK BOIL BOLA BOLD BOLE BOLL BOLT BOND BONE BONK BONY BOOK BOON BOOS BOOT BORA BORE BORK BORN BORT BOSH BOSK BOSS BOTA BOTH BOTS BOTT BRAD BRAE BRAN BRAS BRAT BRAY BREA BRED BREE BREN BRIA BRIE BRIN BRIS BRIT BROS BUCK BULK BULL BUNA BUND BUNK BUNN BUNS BUNT BUOY BURA BURD BURL BURN BURS BURY BUSH BUSK BUSS BUST BUSY BUTE BUTS BUTT BYES BYRE BYRL BYTE CACA CAEL CAID CAIN CALE CALK CALL CANE CANS CANT CARA CARD CARE CARK CARL CARN CARS CART CASA CASE CASH CASK CAST CATE CATS CECA CEES CEIL CELL CELS CELT CENT CERE CESS CETE CHAD CHAT CHAY CHIA CHID CHIN CHIS CHIT CHON CIAN CINE CION CIRE CIST CITE CITY CLAD CLAN CLAY CLOD CLON CLOT CLOY COAL COAT COCA COCK COED COEN COIL COIN COLA COLD COLE COLS COLT COLY CONE CONK CONN CONS CONY COOK COOL COON COOS COOT CORA CORD CORE CORK CORN CORS CORY COSH COSS COST COSY COTE COTS CRED CRIS CRIT CUED CUES CULL CULT CUNT CURD CURE CURL CURN CURS CURT CUSK CUSS CUTE CUTS CYAN CYST DACE DAIS DALE DALS DANA DANE DANK DANS DARE DARK DARN DART DASH DATA DATE DEAD DEAL DEAN DECK DEED DEES DEET DEIL DELE DELL DELS DELT DENE DENS DENT DENY DEON DERE DESK DHAK DHAL DIAL DICE DICK DIED DIEL DIES DIET DILL DINA DINE DINK DINS DINT DIOL DION DIRE DIRK DIRL DIRT DISH DISK DISS DITA DITE DITS DOAT DOCK DOCS DOES DOIT DOLE DOLL DOLS DOLT DONA DONE DONS DORE DORK DORS DORY DOSE DOSS DOST DOTE DOTH DOTS DOTY DRAT DRAY DREE DREK DUAD DUAL DUCE DUCK DUCT DUEL DUES DUET DUIT DULL DULY DUNE DUNK DUNS DUNT DUOS DURA DURE DURN DUSK DUST DUTY DYAD DYED DYES DYNE FACE FACT FAIL FAIN FALL FANE FANS FARD FARE FARL FART FASH FAST FATE FATS FEAL FEAT FECK FEED FEEL FEES FEET FELL FELT FEND FENS FEOD FERE FERN FESS FEST FETA FETE FETS FIAT FICE FILA FILE FILL FILS FIND FINE FINK FINN FINS FIRE FIRN FIRS FISH FIST FITS FLAK FLAN FLAT FLAY FLEA FLED FLEE FLEY FLIT FLOE FOAL FOES FOIL FOIN FOLD FOLK FOND FONS FONT FOOD FOOL FOOT FORA FORD FORE FORK FORT FOSS FRAE FRAT FRAY FRED FREE FRET FRIT FROE FUCK FUEL FULL FUND FUNK FUNS FURL FURS FURY FUSE FUSS FYCE LACE LACK LACS LACY LAID LAIN LALL LANA LAND LANE LANK LARA LARD LARK LARS LASE LASH LASS LAST LATE LATH LATS LEAD LEAH LEAK LEAL LEAN LEAS LECH LEEK LEES LEET LEIA LEIS LELA LENA LEND LENS LENT LEON LESS LEST LETS LIAN LICE LICH LICK LIED LIEN LIES LILA LILT LILY LINA LINE LINK LINN LINS LINT LINY LION LIRA LIRE LISA LIST LITE LITS LOAD LOAN LOCA LOCH LOCK LOID LOIN LOLA LOLL LONE LOOK LOON LOOS LOOT LORD LORE LORN LORY LOSE LOSS LOST LOTA LOTH LOTS LUCA LUCE LUCK LUCY LUES LUIS LULL LUNA LUNE LUNK LUNT LUNY LURE LURK LUSH LUST LUTE LYCH LYES LYLA LYLE LYRA LYRE LYSE MACE MACH MACK MACS MACY MAES MAIA MAID MAIL MAIN MALE MALL MALT MANA MANE MANS MANY MARA MARE MARK MARL MARS MART MARY MASA MASH MASK MASS MAST MATE MATH MATS MATT MEAD MEAL MEAN MEAT MEED MEEK MEET MELD MELL MELS MELT MEND MERE MERK MERL MESA MESH MESS META METE METH MHOS MIAH MICA MICE MICK MICS MIEN MILA MILD MILE MILK MILL MILS MILT MINA MIND MINE MINK MINT MIRA MIRE MIRK MIRS MIRY MISE MISS MIST MITE MITT MITY MOAN MOAS MOAT MOCK MOCS MOIL MOLA MOLD MOLE MOLL MOLS MOLT MOLY MONA MONK MONS MONY MOOD MOOL MOON MOOS MOOT MORA MORE MORN MORS MORT MOSH MOSK MOSS MOST MOTE MOTH MOTS MOTT MUCH MUCK MULE MULL MUNS MUON MURA MURE MURK MUSA MUSE MUSH MUSK MUSS MUST MUTE MUTS MUTT MYAH MYCS MYLA MYNA MYRA MYTH PACA PACE PACK PACS PACT PACY PAID PAIK PAIL PAIN PALE PALL PALS PALY PANE PANS PANT PARA PARD PARE PARK PARS PART PASE PASH PASS PAST PATE PATH PATS PATY PEAK PEAL PEAN PEAS PEAT PECH PECK PECS PEED PEEK PEEL PEEN PEES PEIN PELE PELT PEND PENS PENT PEON PERE PERK PERT PEST PETS PHAT PHIS PHON PHOT PIAL PIAN PIAS PICA PICE PICK PICS PIED PIES PILE PILL PILY PINA PINE PINK PINS PINT PINY PION PIRN PISH PISS PITA PITH PITS PITY PLAN PLAT PLAY PLEA PLED PLIE PLOD PLOT PLOY POCK POET POIS POLE POLL POLS POLY POND PONE PONS PONY POOD POOH POOL POON POOS PORE PORK PORN PORT POSE POSH POST POSY POTS PRAT PRAY PREE PREY PROA PROD PROS PUCE PUCK PULA PULE PULL PULS PUNA PUNK PUNS PUNT PUNY PURE PURL PURS PUSH PUSS PUTS PUTT PYAS PYES PYIN PYRE SAAD SACK SACS SAID SAIL SAIN SALE SALL SALS SALT SANA SAND SANE SANK SANS SARA SARD SARK SASH SASS SATE SEAL SEAN SEAS SEAT SECS SECT SEED SEEK SEEL SEEN SEES SEIS SELL SELS SEND SENE SENT SERA SERE SERS SETA SETH SETS SETT SHAD SHAE SHAH SHAT SHAY SHEA SHED SHES SHIN SHIT SHOD SHOE SHOT SIAL SICE SICK SICS SILD SILK SILL SILT SINE SINH SINK SINS SIRE SIRS SITE SITH SITS SLAT SLAY SLED SLID SLIT SLOE SLOT SOAK SOCA SOCK SOIL SOLA SOLD SOLE SOLS SONE SONS SOOK SOON SOOT SORA SORD SORE SORN SORT SOTH SOTS SPAE SPAN SPAS SPAT SPAY SPED SPIK SPIN SPIT SPOT SPRY SRIS SUCH SUCK SUED SUES SUET SUIT SULK SUNK SUNN SUNS SURA SURD SURE SUSS SYCE SYED SYNE TACE TACH TACK TACT TAEL TAIL TAIN TALA TALE TALK TALL TANK TANS TAOS TARA TARE TARN TARS TART TASK TASS TATE TATS TEAK TEAL TEAS TEAT TECH TEED TEEL TEEN TEES TELA TELE TELL TELS TEND TENS TENT TERN TESS TEST TETH TETS THAE THAN THAT THEA THEE THEN THEY THIN THIS TICK TICS TIED TIES TILE TILL TILS TILT TINA TINE TINS TINT TINY TIRE TIRL TITS TOAD TOEA TOED TOES TOIL TOIT TOLA TOLD TOLE TOLL TONE TONS TONY TOOK TOOL TOON TOOT TORA TORE TORN TORS TORT TORY TOSH TOSS TOST TOTE TOTS TRAD TRAE TRAY TREE TREK TRES TRET TREY TROD TROT TROY TUCK TUIS TULE TUNA TUNE TUNS TURD TURK TURN TUSH TUSK TUTS TYCE TYEE TYES TYIN TYNE TYRE WACK WAES WAIL WAIN WAIT WALE WALK WALL WALY WAND WANE WANK WANS WANT WANY WARD WARE WARK WARN WARS WART WARY WASH WAST WATS WATT WEAK WEAL WEAN WEED WEEK WEEL WEEN WEES WEET WELD WELL WELT WEND WENS WENT WERE WERT WEST WETS WHAT WHEE WHEN WHET WHEY WHID WHIN WHIT WHOA WICH WICK WILD WILE WILL WILT WILY WIND WINE WINK WINS WINY WIRE WIRY WISE WISH WISS WIST WITE WITH WITS WOAD WOES WOLD WONK WONS WONT WOOD WOOL WOOS WORD WORE WORK WORN WORT WOST WOTS WREN WRIT WUSS WYCH WYES WYLE WYND WYNN WYNS WYTE\n" + ] + } + ], + "source": [ + "show(improved_lock(greedy_lock()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How about starting from a random lock? " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: TMSLBPFWCD AEHYLORIWU CNATELISRO LDSYANKETH\n", + "Count: 1240\n", + "Words: BAAL BAAS BACH BACK BAIL BAIT BALD BALE BALK BALL BALS BAND BANE BANK BANS BARD BARE BARK BARN BARS BASE BASH BASK BASS BAST BATE BATH BATS BATT BEAD BEAK BEAN BEAT BECK BEEN BEES BEET BELL BELS BELT BEND BENE BENS BENT BERK BEST BETA BETH BETS BIAS BICE BILE BILK BILL BIND BINE BINS BINT BIOS BIRD BIRK BIRL BISE BISK BITE BITS BITT BLAE BLAH BLAT BLED BLET BLIN BLOT BOAS BOAT BOCK BOIL BOLA BOLD BOLE BOLL BOLT BOND BONE BONK BONY BOOK BOON BOOS BOOT BORA BORE BORK BORN BORT BOSH BOSK BOSS BOTA BOTH BOTS BOTT BRAD BRAE BRAN BRAS BRAT BRAY BREA BRED BREE BREN BRIA BRIE BRIN BRIS BRIT BROS BUCK BULK BULL BUNA BUND BUNK BUNN BUNS BUNT BUOY BURA BURD BURL BURN BURS BURY BUSH BUSK BUSS BUST BUSY BUTE BUTS BUTT BYES BYRE BYRL BYTE CACA CAEL CAID CAIN CALE CALK CALL CANE CANS CANT CARA CARD CARE CARK CARL CARN CARS CART CASA CASE CASH CASK CAST CATE CATS CECA CEES CEIL CELL CELS CELT CENT CERE CESS CETE CHAD CHAT CHAY CHIA CHID CHIN CHIS CHIT CHON CIAN CINE CION CIRE CIST CITE CITY CLAD CLAN CLAY CLOD CLON CLOT CLOY COAL COAT COCA COCK COED COEN COIL COIN COLA COLD COLE COLS COLT COLY CONE CONK CONN CONS CONY COOK COOL COON COOS COOT CORA CORD CORE CORK CORN CORS CORY COSH COSS COST COSY COTE COTS CRED CRIS CRIT CUED CUES CULL CULT CUNT CURD CURE CURL CURN CURS CURT CUSK CUSS CUTE CUTS CYAN CYST DACE DAIS DALE DALS DANA DANE DANK DANS DARE DARK DARN DART DASH DATA DATE DEAD DEAL DEAN DECK DEED DEES DEET DEIL DELE DELL DELS DELT DENE DENS DENT DENY DEON DERE DESK DHAK DHAL DIAL DICE DICK DIED DIEL DIES DIET DILL DINA DINE DINK DINS DINT DIOL DION DIRE DIRK DIRL DIRT DISH DISK DISS DITA DITE DITS DOAT DOCK DOCS DOES DOIT DOLE DOLL DOLS DOLT DONA DONE DONS DORE DORK DORS DORY DOSE DOSS DOST DOTE DOTH DOTS DOTY DRAT DRAY DREE DREK DUAD DUAL DUCE DUCK DUCT DUEL DUES DUET DUIT DULL DULY DUNE DUNK DUNS DUNT DUOS DURA DURE DURN DUSK DUST DUTY DYAD DYED DYES DYNE FACE FACT FAIL FAIN FALL FANE FANS FARD FARE FARL FART FASH FAST FATE FATS FEAL FEAT FECK FEED FEEL FEES FEET FELL FELT FEND FENS FEOD FERE FERN FESS FEST FETA FETE FETS FIAT FICE FILA FILE FILL FILS FIND FINE FINK FINN FINS FIRE FIRN FIRS FISH FIST FITS FLAK FLAN FLAT FLAY FLEA FLED FLEE FLEY FLIT FLOE FOAL FOES FOIL FOIN FOLD FOLK FOND FONS FONT FOOD FOOL FOOT FORA FORD FORE FORK FORT FOSS FRAE FRAT FRAY FRED FREE FRET FRIT FROE FUCK FUEL FULL FUND FUNK FUNS FURL FURS FURY FUSE FUSS FYCE LACE LACK LACS LACY LAID LAIN LALL LANA LAND LANE LANK LARA LARD LARK LARS LASE LASH LASS LAST LATE LATH LATS LEAD LEAH LEAK LEAL LEAN LEAS LECH LEEK LEES LEET LEIA LEIS LELA LENA LEND LENS LENT LEON LESS LEST LETS LIAN LICE LICH LICK LIED LIEN LIES LILA LILT LILY LINA LINE LINK LINN LINS LINT LINY LION LIRA LIRE LISA LIST LITE LITS LOAD LOAN LOCA LOCH LOCK LOID LOIN LOLA LOLL LONE LOOK LOON LOOS LOOT LORD LORE LORN LORY LOSE LOSS LOST LOTA LOTH LOTS LUCA LUCE LUCK LUCY LUES LUIS LULL LUNA LUNE LUNK LUNT LUNY LURE LURK LUSH LUST LUTE LYCH LYES LYLA LYLE LYRA LYRE LYSE MACE MACH MACK MACS MACY MAES MAIA MAID MAIL MAIN MALE MALL MALT MANA MANE MANS MANY MARA MARE MARK MARL MARS MART MARY MASA MASH MASK MASS MAST MATE MATH MATS MATT MEAD MEAL MEAN MEAT MEED MEEK MEET MELD MELL MELS MELT MEND MERE MERK MERL MESA MESH MESS META METE METH MHOS MIAH MICA MICE MICK MICS MIEN MILA MILD MILE MILK MILL MILS MILT MINA MIND MINE MINK MINT MIRA MIRE MIRK MIRS MIRY MISE MISS MIST MITE MITT MITY MOAN MOAS MOAT MOCK MOCS MOIL MOLA MOLD MOLE MOLL MOLS MOLT MOLY MONA MONK MONS MONY MOOD MOOL MOON MOOS MOOT MORA MORE MORN MORS MORT MOSH MOSK MOSS MOST MOTE MOTH MOTS MOTT MUCH MUCK MULE MULL MUNS MUON MURA MURE MURK MUSA MUSE MUSH MUSK MUSS MUST MUTE MUTS MUTT MYAH MYCS MYLA MYNA MYRA MYTH PACA PACE PACK PACS PACT PACY PAID PAIK PAIL PAIN PALE PALL PALS PALY PANE PANS PANT PARA PARD PARE PARK PARS PART PASE PASH PASS PAST PATE PATH PATS PATY PEAK PEAL PEAN PEAS PEAT PECH PECK PECS PEED PEEK PEEL PEEN PEES PEIN PELE PELT PEND PENS PENT PEON PERE PERK PERT PEST PETS PHAT PHIS PHON PHOT PIAL PIAN PIAS PICA PICE PICK PICS PIED PIES PILE PILL PILY PINA PINE PINK PINS PINT PINY PION PIRN PISH PISS PITA PITH PITS PITY PLAN PLAT PLAY PLEA PLED PLIE PLOD PLOT PLOY POCK POET POIS POLE POLL POLS POLY POND PONE PONS PONY POOD POOH POOL POON POOS PORE PORK PORN PORT POSE POSH POST POSY POTS PRAT PRAY PREE PREY PROA PROD PROS PUCE PUCK PULA PULE PULL PULS PUNA PUNK PUNS PUNT PUNY PURE PURL PURS PUSH PUSS PUTS PUTT PYAS PYES PYIN PYRE SAAD SACK SACS SAID SAIL SAIN SALE SALL SALS SALT SANA SAND SANE SANK SANS SARA SARD SARK SASH SASS SATE SEAL SEAN SEAS SEAT SECS SECT SEED SEEK SEEL SEEN SEES SEIS SELL SELS SEND SENE SENT SERA SERE SERS SETA SETH SETS SETT SHAD SHAE SHAH SHAT SHAY SHEA SHED SHES SHIN SHIT SHOD SHOE SHOT SIAL SICE SICK SICS SILD SILK SILL SILT SINE SINH SINK SINS SIRE SIRS SITE SITH SITS SLAT SLAY SLED SLID SLIT SLOE SLOT SOAK SOCA SOCK SOIL SOLA SOLD SOLE SOLS SONE SONS SOOK SOON SOOT SORA SORD SORE SORN SORT SOTH SOTS SRIS SUCH SUCK SUED SUES SUET SUIT SULK SUNK SUNN SUNS SURA SURD SURE SUSS SWAN SWAT SWAY SWOT SYCE SYED SYNE TACE TACH TACK TACT TAEL TAIL TAIN TALA TALE TALK TALL TANK TANS TAOS TARA TARE TARN TARS TART TASK TASS TATE TATS TEAK TEAL TEAS TEAT TECH TEED TEEL TEEN TEES TELA TELE TELL TELS TEND TENS TENT TERN TESS TEST TETH TETS THAE THAN THAT THEA THEE THEN THEY THIN THIS TICK TICS TIED TIES TILE TILL TILS TILT TINA TINE TINS TINT TINY TIRE TIRL TITS TOAD TOEA TOED TOES TOIL TOIT TOLA TOLD TOLE TOLL TONE TONS TONY TOOK TOOL TOON TOOT TORA TORE TORN TORS TORT TORY TOSH TOSS TOST TOTE TOTS TRAD TRAE TRAY TREE TREK TRES TRET TREY TROD TROT TROY TUCK TUIS TULE TUNA TUNE TUNS TURD TURK TURN TUSH TUSK TUTS TWAE TWAS TWAT TWEE TWIN TWIT TWOS TYCE TYEE TYES TYIN TYNE TYRE WACK WAES WAIL WAIN WAIT WALE WALK WALL WALY WAND WANE WANK WANS WANT WANY WARD WARE WARK WARN WARS WART WARY WASH WAST WATS WATT WEAK WEAL WEAN WEED WEEK WEEL WEEN WEES WEET WELD WELL WELT WEND WENS WENT WERE WERT WEST WETS WHAT WHEE WHEN WHET WHEY WHID WHIN WHIT WHOA WICH WICK WILD WILE WILL WILT WILY WIND WINE WINK WINS WINY WIRE WIRY WISE WISH WISS WIST WITE WITH WITS WOAD WOES WOLD WONK WONS WONT WOOD WOOL WOOS WORD WORE WORK WORN WORT WOST WOTS WREN WRIT WUSS WYCH WYES WYLE WYND WYNN WYNS WYTE\n" + ] + } + ], + "source": [ + "show(improved_lock(random_lock()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We got up to 1240 words, but can we go beyond? I'll improve 50 random locks, taking 6000 steps each rather than just 3000 (this will take around 15 minutes):" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15min 48s, sys: 9.03 s, total: 15min 57s\n", + "Wall time: 19min 40s\n" + ] + } + ], + "source": [ + "%time improved_locks = [improved_lock(random_lock(seed=i), 6000) for i in range(50)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what we got:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({1232: 3, 1235: 5, 1240: 42})" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(map(word_count, improved_locks))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So 42/50 locks got a score of 1240.\n", + "My first reaction to this was that if I discovered 42 different locks with score 1240, then probably there is at least one undiscovered lock with a score above 1240. But a discussion with [Matt Chisholm](https://blog.glyphobet.net/faq) changed my thinking. The key is to realize that some locks that look different are actually the same; they just have the letters in a different order. I define the function `alock` to put each tumbler into alphabetical order (and make the lock be a tuple rather than a list, so that it can be an entry in a `dict` or `set`):" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def alock(lock):\n", + " \"Canonicalize lock by alphabetizing the letters in each tumbler.\"\n", + " return tuple(Tumbler(sorted(tumbler)) for tumbler in lock)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Then we can find the unique locks:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{('BCDFHLMPST', 'AEHILORUWY', 'ACELMNORST', 'ADEKLNPSTY'): 1232,\n", + " ('BCDFLMPSTW', 'AEHILOPRUY', 'ACEILNORST', 'ADEHKLNSTY'): 1240,\n", + " ('BCDFLMPSTW', 'AEHILORUWY', 'ACEILNORST', 'ADEHKLNSTY'): 1240,\n", + " ('BCDGLMPSTW', 'AEHILORUWY', 'AEILMNORST', 'ADEKLNPSTY'): 1235}" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def unique_locks(locks):\n", + " \"Return a dict of {lock: word_count} for the distinct locks.\"\n", + " return {alock(lock): word_count(lock) \n", + " for lock in locks}\n", + "\n", + "unique_locks(improved_locks)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So out of the 50 `improved_locks` there are actually only 4 distinct ones. And only two have a score of 1240:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{('BCDFLMPSTW', 'AEHILOPRUY', 'ACEILNORST', 'ADEHKLNSTY'),\n", + " ('BCDFLMPSTW', 'AEHILORUWY', 'ACEILNORST', 'ADEHKLNSTY')}" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "peaks = {alock(lock) for lock in improved_locks if word_count(lock) == 1240}\n", + "peaks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These two differ in just one letter (a `P` or a `W` in the second tumbler). \n", + "\n", + "This discovery changes my whole thinking about the space of scores for locks. Previously I imagined a spiky \"porcupine-shaped\" landscape, with 42 different peaks hitting a height of 1240. But now I have a different picture of the landscape: a single peak containing the two locks (one with a `P` and one with a `W`), surrounded by rolling hills. To verify this picture, I'll look at all the neighbors of the two peak locks, and see which ones are at least 1240:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{('BCDFLMPSTW', 'AEHILOPRUY', 'ACEILNORST', 'ADEHKLNSTY'): 1240,\n", + " ('BCDFLMPSTW', 'AEHILORUWY', 'ACEILNORST', 'ADEHKLNSTY'): 1240}" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alphabetset = set(alphabet)\n", + "\n", + "def neighborhood(lock): \n", + " \"Yield all locks resulting from a change of one letter in one tumbler.\"\n", + " for i in range(len(lock)):\n", + " for new in alphabetset - set(lock[i]):\n", + " for old in lock[i]:\n", + " lock2 = Lock(lock)\n", + " lock2[i] = lock2[i].replace(old, new)\n", + " yield lock2\n", + " \n", + "unique_locks(lock for peak in peaks for lock in neighborhood(peak) if word_count(lock) >= 1240)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Nothing new. This doesn't prove there is no lock with score over 1240, but it does mean we have looked hard to find one and failed.\n", + "\n", + "# Question 3: Simultaneous Words" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can we make a lock that spells 10 words simultaneously? One possible approach would be to start with any lock and randomly change it (just as we did with `improved_lock`), but measure improvements by the number of words formed. My intuition is that this approach would work, eventually, but that progress would be very slow, because most random changes to a letter would not make a word.\n", + "\n", + "An alternative approach is to think of the lock not as a list of 4 vertical tumblers (each with 10 letters), but rather as a list of 10 horizontal words (each with 4 letters). I'll call this the *word list* representation, and note that a lock and a word list are *[matrix transposes](http://en.wikipedia.org/wiki/Transpose)* of each other—they swap rows for columns. There is an [old trick](https://books.google.com/books?id=eH6jBQAAQBAJ&pg=PA574&lpg=PA574&dq=lisp+transpose+matrix&source=bl&ots=Yixwj8m3k4&sig=KoeuJnFhRnJsiD06_Cx56rUOetQ&hl=en&sa=X&ved=0CB4Q6AEwAGoVChMIyM-WiriLxgIVD6OICh2QcwBK#v=onepage&q=transpose%20matrix&f=false) to compute the transpose of a matrix `M` with the expression `zip(*M)`. But `zip` returns tuples; we want strings, so we can define `transpose` as:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def transpose(strings): return [Word(letters) for letters in zip(*strings)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can see the transpose of the `wordlock` is a list of words:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['SLED',\n", + " 'PENS',\n", + " 'HYMN',\n", + " 'MHLM',\n", + " 'TNRP',\n", + " 'WRTY',\n", + " 'DUAL',\n", + " 'LOOK',\n", + " 'FAST',\n", + " 'BIKE']" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "transpose(['SPHMTWDLFB', \n", + " 'LEYHNRUOAI', \n", + " 'ENMLRTAOSK', \n", + " 'DSNMPYLKTE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first row of the word list has the letters SLED, because those are the letters in the first column of the lock. You can see that the WordLock® is designed to spell out LOOK FAST BIKE, among other words.\n", + "\n", + "Now we're ready to find a good word list with this strategy:\n", + "\n", + "1. Start with some word list (e.g., a random sample of 10 words from `WORDS`).\n", + "2. Pick, at random, one word and change it to a new word.\n", + "3. If the change is an improvement, keep the change; otherwise discard the change.\n", + "4. Repeat.\n", + "\n", + "But what counts as an improvement? We can't improve the number of words, because we start with 10 words, and every change also gives us 10 words. Rather, we will try to improve the number of duplicate letters on any tumbler (of the lock that corresponds to the word list). We improve by reducing the number of duplicate letters, and stop when there are no duplicates.\n", + "\n", + "The following code implements this approach:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def improved_wordlist(wordlist):\n", + " \"Find a wordlist that has no duplicate letters, via random changes to wordlist.\"\n", + " score = duplicates(wordlist)\n", + " while score > 0:\n", + " wordlist2 = changed_wordlist(wordlist)\n", + " score2 = duplicates(wordlist2)\n", + " if score2 < score: \n", + " wordlist, score = wordlist2, score2\n", + " return wordlist\n", + " \n", + "def duplicates(wordlist):\n", + " \"The number of duplicate letters across all the tumblers of the lock that corresponds to this wordlist.\"\n", + " lock = transpose(wordlist) \n", + " def duplicates(tumbler): return len(tumbler) - len(set(tumbler))\n", + " return sum(duplicates(tumbler) for tumbler in lock)\n", + "\n", + "def changed_wordlist(wordlist, words=list(WORDS)):\n", + " \"Make a copy of wordlist and replace one of the words.\"\n", + " copy = list(wordlist)\n", + " i = random.randrange(len(wordlist))\n", + " copy[i] = random.choice(words)\n", + " return copy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The structure of `improved_wordlist` is similar to `improved_lock`, with a few differences:\n", + "1. We are minimizing duplicates, not maximizing word count. \n", + "2. We stop when the score is 0, rather than continuing for a given number of iterations.\n", + "3. We want to make a `random.choice` from `WORDS`. But `random.choice` can't operate on a `set`, so we\n", + "have to introduce `words=list(WORDS)`.\n", + "\n", + "Now we can find some wordlists:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['KNUR',\n", + " 'FLAG',\n", + " 'APES',\n", + " 'EVIL',\n", + " 'COZY',\n", + " 'TICK',\n", + " 'PHON',\n", + " 'LATU',\n", + " 'DUPE',\n", + " 'REFT']" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "improved_wordlist(random.sample(WORDS, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was easy! Can we go to 11?" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['BRAS',\n", + " 'EMIR',\n", + " 'NIPA',\n", + " 'PESO',\n", + " 'ONYX',\n", + " 'WYNN',\n", + " 'CUKE',\n", + " 'MOLY',\n", + " 'FLOC',\n", + " 'THEM',\n", + " 'HARL']" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "improved_wordlist(random.sample(WORDS, 11))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Improving Anything" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now have two similar functions, `improved_lock` and `improved_wordlist`. Could (and should?) we replace them by a single function, say, `improved`, that could improve locks, wordlists, and anything else?\n", + "\n", + "The answer is: *yes* we could, and *maybe* we should.\n", + "\n", + "It is nice to form an abstraction for the idea of *improvement*. (Traditionally, the method we have used for improvement has been called *hill-climbing*, because of the analogy that the score is like the elevation on a topological map, and we are trying to find our way to a peak.)\n", + "\n", + "However, there are many variations on the theme of *improvement*: maximizing or minimizing? Repeat for a given number of iterations, or continue until we meet a goal? I don't want `improved` to have an argument list a mile long, and I felt that five arguments is right on the border of acceptable. The arguments are:\n", + "1. `item`: The object to start with; this is what we will try to improve.\n", + "2. `changed`: a function that generates a new item.\n", + "3. `scorer`: a function that evaluates the quality of an item.\n", + "4. `extremum`: should be `max` if we are maximizing scores, or `min` if we are minimizing scores.\n", + "5. `stop`: a predicate with args `(i, score, item)`, where `i` is the iteration number, and `score` is `scorer(item)`. Return `True` to stop.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def improved(item, changed, scorer, extremum, stop):\n", + " \"\"\"Apply the function `changed` to `item` and evaluate with the function `scorer`;\n", + " When `stop(i, score)` is true, return `item`.\"\"\"\n", + " score = scorer(item)\n", + " for i in itertools.count(0):\n", + " if stop(i, score):\n", + " return item\n", + " item2 = changed(item)\n", + " score2 = scorer(item2)\n", + " if score2 == extremum(score, score2):\n", + " item, score = item2, score2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can re-implement `improved_lock` and `improved_wordlist` using `improved`:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def improved_lock(lock, steps=3000):\n", + " \"Randomly change letters in lock, keeping changes that improve the score.\"\n", + " return improved(lock, changed_lock, word_count, max,\n", + " lambda i, _: i == steps)\n", + "\n", + "def improved_wordlist(wordlist):\n", + " \"Find a wordlist that has no duplicate letters, via random changes to wordlist.\"\n", + " return improved(wordlist, changed_wordlist, duplicates, min,\n", + " lambda _, score: score == 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lock: TMSLBPFWCD AEHYLORIWU CNATELISRO LDSYANKETH\n", + "Count: 1240\n", + "Words: BAAL BAAS BACH BACK BAIL BAIT BALD BALE BALK BALL BALS BAND BANE BANK BANS BARD BARE BARK BARN BARS BASE BASH BASK BASS BAST BATE BATH BATS BATT BEAD BEAK BEAN BEAT BECK BEEN BEES BEET BELL BELS BELT BEND BENE BENS BENT BERK BEST BETA BETH BETS BIAS BICE BILE BILK BILL BIND BINE BINS BINT BIOS BIRD BIRK BIRL BISE BISK BITE BITS BITT BLAE BLAH BLAT BLED BLET BLIN BLOT BOAS BOAT BOCK BOIL BOLA BOLD BOLE BOLL BOLT BOND BONE BONK BONY BOOK BOON BOOS BOOT BORA BORE BORK BORN BORT BOSH BOSK BOSS BOTA BOTH BOTS BOTT BRAD BRAE BRAN BRAS BRAT BRAY BREA BRED BREE BREN BRIA BRIE BRIN BRIS BRIT BROS BUCK BULK BULL BUNA BUND BUNK BUNN BUNS BUNT BUOY BURA BURD BURL BURN BURS BURY BUSH BUSK BUSS BUST BUSY BUTE BUTS BUTT BYES BYRE BYRL BYTE CACA CAEL CAID CAIN CALE CALK CALL CANE CANS CANT CARA CARD CARE CARK CARL CARN CARS CART CASA CASE CASH CASK CAST CATE CATS CECA CEES CEIL CELL CELS CELT CENT CERE CESS CETE CHAD CHAT CHAY CHIA CHID CHIN CHIS CHIT CHON CIAN CINE CION CIRE CIST CITE CITY CLAD CLAN CLAY CLOD CLON CLOT CLOY COAL COAT COCA COCK COED COEN COIL COIN COLA COLD COLE COLS COLT COLY CONE CONK CONN CONS CONY COOK COOL COON COOS COOT CORA CORD CORE CORK CORN CORS CORY COSH COSS COST COSY COTE COTS CRED CRIS CRIT CUED CUES CULL CULT CUNT CURD CURE CURL CURN CURS CURT CUSK CUSS CUTE CUTS CYAN CYST DACE DAIS DALE DALS DANA DANE DANK DANS DARE DARK DARN DART DASH DATA DATE DEAD DEAL DEAN DECK DEED DEES DEET DEIL DELE DELL DELS DELT DENE DENS DENT DENY DEON DERE DESK DHAK DHAL DIAL DICE DICK DIED DIEL DIES DIET DILL DINA DINE DINK DINS DINT DIOL DION DIRE DIRK DIRL DIRT DISH DISK DISS DITA DITE DITS DOAT DOCK DOCS DOES DOIT DOLE DOLL DOLS DOLT DONA DONE DONS DORE DORK DORS DORY DOSE DOSS DOST DOTE DOTH DOTS DOTY DRAT DRAY DREE DREK DUAD DUAL DUCE DUCK DUCT DUEL DUES DUET DUIT DULL DULY DUNE DUNK DUNS DUNT DUOS DURA DURE DURN DUSK DUST DUTY DYAD DYED DYES DYNE FACE FACT FAIL FAIN FALL FANE FANS FARD FARE FARL FART FASH FAST FATE FATS FEAL FEAT FECK FEED FEEL FEES FEET FELL FELT FEND FENS FEOD FERE FERN FESS FEST FETA FETE FETS FIAT FICE FILA FILE FILL FILS FIND FINE FINK FINN FINS FIRE FIRN FIRS FISH FIST FITS FLAK FLAN FLAT FLAY FLEA FLED FLEE FLEY FLIT FLOE FOAL FOES FOIL FOIN FOLD FOLK FOND FONS FONT FOOD FOOL FOOT FORA FORD FORE FORK FORT FOSS FRAE FRAT FRAY FRED FREE FRET FRIT FROE FUCK FUEL FULL FUND FUNK FUNS FURL FURS FURY FUSE FUSS FYCE LACE LACK LACS LACY LAID LAIN LALL LANA LAND LANE LANK LARA LARD LARK LARS LASE LASH LASS LAST LATE LATH LATS LEAD LEAH LEAK LEAL LEAN LEAS LECH LEEK LEES LEET LEIA LEIS LELA LENA LEND LENS LENT LEON LESS LEST LETS LIAN LICE LICH LICK LIED LIEN LIES LILA LILT LILY LINA LINE LINK LINN LINS LINT LINY LION LIRA LIRE LISA LIST LITE LITS LOAD LOAN LOCA LOCH LOCK LOID LOIN LOLA LOLL LONE LOOK LOON LOOS LOOT LORD LORE LORN LORY LOSE LOSS LOST LOTA LOTH LOTS LUCA LUCE LUCK LUCY LUES LUIS LULL LUNA LUNE LUNK LUNT LUNY LURE LURK LUSH LUST LUTE LYCH LYES LYLA LYLE LYRA LYRE LYSE MACE MACH MACK MACS MACY MAES MAIA MAID MAIL MAIN MALE MALL MALT MANA MANE MANS MANY MARA MARE MARK MARL MARS MART MARY MASA MASH MASK MASS MAST MATE MATH MATS MATT MEAD MEAL MEAN MEAT MEED MEEK MEET MELD MELL MELS MELT MEND MERE MERK MERL MESA MESH MESS META METE METH MHOS MIAH MICA MICE MICK MICS MIEN MILA MILD MILE MILK MILL MILS MILT MINA MIND MINE MINK MINT MIRA MIRE MIRK MIRS MIRY MISE MISS MIST MITE MITT MITY MOAN MOAS MOAT MOCK MOCS MOIL MOLA MOLD MOLE MOLL MOLS MOLT MOLY MONA MONK MONS MONY MOOD MOOL MOON MOOS MOOT MORA MORE MORN MORS MORT MOSH MOSK MOSS MOST MOTE MOTH MOTS MOTT MUCH MUCK MULE MULL MUNS MUON MURA MURE MURK MUSA MUSE MUSH MUSK MUSS MUST MUTE MUTS MUTT MYAH MYCS MYLA MYNA MYRA MYTH PACA PACE PACK PACS PACT PACY PAID PAIK PAIL PAIN PALE PALL PALS PALY PANE PANS PANT PARA PARD PARE PARK PARS PART PASE PASH PASS PAST PATE PATH PATS PATY PEAK PEAL PEAN PEAS PEAT PECH PECK PECS PEED PEEK PEEL PEEN PEES PEIN PELE PELT PEND PENS PENT PEON PERE PERK PERT PEST PETS PHAT PHIS PHON PHOT PIAL PIAN PIAS PICA PICE PICK PICS PIED PIES PILE PILL PILY PINA PINE PINK PINS PINT PINY PION PIRN PISH PISS PITA PITH PITS PITY PLAN PLAT PLAY PLEA PLED PLIE PLOD PLOT PLOY POCK POET POIS POLE POLL POLS POLY POND PONE PONS PONY POOD POOH POOL POON POOS PORE PORK PORN PORT POSE POSH POST POSY POTS PRAT PRAY PREE PREY PROA PROD PROS PUCE PUCK PULA PULE PULL PULS PUNA PUNK PUNS PUNT PUNY PURE PURL PURS PUSH PUSS PUTS PUTT PYAS PYES PYIN PYRE SAAD SACK SACS SAID SAIL SAIN SALE SALL SALS SALT SANA SAND SANE SANK SANS SARA SARD SARK SASH SASS SATE SEAL SEAN SEAS SEAT SECS SECT SEED SEEK SEEL SEEN SEES SEIS SELL SELS SEND SENE SENT SERA SERE SERS SETA SETH SETS SETT SHAD SHAE SHAH SHAT SHAY SHEA SHED SHES SHIN SHIT SHOD SHOE SHOT SIAL SICE SICK SICS SILD SILK SILL SILT SINE SINH SINK SINS SIRE SIRS SITE SITH SITS SLAT SLAY SLED SLID SLIT SLOE SLOT SOAK SOCA SOCK SOIL SOLA SOLD SOLE SOLS SONE SONS SOOK SOON SOOT SORA SORD SORE SORN SORT SOTH SOTS SRIS SUCH SUCK SUED SUES SUET SUIT SULK SUNK SUNN SUNS SURA SURD SURE SUSS SWAN SWAT SWAY SWOT SYCE SYED SYNE TACE TACH TACK TACT TAEL TAIL TAIN TALA TALE TALK TALL TANK TANS TAOS TARA TARE TARN TARS TART TASK TASS TATE TATS TEAK TEAL TEAS TEAT TECH TEED TEEL TEEN TEES TELA TELE TELL TELS TEND TENS TENT TERN TESS TEST TETH TETS THAE THAN THAT THEA THEE THEN THEY THIN THIS TICK TICS TIED TIES TILE TILL TILS TILT TINA TINE TINS TINT TINY TIRE TIRL TITS TOAD TOEA TOED TOES TOIL TOIT TOLA TOLD TOLE TOLL TONE TONS TONY TOOK TOOL TOON TOOT TORA TORE TORN TORS TORT TORY TOSH TOSS TOST TOTE TOTS TRAD TRAE TRAY TREE TREK TRES TRET TREY TROD TROT TROY TUCK TUIS TULE TUNA TUNE TUNS TURD TURK TURN TUSH TUSK TUTS TWAE TWAS TWAT TWEE TWIN TWIT TWOS TYCE TYEE TYES TYIN TYNE TYRE WACK WAES WAIL WAIN WAIT WALE WALK WALL WALY WAND WANE WANK WANS WANT WANY WARD WARE WARK WARN WARS WART WARY WASH WAST WATS WATT WEAK WEAL WEAN WEED WEEK WEEL WEEN WEES WEET WELD WELL WELT WEND WENS WENT WERE WERT WEST WETS WHAT WHEE WHEN WHET WHEY WHID WHIN WHIT WHOA WICH WICK WILD WILE WILL WILT WILY WIND WINE WINK WINS WINY WIRE WIRY WISE WISH WISS WIST WITE WITH WITS WOAD WOES WOLD WONK WONS WONT WOOD WOOL WOOS WORD WORE WORK WORN WORT WOST WOTS WREN WRIT WUSS WYCH WYES WYLE WYND WYNN WYNS WYTE\n" + ] + } + ], + "source": [ + "show(improved_lock(random_lock()))" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['UMAR',\n", + " 'DISH',\n", + " 'TEMP',\n", + " 'JUDE',\n", + " 'WORM',\n", + " 'STOW',\n", + " 'BHUT',\n", + " 'YAGI',\n", + " 'ACTA',\n", + " 'GYPS']" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "improved_wordlist(random.sample(WORDS, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Question 4: Coincidence?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is still one unanswered question: did the designers of WordLock® deliberately put \"FRED BUNS\" in, or was it a coincidence? Hacker News reader [emhart](https://news.ycombinator.com/user?id=emhart) (aka the competitive lockpicker Schyler Towne) astutely commented that he had found the [patent](https://www.google.com/patents/US6621405) assigned to WordLock; it describes an algorithm similar to my `greedy_lock`.\n", + "After seeing that, I'm inclined to believe that \"FRED BUNS\" is the coincidental result of running the algorithm. On\n", + "the other hand, there is a [followup patent](https://www.google.com/patents/US20080053167) that discusses a refinement\n", + "\"wherein the letters on the wheels are configured to spell a first word displayed on a first row of letters and a second word displayed on a second row of letters.\" So the possibility of a two-word phrase was somthing that Wordlock LLc. was aware of.\n", + "\n", + "We see below that the procedure described in the [patent](https://www.google.com/patents/US6621405) is not quite as good as `greedy_lock`, because the patent states that at each tumbler position \"*the entire word list is scanned*\" to produce the letter frequencies, whereas `greedy_lock` scans only the words that are consistent with the previous tumblers. Because of that difference, `greedy_lock` produces more words, 1177 to 1161:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1177, 1161)" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def greedy_lock_patented(t=4, c=10, words=WORDS):\n", + " \"Make a lock with t tumblers, each consisting of the c letters that cover the most words at that position.\"\n", + " lock = Lock()\n", + " for i in range(t):\n", + " # Make a tumbler of c letters, such that the tumbler covers the most words.\n", + " # Then update words to only include the ones that can be made with this tumbler\n", + " counter = Counter(word[i] for word in words)\n", + " tumbler = Tumbler(L for (L, _) in counter.most_common(c))\n", + " # words = [w for w in words if w[i] in tumbler] # <<<< The patent does not update the word list\n", + " lock.append(tumbler)\n", + " return lock\n", + "\n", + "word_count(greedy_lock()), word_count(greedy_lock_patented())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tests" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is a \n", + "good idea to have some tests, in case you want to change some code and see if you have introduced an error. Also, tests serve as examples of usage of functions. The following tests have poor coverage, because it is hard to test non-deterministic functions, and I didn't attempt that here." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " assert 'WORD' in WORDS\n", + " assert 'FRED' in WORDS\n", + " assert 'BUNS' in WORDS\n", + " assert 'XYZZ' not in WORDS\n", + " assert 'word' not in WORDS\n", + " assert 'FIVE' in WORDS\n", + " assert 'FIVER' not in WORDS\n", + " assert len(WORDS) == 4360\n", + " \n", + " assert fredbuns == ['FB', 'RU', 'EN', 'DS']\n", + " assert combinations(fredbuns) == ['FRED','FRES','FRND','FRNS','FUED','FUES','FUND','FUNS',\n", + " 'BRED','BRES','BRND','BRNS','BUED','BUES','BUND','BUNS']\n", + " assert words_from(fredbuns) == ['FRED', 'FUND', 'FUNS', 'BRED', 'BUND', 'BUNS']\n", + " assert \"FRED\" in words_from(wordlock) and \"BUNS\" in words_from(wordlock)\n", + "\n", + " assert wordlock == ['SPHMTWDLFB', 'LEYHNRUOAI', 'ENMLRTAOSK', 'DSNMPYLKTE']\n", + " assert len(combinations(wordlock)) == 10000\n", + " assert word_count(wordlock) == 1118\n", + " \n", + " assert transpose(['HIE', 'BYE']) == ['HB', 'IY', 'EE']\n", + " assert transpose(transpose(wordlock)) == wordlock\n", + " \n", + " return 'pass'\n", + " \n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# One More Question" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I wonder if [@BIKESNOBNYC](https://twitter.com/bikesnobnyc) would appreciate this notebook? On the one hand, he is the kind of guy who, in discussing the fact that bicycling is the seventh most popular recreational activity, [wrote]() \"*the number seven is itself a highly significant number. It is the lowest number that cannot be represented as the sum of the square of three integers*,\" so it seems he has some interest in mathematical oddities. On the other hand, he followed that up by writing \"*I have no idea what that means, but it's true*,\" so maybe not." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{7, 15, 23, 28, 31, 39, 47, 55, 60, 63, 71, 79, 87, 92, 95}" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Numbers up to 100 that are not the sum of 3 squares\n", + "nums = range(11)\n", + "sums = {A**2 + B**2 + C**2 for A in nums for B in nums for C in nums}\n", + "set(range(max(nums)**2)) - sums" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Gesture Typing.ipynb b/pytudes/ipynb/Gesture Typing.ipynb new file mode 100644 index 0000000..1ec2c2d --- /dev/null +++ b/pytudes/ipynb/Gesture Typing.ipynb @@ -0,0 +1,2111 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Gesture Typing \n", + "===\n", + "\n", + "Typing quickly and accurately on a smartphone screen is hard! One invention to make it easier is **gesture typing**, in which your finger can trace a **path** consisting of letter-to-letter **segments**. When you lift your finger the path (and the word) is complete. Below we see the path for the word \"hello.\" Note that the path is imprecise; it didn't quite hit the \"L\", but the word was recognized anyways, because \"Hello\" is a known word, whereas \"Hekko\", \"Hwerklo\", etc., are not.\n", + "\n", + "\n", + "\n", + "Questions About Gesture Typing\n", + "===\n", + "\n", + "My colleague Nicolas Schank examined (and answered) the question of what word has the longest path length. I mentioned this to [Shumin Zhai](http://www.shuminzhai.com/), the pioneer of gesture typing, and between the three of us we expanded the list of questions:\n", + "\n", + " 1. What words have the longest path length?\n", + " 2. What words have the highest ratio of path length to word length? \n", + " 3. What is the average segment length, over a typical typing work load?\n", + " 3. Is there a better keyboard layout to minimize the average segment length over a work load?\n", + " 4. How often are two words confused because they have similar paths?\n", + " 5. Is there a better keyboard layout to minimize confusion? \n", + " 6. Is there a better keyboard layout to maximize overall user satisfaction?\n", + "\n", + "Let's look at each of these questions, but first, let's get a rough idea for of the concepts we will need to model.\n", + "\n", + "Vocabulary\n", + "===\n", + "\n", + "We will need to talk about the following concepts:\n", + "\n", + "* **Keyboard**: We'll need to know the **location** of each letter on the keyboard (we consider only letters, not the other symbols).\n", + "* **Location**: A location is a **point** in two-dimensional space (we assume keyboards are flat).\n", + "* **Path**: A path connects the letters in a word. In the picture above the path is curved, but a shortest path is formed by connecting straight line **segments**, so maybe we need only deal with straight lines.\n", + "* **Segment**: A line segment is a straight line between two points.\n", + "* **Length**: Paths and Segments have lengths; the distance traveled along them.\n", + "* **Words**: We will need a list of allowable words (in order to find the one with the longest path).\n", + "* **Work Load**: If we want to find the average path length over a typical work load, we'll have to represent a work load: not\n", + "just a list of words, but a measure of how frequent each word (or each segment) is.\n", + "* **Confusion**: We need some measure of *whether* (or perhaps *to what degree*) the paths for two words can be confused with each other.\n", + "* **Satisfaction**: This is a very difficult concept to define. A user will be more satisfied with a keyboard if it allows for fast, accurate typing, and if it gives the user a feeling of mastery, not frustration.\n", + "\n", + "**Note**: Before we get started writing any real code, I've taken all the `import`s I will need throughout this notebook and gathered them together here:\n", + "\n", + "\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import Counter\n", + "from statistics import mean\n", + "import matplotlib.pyplot as plt\n", + "import urllib\n", + "import itertools\n", + "import random \n", + "import re" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Representing Keyboards and Points\n", + "===\n", + "\n", + "The representation for a keyboard needs to describe the location of each of the letters. Using the principle of *\"Do the simplest thing that could possibly work,\"* I represent a keyboard as a `dict` of `{letter: point}` pairs, where there will be 26 letters, A-Z,\n", + "and each point will mark the x-y coordinates of the center of the corresponding key. In a standard keyboard the letters are not all on a strict rectangular grid; the **A** key is half way between the **Q** and **W** in the horizontal direction. I would like to have a programmer-friendly way of defining keyboard layouts. For example, a programmer should be able to write:\n", + "\n", + " Keyboard(('Q W E R T Y U I O P',\n", + " ' A S D F G H J K L ',\n", + " ' Z X C V B N M '))\n", + " \n", + "and this would be equivalent to the `dict`:\n", + "\n", + " {'Q': Point(0, 0), 'W': Point(1, 0), ...\n", + " 'A': Point(0.5, 1), 'S': Point(1.5, 1), ...\n", + " 'Z': Point(1.5, 2), 'X': Point(2.5, 2), ...}\n", + " \n", + "Note that one key width is two characters in the input to `Keyboard`. Here is the implementation:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Keyboard(rows):\n", + " \"A keyboard is a {letter: location} map, e.g. {'Q':Point(0, 0), 'A': Point(0.5, 1)}.\"\n", + " return {ch: Point(x/2, y) \n", + " for (y, row) in enumerate(rows)\n", + " for (x, ch) in enumerate(row)\n", + " if ch != ' '}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about `Point`? At first glance, Python does not appear to have a two-dimensional point as a builtin data type, but\n", + "on second thought, it does: `complex`. A complex number is a point in the two-dimensional complex plane;\n", + "we can use that to model the two-dimensional (x, y) plane. Because complex numbers are built in, manipulating them will be efficient. A bonus is that the distance between points `A` and `B` is simply `abs(A-B)`; easier than the usual formula involving squares and a square root. Thus, the simplest possible thing I could do to represent points is\n", + "\n", + "
\n",
+    "Point = complex\n",
+    "
\n", + "\n", + "That would work fine. However, I would like to refer to the x coordinate of point `p` as `p.x` rather than `p.real`, and I would like points to display nicely, so I will do the second-simplest thing: make `Point` be a subclass of `complex` with `x` and `y` properties and a `__repr__` method:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Point(complex):\n", + " \"A point in the (x, y) plane.\"\n", + " def __repr__(self): return 'Point({}, {})'.format(self.x, self.y)\n", + " x = property(lambda p: p.real)\n", + " y = property(lambda p: p.imag)\n", + " \n", + "def distance(A, B):\n", + " \"The distance between two points.\"\n", + " return abs(A - B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternative representations for points include an `(x, y)` tuple or namedtuple, or a NumPy two-element array, or a class. \n", + "\n", + "Alternatives for `Keyboard` include a subclass of `dict`, or a class that contains a `dict`. \n", + "\n", + "\n", + "Now we can check that `Keyboard` works:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'A': Point(0.5, 1.0),\n", + " 'B': Point(5.5, 2.0),\n", + " 'C': Point(3.5, 2.0),\n", + " 'D': Point(2.5, 1.0),\n", + " 'E': Point(2.0, 0.0),\n", + " 'F': Point(3.5, 1.0),\n", + " 'G': Point(4.5, 1.0),\n", + " 'H': Point(5.5, 1.0),\n", + " 'I': Point(7.0, 0.0),\n", + " 'J': Point(6.5, 1.0),\n", + " 'K': Point(7.5, 1.0),\n", + " 'L': Point(8.5, 1.0),\n", + " 'M': Point(7.5, 2.0),\n", + " 'N': Point(6.5, 2.0),\n", + " 'O': Point(8.0, 0.0),\n", + " 'P': Point(9.0, 0.0),\n", + " 'Q': Point(0.0, 0.0),\n", + " 'R': Point(3.0, 0.0),\n", + " 'S': Point(1.5, 1.0),\n", + " 'T': Point(4.0, 0.0),\n", + " 'U': Point(6.0, 0.0),\n", + " 'V': Point(4.5, 2.0),\n", + " 'W': Point(1.0, 0.0),\n", + " 'X': Point(2.5, 2.0),\n", + " 'Y': Point(5.0, 0.0),\n", + " 'Z': Point(1.5, 2.0)}" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qwerty = Keyboard(('Q W E R T Y U I O P',\n", + " ' A S D F G H J K L ',\n", + " ' Z X C V B N M '))\n", + "qwerty" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Computing Path Length\n", + "===\n", + "\n", + "Now let's figure out the path length for a word: the sum of the lengths of segments between letters. So the path length for `'WORD'` would be the sum of the segment lengths for `'WO'` plus `'OR'` plus `'RD'`:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.118033988749895" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "W, O, R, D = qwerty['W'], qwerty['O'], qwerty['R'], qwerty['D'], \n", + "distance(W, O) + distance(O, R) + distance(R, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make a function to compute this:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def path_length(word, kbd=qwerty):\n", + " \"The total path length for a word on this keyboard: the sum of the segment lengths.\"\n", + " return sum(distance(kbd[word[i]], kbd[word[i+1]])\n", + " for i in range(len(word)-1))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "13.118033988749895" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path_length('WORD')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check with a simpler example that we know the answer to:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "4.0" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path_length('TO')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That makes it clearer—the **O** is four keys to the right of the **T**, on the same row, so the distance between them is 4.\n", + "\n", + "Here's another one that you can verify on your own:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "path_length('TYPEWRITER') == 1 + 4 + 7 + 1 + 2 + 4 + 3 + 2 + 1 == 25" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 1: Longest Path Length?\n", + "===\n", + "\n", + "To know what the longest word is, we'll have to know what the allowable words are. The so-called TWL06 word list gives all the words that are legal in the game of Scrabble; that seems like a reasonable list (although it omits proper nouns). Here's how to load a copy:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "! [ -e TWL06.txt ] || curl -O http://norvig.com/ngrams/TWL06.txt\n", + " \n", + "WORDS = set(open('TWL06.txt').read().split())" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "178691" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(WORDS)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a lot of words; which one has the longest path?" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'PALEOMAGNETISMS'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(WORDS, key=path_length)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the ten longest paths? Including the lengths? We'll use a helper function, `print_top`, which prints the top *n* items in a seqence according to some key function:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "72.2 PALEOMAGNETISMS\n", + "70.0 ANTIQUARIANISMS\n", + "69.9 ELECTROANALYSIS\n", + "69.9 ANTIAPHRODISIAC\n", + "69.3 PARLIAMENTARIAN\n", + "68.9 BLEPHAROSPASMS\n", + "68.6 BIDIALECTALISMS\n", + "67.6 PALEOGEOGRAPHIC\n", + "67.6 SPERMATOZOANS\n", + "67.1 APOCALYPTICISMS\n" + ] + } + ], + "source": [ + "def print_top(n, sequence, key=None, formatter='{:.1f} {}'.format):\n", + " \"Find the top n elements of sequence as ranked by key function, and print them.\"\n", + " for x in sorted(sequence, key=key, reverse=True)[:n]:\n", + " print(formatter(key(x), x))\n", + " \n", + "print_top(10, WORDS, path_length)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 2: Highest Path Length to Word Length Ratio?\n", + "===\n", + "\n", + "Very long words tend to have long path lengths. But what words have the highest *ratio*\n", + "of path length to word length? (I decided to measure word length by number of letters; an alternative is number of segments.) " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def path_length_ratio(word, kbd=qwerty): return path_length(word, kbd) / len(word)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "6.9 PALAPA\n", + "6.7 PAPAL\n", + "6.4 PAPA\n", + "6.4 JALAPS\n", + "6.2 SLAPS\n", + "6.2 KAMALA\n", + "6.2 LAPELS\n", + "6.2 PAPS\n", + "6.2 HALALA\n", + "6.1 SPALE\n" + ] + } + ], + "source": [ + "print_top(10, WORDS, path_length_ratio)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 3: Average Segment Length on Work Load?\n", + "===\n", + "\n", + "What is the average segment length for a typical typing work load? To answer that, we need to know what a typical work load is. We will read a file of \"typical\" text, and count how many times each segment is used. A `Workload` is a `dict` of the form `{segment: proportion, ...},` e.g. `{'AB': 0.02}`, where each key is a two-letter string (or *bigram*) representing a segment, and each value is the proportion of time that segment appears in the workload. Since the distance from `A` to `B` on a keyboard is the same as the distance from `B` to `A`, we can combine them together into one count;\n", + "I'll arbitrarily choose count them both under the alphabetically first one. I make a `Counter` of all two-letter segments, and `normalize` it so that the counts sum to 1 (and are thus probabilities)." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Workload(text):\n", + " \"\"\"Create a Workload--a dict of the form {'AB': 1000, ...} \n", + " saying how often each letter pair occurs in text.\"\"\"\n", + " segments = (min(AB, AB[::-1]) for AB in bigrams(text))\n", + " return normalize(Counter(segments))\n", + "\n", + "def bigrams(text): return re.findall(r'(?=([A-Z][A-Z]))', text)\n", + "\n", + "def normalize(dictionary):\n", + " \"Normalize a {key: val} dict so that the sum of the vals is 1.0.\"\n", + " total = sum(dictionary.values())\n", + " for k in dictionary:\n", + " dictionary[k] /= total\n", + " return dictionary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Note:* Some `re` trickiness here: `([A-Z][A-Z])` means a group of two consecutive letters. But if I only looked for that, then in the text `'FOUR'` I would find `['FO', 'UR']`. So I use the `?=` operator, which says to check for a match, but don't consume the matched characters. So I can find `['FO', 'OU', 'UR']`, which is what I want.\n", + "\n", + "Let's see what a workload looks like for a tiny text:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({'AL': 0.05,\n", + " 'AO': 0.05,\n", + " 'DO': 0.05,\n", + " 'GO': 0.1,\n", + " 'HO': 0.05,\n", + " 'HS': 0.05,\n", + " 'IS': 0.05,\n", + " 'OO': 0.55,\n", + " 'OT': 0.05})" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Workload('SHOT IS GOOD -- GOOOOOOOOOOOAL!')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I happened to have a file of about a megabyte of random text, `smaller.txt`; that should work fine as a typical work load:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "! [ -e smaller.txt ] || curl -O http://norvig.com/ngrams/smaller.txt\n", + " \n", + "WORKLOAD = Workload(open('smaller.txt').read().upper())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's peek at the most common segments:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[('HT', 0.04144819308354474),\n", + " ('ER', 0.04050225926898767),\n", + " ('EH', 0.03576926529702987),\n", + " ('IN', 0.02699818128015268),\n", + " ('AN', 0.02320447132440709),\n", + " ('NO', 0.022344984888333263),\n", + " ('EN', 0.021994208025641622),\n", + " ('IT', 0.021467211506811055),\n", + " ('ES', 0.020667573255841017),\n", + " ('DE', 0.020619362217840744)]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "WORKLOAD.most_common(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most popular segments, at about 4% each are `HT/TH` and `ER/RE`. Now we can compute the workload average:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def workload_average(kbd, workload=WORKLOAD):\n", + " \"The average segment length over a workload of segments.\"\n", + " return sum(distance(kbd[A], kbd[B]) * workload[A+B]\n", + " for (A, B) in workload)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.2333097802127653" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "workload_average(qwerty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, on average, your finger has to travel a little over 3 keys from one letter to the next over a typical workload." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aside: Visualizing a Keyboard\n", + "---\n", + "\n", + "We'll need a way of visualizing what a keyboard looks like. I could just `print` letters, but I think it is more compelling to use IPython's `matplotlib` module. In the function `show_kbd` we'll draw a square around the center point of each key, and annotate the square with the key letter. " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def show_kbd(kbd, name='keyboard', K=20):\n", + " \"Plot the keyboard with square keys, K units on a side.\"\n", + " H = K / 2 # (K is Key width/height; H is half K)\n", + " for L in kbd:\n", + " x, y = K * kbd[L].x, -K * kbd[L].y\n", + " plot_square(x, y, H, label=L)\n", + " plt.axis('equal'); plt.axis('off')\n", + " plt.title(title(kbd, name));\n", + " plt.show()\n", + "\n", + "def plot_square(x, y, H, label='', style='k-'):\n", + " \"Plot a square with center (x, y), half-width H, and optional label.\"\n", + " plt.plot([x-H, x+H, x+H, x-H, x-H], \n", + " [y-H, y-H, y+H, y+H, y-H], style) \n", + " plt.annotate(label, (x-H/4, y-H/4)) # H/4 seems to place label well.\n", + " \n", + "def title(kbd, name): return '{}: path length = {:.1f}'.format(name, workload_average(kbd))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty, 'qwerty')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 4: Keyboard with Minimal Workload Average?\n", + "===\n", + "\n", + "Now for a much harder question: can we find a different keyboard layout that has a smaller average segment length over the workload? First, let's note that there are two ways to modify a keyboard: \n", + "\n", + "* Keep the keys in the same locations but swap letters. (This is an operation you can do on a physical keyboard just by prying off the key caps and swapping them.) \n", + "* Change the locations of keys. (On a physical keyboard you'd need a saw and glue to do this, but it is easier on a virtual keyboard.) \n", + "\n", + "Let's start by limiting ourselves to just swapping letters. \n", + "\n", + "This is an **optimization** problem. There are many permutations of letters; too many to try them all. To be precise, there are 26! (26 factorial) permutations, which is about 1026 (fun fact: 25 and 26 are the only integers for which n! ≈ 10n). If we can't try them all, we need some way to sample the configurations, trying to make progress towards a better one. Again, we'll try the simplest thing that could possibly work: \n", + "\n", + " 1. Pick two keys at random.\n", + " 2. Swap them.\n", + " 3. If that gives a better (lower) workload total, keep them that way.\n", + " 4. If not, swap back.\n", + " 5. Repeat this for a given number of times, say 1000." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def improved(kbd, swaps=1000, scorer=workload_average):\n", + " \"Minimize scorer(kbd) by swapping keys and keeping improvements.\"\n", + " kbd = kbd.copy()\n", + " score = scorer(kbd)\n", + " letters = list(kbd)\n", + " for _ in range(swaps):\n", + " A, B = random.sample(letters, 2) # Step 1: pick two keys\n", + " swap(kbd, A, B) # Step 2: swap them\n", + " score2 = scorer(kbd)\n", + " if score2 < score: # Step 3: If better, keep them\n", + " score = score2 # (and record the new best total)\n", + " else:\n", + " swap(kbd, B, A) # Step 4: swap back if not better\n", + " return kbd\n", + "\n", + "def swap(kbd, A, B): kbd[A], kbd[B] = kbd[B], kbd[A]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note 1:** This strategy is called **hillclimbing**, drawing on the metaphor of getting to a high peak by trying to take a step, and continuing if the step is uphill, and returning if it is not. This technique often finds a local maximum—a solution that is better than all its neighbors, but not as good as another solution that is many steps away.\n", + "\n", + "**Note 2:** I make `scorer` be a parameter, in case we later decide we want to minimize something else other than `workload_average`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see how well we can do:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(improved(qwerty, 3000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a pretty good improvement! We decreased the workload average by about a third. (If you are reading this in an active IPython notebook, you can re-run the cell above and see a different result each time.) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualizing `improved`\n", + "---\n", + "\n", + "Let's get a better feeling for what `improved` does. We will keep track of the workload average after each swap, and plot that as a curve. We will repeat that 10 times (because each run has random variation).\n", + "\n", + "I'll add another parameter, `scores`, to `improved`, If it is not `None`, then it should be a list into which we can accumulate all the scores (after each time step). Then I'll add a new function, `plot_improvements`, that plots the scores that `improved` accumulates." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "def improved(kbd, swaps=1000, scorer=workload_average, scores=[]):\n", + " \"Minimize scorer(kbd) by swapping keys and keeping improvements.\"\n", + " kbd = kbd.copy()\n", + " score = scorer(kbd)\n", + " letters = list(kbd)\n", + " for _ in range(swaps):\n", + " A, B = random.sample(letters, 2) # Step 1: pick two keys\n", + " swap(kbd, A, B) # Step 2: swap them\n", + " score2 = scorer(kbd)\n", + " if score2 < score: # Step 3: If better, keep them\n", + " score = score2 # (and record the new best total)\n", + " else:\n", + " swap(kbd, B, A) # Step 4: swap back if not better\n", + " scores.append(score) # <<< NEW\n", + " return kbd" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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G730PXnutUV2OENUozx12GAcvVQY9/CxHTP2QjTWLmPNlAs+L0Ts7m/k1NSTU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\n9mN84YX+KbTGFwJcdBF85zt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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_improvements(kbd, swaps, scorer=workload_average, repeats=10):\n", + " plt.ylabel('Workload average segment length') \n", + " plt.xlabel('Number of swaps'); \n", + " for _ in range(repeats):\n", + " scores = []\n", + " improved(kbd.copy(), swaps, scorer, scores)\n", + " plt.plot(scores)\n", + " plt.show()\n", + " \n", + "plot_improvements(qwerty, 2500)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This plot is interesting. I note the following:\n", + "\n", + "* Each curve follows a slightly different path (because the swaps are random).\n", + "* The curves are grouped very tightly together; the variance is small. Almost everywhere, the difference between the best and the worst is about 0.2 or less. By the end, almost all the curves are between 1.9 and 2.0.\n", + "* We make rapid progress, decreasing from 3.2 to around 2.2 in about 200 swaps, and to around 2.0 in about 500 swaps.\n", + "* After 1000 swaps, progress is slow, and after 2000, even slower." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I can't say we've found the best possible keyboard, but it looks like progress will be slow in improving over about 1.9. \n", + "\n", + "Keys in Different Physical Locations\n", + "---\n", + "\n", + "Now let's allow keys to be in different physical locations. Rather than allowing complete freedom of movement, we'll start from a few different fixed key layouts and swap keys from there. I'll define three layouts and gather them into a `dict`:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "keyboards = {\n", + " 'qwerty': Keyboard(('Q W E R T Y U I O P',\n", + " ' A S D F G H J K L ', \n", + " ' Z X C V B N M ')),\n", + "\n", + " '4-by-7': Keyboard((' A B C D E F ',\n", + " 'G H I J K L M',\n", + " ' N O P Q R S ',\n", + " 'T U V W X Y Z')),\n", + "\n", + " '5-by-6': Keyboard((' A B C D E ',\n", + " 'F G H I J K',\n", + " 'L M N O P Q',\n", + " ' R S T U V',\n", + " ' W X Y Z '))\n", + " }" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a function to report on a collection of keyboards such as this (after improving them):" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def report(keyboards=keyboards, swaps=3000, scorer=workload_average):\n", + " \"Iterate through a dict of {name: kbd} pairs, showing kbd before and after repeated_improved(kbd).\"\n", + " for (name, kbd) in keyboards.items():\n", + " show_kbd(improved(kbd, swaps=swaps, scorer=scorer), \n", + " ('improved ' if swaps else '') + name)\n", + " \n", + "report()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(**Note:** The plots of different-shaped keyboards have different-sized squares around the keys. Some of the plots have a lot of whitespace around them. If anyone knows an easy way to tell `plot` to display them better, let me know.)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "So the more compact keyboards with a smaller diameter (`4-by-7` and `5-by-6`) seem to perform slightly better than `qwerty`. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 5: How often are two words confused because of similar paths?\n", + "===\n", + "\n", + "When can one word be confused with another? When their paths are similar (which means that their corresponding letters are in similar locations). For example, on a Qwerty keyboard, the paths for \"HELLO\" and \"JELLO\" are similar, because **H** and **J** are adjacent, and the other letters are the same.\n", + "\n", + "\n", + "\n", + "We'd like to know, for a given keyboard, how confusing is it? How many words have paths on the keyboard that can be confused for other words? We have our work cut out for us:\n", + "\n", + "1. Determine what letters could be confused for each other.\n", + "2. Determine what words/paths can be confused.\n", + "3. Invent some metric for the overall confusingness of a keyboard. \n", + "4. Try to find less-confusing keyboards.\n", + "\n", + "Letter Confusions\n", + "---\n", + "\n", + "So, as a first step, we will make a mapping from each key to the keys that it can be confused with. I'll say that any key within a distance of 1.5 units on the keyboard is a **neighboring** key, and thus a potential confusion:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def neighboring_keys(kbd, radius=1.5):\n", + " \"Build a dict of {Letter:NeighboringLetters}, e.g. {'Q':'AQW', ...}.\"\n", + " return {A: cat(sorted(B for B in kbd if distance(kbd[A], kbd[B]) <= radius))\n", + " for A in kbd}\n", + "\n", + "cat = ''.join ## Function to join letters (or strings) into one string" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'A': 'AQSWZ',\n", + " 'B': 'BGHJNV',\n", + " 'C': 'CDFGVX',\n", + " 'D': 'CDEFRSXZ',\n", + " 'E': 'DERSW',\n", + " 'F': 'CDFGRTVX',\n", + " 'G': 'BCFGHTVY',\n", + " 'H': 'BGHJNUVY',\n", + " 'I': 'IJKOU',\n", + " 'J': 'BHIJKMNU',\n", + " 'K': 'IJKLMNO',\n", + " 'L': 'KLMOP',\n", + " 'M': 'JKLMN',\n", + " 'N': 'BHJKMN',\n", + " 'O': 'IKLOP',\n", + " 'P': 'LOP',\n", + " 'Q': 'AQW',\n", + " 'R': 'DEFRT',\n", + " 'S': 'ADESWXZ',\n", + " 'T': 'FGRTY',\n", + " 'U': 'HIJUY',\n", + " 'V': 'BCFGHV',\n", + " 'W': 'AEQSW',\n", + " 'X': 'CDFSXZ',\n", + " 'Y': 'GHTUY',\n", + " 'Z': 'ADSXZ'}" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qwerty_neighbors = neighboring_keys(qwerty) \n", + "qwerty_neighbors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see, for example, that **Q**, off in the corner, has only **A**, **W**, and itself as neighbors, while **G**, in the middle of the keyboard, has 8 neighbors. \n", + "\n", + "Word Confusions\n", + "---\n", + "\n", + "Consider each of the letters in the word \"HELLO,\" and all the possible choices for neighbors of each letter:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['BGHJNUVY', 'DERSW', 'KLMOP', 'KLMOP', 'IKLOP']" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "columns = [qwerty_neighbors[L] for L in 'HELLO']\n", + "columns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are five columns of letters, and if we pick one letter from each column, we get a path that is formed by letters that are each confusions of letters in the original word, and so the whole path is a confusion for the original word. So \"JELLO\" is a confusion for \"HELLO\", as would be \"BDKKI\" and \"YWPPP\", except those are not words.\n", + "\n", + "It turns out that there is a library function, `itertools.product`, that will take alternative choices, and generate all possible ways of assembling a sequence consisting of one selection (letter) from each alternative choice." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "paths = {cat(picks) for picks in itertools.product(*columns)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How many paths are there?" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "5000" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(paths)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at a few of them:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['NWPOO', 'HEOOP', 'JRMLI', 'HWPKL', 'VEMKO', 'UWOPI', 'VDOMK', 'HELLI']" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(paths, 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And let's see all the paths that are also words:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BROMO', 'BROOK', 'HELLO', 'JELLO'}" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "WORDS & paths" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Only 4 out of 5000; That's pretty good, but it means \"HELLO\" is still a confusing word. We can package this as the function `confusions`:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def confusions(word, neighbors=neighboring_keys(qwerty)):\n", + " \"All valid words whose paths could be confused with the path for the given word.\"\n", + " columns = [neighbors[L] for L in word]\n", + " return {cat(picks) for picks in itertools.product(*columns)} & WORDS" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BROMO', 'BROOK', 'HELLO', 'JELLO'}" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "confusions('HELLO')" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'ALTOS', 'EIDOS', 'SIDLE', 'SKEPS', 'WIELD', 'WORKS', 'WORLD', 'WORMS'}" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "confusions('WORLD')" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'FEARING',\n", + " 'FRAYING',\n", + " 'GEARING',\n", + " 'GRATING',\n", + " 'GRAYING',\n", + " 'GREYING',\n", + " 'REARING',\n", + " 'REEFING',\n", + " 'RESTING',\n", + " 'TEARING',\n", + " 'TESTING'}" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "confusions('TESTING')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far, so good. But I'm worried about the efficiency of `confusions`.\n", + "\n", + "My first concern is that `WORDS` has 178,691 words, including many unusual words, so there might be too many confusions. I will read in a smaller word set, with only common words:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "! [ -e words.js ] || curl -O https://xkcd.com/simplewriter/words.js\n", + " \n", + "COMMON = set(re.findall('[A-Z]+', open('words.js').read().upper()))" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(3614, 'SPECIALS', 'UNDERSTANDINGS')" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(COMMON), max(COMMON, key=path_length), max(COMMON, key=len)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More Efficient `confusions`\n", + "---\n", + "\n", + "Another issue is that `confusions` is really slow:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 3.14 s, sys: 306 ms, total: 3.44 s\n", + "Wall time: 3.45 s\n" + ] + }, + { + "data": { + "text/plain": [ + "{'SOMETHING'}" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time confusions('SOMETHING')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It took (on my computer) 3 seconds to compute this. Why so long? Let's count:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[7, 5, 5, 5, 5, 8, 5, 6, 8]" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[len(neighboring_keys(qwerty)[L]) for L in 'SOMETHING']" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are 7 × 5 × 5 × 5 × 5 × 8 × 5 × 6 × 8 = 8,400,000 paths for `confusions` to consider. `'PALEOMAGNETISMS'` would have about 10,000 times more paths. Looking at every path is slow, but for most paths, we're wasting our time. For example, one choice for the first two neighboring letters of 'SO' is 'XP', but 'XP' does not start any word in the dictionary. Nevertheless, `itertools.product` will generate 240,000 combinations that start with 'XP', and will then rule them out one at a time. It would be better to stop as soon as we see 'XP', and never consider continuations of this path.\n", + "\n", + "So that gives us the key idea for a more efficient version of `confusions`: *only follow paths that form a prefix of some word.* I'll make a set of all the prefixes of the `COMMON` words:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def prefixes(words):\n", + " \"Return a set of prefixes (1 to N characters) of this collection of words.\"\n", + " return {word[:i] for word in words for i in range(1, len(word)+1)}\n", + "\n", + "PREFIXES = prefixes(COMMON)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'T', 'TH', 'THE', 'THES', 'THESE', 'THEY', 'THO', 'THOS', 'THOSE'}" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "prefixes(['THESE', 'THEY', 'THOSE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can describe the more efficient version of the `confusions` algorithm:\n", + "\n", + "1. Maintain a queue of partial paths, where a partial path is a string representing choices for neighboring letters for a prefix of the word. For example, 'HE' and 'JE' are both partial paths for the word 'HELLO'. Initialize the queue to have just one partial path, the empty string.\n", + "2. Remove a partial path from the queue. Find all possible ways to extend the path by adding a neighboring letter, but only if doing so creates a path that is a prefix of some word in the dictionary. For example, given the word 'HELLO', and the partial path 'JE', consider all the neighbors of 'L' (namely, 'K', 'M', 'L', 'O', or 'P'), but only 'JEM', 'JEL', and 'JEO' are prefixes of words, so add just those to the queue.\n", + "3. When a partial path reaches the same length as the word ('HELLO' in this example), then don't extend it any farther; instead check to see if the path is a word. If it is, yield it as a result.\n", + "\n", + "A word is `confusable` if it has a confusion word (other than itself)." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def confusions(word, neighbors=neighboring_keys(qwerty)):\n", + " \"All valid words whose paths could be confused with the path for this word.\"\n", + " Q = [''] # A queue of partial paths \n", + " while Q:\n", + " path = Q.pop()\n", + " if len(path) < len(word):\n", + " for L in neighbors[word[len(path)]]:\n", + " if path + L in PREFIXES:\n", + " Q.append(path + L)\n", + " elif path in COMMON:\n", + " yield path\n", + "\n", + "def confusable(word, neighbors=neighboring_keys(qwerty)) -> bool: \n", + " \"Is this word confusable with another, given this keyboard's neighboring keys?\"\n", + " return any(c != word for c in confusions(word, neighbors))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check the speed (remember the old version took over 3 seconds):" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 94 µs, sys: 0 ns, total: 94 µs\n", + "Wall time: 95.8 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "{'SOMETHING'}" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time set(confusions('SOMETHING'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We went from about 3 seconds to about 100 microseconds: that's 30,000 times faster! We can look at some more confusions:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BELIEVED': 'BELIEVES BELIEVER BELIEVED',\n", + " 'BENDS': 'BENDS',\n", + " 'BITEY': 'HURRY BITEY',\n", + " 'CEILINGS': 'CEILINGS',\n", + " 'COATING': 'COATING',\n", + " 'COLORERS': 'COLORERS',\n", + " 'COUPLES': 'COUPLES',\n", + " 'DUSTING': 'SHARING DUSTING',\n", + " 'DYING': 'EYING DYING',\n", + " 'ENJOYS': 'ENJOYS',\n", + " 'FREED': 'TREES TREED FREES FREER FREED FEWER FEEDS DRESS',\n", + " 'GET': 'YET TRY HEY HER GET CRY',\n", + " 'GUESSES': 'GUESSES GUESSED',\n", + " 'HOSPITAL': 'HOSPITAL',\n", + " 'IMAGING': 'OKAYING IMAGING',\n", + " 'LETTER': 'LETTER',\n", + " 'LUCKY': 'LUCKY',\n", + " 'MAY': 'MAY LAY',\n", + " 'ONCE': 'ONCE',\n", + " 'PALE': 'PALE',\n", + " 'PARTIES': 'PARTIES PARTIED',\n", + " 'PLAYER': 'PLAYER PLAYED PLATED OKAYED',\n", + " 'REPEAT': 'REPEAT',\n", + " 'RUSHES': 'RUSHES RUSHED FISHES FISHED',\n", + " 'SAMES': 'WAKES WAKED SANDS SAMES ASKED',\n", + " 'SHARP': 'SHARP',\n", + " 'SINGE': 'WINGS SONGS SINGS SINGE SINCE AUNTS',\n", + " 'SPEND': 'WORKS SPEND DOWNS',\n", + " 'TAUGHT': 'TAUGHT',\n", + " 'WALLED': 'WALLED WALKER WALKED'}" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{w: ' '.join(confusions(w))\n", + " for w in random.sample(COMMON, 30)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualizing Paths on a Keyboard\n", + "----\n", + "\n", + "It would be nice to see potentially confusable word paths on a keyboard.\n", + "I'll add functionality to `show_kbd` to call the new function `plot_paths` if any `words` are passed to `show_kbd`:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def show_kbd(kbd, name='keyboard', K=20, words=()):\n", + " \"Plot the keyboard with square keys, K units on a side.\"\n", + " H = K / 2 # (K is Key width/height; H is half K)\n", + " for L in kbd:\n", + " x, y = K * kbd[L].x, -K * kbd[L].y\n", + " plot_square(x, y, H, label=L)\n", + " plot_paths(kbd, K, words)\n", + " plt.axis('equal'); plt.axis('off')\n", + " plt.title(title(kbd, name));\n", + " plt.show()\n", + " \n", + "def plot_paths(kbd, K, words):\n", + " \"Plot paths for each word.\"\n", + " for (i, word) in enumerate(words):\n", + " Xs = [+K * kbd[L].x for L in word]\n", + " Ys = [-K * kbd[L].y for L in word]\n", + " plt.plot(Xs, Ys, '-o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see how it works on three similar paths:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty, words=['VALUE', 'VALOR', 'CAKE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " OK, we're on the right track, but I see three problems, which I think I can solve: \n", + "\n", + "- The letters are obscured by the circles. Solution: offset paths away from the center.\n", + "- When the paths are the same, they overwrite each other. Solution: offset each path towards a different corner.\n", + "- There is no indication what direction the path is going in. Solution: put a diamond on the start position.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def plot_paths(kbd, K, words):\n", + " \"Plot paths for each word, each with a different offset (and color).\"\n", + " Q = K / 5 # Q originally meant a quarter of a key width; but 1/5 looks nicer.\n", + " offsets = [Point(-Q, -Q), Point(-Q, +Q), Point(Q, +Q), Point(Q, -Q)]\n", + " for (i, word) in enumerate(words):\n", + " Xs = [+K * kbd[L].x + offsets[i % 4].x for L in word]\n", + " Ys = [-K * kbd[L].y + offsets[i % 4].y for L in word]\n", + " plt.plot(Xs, Ys, '-o')\n", + " plt.plot(Xs[:1], Ys[:1], 'kd')" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty, words=['VALUE', 'VALOR', 'CAKE'])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks busier, but it is easier to follow the paths. Another example:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty, words={'HOUSED', 'HOUSES', 'NOISES'})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Average Confusions of a Keyboard\n", + "===\n", + "\n", + "The question is: how confusing is a keyboard? One metric for confusingness is the percentage of words that are confused with other words:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def confusingness(kbd):\n", + " \"The proportion of words in COMMON that are confused with other words on this keyboard.\"\n", + " neighbors = neighboring_keys(kbd)\n", + " return mean([confusable(w, neighbors) for w in COMMON])\n", + "\n", + "def title(kbd, name): \n", + " return ('{}: path length = {:.1f}, confuse = {:.0%}'\n", + " .format(name, workload_average(kbd), confusingness(kbd)))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'4-by-7': 0.4571112340896514,\n", + " '5-by-6': 0.5282235749861649,\n", + " 'qwerty': 0.5398450470392916}" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{name: confusingness(kbd) for (name, kbd) in keyboards.items()}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "About half the common words are confusable, with a little bit of variation between keyboards." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 6: Is there a Keyboard that Minimizes Confusion?\n", + "===\n", + "\n", + "Consider this:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 112 ms, sys: 990 µs, total: 113 ms\n", + "Wall time: 112 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "0.5398450470392916" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time confusingness(qwerty)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 168 µs, sys: 0 ns, total: 168 µs\n", + "Wall time: 171 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "3.2333097802127653" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time workload_average(qwerty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Computing `confusingness` takes about 500 times longer than computing `workload_average`, so if we want to use `confusingness` as a scoring function, we will have to settle for fewer swaps:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 10.4 s, sys: 19.7 ms, total: 10.4 s\n", + "Wall time: 10.4 s\n" + ] + } + ], + "source": [ + "%time show_kbd(improved(qwerty, swaps=100, scorer=confusingness))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This did indeed reduce confusingness (which was 54%); not bad for only 100 swaps." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Question 7: Is there a Keyboard that Maximizes User Satisfaction?\n", + "===\n", + "\n", + "What is user satisfaction? I don't know, but for now I'll approximate satisfaction (or rather, *dissatisfaction*, since lower scores are better) with a combined score that is the product of workload average and confusingness. Then I (rather arbitrarily) scale the result by 5, just because I think a number like \"2.1\" looks better than \"0.42\".\n", + "\n", + "First we'll define the combined scorer function and incorporate it into `title`:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def dissatisfaction(kbd):\n", + " \"The product of workload average and confusingness, scaled by 5.\"\n", + " return 5 * workload_average(kbd) * confusingness(kbd)\n", + "\n", + "def title(kbd, name): \n", + " return ('{}: path length = {:.1f}, confuse = {:.0%}, overall = {:.1f}'\n", + " .format(name, workload_average(kbd), confusingness(kbd), \n", + " dissatisfaction(kbd)))" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let'stry to minimize confusion. This should take around 2 minutes:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2min 30s, sys: 482 ms, total: 2min 31s\n", + "Wall time: 2min 31s\n" + ] + } + ], + "source": [ + "%time report(swaps=500, scorer=dissatisfaction)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Success! We were in fact able to make progress on the combined metric. If we could run 50,000 swaps instead of just 500, we could probably do even better. To do so would require either (1) more computers, (2) more patience, or (3) more efficient algorithms. I'll leave it up to you to make more progress.\n", + "\n", + "**Note**: Each time this notebook is run, different random results can occur. I'll record a keyboard found by one\n", + "of the good runs (only 11% confusingness) here, just in case another run is not as good:" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(Keyboard((' U D J K N W ',\n", + " 'T V H E B Q R',\n", + " ' Z I M X A C ',\n", + " 'S P G O F Y L')))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Summary\n", + "=====\n", + " \n", + " So where are we? Let's revisit our initial questions and see what answers we have:\n", + " \n", + " 1. What words have the longest path length?
**Answered**: \"PALEOMAGNETISMS\" etc.\n", + " 2. What words have the highest ratio of path length to word length?
**Answered**: \"PALAPA\" etc.\n", + " 3. What is the average segment length, over a typical typing work load?
**Answered**: 3.23 keys, for Qwerty keyboard, on our sample workload.\n", + " 4. Is there a better keyboard layout to minimize the average segment length over a work load?
**Answered**: Yes, many layouts at around 1.9 on Qwerty; or 1.7 or 1.8 on more square keyboards.\n", + " 5. How often are two words confused because they have similar paths?
**Answered**: On Qwerty, 26% of the words in a small dictionary, and 55% of the words in running text have at least one possible confusion. Other layouts are worse.\n", + " 6. Is there a better keyboard layout to minimize confusion?
**Partially Answered**: We found a keyboard with less confusingness than Qwerty. The computation of confusingness takes too long to do very much hillclimbing search. \n", + " 7. Is there a better keyboard layout to maximize overall user satisfaction?
**Partially Answered**: We defined a combined metric, and found\n", + "a keyboard with a better score. There are no doubt better metrics, and better keyboards to be found.\n", + " \n", + "\n", + "\n", + "\n", + "Going Beyond\n", + "===\n", + "\n", + "Now it is your turn to answer the open questions, or make up some questions of your own. Good luck! Here are a few ideas to get you started:\n", + "\n", + "* Hillclimbing just keeps the one best keyboard it has found so far. Other optimization techniques such as\n", + "[beam search](http://en.wikipedia.org/wiki/Beam_search) or [genetic algorithms](http://en.wikipedia.org/wiki/Genetic_algorithm) or [ant colony optimization](http://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms) maintain several candidates at a time. Is that a good idea?\n", + "\n", + "* The code in this notebook emphasizes clarity, not efficiency. Can you modify the code (or perhaps port it to another language) and make it twice as efficient? 10 times? 100 times?\n", + "\n", + "* What other factors do you think are important to user satisfaction with a keyboard. Can you measure them?\n", + "\n", + "* Consider the 5 paths below. They all start at 'P', move in a straight line to 'T', and then go to 'S', but they all make different stops along the top row. In other words, the 5 paths all trace exacty the same lines, so they are very confusing, but our definition of `confusions` makes most of them different. Can you think\n", + "of a better way to handle confusions for paths like this?" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_kbd(qwerty, words=['POUTS', 'POIUYTS', 'PUTTS', 'PUTS', 'POTS', 'PITS'])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Ghost.ipynb b/pytudes/ipynb/Ghost.ipynb new file mode 100644 index 0000000..de05e0c --- /dev/null +++ b/pytudes/ipynb/Ghost.ipynb @@ -0,0 +1,1231 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ghost\n", + "\n", + "According to [Wikipedia](https://en.wikipedia.org/wiki/Ghost_(game)):\n", + "\n", + "> **Ghost** *is a written or spoken word game in which players take turns adding letters to a growing word fragment, trying not to be the one to complete a valid word. Each fragment must be the beginning of an actual word, and usually some minimum is set on the length of a word that counts, such as three or four letters. The player who completes a word loses.*\n", + "\n", + "I'd like to create a program to allow any two players (human or computer) to play the game, and I'd like to figure out who wins if both players play optimally. The concepts I will need to define, and my implementation choices, are as follows:\n", + "\n", + "- **Words**: I will read a standard online word list, `enable1`, and make a set of all the words of sufficient length.\n", + "- **Fragment**: a fragment is a `str` of letters, such as `'gho'`.\n", + "- **Beginning**: each word has a set of valid beginnings: for `ghost` it is `{'', g, gh, gho, ghos, ghost}`. \"Prefix\" is a synonym of \"beginning\".\n", + "- **Vocabulary**: A `Vocabulary` object holds a set of all the `words` in a dictionary, as well as all the valid `fragments` (beginnings) of the words.\n", + "- **Player**: The first player will be called player `0`; the second player `1`. \n", + "- **Play**: A play is a new fragment formed by adding one letter to the end of the existing fragment.\n", + "- **Legal Play**: A play that is a valid prefix of some word. `enable1.legal_plays('gho') = {'ghos, 'ghou'}`.\n", + "- **Strategy**: A strategy is a function with signature `strategy(vocab, fragment) -> play`.\n", + "- **Game**: `play_game(vocab, *strategies)` plays a game between two (or more) player strategies.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Vocabulary: Words, Fragments, Legal Plays, and `enable1`\n", + "\n", + "`Vocabulary(words)` takes a collection of words as input, stores the words as a set, and also stores all the legal fragments of those words. `legal_plays(fragments)` gives a set of all plays that can be formed by adding a letter to create a legal word fragment. I also define the function `words` to split any string into component words." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class Vocabulary:\n", + " \"Holds a set of legal words and a set of legal prefix fragments of those words.\"\n", + " def __init__(self, words, minlength=3):\n", + " self.words = {word for word in words if len(word) >= minlength}\n", + " self.fragments = {word[:i] for word in self.words for i in range(len(word) + 1)}\n", + " \n", + " def legal_plays(self, fragment): \n", + " return {fragment + L for L in alphabet} & self.fragments \n", + " \n", + "alphabet = 'abcdefghijklmnopqrstuvwxyz'\n", + " \n", + "words = str.split # Function to split a str into words" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a small example with a vocabulary of just three words:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'game', 'ghost', 'ghoul'}" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v = Vocabulary(words('game ghost ghoul'))\n", + "\n", + "v.words" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'', 'g', 'ga', 'gam', 'game', 'gh', 'gho', 'ghos', 'ghost', 'ghou', 'ghoul'}" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "v.fragments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is a large vocabulary, from a standard online Scrabble™ word list known as `enable1`:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "! [ -e enable1.txt ] || curl -O http://norvig.com/ngrams/enable1.txt" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "enable1 = Vocabulary(words(open('enable1.txt').read()))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's explore `enable1`:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(172724, 387878, 'ethylenediaminetetraacetates')" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(enable1.words), len(enable1.fragments), max(enable1.words, key=len)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'ghos', 'ghou'}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "enable1.legal_plays('gho')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'ewe'}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "enable1.legal_plays('ew')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'tha', 'the', 'thi', 'tho', 'thr', 'thu', 'thw', 'thy'}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "enable1.legal_plays('th')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Players and Winners\n", + "\n", + "The first player is `0` and the second player is `1`. These names are convenient because:\n", + "- During the course of the game, the player whose turn it is to play next is always the length of the current fragment mod 2.\n", + "- When the game ends, the winning player is the length of the current fragment mod 2.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "to_play = winner = lambda fragment: len(fragment) % 2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Who Wins?\n", + "\n", + "Who wins a game if both players play rationally? To answer that, consider the general situation at some point\n", + "during the game where\n", + "a player is presented with a fragment. That player can win if either:\n", + "- The fragment is a complete word (meaning the other player just formed the word, and thereby lost).\n", + "- The fragment is not a legal fragment (meaning the other player made a mistake, and thereby lost).\n", + "- At least one of the legal plays in this position puts the opponent in a position from which they *cannot* win.\n", + "\n", + "The function `win(vocab, fragment)` implements this. It returns a winning fragment if there is one, otherwise `False`. In particular, it returns `fragment` if the current player has already won (because `fragment` is\n", + "a word or illegal fragment), and it returns one of the legal plays if that play leads to a position from\n", + "which the opponent *cannot* `win`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def win(vocab, fragment=''):\n", + " \"\"\"Does the current player have a forced win? \n", + " If so, return a play (or the current fragment) that leads to a win.\"\"\"\n", + " if fragment in vocab.words or fragment not in vocab.fragments:\n", + " return fragment\n", + " for play in vocab.legal_plays(fragment):\n", + " if not win(vocab, play):\n", + " return play \n", + " return False" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's test `win` to gain some confidence that we got it right:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# No winning play because all words have odd number of letters.\n", + "win(Vocabulary(words('cat camel gecko'))) " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'g'" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 'g' is a winning play (but 'c' would be a loser)\n", + "win(Vocabulary(words('cat camel goat gerbil'))) " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# No winning play; doomed to 'camel' or 'gar'\n", + "win(Vocabulary(words('cat camel goat gecko gerbil gar'))) " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'g'" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 'g' wins because 'ga' can be answered with 'gan' and 'ge' with 'ge'\n", + "win(Vocabulary(words('cat camel goat gecko gerbil gar gannet'))) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# TL;DR: The Answer\n", + "\n", + "Can the first player win with the `enable1` vocabulary?" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "win(enable1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**No.** The game is a win for the second player, not the first.\n", + "This agrees with [xkcd](https://xkcd.com/)'s Randall Monroe, who [says](https://blog.xkcd.com/2007/12/31/ghost/) *\"I hear if you use the Scrabble wordlist, it’s always a win for the second player.\"*\n", + "\n", + "But ... Wikipedia says that the minimum word length can be \"three or four letters.\" In `enable1` the limit was three; let's try again with a limit of four:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'n'" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "enable1_4 = Vocabulary(enable1.words, 4)\n", + "\n", + "win(enable1_4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Yes.** The first player can win with this vocabulary, by playing `'n'` first (and there might be other first plays that also force a win). It makes sense that it is easier for the first player to win, because we've eliminated a bunch of three-letter words from the vocabulary, all of which are losers for the first player. So here's a good meta-strategy: Say \"*Hey, let's play a game of Ghost. We can use the `enable1` word list. Would you like the limit to be 3 or 4 letters?*\" Then if your opponent says three (or four) you can say \"*OK, since you decided that, I'll decide to go second (or first).*\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Playing the Game: Strategies\n", + "\n", + "We define a *strategy* as a function that is given a vocabulary and a fragment as arguments, and returns a legal play. Below we define `rational`, a strategy that wins whenever it is possible to do so and plays randomly otherwise, and `ask` (a strategy factory that returns a strategy that, when called, will ask the named person to input a fragment)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "\n", + "def rational(vocab, fragment): \n", + " \"Select a play that makes opponent not win (if possible), otherwise a random play.\"\n", + " return win(vocab, fragment) or random.choice(list(vocab.legal_plays(fragment)))\n", + "\n", + "def ask(name):\n", + " \"Return a strategy that asks for the next letter.\"\n", + " return lambda _, fragment: input('Player ' + name + ' given \"' + fragment + '\" plays? ')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a function to play a game. You give it a vocabulary, two (or possibly more) strategies, and optionally a `verbose` keyword to say if you want a line printed for each play or not." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "from itertools import cycle\n", + "\n", + "def play(vocab, *strategies, verbose=False):\n", + " \"Return (winner, final_fragment) for a game of Ghost between these strategies.\"\n", + " fragment = ''\n", + " for (p, strategy) in cycle(enumerate(strategies)): # p is the player number\n", + " play = strategy(vocab, fragment)\n", + " if verbose:\n", + " print('Player {}, given \"{}\", plays \"{}\".'.format(p, fragment, play))\n", + " if play not in vocab.legal_plays(fragment):\n", + " return (winner(fragment + '?'), play) # Player loses for making an illegal play\n", + " elif play in vocab.words:\n", + " return (winner(play), play) # Player loses for making a word\n", + " else:\n", + " fragment = play # Keep playing" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, 'odyssey')" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play(enable1, rational, rational) " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 'truancies'),\n", + " (1, 'xebec'),\n", + " (1, 'ods'),\n", + " (1, 'vying'),\n", + " (1, 'ewe'),\n", + " (1, 'bwana'),\n", + " (1, 'vying'),\n", + " (1, 'knell'),\n", + " (1, 'zloty'),\n", + " (1, 'flirt'),\n", + " (1, 'zlote'),\n", + " (1, 'bwana'),\n", + " (1, 'gjetost'),\n", + " (1, 'pliancies'),\n", + " (1, 'flounce'),\n", + " (1, 'ufologist'),\n", + " (1, 'flour'),\n", + " (1, 'dweeb'),\n", + " (1, 'flirt'),\n", + " (1, 'ignatia')]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Does player 1 win every time?\n", + "\n", + "[play(enable1, rational, rational, verbose=False) for _ in range(20)]" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 'nyctalopia')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play(enable1_4, rational, rational)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Player P given \"\" plays? d\n", + "Player P given \"dw\" plays? dwa\n", + "Player P given \"dwar\" plays? dwarv\n", + "Player P given \"dwarve\" plays? dwarves\n" + ] + }, + { + "data": { + "text/plain": [ + "(1, 'dwarves')" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play(enable1, ask('P'), rational)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Minimizing Possible Outcomes\n", + "\n", + "Now we know how to play perfectly, if we have a computer handy to execute the strategy.\n", + "But can we summarize the strategy into a form that is small enough that a human can memorize it? I will define the function `outcomes(vocab, fragment, player)` to return a set of all the words that are possible outcomes of a game, where the opponent can use any strategy whatsoever, but `player` uses a strategy that is:\n", + "\n", + "- *Rational*: plays towards a forced win whenever there is one.\n", + "- *Exploitive*: otherwise tries to give the opponent an opportunity to make a mistake that can be exploited.\n", + "- *Minimizing*: within the above constraints, returns the smallest possible set of words." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [], + "source": [ + "import textwrap \n", + "\n", + "def outcomes(vocab, fragment, player):\n", + " \"The smallest set of outcome words, if player tries to win, and make the set small.\"\n", + " if fragment in vocab.words:\n", + " return {fragment}\n", + " else:\n", + " cases = [outcomes(vocab, play, player) for play in vocab.legal_plays(fragment)]\n", + " if to_play(fragment) == player: # Player picks the top priority case\n", + " return min(cases, key=lambda words: priority(words, player))\n", + " else: # Oher player could pick anything\n", + " return set.union(*cases)\n", + " \n", + "def priority(words, player):\n", + " \"\"\"Return (lossiness, number_of_words, total_number_of_letters),\n", + " where lossiness is 0 if no losses, 1 if mixed losses/wins, 2 if all losses.\n", + " The idea is to find the list of outcome words that minimizes this triple.\"\"\"\n", + " lossiness = (0 if all(winner(word) == player for word in words) else\n", + " 1 if any(winner(word) == player for word in words) else\n", + " 2) \n", + " return (lossiness, len(words), sum(map(len, words)))\n", + "\n", + "def report_outcomes(vocab, player):\n", + " \"Find minimal outcomes for player; print info.\"\n", + " oc = outcomes(vocab, '', player)\n", + " winners = {w for w in oc if winner(w) == player}\n", + " def fill(label, words): \n", + " if words:\n", + " text = '{} ({}): {}'.format(label, len(words), ' '.join(sorted(words)))\n", + " print(textwrap.fill(text))\n", + " print('Outcomes ({}) for player {}:'.format(len(oc), player))\n", + " fill('Losers', oc - winners)\n", + " fill('Winners', winners)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Minimizing Outcomes for Player 0\n", + "\n", + "Let's see what minimal set of words player 0 can force the game into (with both vocabularies):" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Outcomes (6) for player 0:\n", + "Losers (1): qursh\n", + "Winners (5): qaid qiviut qoph qurush qwerty\n" + ] + } + ], + "source": [ + "report_outcomes(enable1, 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Interesting!** There are only 6 words; it wouldn't be hard for a human to memorize these. Then, when you are playing as player 0, pick `'q'` first, and then try to steer the game to one of the 5 words with an even number of letters. Unfortunately, one word, `'qursh'` (a monetary unit of Saudi Arabia), has an odd number of letters, which means that if the opponent replies to `'q'` with `'qu'` and to `'qur'` with `'qurs'`, then player 0 will lose. But if the opponent makes any other responses, player 0 will win." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Outcomes (7) for player 0:\n", + "Winners (7): naan nene ngultrum nirvanic nolo null nyctalopia\n" + ] + } + ], + "source": [ + "report_outcomes(enable1_4, 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Neat!** Only 7 words, and the first player can always win by forcing the opponent to one of these words.\n", + "\n", + "## Minimizing Outcomes for Player 1\n", + "\n", + "Since player 0 can pick any letter, the minimal `outcomes` set for player 1 must be at least 26 words. Let's see how much bigger it turns out to be. \n", + "\n", + "With `enable1` we already know that player 1 can force a win, so all the words in the `outcomes` set will have odd length:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Outcomes (55) for player 1:\n", + "Winners (55): aah aal aargh aas bwana cwm drave dreck drink droit\n", + "druid dry ewe fjeld fjord gjetost hmm ihram jnana kwashiorkor llano\n", + "mho nth oquassa prawn prequel prill pro prurigo pry qua quell quiff\n", + "quomodo qursh rhamnus rheum rhizoid rho rhumb rhyolitic squoosh\n", + "tchotchke uhlan vying wrath wrest wrist wrong wrung wry xanthic\n", + "xanthin yttrium zucchetto\n" + ] + } + ], + "source": [ + "report_outcomes(enable1, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Memorize this list and you will never lose as player 1.\n", + "\n", + "How about with the other vocabulary?" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Outcomes (85) for player 1:\n", + "Losers (4): hybris hyphen hyte ngultrum\n", + "Winners (81): aquiculture aquifer aquilegia aquiver bwana cnidarian\n", + "drave dreck drink droit druid dryness eschatologies eschatology\n", + "escheat eserine esker esophagus esplanade esquire esquiring essay\n", + "estuarine estuary esurience fjeld fjord gjetost hyaenic hydatid hyena\n", + "hyenine hyenoid hygeist hying hylozoism hylozoist hymen hyoid hypha\n", + "hyraces hyrax hyson ihram jnana kwashiorkor llano mbira ngwee oquassa\n", + "plaza plethoric plica plonk pluck plyer quaff quell quiff quomodo\n", + "qursh rhamnus rheum rhizoid rhomb rhumb rhyolitic squoosh tchotchke\n", + "uhlan vying wrath wrest wrist wrong wrung wryly xanthic xanthin\n", + "yttrium zucchetto\n" + ] + } + ], + "source": [ + "report_outcomes(enable1_4, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case there are 85 words, four of which are losses for player 1. But the other 81 words are wins, so with this strategy you'd have a good chance against an imperfect opponent." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SuperGhost\n", + "\n", + "In the variant *SuperGhost*, players can add a letter to either the beginning or the end of a fragment, as long as this forms a fragment that is part of some word. As Wikipedia says, given the fragment `era`, a player might play `bera` or `erad`. I was thinking of SuperGhost when I made the design decision to encapsulate `legal_plays` as a method of `Vocabulary`, rather than as a separate function. Because I did that, I should be able to use all the existing code if I just make a new class, `SuperVocabulary`, that finds *all* fragments (i.e. infixes) rather than just the beginning fragments (i.e. prefixes), and if I change `legal_plays` to add letters to both ends." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "class SuperVocabulary(Vocabulary):\n", + " \"Holds a set of legal words and a set of legal infix fragments of those words.\"\n", + " def __init__(self, words, minlength=3):\n", + " self.words = {word for word in words if len(word) >= minlength}\n", + " self.fragments = {word[i:j] for word in self.words \n", + " for i in range(len(word)) \n", + " for j in range(i, len(word) + 1)}\n", + " \n", + " def legal_plays(self, fragment):\n", + " \"All plays (adding a letter to fragment) that form a valid infix.\"\n", + " return {p for L in alphabet for p in (fragment + L, L + fragment)} & self.fragments" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I will create `SuperVocabulary` objects for 3- and 4-letter versions of `enable1`, and check out how many fragments there are in each variant:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "enable1_3super = SuperVocabulary(enable1.words, 3)\n", + "enable1_4super = SuperVocabulary(enable1.words, 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'acrop',\n", + " 'cropa',\n", + " 'crope',\n", + " 'croph',\n", + " 'cropi',\n", + " 'cropl',\n", + " 'cropo',\n", + " 'cropp',\n", + " 'cropr',\n", + " 'crops',\n", + " 'cropt',\n", + " 'cropu',\n", + " 'cropy',\n", + " 'ecrop',\n", + " 'icrop',\n", + " 'ncrop',\n", + " 'rcrop',\n", + " 'tcrop'}" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Example legal plays\n", + "enable1_3super.legal_plays('crop')" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'u'" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Can the first player win in SuperGhost with 3-letter words?\n", + "\n", + "win(enable1_3super)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'u'" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# How about with a 4-letter limit?\n", + "\n", + "win(enable1_4super)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first player can win with or without three-letter words. And unless the first player is perfect, the rational strategy can do pretty well as seond player as well. Here is a sample game:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Player P given \"\" plays? q\n", + "Player P given \"cq\" plays? cqu\n", + "Player P given \"cque\" plays? acque\n", + "Player P given \"acques\" plays? acquest\n" + ] + }, + { + "data": { + "text/plain": [ + "(1, 'acquest')" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play(enable1_3super, ask('P'), rational)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I would like to give a concise summary of the strategy for SuperGhost, but my existing `outcomes` function won't do it. That's because it is not enough to know that a particular word results in a win; we have to know in what order the letters of the word are added. I'll leave it as an exercise to find a good way to summarize SuperGhost strategies.\n", + "\n", + "# SuperDuperGhost\n", + "\n", + "In the variant *SuperDuperGhost*, players have an option to reverse the fragment before adding a letter to the beginning or end. As Wikipedia says, given the fragment `era`, a player might play `bera, erad, nare,` or `aren`.\n", + "Wikipedia is not clear, but I interpret this as meaning that the fragment played must still be a fragment of a word (not a reversed fragment of a word). Again, all we need is a new subclass:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "class SuperDuperVocabulary(SuperVocabulary):\n", + " \"Holds a set of legal words and a set of legal infix fragments of those words.\"\n", + " \n", + " def legal_plays(self, fragment):\n", + " \"All plays that form a valid infix; optionally reverse fragment first.\"\n", + " def all4(f, L): return (f + L, f[::-1] + L, L + f, L + f[::-1])\n", + " return {p for L in alphabet for p in all4(fragment, L)} & self.fragments" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "enable1_3duper = SuperDuperVocabulary(enable1.words)\n", + "enable1_4duper = SuperDuperVocabulary(enable1.words, 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'acrop',\n", + " 'cropa',\n", + " 'crope',\n", + " 'croph',\n", + " 'cropi',\n", + " 'cropl',\n", + " 'cropo',\n", + " 'cropp',\n", + " 'cropr',\n", + " 'crops',\n", + " 'cropt',\n", + " 'cropu',\n", + " 'cropy',\n", + " 'ecrop',\n", + " 'icrop',\n", + " 'iporc',\n", + " 'ncrop',\n", + " 'nporc',\n", + " 'porce',\n", + " 'porch',\n", + " 'porci',\n", + " 'porcu',\n", + " 'rcrop',\n", + " 'tcrop'}" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Example legal plays\n", + "enable1_3duper.legal_plays('crop')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we should check who wins. But I'm impateint: I tried `win(enable1_3duper)`, waited a minute, and it still hadn't returned, so I interrupted that computation and threw in a `lru_cache` decorator; which stops `win` from wasting time repeating the same computation over and over. This brings the time down to about 2 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "from functools import lru_cache\n", + "\n", + "@lru_cache(None)\n", + "def win(vocab, fragment=''):\n", + " \"\"\"Does the current player have a forced win? \n", + " Return fragment if the player has already won, or return a play that forces a win.\"\"\"\n", + " if fragment in vocab.words or fragment not in vocab.fragments:\n", + " return fragment\n", + " for play in vocab.legal_plays(fragment):\n", + " if not win(vocab, play):\n", + " return play \n", + " return False" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'p'" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "win(enable1_3duper)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'p'" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "win(enable1_4duper)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first player can win with either vocabulary. Here's a sample game." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Player 0, given \"\", plays \"p\".\n", + "Player 1, given \"p\", plays \"pr\".\n", + "Player 0, given \"pr\", plays \"lpr\".\n", + "Player 1, given \"lpr\", plays \"rple\".\n", + "Player 0, given \"rple\", plays \"rplex\".\n", + "Player 1, given \"rplex\", plays \"rplexe\".\n", + "Player 0, given \"rplexe\", plays \"urplexe\".\n", + "Player 1, given \"urplexe\", plays \"urplexes\".\n", + "Player 0, given \"urplexes\", plays \"ourplexes\".\n", + "Player 1, given \"ourplexes\", plays \"fourplexes\".\n" + ] + }, + { + "data": { + "text/plain": [ + "(0, 'fourplexes')" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play(enable1_3duper, rational, rational, verbose=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see how many fragments each vocabulary takes:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[387878, 387844, 1076434, 1076431, 1076434, 1076431]" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[len(v.fragments) \n", + " for v in [enable1, enable1_4, enable1_3super, enable1_4super, enable1_3duper, enable1_4duper]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Summary\n", + "\n", + "Here's a summary of what we have learned. (*Note:* the bold **qursh** means it is a losing word):\n", + "\n", + "| Variant \t| Shortest \t| Winner \t| First Player Forced Outcomes | 2nd Outcomes | Fragments\n", + "|:----:\t|:---:\t |:---:\t |:---: |:---: |---:\n", + "| Ghost | 3 \t | Second \t| qaid qiviut qoph **qursh** qurush qwerty | 55 words | 387,878\n", + "| Ghost | 4 \t | First \t| naan nene ngultrum nirvanic nolo null nyctalopia | 85 words | 387,844\n", + "| Super | 3\t| First \t| ? | ? | 1,076,434\n", + "| Super | 4 \t| First \t| ? | ? | 1,076,431\n", + "| SuperDuper | 3 | First| ? | ? | 1,076,434\n", + "| SuperDuper | 4 | First| ? | ? | 1,076,431\n", + "\n", + "# Further Work\n", + "\n", + "Here are some additional ideas to play with:\n", + "\n", + "- **Exploitation:** What are some good strategies when you are not guaranteed to win, to exploit an imperfect human opponent? Can you steer the game so that you win if the opponent is unfamiliar with some obscure word(s)? You might need a file of [word frequencies](http://norvig.com/ngrams/count_1w.txt).\n", + "- **Security:** A strategy function could *cheat*, and modify `vocab.words`, inserting or deleting some crucial words to ensure victory. Can you harden `play` (and/or change `Vocabulary`) to protect against that?\n", + "- **Pruning:** Currently `Vocabulary` saves words and fragments that could never be reached in a game. For example, because `'the'` is a word that ends the game, we could never reach `'them'` or `'theme'` or `'thermoluminescences'`. Can you prune away these redundant words/fragments?\n", + "- **Multi-player:** `play(enable1, ask('A'), ask('B'), ask('C'))` will play a three-player game. But `rational` (along with `win` and `winner`) would no longer work, since they assume there are exactly two players. Can you alter them to allow *n* players?\n", + "- **SuperGhost Summary:** Can you summarize a SuperGhost or SuperDuperGhost strategy in a way that a human can memorize?\n", + "- **Xghost:** In *Xghost*, a letter can be added anywhere, so from the fragment `'era'` you could play `'erba'`.\n", + "- **Spook:** In *Spook*, letters can be rearranged before adding one, so from the fragment `'era'` you could play `'bear'`." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Golomb-Puzzle.ipynb b/pytudes/ipynb/Golomb-Puzzle.ipynb new file mode 100644 index 0000000..f7480ea --- /dev/null +++ b/pytudes/ipynb/Golomb-Puzzle.ipynb @@ -0,0 +1,1326 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Sol Golomb’s Rectangle Puzzle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This problem by Solomon Golomb was presented by Gary Antonik in his 14/4/14 New York Times [Numberplay column](http://wordplay.blogs.nytimes.com/2014/04/14/rectangle):\n", + "\n", + ">Say you’re given the following challenge: create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units. You can combine sides in a variety of ways: for example, you could create a set of rectangles with dimensions 1 x 3, 2 x 4, 5 x 7, 6 x 8 and 9 x 10.\n", + ">\n", + ">1. How many different sets of five rectangles are possible?\n", + ">\n", + ">2. What are the maximum and minimum values for the total areas of the five rectangles?\n", + ">\n", + ">3. What other values for the total areas of the five rectangles are possible?\n", + ">\n", + ">4. Which sets of rectangles may be assembled to form a square?\n", + "\n", + "To me, these are interesting questions because, first, I have a (slight) personal connection to Solomon Golomb (my former colleague at USC) and to Nelson Blachman (the father of my colleague Nancy Blachman), who presented the problem to Antonik, and second, I find it interesting that the problems span the range from mathematical to computational. Let's answer them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. How many different sets of five rectangles are possible?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a basic [combinatorics](http://en.wikipedia.org/wiki/Combinatorics) or counting problem. I will present *three* methods to count the sets. If all goes well they will give the same answer. The example set of rectangles given in the problem was\n", + "\n", + "> {1 × 3, 2 × 4, 5 × 7, 6 × 8, 9 × 10}\n", + " \n", + "and in general it would be\n", + "\n", + "> {A × B, C × D, E × F, G × H, I × J}\n", + "\n", + "The question is: how many distinct ways can we assign the integers 1 through 10 to the variables A through J?\n", + " \n", + "**Method 1: Count all permutations and divide by repetitions:** There are 10 variables to be filled, so there are 10! = 3,628,800 permutations. But if we fill the first two variables with 1 × 3, that is the same rectangle as 3 × 1. So divide 10! by 25 to account for the fact that each of 5 rectangles can appear 2 ways. Similarly, if we fill A and B with 1 × 3, that yields the same set as if we filled C and D with 1 × 3. So divide again by 5! (the number of permutations of 5 things) to account for this.\n", + "That gives us:\n", + "\n", + "> 10! / 25 / 5! = 945. \n", + "\n", + "(It is always a relief when this \"count and divide\" method comes out to a whole number.)\n", + "\n", + "**Method 2: Count without repetitions**: in each rectangle of the example set the smaller component is listed first, and in each set, the rectangles with smaller first components are listed first. An alternate to \"count and divide\" is to count directly how many sets there are that respect this ordering. We'll work from left to right. How many choices are there for variable A? Only one: A must always be 1, because we agreed that the smallest number comes first. Then, given A, there are 9 remaining choices for B. For C, given A and B, there is again only one choice: C must be the smallest of the remaining 8 numbers (it will be 3 if the first rectangle was 1 × 2; otherwise it will be 2, but either way there is only one choice). That leaves 7 choices for D, 5 for F, 3 for H and 1 for J. So:\n", + "\n", + "> 9 × 7 × 5 × 3 × 1 = 945.\n", + "\n", + "(It is always a relief when two methods give the same answer.)\n", + " \n", + "**Method 3: Write a program to enumerate the sets:** We'll represent the 1 × 3 rectangle as the tuple `(1, 3)` and the example set of rectangles as the set\n", + "\n", + " {(1, 3), (2, 4), (5, 7), (6, 8), (9, 10)}\n", + "\n", + "We'll write a program to generate all possible sets of rectangles, following method 2, and then just count how many there are. To implement method 2, the minimum side will always be the first element, A, in an (A, B) pair. We iterate through all possible values for B, and then join that pair with all possible rectangles made from the remaining sides. We also have to handle the case when there are no sides; then there is one possible set of rectangles: the empty set." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "def rectangle_sets(sides):\n", + " \"Given a set of sides, list all distinct sets of rectangles that can be made.\"\n", + " if not sides:\n", + " return [ set() ]\n", + " else:\n", + " A = min(sides)\n", + " return [ {(A, B)} | other_rects\n", + " for B in sides if B is not A\n", + " for other_rects in rectangle_sets(sides - {A, B}) ]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[{(1, 2), (3, 4)}, {(1, 3), (2, 4)}, {(1, 4), (2, 3)}]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rectangle_sets({1, 2, 3, 4})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see above that there are three possible rectangle sets for 4 sides (the 1 can pair with any other side, and then a second rectangle can only be made one way from the remaining 2 sides). Below we count how many can be made with 10 sides:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "945" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sides = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\n", + "\n", + "all_sets = rectangle_sets(sides)\n", + "\n", + "len(all_sets)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(It is a relief that once again we get the same answer, 945.) \n", + "\n", + "I don't want to print all 945 sets, but let's peek at every 100th one:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[{(1, 2), (3, 4), (5, 6), (7, 8), (9, 10)},\n", + " {(1, 2), (3, 10), (4, 8), (5, 6), (7, 9)},\n", + " {(1, 3), (2, 10), (4, 6), (5, 7), (8, 9)},\n", + " {(1, 4), (2, 10), (3, 5), (6, 8), (7, 9)},\n", + " {(1, 5), (2, 9), (3, 8), (4, 6), (7, 10)},\n", + " {(1, 6), (2, 9), (3, 5), (4, 7), (8, 10)},\n", + " {(1, 7), (2, 9), (3, 4), (5, 8), (6, 10)},\n", + " {(1, 8), (2, 7), (3, 9), (4, 5), (6, 10)},\n", + " {(1, 9), (2, 7), (3, 5), (4, 6), (8, 10)},\n", + " {(1, 10), (2, 7), (3, 4), (5, 8), (6, 9)}]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all_sets[::100]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. What are the maximum and minimum values for the total areas of the five rectangles?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "I think I know this one, but I'm not completely sure. I know that a rectangle with a fixed perimeter has maximum area when it is a square. My guess is that the maximum total area occurs when each rectangle is *almost* square: a 9 × 10 rectangle; 7 × 8; and so on. So that would give us a maximum area of:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "190" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(1 * 2) + (3 * 4) + (5 * 6) + (7 * 8) + (9 * 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the minimum area should be when the rectangles deviate the most from squares: a 1 × 10, and so on:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "110" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(1 * 10) + (2 * 9) + (3 * 8) + (4 * 7) + (5 * 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since I am not sure, I will double check by finding the rectangle sets with the min and max total areas:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def total_area(rectangles): return sum(w * h for (w, h) in rectangles)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2), (3, 4), (5, 6), (7, 8), (9, 10)}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(all_sets, key=total_area)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 10), (2, 9), (3, 8), (4, 7), (5, 6)}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "min(all_sets, key=total_area)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This verifies my intuitions. But I still don't completely understand the situation. Suppose there are *N* sides that are not consecutive integers. Will the maximum total area always be formed by combining the two biggest sides, and so on?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. What other values for the total areas of the five rectangles are possible?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I have no idea how to figure this out mathematically from first principles, but it is easy to compute with the code we already have:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 184, 186, 187, 190]\n" + ] + } + ], + "source": [ + "areas = {total_area(s) for s in all_sets}\n", + "print(sorted(areas))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Is there a more succint way to describe these values? Let's see ..." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{176, 185, 188, 189}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(range(110, 191)) - areas" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The answer is: \"All the integers between 110 and 190 inclusive, except 176, 185, 188, and 189.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Which sets of rectangles may be assembled to form a square?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The only way I can think about this is to write a program; I don't see any way to work it out by hand. I do know that the total area will have to be a perfect square, and since the total area is between 110 and 191, that means either 121, 144, or 169:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(121, {(1, 6), (2, 9), (3, 10), (4, 8), (5, 7)}),\n", + " (121, {(1, 6), (2, 10), (3, 8), (4, 9), (5, 7)}),\n", + " (121, {(1, 6), (2, 10), (3, 9), (4, 7), (5, 8)}),\n", + " (121, {(1, 7), (2, 10), (3, 6), (4, 9), (5, 8)}),\n", + " (121, {(1, 8), (2, 6), (3, 10), (4, 9), (5, 7)}),\n", + " (121, {(1, 8), (2, 7), (3, 10), (4, 6), (5, 9)}),\n", + " (121, {(1, 8), (2, 9), (3, 7), (4, 6), (5, 10)}),\n", + " (121, {(1, 8), (2, 10), (3, 5), (4, 9), (6, 7)}),\n", + " (121, {(1, 9), (2, 7), (3, 6), (4, 10), (5, 8)}),\n", + " (121, {(1, 9), (2, 7), (3, 8), (4, 6), (5, 10)}),\n", + " (121, {(1, 9), (2, 7), (3, 10), (4, 5), (6, 8)}),\n", + " (121, {(1, 9), (2, 8), (3, 6), (4, 7), (5, 10)}),\n", + " (121, {(1, 10), (2, 5), (3, 9), (4, 8), (6, 7)}),\n", + " (121, {(1, 10), (2, 8), (3, 7), (4, 5), (6, 9)}),\n", + " (144, {(1, 3), (2, 9), (4, 10), (5, 7), (6, 8)}),\n", + " (144, {(1, 3), (2, 10), (4, 7), (5, 9), (6, 8)}),\n", + " (144, {(1, 3), (2, 10), (4, 8), (5, 7), (6, 9)}),\n", + " (144, {(1, 5), (2, 6), (3, 8), (4, 10), (7, 9)}),\n", + " (144, {(1, 7), (2, 4), (3, 8), (5, 9), (6, 10)}),\n", + " (144, {(1, 7), (2, 9), (3, 5), (4, 6), (8, 10)}),\n", + " (144, {(1, 9), (2, 5), (3, 7), (4, 6), (8, 10)}),\n", + " (144, {(1, 9), (2, 6), (3, 5), (4, 7), (8, 10)}),\n", + " (144, {(1, 10), (2, 4), (3, 5), (6, 8), (7, 9)}),\n", + " (169, {(1, 2), (3, 5), (4, 9), (6, 10), (7, 8)}),\n", + " (169, {(1, 2), (3, 7), (4, 6), (5, 10), (8, 9)}),\n", + " (169, {(1, 2), (3, 7), (4, 9), (5, 6), (8, 10)}),\n", + " (169, {(1, 2), (3, 8), (4, 5), (6, 10), (7, 9)}),\n", + " (169, {(1, 3), (2, 5), (4, 8), (6, 9), (7, 10)}),\n", + " (169, {(1, 3), (2, 7), (4, 5), (6, 10), (8, 9)}),\n", + " (169, {(1, 3), (2, 7), (4, 8), (5, 6), (9, 10)}),\n", + " (169, {(1, 4), (2, 5), (3, 7), (6, 9), (8, 10)}),\n", + " (169, {(1, 5), (2, 3), (4, 9), (6, 7), (8, 10)}),\n", + " (169, {(1, 5), (2, 4), (3, 8), (6, 7), (9, 10)}),\n", + " (169, {(1, 5), (2, 7), (3, 4), (6, 8), (9, 10)}),\n", + " (169, {(1, 6), (2, 3), (4, 8), (5, 7), (9, 10)})]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "perfect_squares = {i ** 2 for i in range(100)}\n", + "\n", + "sorted((total_area(s), s) \n", + " for s in all_sets if total_area(s) in perfect_squares)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "35" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So 35 out of 945 rectangle sets *might* be assembled into a square; we don't know yet if they *can* be. \n", + "\n", + "# Packing Rectangles into a Square\n", + "\n", + "I would like to see *how* the rectangles are packed into the square, not just *which* sets can be packed, so I'll need a data structure to hold information on which rectangle goes where, and a way to visually display the results.\n", + "I'll represent a *Grid* as a two-dimensional array: a list of rows, each of which is a list of cells, with the idea that each cell will be covered by a rectangle by assigning `grid[y][x] = rect` (and the special rectangle `empty` will be used to mark a cell as uncovered). I only need to deal with square grids:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "empty = (0, 0)\n", + "\n", + "def Square(n):\n", + " \"Create an [n x n] grid of empty cells.\"\n", + " return [[empty for col in range(n)] \n", + " for row in range(n)]" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)],\n", + " [(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)],\n", + " [(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)],\n", + " [(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)],\n", + " [(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)]]" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Square(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make a function to place a single rectangle onto a grid: `place_rectangle_at((w, h), grid, (x0, y0))` places a rectangle of width *w* and height *h* onto a grid at position (x0, y0). If the rectangle overlaps a non-empty cell, or goes off the grid, we return `None` to indicate that this is not a legal placement. If the rectangle does fit, we return a new grid with the new rectangle placed on it (we do not modify the original grid):" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def place_rectangle_at(rect, grid, pos):\n", + " \"\"\"Place the rectangle of size (w, h) onto grid at position (x0, y0).\n", + " Return a new grid, or None if the rectangle cannot be placed.\"\"\"\n", + " (w, h) = rect\n", + " (x0, y0) = pos\n", + " newgrid = [row.copy() for row in grid] \n", + " for x in range(x0, x0+w):\n", + " for y in range(y0, y0+h):\n", + " if y >= len(grid) or x >= len(grid[y]) or newgrid[y][x] is not empty:\n", + " return None \n", + " newgrid[y][x] = rect\n", + " return newgrid" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[(0, 0), (0, 0), (0, 0), (0, 0), (0, 0)],\n", + " [(0, 0), (0, 0), (3, 4), (3, 4), (3, 4)],\n", + " [(0, 0), (0, 0), (3, 4), (3, 4), (3, 4)],\n", + " [(0, 0), (0, 0), (3, 4), (3, 4), (3, 4)],\n", + " [(0, 0), (0, 0), (3, 4), (3, 4), (3, 4)]]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Place a 3 x 4 rectangle on a 5 x 5 square grid, 2 cells over and 1 down:\n", + "place_rectangle_at((3, 4), Square(5), (2, 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[(2, 5), (2, 5), (0, 0), (0, 0), (0, 0)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)]]" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Place two rectangles on a grid\n", + "grid0 = Square(5)\n", + "grid1 = place_rectangle_at((3, 4), grid0, (2, 1))\n", + "grid2 = place_rectangle_at((2, 5), grid1, (0, 0))\n", + "grid2" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[(2, 5), (2, 5), (3, 1), (3, 1), (3, 1)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)]]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Place a third rectangle that just barely fits\n", + "place_rectangle_at((3, 1), grid2, (2, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "None\n" + ] + } + ], + "source": [ + "# Alternatively, try to place a third rectangle that does not fit\n", + "print(place_rectangle_at((4, 1), grid2, (2, 0)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we need a strategy for packing a set of rectangles onto a grid. I know that many variants of [bin packing problems](http://en.wikipedia.org/wiki/Bin_packing_problem) are NP-hard, but we only have 5 rectangles, so it should be easy: just exhaustively try each rectangle in each possible position, and in both possible orientations (horizontal and vertical). But placing rectangles is commutative, so we can do this two ways:\n", + "\n", + "> Way 1: Considering the *rectangles* in a fixed order, try every possible *position* for each *rectangle*.\n", + "\n", + "or\n", + "\n", + "> Way 2: Considering the *positions* in a fixed order, try every possible *rectangle* for each *position*.\n", + "\n", + "In Way 1, we could pre-sort the rectangles (say, biggest first). Then we try to put the biggest rectangle in all possible positions on the grid, and for each position that fits, try putting the second biggest rectangle in all remaining positions, and so on. As a rough estimate, assume there are on average about 10 ways to place a rectangle. Then this way will look at about 105 = 100,000 combinations.\n", + "\n", + "In Way 2, we consider the positions in some fixed order; say top-to-bottom, left-to right. Take the first empty position (say, the upper left corner). Try putting each of the rectangles there, and for each one that fits, try all possible rectangles in the next empty position, and so on. There are only 5! permutations of rectangles, and each rectangle can go either horizontally or vertically, so we would have to consider 5! × 25 = 3840 combinations. Since 3840 < 100,000, I'll go with Way 2. Here is a more precise description:\n", + "\n", + "> Way 2: To `pack` a set of rectangles onto a grid, find the first empty cell on the grid. Try in turn all possible placements of any rectangle (in either orientation) at that position. For each one that fits, try to `pack` the remaining rectangles, and return the resulting grid if one of these packings succeeds. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "def pack(rectangles, grid):\n", + " \"\"\"Find a way to pack all rectangles onto grid and return the packed grid,\n", + " or return None if not possible.\"\"\"\n", + " if not rectangles:\n", + " return grid \n", + " pos = first_empty_cell(grid)\n", + " if grid and pos:\n", + " for (rectangles2, grid2) in rectangle_placements(rectangles, grid, pos):\n", + " solution = pack(rectangles2, grid2)\n", + " if solution:\n", + " return solution\n", + "\n", + "def rectangle_placements(rectangles, grid, pos):\n", + " \"Yield all (rectangles2, grid2) pairs that are the result of placing any rectangle at pos on grid.\"\n", + " for (w, h) in rectangles:\n", + " for rect in [(w, h), (h, w)]:\n", + " grid2 = place_rectangle_at(rect, grid, pos)\n", + " if grid2: \n", + " yield rectangles - {(w, h)}, grid2 \n", + " \n", + "def first_empty_cell(grid):\n", + " \"The uppermost, leftmost empty cell.\"\n", + " for (y, row) in enumerate(grid):\n", + " for (x, cell) in enumerate(row):\n", + " if cell is empty:\n", + " return (x, y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try a simple example that I know will fit:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[[(2, 5), (2, 5), (3, 1), (3, 1), (3, 1)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)],\n", + " [(2, 5), (2, 5), (3, 4), (3, 4), (3, 4)]]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pack({(1, 3), (2, 5), (3, 4)}, Square(5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It works! But it is not pretty.\n", + "\n", + "# Colored Rectangles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It would be nicer to have a graphical display of colored rectangles. I will define the function `show` which displays a grid as colored rectangles, by calling upon `html_table`, which formats any grid into HTML text." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "from IPython.display import HTML, display, clear_output\n", + "\n", + "def show(grid):\n", + " \"Display a colored HTML representation of this grid, unless it is None.\"\n", + " if grid:\n", + " display(html_table(grid, colored_cell))\n", + " \n", + "def html_table(grid, cell_function='{}'.format):\n", + " \"Return an HTML , where each cell's contents comes from calling cell_function(grid[y][x])\"\n", + " return HTML('
{}
'\n", + " .format(cat('\\n' + cat(map(cell_function, row)) \n", + " for row in grid)))\n", + "\n", + "def colored_cell(rect): \n", + " x, y = sorted(rect)\n", + " return '{}{}'.format(colors[x], x%10, y%10)\n", + "\n", + "colors = 'lightgrey yellow plum chartreuse cyan coral red olive slateblue lightgrey wheat'.split()\n", + "\n", + "cat = ''.join" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def pack_square(rectangles):\n", + " \"Pack rectangles into a square of appropriate size, if possible.\"\n", + " A = total_area(rectangles)\n", + " if A in perfect_squares:\n", + " return pack(rectangles, Square(int(A ** 0.5)))\n", + "\n", + "for s in all_sets:\n", + " show(pack_square(s))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So there are 4 sets of rectangles that work." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Animated Colored Rectangles" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is gratifying to see the final results, and have the computation be so fast, but I'd like to get a better understanding of the process of finding the results. I can try to visualize the process by *animating* the search that `pack` does: every time we successfully call `place_rectangle_at`, I can show the new grid, and then pause for a short period. I accomplish this by modifying `pack` to take an optional argument, `animation`, which when false gives the same behavior as before, but when it is a number, pauses for that number of seconds in between displaying each step of the packing." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import time\n", + "\n", + "def pack(rectangles, grid, animation=False): \n", + " \"\"\"Find a way to pack all rectangles onto grid and return the packed grid,\n", + " or return None if not possible. \n", + " Pause `animation` seconds between displaying each rectangle placement if `animation` is not false.\"\"\"\n", + " if animation: \n", + " clear_output()\n", + " show(grid)\n", + " time.sleep(animation) \n", + " if not rectangles:\n", + " return grid \n", + " pos = first_empty_cell(grid)\n", + " if grid and pos:\n", + " for (rectangles2, grid2) in rectangle_placements(rectangles, grid, pos): \n", + " solution = pack(rectangles2, grid2, animation)\n", + " if solution:\n", + " return solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are running this in a live IPython notebook (not in nbviewer), you can see for yourself by re-running this cell:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pack({(1, 2), (3, 7), (4, 6), (5, 10), (8, 9)}, Square(13), 1);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Now For Something Completely Different: Cryptarithmetic" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On April 28, Gary Antonik had another [Numberplay column](http://wordplay.blogs.nytimes.com/2014/04/28/num/) that quotes my friend Bill Gosper. (Gosper often presents more advanced puzzles in the [math-fun](http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun) mailing list.) This puzzle was:\n", + "\n", + ">For the expression N U M + B E R = P L A Y,\n", + "\n", + "> Which distinct numerals (each different) can be substituted for letters to make a valid expression?\n", + "\n", + "> How many solutions are there?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I tackled this type of problem (known as a [cryptarithmetic](http://mathworld.wolfram.com/Cryptarithmetic.html) or [alphametic](http://mathworld.wolfram.com/Alphametic.html) problem) in my Udacity class [CS 212](https://www.udacity.com/wiki/cs212/unit-2#cryptarithmetic). My approach was simple: try all permutations of digits replacing letters (that should be quick and easy—there can be at most 10 factorial or 3.6 million permutations), then for each one, use Python's `eval` function to see if the resulting string is a true expression. The basic idea is simple, but there are complications to worry about:\n", + "\n", + "1. Math uses `=` and Python uses `==` for equality; we'll allow either one.\n", + "2. The more detailed rules for these problems say that a number with a leading zero (like `012`) is illegal (but `0` itself is ok).\n", + "3. By default, Python thinks that 3/2 is 1, because integer division rounds down. But we can import \"proper\" division from the future.\n", + "4. If we try to eval an expression like 1/0, Python raises an error; we'll have to handle it." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "from __future__ import division\n", + "import itertools\n", + "import re\n", + "\n", + "def solve_all(formula):\n", + " \"\"\"Given a formula like 'NUM + BER = PLAY', fill in digits to solve it.\n", + " Input formula is a string; generate each digit-filled-in string.\"\"\"\n", + " formula = formula.replace(' = ', ' == ')\n", + " for exp in replace_letters(formula):\n", + " if valid(exp):\n", + " yield exp\n", + "\n", + "def replace_letters(formula):\n", + " \"Generate all possible replacements of letters with digits in formula.\"\n", + " letters = ''.join(set(re.findall('[A-Z]', formula)))\n", + " for digits in itertools.permutations('1234567890', len(letters)):\n", + " trans = str.maketrans(letters, ''.join(digits))\n", + " yield formula.translate(trans)\n", + "\n", + "def valid(exp):\n", + " \"Expression is valid iff it has no numbers with leading zero, and evals true.\"\n", + " try:\n", + " return not leading_zero(exp) and eval(exp)\n", + " except ArithmeticError:\n", + " return False\n", + " \n", + "leading_zero = re.compile(r'\\b0[0-9]').search" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'857 + 349 == 1206'" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "next(solve_all('NUM + BER = PLAY'))" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 29 s, sys: 42.2 ms, total: 29.1 s\n", + "Wall time: 29.1 s\n" + ] + }, + { + "data": { + "text/plain": [ + "96" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time len(list(solve_all('NUM + BER = PLAY')))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So there are 96 solutions, but it is a bit slow to find them all. For each of the permutations of digits, we substitute the digits for letters, and then call `eval(exp)` on the resulting string. The majority of time is spent inside `eval`. But the expression is basically the same each time; we could save a lot of work if we eval the expression just once, yielding a Python function, and then call that function once for each permutation of digits. In other words, we want to take an expression such as\n", + "\n", + " \"NUM + BER == PLAY\"\n", + " \n", + "and transform it into the Python function\n", + "\n", + "\n", + " lambda A,B,E,M,L,N,P,R,U,Y: (100*N+10*U+M) + (100*B+10*E+R) == (1000*P+100*L+10*A+Y)\n", + " \n", + "Actually that's not quite right. The rules are that the first letter of each multi-letter word (the \"N\" in \"NEW\"; the \"B\" in \"BER\"; and the \"P\" in \"PLAY\") cannot be a zero. So the function should be:\n", + "\n", + " lambda A,B,E,M,L,N,P,R,U,Y: N and B and P and (100*N+10*U+M) + (100*B+10*E+R) == (1000*P+100*L+10*A+Y)\n", + "\n", + "In my Udacity class I show a solution to this problem; you can [go there](https://www.udacity.com/wiki/cs212/unit-2#rethinking-eval) or see it here. Here is the code to compile a formula (or expression) into a Python function: " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def compile_formula(formula, verbose=False):\n", + " \"\"\"Compile formula into a function. Also return letters found, as a str,\n", + " in same order as parms of function. For example, 'YOU == ME**2' returns\n", + " (lambda Y,M,E,U,O: Y and M and ((100*Y+10*O+U) == (10*M+E)**2)), 'YMEUO'\"\"\"\n", + " formula = formula.replace(' = ', ' == ')\n", + " letters = ''.join(set(re.findall('[A-Z]', formula)))\n", + " firstletters = set(re.findall(r'\\b([A-Z])[A-Z]', formula))\n", + " body = re.sub('[A-Z]+', compile_word, formula)\n", + " if firstletters:\n", + " body = '{} and ({})'.format(' and '.join(firstletters), body)\n", + " fn = 'lambda {}: {}'.format(','.join(letters), body)\n", + " if verbose: print(fn)\n", + " return eval(fn), letters\n", + "\n", + "def compile_word(matchobj):\n", + " \"Compile the word 'YOU' as '(100*Y + 10*O + U)'.\"\n", + " word = matchobj.group()\n", + " terms = reversed([mult(10**i, L) for (i, L) in enumerate(reversed(word))])\n", + " return '(' + '+'.join(terms) + ')'\n", + "\n", + "def mult(factor, var): return var if factor == 1 else str(factor) + '*' + var" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lambda Y,M,E,O,U: Y and M and ((100*Y+10*O+U) == (10*M+E)**2)\n" + ] + }, + { + "data": { + "text/plain": [ + "(>, 'YMEOU')" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "compile_formula(\"YOU == ME**2\", verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lambda L,A,Y,P,M,E,R,U,B,N: P and B and N and ((100*N+10*U+M) + (100*B+10*E+R) == (1000*P+100*L+10*A+Y))\n" + ] + }, + { + "data": { + "text/plain": [ + "(>, 'LAYPMERUBN')" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "compile_formula(\"NUM + BER == PLAY\", verbose=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def faster_solve_all(formula):\n", + " \"\"\"Given a formula like 'ODD + ODD == EVEN', fill in digits to solve it.\n", + " Input formula is a string; output is a digit-filled-in string or None.\n", + " Capital letters are variables. This version precompiles the formula; only one eval per formula.\"\"\"\n", + " fn, letters = compile_formula(formula)\n", + " for digits in itertools.permutations((1,2,3,4,5,6,7,8,9,0), len(letters)):\n", + " try:\n", + " if fn(*digits):\n", + " yield replace_all(formula, letters, digits)\n", + " except ZeroDivisionError: \n", + " pass\n", + " \n", + "def replace_all(text, olds, news):\n", + " \"Replace each occurrence of each old in text with the corresponding new.\"\n", + " # E.g. replace_all('A + B', ['A', 'B'], [1, 2]) == '1 + 2'\n", + " for (old, new) in zip(olds, news):\n", + " text = text.replace(str(old), str(new))\n", + " return text" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'857 + 349 = 1206'" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "next(faster_solve_all('NUM + BER = PLAY'))" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.75 s, sys: 3.29 ms, total: 1.76 s\n", + "Wall time: 1.76 s\n" + ] + }, + { + "data": { + "text/plain": [ + "96" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time len(list(faster_solve_all('NUM + BER = PLAY')))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We get the same answer, but 15 times faster." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/How To Count Things.ipynb b/pytudes/ipynb/How To Count Things.ipynb new file mode 100644 index 0000000..2edcae5 --- /dev/null +++ b/pytudes/ipynb/How To Count Things.ipynb @@ -0,0 +1,1196 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "import re\n", + "from itertools import product, chain, permutations\n", + "from collections import defaultdict\n", + "from functools import lru_cache as cache\n", + "from math import factorial" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# How to Count Things\n", + "\n", + "This notebook contains problems designed to show how to count things. So far there are five example problems.\n", + "\n", + "# (1) Student Records: Late, Absent, Present\n", + "\n", + "Consider this problem:\n", + "\n", + "> (1) Students at a school must meet with the guidance counselor if they have two total absences, or three consecutive late days. Each student's attendance record consists of a string of 'A' for absent, 'L' for late, or 'P' for present. For example: \"LAPLPA\" requires a meeting (because there are two absences), and \"LAPLPL\" is OK (there are three late days, but they are not consecutive). Write a function that takes such a string as input and returns `True` if the student's record is OK. \n", + "\n", + "> (2) Write a function to calculate the number of attendance records of length N that are OK.\n", + "\n", + "For part (1), the simplest approach is to use `re.search`:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def ok(record: str) -> bool: return not re.search(r'LLL|A.*A', record)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_ok():\n", + " assert ok(\"LAPLLP\")\n", + " assert not ok(\"LAPLLL\") # 3 Ls in a row\n", + " assert not ok(\"LAPLLA\") # 2 As overall\n", + " assert ok(\"APLLPLLP\")\n", + " assert not ok(\"APLLPLLL\") # 3 Ls in a row\n", + " assert not ok(\"APLLPLLA\") # 2 As overall\n", + " return 'pass'\n", + " \n", + "test_ok() " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For part (2), I'll start with a simple (but slow) solution called `total_ok_slow` that enumerates `all_strings` (using `itertools.product`) and counts how many are `ok`. I use the `quantify` recipe ([from `itertools`](https://docs.python.org/3.6/library/itertools.html#itertools-recipes)) to count them:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def total_ok_slow(N: int) -> int:\n", + " \"How many strings over 'LAP' of length N are ok?\"\n", + " return quantify(all_strings('LAP', N), ok)\n", + "\n", + "def all_strings(alphabet, N): \n", + " \"All length-N strings over the given alphabet.\"\n", + " return map(cat, product(alphabet, repeat=N))\n", + "\n", + "def quantify(iterable, pred=bool) -> int:\n", + " \"Count how many times the predicate is true of items in iterable.\"\n", + " return sum(map(pred, iterable))\n", + "\n", + "cat = ''.join" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 1,\n", + " 1: 3,\n", + " 2: 8,\n", + " 3: 19,\n", + " 4: 43,\n", + " 5: 94,\n", + " 6: 200,\n", + " 7: 418,\n", + " 8: 861,\n", + " 9: 1753,\n", + " 10: 3536}" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{N: total_ok_slow(N) for N in range(11)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks good, but\n", + "I will need a more efficient algorithm to handle large values of *N*. Here's how I think about it:\n", + "\n", + "* I can't enumerate all the strings; there are too many of them, 3N. \n", + "* Even if I only enumerate the ok strings, there are still too many, O(2N).\n", + "* Instead, I'll want to keep track of a *summary* of all the ok strings of length *N*, and use that to quickly compute a summary of the ok strings of length *N*+1. I recognize this as a *[dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming)* approach.\n", + "\n", + "* What is in the summary? A list of all ok strings is too much. A count of the number of ok strings is not enough. Instead, I will group together the strings that have the same number of `'A'` characters in them, and the same number of consecutive `'L'` characters at the end of the string, and count them. I don't need to count strings that have two or more `'A'` characters, or 3 consecutive `'L'` characters anywhere in the string. And I don't need to worry about runs of 1 or 2 `'L'` characters embedded in the middle of the string. So the summary is a mapping of the form `{(A, L): count, ...}`. \n", + "\n", + "Here is a function to create the summary for `N+1`, given the summary for `N`:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def next_summary(prev_summary: dict) -> dict:\n", + " \"Given a summary of the form {(A, L): count}, return summary for one char more.\"\n", + " summary = defaultdict(int)\n", + " for (A, L), c in prev_summary.items():\n", + " if A < 1: summary[A+1, 0] += c # transition with 'A'\n", + " if L < 2: summary[A, L+1] += c # transition with 'L'\n", + " summary[A, 0] += c # transition with 'P'\n", + " return summary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For `N = 0`, the summary is `{(0, 0): 1}`, because there is one string, the empty string, which has no `'A'` nor `'L'`. From there we can proceed in a \"bottom-up\" fashion to compute the total number of OK strings for any value of `N`:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(int, {(0, 0): 1, (0, 1): 1, (1, 0): 1})" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "next_summary({(0, 0): 1})" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(int, {(0, 0): 2, (0, 1): 1, (0, 2): 1, (1, 0): 3, (1, 1): 1})" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "next_summary(_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I can annotate that result with the two-letter strings that form each count:\n", + "\n", + " {(0, 0): 2, # LP, PP\n", + " (0, 1): 1, # PL\n", + " (0, 2): 1, # LL\n", + " (1, 0): 1, # AP, LA, PA\n", + " (1, 1): 1} # AL\n", + "\n", + "\n", + "Here's an implementation of `total_ok`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def total_ok(N) -> int:\n", + " \"How many strings of length N are ok?\"\n", + " summary = {(0, 0): 1}\n", + " for _ in range(N):\n", + " summary = next_summary(summary)\n", + " return sum(summary.values()) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use this to go way beyond what we could do with `total_ok_slow`:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.21 ms, sys: 111 µs, total: 1.32 ms\n", + "Wall time: 1.35 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "5261545087067582125179062608958232695543100705754634272071166414871321070487675367" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time total_ok(300)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.3689147905858837e+143" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "3. ** 300" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are over 1080 ok strings of length 300; more than the number of atoms in the universe. But it only took around a millisecond to count them (while ignoring the 3300 = 10143 not-ok strings of length 300).\n", + "\n", + "Dynamic programming can also be done top-down (where we start at `N` and work down to `0`):" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def total_ok(N) -> int:\n", + " \"How many strings of length N are ok?\"\n", + " return sum(summary_for(N).values())\n", + " \n", + "def summary_for(N) -> dict: \n", + " \"The {(A, L): count} summary for strings of length N.\"\n", + " return ({(0, 0): 1} if N == 0 else next_summary(summary_for(N - 1)))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 1.82 ms, sys: 46 µs, total: 1.87 ms\n", + "Wall time: 1.88 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "5261545087067582125179062608958232695543100705754634272071166414871321070487675367" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time total_ok(300)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We get the same answer in about the same amount of time.\n", + "\n", + "Let's verify our results against the slow, reliable `total_ok_slow`, and look at the summaries for the first few values of `N`:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " N ok summary(N)\n", + "-- ---- ----------\n", + " 0 1 {(0, 0): 1}\n", + " 1 3 {(0, 1): 1, (1, 0): 1, (0, 0): 1}\n", + " 2 8 {(0, 1): 1, (1, 0): 3, (0, 0): 2, (0, 2): 1, (1, 1): 1}\n", + " 3 19 {(0, 1): 2, (1, 2): 1, (0, 0): 4, (1, 0): 8, (0, 2): 1, (1, 1): 3}\n", + " 4 43 {(0, 1): 4, (1, 2): 3, (0, 0): 7, (1, 0): 19, (0, 2): 2, (1, 1): 8}\n", + " 5 94 {(0, 1): 7, (1, 2): 8, (0, 0): 13, (1, 0): 43, (0, 2): 4, (1, 1): 19}\n", + " 6 200 {(0, 1): 13, (1, 2): 19, (0, 0): 24, (1, 0): 94, (0, 2): 7, (1, 1): 43}\n", + " 7 418 {(0, 1): 24, (1, 2): 43, (0, 0): 44, (1, 0): 200, (0, 2): 13, (1, 1): 94}\n", + " 8 861 {(0, 1): 44, (1, 2): 94, (0, 0): 81, (1, 0): 418, (0, 2): 24, (1, 1): 200}\n", + " 9 1753 {(0, 1): 81, (1, 2): 200, (0, 0): 149, (1, 0): 861, (0, 2): 44, (1, 1): 418}\n", + "10 3536 {(0, 1): 149, (1, 2): 418, (0, 0): 274, (1, 0): 1753, (0, 2): 81, (1, 1): 861}\n" + ] + } + ], + "source": [ + "print(' N ok summary(N)')\n", + "print('-- ---- ----------')\n", + "for N in range(11): \n", + " assert total_ok(N) == total_ok_slow(N)\n", + " print('{:2} {:4} {}'.format(N, total_ok(N), dict(summary_for(N))))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# (2) Count Strings with Alphabetic First Occurrences\n", + "\n", + "Here's another problem:\n", + "\n", + "> Given an alphabet of length k, how many strings of length k can be formed such that the first occurrences of each character in the string are a prefix of the alphabet?\n", + "\n", + "Let's first make sure we understand the problem. Since *k* could go well beyond 26, I will choose as my alphabet the integers, not the letters `'abc...'`. An alphabet of length *k* is `range(k)`, and a valid string of length 3 could be\n", + "`[0, 1, 2]` or `[0, 0, 1]` (or other possibilities). These are valid because the first occurrence of each character for these strings are `[0, 1, 2]` and `[0, 1]`, respectively, and these are prefixes of `range(3)`. But `[0, 0, 2]` is not valid, because the first occurrences are `[0, 2]`, and this is not a prefix (because it is missing the `1`). \n", + "\n", + "I'll define four key concepts:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def valid(s) -> bool: \n", + " \"A string is valid if its first occurrences are a prefix of the alphabet.\"\n", + " return is_prefix(first_occurrences(s))\n", + "\n", + "def is_prefix(s) -> bool: \n", + " \"A string is a valid prefix if it is consecutive integers starting from 0.\"\n", + " return s == list(range(len(s)))\n", + "\n", + "def first_occurrences(s) -> list:\n", + " \"The unique elements of s, in the order they first appear.\" \n", + " firsts = []\n", + " for x in s:\n", + " if x not in firsts: firsts.append(x)\n", + " return firsts \n", + "\n", + "def all_strings(k): \n", + " \"All strings of length k over an alphabet of k ints.\"\n", + " return product(range(k), repeat=k)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test(): \n", + " assert valid([0, 1, 2]) and valid([0, 0, 1])\n", + " assert not valid([0, 0, 2])\n", + " assert is_prefix([0, 1, 2])\n", + " assert first_occurrences([0, 0, 2]) == [0, 2]\n", + " assert set(all_strings(2)) == {(0, 0), (0, 1), (1, 0), (1, 1)}\n", + " # s first_occurrences(s) valid(s)\n", + " assert test1([0, 1, 2], [0, 1, 2], True) \n", + " assert test1([0, 0, 0], [0], True) \n", + " assert test1([1], [1], False) \n", + " assert test1([0, 1, 3], [0, 1, 3], False)\n", + " assert test1([0, 1, 3, 2], [0, 1, 3, 2], False)\n", + " assert test1([0, 1, 0, 1, 0, 2, 1], [0, 1, 2], True)\n", + " assert test1([0, 1, 0, 2, 1, 3, 1, 2, 5, 4, 3], [0, 1, 2, 3, 5, 4], False)\n", + " assert test1([0, 1, 0, 2, 1, 3, 1, 2, 4, 5, 3], [0, 1, 2, 3, 4, 5], True)\n", + " return 'ok'\n", + "\n", + "def test1(s, firsts, is_valid):\n", + " return first_occurrences(s) == firsts and valid(s) == is_valid\n", + " \n", + "test()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, I will solve the problem in a slow but sure way: generate all possible strings, then count the number that are valid. The complexity of this algorithm is $O(k^{k+1})$, because there are $k^k$ strings, and to validate a string requires looking at all $k$ characters." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 1, 2, 5, 15, 52, 203]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def how_many_slow(k) -> int: \n", + " \"\"\"Count the number of valid strings. (Try all possible strings.)\"\"\"\n", + " return quantify(all_strings(k), valid)\n", + "\n", + "[how_many_slow(k) for k in range(7)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's think about how to speed that up. I don't want to have to consider every possible string, because there are too many ($k^k$) of them. Can I group together many strings and just count the number of them, without enumerating each one? For example, if I knew there were 52 valid strings of length $k-1$ (and didn't know anything else about them), can I tell how many valid strings of length $k$ there are? I don't see a way to do this directly, because the number of ways to extend a valid string is dependent on the number of distinct characters in the string. If a string has $m$ distinct characters, then I can extend it in $m$ waysby repeating any of those $m$ characters, or I can introduce a first occurrence of character number $m+1$ in just 1 way.\n", + "\n", + "So I need to keep track of the number of valid strings of length $k$ that have exactly $m$ distinct characters (those characters must be exactly `range(m)`). I'll call that number `C(k, m)`. Because I can reach a recursive call to `C(k, m)` by many paths, I will use the `cache` decorator to keep track of the computations that I have already done. Then I can define `how_many(k)` as the sum over all values of `m` of `C(k, m)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "@cache()\n", + "def C(k, m) -> int:\n", + " \"Count the number of valid strings of length k, that use m distinct characters.\"\n", + " return (1 if k == 0 == m else\n", + " 0 if k == 0 != m else\n", + " C(k-1, m) * m + C(k-1, m-1)) # m ways to add an old character; 1 way to add new\n", + "\n", + "def how_many(k): return sum(C(k, m) for m in range(k+1))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "47585391276764833658790768841387207826363669686825611466616334637559114497892442622672724044217756306953557882560751" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "how_many(100)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "assert all(how_many(k) == how_many_slow(k) for k in range(7))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0 1\n", + " 1 1\n", + " 2 2\n", + " 3 5\n", + " 4 15\n", + " 5 52\n", + " 6 203\n", + " 7 877\n", + " 8 4140\n", + " 9 21147\n", + " 10 115975\n", + " 20 5.17242e+13\n", + " 30 8.46749e+23\n", + " 40 1.57451e+35\n", + " 50 1.85724e+47\n", + " 60 9.76939e+59\n", + " 70 1.8075e+73\n", + " 80 9.91268e+86\n", + " 90 1.4158e+101\n", + "100 4.75854e+115\n", + "110 3.46846e+130\n", + "120 5.1263e+145\n" + ] + } + ], + "source": [ + "for k in chain(range(10), range(10, 121, 10)):\n", + " print('{:3} {:12g}'.format(k, how_many(k)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# (3) Sol Golomb’s Rectangle Puzzle\n", + "\n", + "This problem is covered in depth in [another notebook](Golomb-puzzle.ipynb), so here I present just the part that has to do with counting things:\n", + "\n", + "> *Say you’re given the following challenge: create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units. You can combine sides in a variety of ways: for example, you could create a set of rectangles with dimensions 1 x 3, 2 x 4, 5 x 7, 6 x 8 and 9 x 10. How many different sets of five rectangles are possible?*\n", + "\n", + "This is a basic [combinatorics](http://en.wikipedia.org/wiki/Combinatorics) or counting problem. I will present *three* methods to count the sets. If all goes well they will give the same answer. The example set of rectangles given in the problem was\n", + "\n", + "> {1 × 3, 2 × 4, 5 × 7, 6 × 8, 9 × 10}\n", + " \n", + "and in general it would be\n", + "\n", + "> {A × B, C × D, E × F, G × H, I × J}\n", + "\n", + "The question is: how many distinct ways can we assign the integers 1 through 10 to the variables A through J?\n", + " \n", + "**Method 1: Count all permutations and divide by repetitions:** There are 10 variables to be filled, so there are 10! = 3,628,800 permutations. But if we fill the first two variables with 1 × 3, that is the same rectangle as 3 × 1. So divide 10! by 25 to account for the fact that each of 5 rectangles can appear 2 ways. Similarly, if we fill A and B with 1 × 3, that yields the same set as if we filled C and D with 1 × 3. So divide again by 5! (the number of permutations of 5 things) to account for this.\n", + "That gives us:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "945.0" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factorial(10) / 2 ** 5 / factorial(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(It is always a relief when this \"count and divide\" method comes out to a whole number.)\n", + "\n", + "**Method 2: Count without repetitions**: in each rectangle of the example set the smaller component is listed first, and in each set, the rectangles with smaller first components are listed first. An alternate to \"count and divide\" is to count directly how many sets there are that respect this ordering. We'll work from left to right. How many choices are there for variable A? Only one: A must always be 1, because we agreed that the smallest number comes first. Then, given A, there are 9 remaining choices for B. For C, given A and B, there is again only one choice: C must be the smallest of the remaining 8 numbers (it will be 3 if the first rectangle was 1 × 2; otherwise it will be 2, but either way there is only one choice). That leaves 7 choices for D, 5 for F, 3 for H and 1 for J. So:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "945" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "9 * 7 * 5 * 3 * 1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(It is always a relief when two methods give the same answer.)\n", + " \n", + "**Method 3: Write a program to enumerate the sets:** We'll represent the 1 × 3 rectangle as the tuple `(1, 3)` and the example set of rectangles as the set\n", + "\n", + " {(1, 3), (2, 4), (5, 7), (6, 8), (9, 10)}\n", + "\n", + "We'll write a program to generate all possible sets of rectangles, following method 2, and then just count how many there are. To implement method 2, the minimum side will always be the first element, A, in an (A, B) pair. We iterate through all possible values for B, and then join that pair with all possible rectangles made from the remaining sides. We also have to handle the case when there are no sides; then there is one possible set of rectangles: the empty set." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "945" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def rectangle_sets(sides):\n", + " \"Given a set of sides, list all distinct sets of rectangles that can be made.\"\n", + " if not sides:\n", + " return [ set() ]\n", + " else:\n", + " A = min(sides)\n", + " return [ {(A, B)} | other_rects\n", + " for B in sides if B is not A\n", + " for other_rects in rectangle_sets(sides - {A, B}) ]\n", + " \n", + "len(rectangle_sets({1, 2, 3, 4, 5, 6, 7, 8, 9, 0}))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(It is a relief that once again we get the same answer, 945.) \n", + "\n", + "Here is a list of the rectangle sets with just 6 sides:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[{(1, 2), (3, 4), (5, 6)},\n", + " {(1, 2), (3, 5), (4, 6)},\n", + " {(1, 2), (3, 6), (4, 5)},\n", + " {(1, 3), (2, 4), (5, 6)},\n", + " {(1, 3), (2, 5), (4, 6)},\n", + " {(1, 3), (2, 6), (4, 5)},\n", + " {(1, 4), (2, 3), (5, 6)},\n", + " {(1, 4), (2, 5), (3, 6)},\n", + " {(1, 4), (2, 6), (3, 5)},\n", + " {(1, 5), (2, 3), (4, 6)},\n", + " {(1, 5), (2, 4), (3, 6)},\n", + " {(1, 5), (2, 6), (3, 4)},\n", + " {(1, 6), (2, 3), (4, 5)},\n", + " {(1, 6), (2, 4), (3, 5)},\n", + " {(1, 6), (2, 5), (3, 4)}]" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rectangle_sets({1, 2, 3, 4, 5, 6})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# (4) Counting Positions in Fischerandom Chess\n", + "\n", + "In this [variant](https://en.wikipedia.org/wiki/Chess960) of chess, the pieces are set up in a random but restricted fashion. The pawns are in their regular positions, and the major white pieces are placed randomly on the first rank, with two restrictions: the bishops must be placed on opposite-color squares, and the king must be placed between the rooks. The black pieces are set up to mirror the white pieces. How many starting positions are there?\n", + "\n", + "We can answer by generating all distinct permutations of the eight pieces and quantifying (counting) the number of permutations that are legal according to the two restrictions:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "960" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from statistics import median\n", + "\n", + "def legal(pieces):\n", + " B, R, K = map(pieces.index, 'BRK')\n", + " b, r = map(cat(pieces).rindex, 'BR')\n", + " return (B % 2 != b % 2) and median([R, K, r]) == K\n", + "\n", + "quantify(set(permutations('RNBKQBNR')), legal)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Note:* initially I wrote `pieces.rindex`, because I forgot that while tuples, lists and strings all have an `index` method, only strings have `rindex`. How annoying! In Ruby, both strings and arrays have `index` and `rindex`. In Java and Javascript, both strings and lists/arrays have both `indexOf` and `lastIndexOf`. What's wrong with Python?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# (5) Counting Paths on a Grid\n", + "\n", + "Consider the following grid, where the goal is to find a path from `S` to `G`, making only \"right\" or \"down\" moves:\n", + "\n", + " S..........\n", + " ...........\n", + " ...........\n", + " ...........\n", + " ...........\n", + " ..........G\n", + " \n", + "One solution path would be to go right 10 times, then go down 5 times. But you could also go down 3 times, then right 10 times, then down 2 times; or take many other paths. How many paths are there? We can use the same three methods we used for the previous puzzle:\n", + "\n", + "**Method 1: Count all permutations and divide by repetitions:** Any path must consist of 10 right and 5 down moves, but they can appear in any order. Arranging 15 things in any order gives 15! = 1,307,674,368,000 possible paths. But that counts all the moves as being distinct, when actually the 10 right moves are indistinguishable, as are the 5 down moves, so we need to divide by the number of ways that they can be arranged. That gives us:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3003.0" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "factorial(15) / factorial(10) / factorial(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Method 2: Count without repetitions**: Another way to look at it is that there will be 15 total moves, so start with all 15 being \"right\" moves and then choose 5 of them to become \"down\" moves. So the answer is (15 choose 5), which leads to the same formula we just used.\n", + "\n", + "**Method 3: Write a program to count the paths:** We can define the function `paths(start, goal)` to count the number of paths from start location to goal location, where a location is a `(column, row)` pair of integers.\n", + "In general, the number of paths to the goal is the number of paths to the location just to the left of the goal, plus the number of paths to the location just above the goal. But there are two special cases: there is only one path (the empty path) when the start is equal to the goal, and there are zero paths when the goal is off the board." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3003" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@cache()\n", + "def paths(start, goal):\n", + " \"Number of paths to goal, using only 'right' and 'down' moves.\"\n", + " (col, row) = goal\n", + " return (1 if goal == start else\n", + " 0 if col < 0 or row < 0 else\n", + " paths(start, (col - 1, row)) + paths(start, (col, row - 1)))\n", + " \n", + "paths((0, 0), (5, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can handle much larger grids (while checking the time taken, and then verifying that the answer agrees with the factorial formula):" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 222 ms, sys: 2.81 ms, total: 225 ms\n", + "Wall time: 225 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "4158251463258564744783383526326405580280466005743648708663033657304756328324008620" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "goal = (C, R) = (100, 200)\n", + "\n", + "%time paths((0, 0), goal)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "_ == factorial(C + R) // factorial(C) // factorial(R)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Why bother with the recursive function when the formula works so well? Good question. One reason is that the two different approaches validate each other by giving the same answer. Another reason is that we can modify the `paths` function to handle grids that have obstacles in them. I'll define a `Grid` constructor, and any cell in the grid that is not a `'.'` will be considered an impassible barrier." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Grid(text): return tuple(text.split())\n", + "\n", + "@cache()\n", + "def paths2(grid, start=(0, 0), goal=None):\n", + " \"Number of paths to goal, using only 'right' and 'down' moves.\"\n", + " goal = goal or bottom_right(grid)\n", + " (col, row) = goal\n", + " return (1 if goal == start else\n", + " 0 if col < 0 or row < 0 or grid[col][row] != '.' else\n", + " paths2(grid, start, (col - 1, row)) + \n", + " paths2(grid, start, (col, row - 1)))\n", + "\n", + "def bottom_right(grid): return (len(grid) - 1, len(grid[0]) - 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can verify that we get the same answer on the 11 by 6 empty grid:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3003" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paths2(Grid(\"\"\"\n", + "...........\n", + "...........\n", + "...........\n", + "...........\n", + "...........\n", + "...........\n", + "\"\"\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a grid where there should be only two paths:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paths2(Grid(\"\"\"\n", + "...........\n", + ".........|.\n", + ".........|.\n", + ".........|.\n", + ".--------+.\n", + "...........\n", + "\"\"\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we tear down that wall, there should be many paths (but less than 3003 because some of the wall remains):" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "992" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paths2(Grid(\"\"\"\n", + "...........\n", + ".........|.\n", + ".........|.\n", + "...........\n", + ".-------...\n", + "...........\n", + "\"\"\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's a bigger, and a much bigger example:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "58975" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paths2(Grid(r\"\"\"\n", + "................\\---\n", + "../......|..........\n", + "./..()...|.().|...\\.\n", + ".\\............|.....\n", + "..\\----....|..|.....\n", + ".......\\...|........\n", + "\\.......\\...........\n", + "-\\.............()...\n", + "--\\.................\n", + "---\\....../\\........\n", + "\"\"\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "121480689204" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paths2(Grid(r\"\"\"\n", + "....................http://www.ascii-art-generator.org/.................\n", + "........................................................................\n", + ".......................WWNK0OkxdoooolooddxkO0KXW........................\n", + ".................WX0kdolc::::::::::cc::::::::::clodk0XW.................\n", + "............WXOdl::::cldxkO0KKKKKKXXXXKKKKKK0Okxdlc:;;:ldOXW............\n", + ".........N0dc;;coxkxxdxKXXXXXXXKddKXXKxdKXXXXXXXKxdxxxxoc;;cd0N.........\n", + "........d:,:oxkdl:,..'xXXXXXXXX0:.,;;;.:0XXXXXXXXx'..':ldkxo:,:d0W......\n", + "....W0l.;okxl;.......cKXXXXXXXXO,......,kXXXXXXXXKc.......;lxko;,l0W....\n", + "...Xo';.Od;..........;OXXXXXXXKl........lKXXXXXXXO:..........;dkd;,oX...\n", + "..K:'lO.,.............;dOKKK0x:..........:x0KKKOd;.............,xOl':K..\n", + ".Xc.o0o..................,,,'...............,,,..................o0o.cX.\n", + ".k';0k'..........................................................'k0;'k.\n", + ".d.cKd............................................................dKc.d.\n", + ".k';Ok,...........................................................kO;'k.\n", + ".Xl.l0d'.........''..................................''...........0l.cX.\n", + "..Kc'cOk;......;x000ko;..,okOOd;........;dOOko,..;ok000x;......;x..'cK..\n", + "...Xd,,dkd:....oXXXXXXKkx0XXXXXKd'....'dKXXXXX0xkKXXXXXXo....;dkd;.dX...\n", + "....WKo,;lxxo;':OXXXXXXXXXXXXXXXXx,..'xXNXXXXXXXXXXXXXXO:'.oxxl;,l.W....\n", + "......WKx:,:lxxxOXXXXXXXXXXXXXXXXXx::xXXXXXXXXXXXXXXXXXOxx..:,:dKW......\n", + ".........WKxl;;:ldk0KXXXXNNXXXXXXXXKKXXXXXXXXXXXXXXK0kdl:;.cxKW.........\n", + "............WN0xoc:;:clodxkO00KKKXXXXXXKKK00Okxdol::;:cox0.W............\n", + ".................WNKOxdlcc::::::::::::::::::::ccldxOKNW.................\n", + "........................WWXK0OkkxxddddxxkkO0KXNW........................\n", + "........................................................................\n", + "\"\"\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can you verify that these last three answers are correct?" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/How to Do Things with Words.ipynb b/pytudes/ipynb/How to Do Things with Words.ipynb new file mode 100644 index 0000000..e3c68a3 --- /dev/null +++ b/pytudes/ipynb/How to Do Things with Words.ipynb @@ -0,0 +1,2307 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Boring preliminaries\n", + "import re\n", + "import math\n", + "import string\n", + "from collections import Counter\n", + "from __future__ import division" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "

Statistical Natural Language Processing in Python.\n", + "
or\n", + "
How To Do Things With Words. And Counters.\n", + "
or\n", + "
Everything I Needed to Know About NLP I learned From Sesame Street.\n", + "
Except Kneser-Ney Smoothing.\n", + "
The Count Didn't Cover That.\n", + "
\n", + "
\n", + "
*One, two, three, ah, ah, ah!* — The Count\n", + "

\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(1) Data: Text and Words\n", + "========\n", + "\n", + "Before we can do things with words, we need some words. First we need some *text*, possibly from a *file*. Then we can break the text into words. I happen to have a big text called [big.txt](file:///Users/pnorvig/Documents/ipynb/big.txt). We can read it, and see how big it is (in characters):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "6488409" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "TEXT = file('big.txt').read()\n", + "len(TEXT)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, six million characters.\n", + "\n", + "Now let's break the text up into words (or more formal-sounding, *tokens*). For now we'll ignore all the punctuation and numbers, and anything that is not a letter." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def tokens(text):\n", + " \"List all the word tokens (consecutive letters) in a text. Normalize to lowercase.\"\n", + " return re.findall('[a-z]+', text.lower()) " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['this', 'is', 'a', 'test', 'this', 'is']" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tokens('This is: A test, 1, 2, 3, this is.')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1105211" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "WORDS = tokens(TEXT)\n", + "len(WORDS)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, a million words. Here are the first 10:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['the', 'project', 'gutenberg', 'ebook', 'of', 'the', 'adventures', 'of', 'sherlock', 'holmes']\n" + ] + } + ], + "source": [ + "print(WORDS[:10])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(2) Models: Bag of Words\n", + "====\n", + "\n", + "The list `WORDS` is a list of the words in the `TEXT`, but it can also serve as a *generative model* of text. We know that language is very complicated, but we can create a simplified model of language that captures part of the complexity. In the *bag of words* model, we ignore the order of words, but maintain their frequency. Think of it this way: take all the words from the text, and throw them into a bag. Shake the bag, and then generating a sentence consists of pulling words out of the bag one at a time. Chances are it won't be grammatical or sensible, but it will have words in roughly the right proportions. Here's a function to sample an *n* word sentence from a bag of words:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def sample(bag, n=10):\n", + " \"Sample a random n-word sentence from the model described by the bag of words.\"\n", + " return ' '.join(random.choice(bag) for _ in range(n))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'the mucous acute ordered inevitability collision collection a attained august'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sample(WORDS)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another representation for a bag of words is a `Counter`, which is a dictionary of `{'word': count}` pairs. For example," + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({'a': 2, 'is': 2, 'test': 2, 'this': 1, 'it': 1})" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(tokens('Is this a test? It is a test!'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A `Counter` is like a `dict`, but with a few extra methods. Let's make a `Counter` for the big list of `WORDS` and get a feel for what's there:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[('the', 80029), ('of', 40025), ('and', 38312), ('to', 28766), ('in', 22047), ('a', 21155), ('that', 12512), ('he', 12401), ('was', 11410), ('it', 10681)]\n" + ] + } + ], + "source": [ + "COUNTS = Counter(WORDS)\n", + "\n", + "print COUNTS.most_common(10)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80029 the\n", + "83 rare\n", + "38312 and\n", + "0 neverbeforeseen\n", + "460 words\n" + ] + } + ], + "source": [ + "for w in tokens('the rare and neverbeforeseen words'):\n", + " print COUNTS[w], w" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In 1935, linguist George Zipf noted that in any big text, the *n*th most frequent word appears with a frequency of about 1/*n* of the most frequent word. He get's credit for *Zipf's Law*, even though Felix Auerbach made the same observation in 1913. If we plot the frequency of words, most common first, on a log-log plot, they should come out as a straight line if Zipf's Law holds. Here we see that it is a fairly close fit:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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RnliOM/2K8orzsDhpMaIvRCOEHwJ/G38oKihWWZ4x7iKvOXOAjh25lbs6dAA6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\nP3s2tzzjkSM0tp9IF2X6hNT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "M = COUNTS['the']\n", + "yscale('log'); xscale('log'); title('Frequency of n-th most frequent word and 1/n line.')\n", + "plot([c for (w, c) in COUNTS.most_common()])\n", + "plot([M/i for i in range(1, len(COUNTS)+1)]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(3) Task: Spelling Correction\n", + "========\n", + "\n", + "Given a word *w*, find the most likely correction *c* = `correct(`*w*`)`.\n", + "\n", + "**Approach:** Try all candidate words *c* that are known words that are near *w*. Choose the most likely one.\n", + "\n", + "How to balance *near* and *likely*?\n", + "\n", + "For now, in a trivial way: always prefer nearer, but when there is a tie on nearness, use the word with the highest `WORDS` count. Measure nearness by *edit distance*: the minimum number of deletions, transpositions, insertions, or replacements of characters. By trial and error, we determine that going out to edit distance 2 will give us reasonable results. Then we can define `correct(`*w*`)`:\n", + " \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def correct(word):\n", + " \"Find the best spelling correction for this word.\"\n", + " # Prefer edit distance 0, then 1, then 2; otherwise default to word itself.\n", + " candidates = (known(edits0(word)) or \n", + " known(edits1(word)) or \n", + " known(edits2(word)) or \n", + " [word])\n", + " return max(candidates, key=COUNTS.get)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The functions `known` and `edits0` are easy; and `edits2` is easy if we assume we have `edits1`:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def known(words):\n", + " \"Return the subset of words that are actually in the dictionary.\"\n", + " return {w for w in words if w in COUNTS}\n", + "\n", + "def edits0(word): \n", + " \"Return all strings that are zero edits away from word (i.e., just word itself).\"\n", + " return {word}\n", + "\n", + "def edits2(word):\n", + " \"Return all strings that are two edits away from this word.\"\n", + " return {e2 for e1 in edits1(word) for e2 in edits1(e1)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now for `edits1(word)`: the set of candidate words that are one edit away. For example, given `\"wird\"`, this would include `\"weird\"` (inserting an `e`) and `\"word\"` (replacing a `i` with a `o`), and also `\"iwrd\"` (transposing `w` and `i`; then `known` can be used to filter this out of the set of final candidates). How could we get them? One way is to *split* the original word in all possible places, each split forming a *pair* of words, `(a, b)`, before and after the place, and at each place, either delete, transpose, replace, or insert a letter:\n", + "\n", + "\n", + "
pairs: Ø+wird w+ird wi+rd wir+dwird+ØNotes: (a, b) pair\n", + "
deletions: Ø+ird w+rd wi+d wir+ØDelete first char of b\n", + "
transpositions: Ø+iwrd w+rid wi+drSwap first two chars of b\n", + "
replacements: Ø+?ird w+?rd wi+?d wir+?Replace char at start of b\n", + "
insertions: Ø+?+wird w+?+ird wi+?+rd wir+?+d wird+?+ØInsert char between a and b\n", + "
" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def edits1(word):\n", + " \"Return all strings that are one edit away from this word.\"\n", + " pairs = splits(word)\n", + " deletes = [a+b[1:] for (a, b) in pairs if b]\n", + " transposes = [a+b[1]+b[0]+b[2:] for (a, b) in pairs if len(b) > 1]\n", + " replaces = [a+c+b[1:] for (a, b) in pairs for c in alphabet if b]\n", + " inserts = [a+c+b for (a, b) in pairs for c in alphabet]\n", + " return set(deletes + transposes + replaces + inserts)\n", + "\n", + "def splits(word):\n", + " \"Return a list of all possible (first, rest) pairs that comprise word.\"\n", + " return [(word[:i], word[i:]) \n", + " for i in range(len(word)+1)]\n", + "\n", + "alphabet = 'abcdefghijklmnopqrstuvwxyz'" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('', 'wird'), ('w', 'ird'), ('wi', 'rd'), ('wir', 'd'), ('wird', '')]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "splits('wird')" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "set(['wird'])\n" + ] + } + ], + "source": [ + "print edits0('wird')" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "set(['wirdh', 'wirdw', 'jird', 'wiid', 'wirj', 'wiprd', 'rird', 'wkird', 'wiqrd', 'wrird', 'wisrd', 'zwird', 'wiqd', 'wizrd', 'wirs', 'wrd', 'wqird', 'tird', 'wirdp', 'wrrd', 'wzrd', 'wiad', 'nird', 'wirsd', 'wixd', 'wxird', 'lird', 'eird', 'wmird', 'wihd', 'wirp', 'lwird', 'wirzd', 'widrd', 'wxrd', 'ewird', 'wirdx', 'wirkd', 'hwird', 'wipd', 'wirnd', 'uwird', 'wirz', 'mwird', 'wjrd', 'wirjd', 'wirrd', 'wirdd', 'wsird', 'bwird', 'wcrd', 'xwird', 'wdird', 'wibrd', 'wikd', 'wiryd', 'wiord', 'gird', 'wtird', 'wbrd', 'nwird', 'wlrd', 'wgird', 'wmrd', 'wirf', 'wirg', 'wird', 'wire', 'wirb', 'wirc', 'wira', 'wkrd', 'wiro', 'wirl', 'wirm', 'iird', 'wirk', 'wirh', 'wiri', 'wirv', 'wirw', 'wirt', 'wiru', 'wirr', 'wicd', 'cird', 'wirq', 'wirqd', 'wizd', 'wirhd', 'ird', 'bird', 'wirx', 'wiry', 'wvrd', 'widr', 'wprd', 'wirad', 'wijd', 'wirxd', 'uird', 'wirdb', 'qwird', 'dird', 'wnrd', 'wjird', 'gwird', 'whrd', 'wtrd', 'woird', 'rwird', 'wurd', 'wijrd', 'witrd', 'wwrd', 'dwird', 'vwird', 'wibd', 'wiyd', 'wicrd', 'weird', 'yird', 'wiwrd', 'wirdv', 'wirdu', 'wid', 'wirds', 'wirdr', 'sird', 'wirbd', 'wirdq', 'wirdy', 'wivrd', 'wirdg', 'wirdf', 'wirde', 'wiud', 'wirdc', 'wir', 'wirda', 'wfird', 'kwird', 'wirdn', 'wirdm', 'wirdl', 'wirdk', 'wirdj', 'wiird', 'wnird', 'wiurd', 'wied', 'aird', 'wirod', 'wpird', 'wcird', 'wzird', 'jwird', 'wirdo', 'wsrd', 'wimd', 'wirwd', 'mird', 'fird', 'wuird', 'wirdt', 'wired', 'wirgd', 'wirfd', 'witd', 'wfrd', 'wyrd', 'wihrd', 'zird', 'ward', 'wilrd', 'widd', 'iwrd', 'hird', 'word', 'wisd', 'wvird', 'pird', 'wlird', 'wyird', 'wdrd', 'werd', 'wild', 'oird', 'wirid', 'wgrd', 'wirvd', 'wiod', 'wirud', 'wircd', 'wiyrd', 'wigrd', 'wixrd', 'wiard', 'vird', 'wiwd', 'wigd', 'wirmd', 'swird', 'wierd', 'xird', 'qird', 'waird', 'wqrd', 'kird', 'cwird', 'wirtd', 'wirdz', 'awird', 'fwird', 'wirpd', 'wifrd', 'pwird', 'owird', 'wivd', 'wimrd', 'iwird', 'winrd', 'wirdi', 'wrid', 'wifd', 'wirld', 'wwird', 'ywird', 'wirn', 'wbird', 'whird', 'wikrd', 'wind', 'twird'])\n" + ] + } + ], + "source": [ + "print edits1('wird')" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "24254\n" + ] + } + ], + "source": [ + "print len(edits2('wird'))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['spelling',\n", + " 'errors',\n", + " 'in',\n", + " 'something',\n", + " 'whatever',\n", + " 'unusual',\n", + " 'mistakes',\n", + " 'everywhere']" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "map(correct, tokens('Speling errurs in somethink. Whutever; unusuel misteakes everyware?'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can we make the output prettier than that?" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def correct_text(text):\n", + " \"Correct all the words within a text, returning the corrected text.\"\n", + " return re.sub('[a-zA-Z]+', correct_match, text)\n", + "\n", + "def correct_match(match):\n", + " \"Spell-correct word in match, and preserve proper upper/lower/title case.\"\n", + " word = match.group()\n", + " return case_of(word)(correct(word.lower()))\n", + "\n", + "def case_of(text):\n", + " \"Return the case-function appropriate for text: upper, lower, title, or just str.\"\n", + " return (str.upper if text.isupper() else\n", + " str.lower if text.islower() else\n", + " str.title if text.istitle() else\n", + " str)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[,\n", + " ,\n", + " ,\n", + " str]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "map(case_of, ['UPPER', 'lower', 'Title', 'CamelCase'])" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Spelling Errors IN something. Whatever; unusual mistakes?'" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "correct_text('Speling Errurs IN somethink. Whutever; unusuel misteakes?')" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Audience says: tumbler ...'" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "correct_text('Audiance sayzs: tumblr ...')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So far so good. You can probably think of a dozen ways to make this better. Here's one: in the text \"three, too, one, blastoff!\" we might want to correct \"too\" with \"two\", even though \"too\" is in the dictionary. We can do better if we look at a *sequence* of words, not just an individual word one at a time. But how can we choose the best corrections of a sequence? The ad-hoc approach worked pretty well for single words, but now we could use some real theory ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(4) Models: Word and Sequence Probabilities\n", + "===\n", + "\n", + "If we have a bag of words, what's the probability of picking a particular word out of the bag? We'll denote that probability as $P(w)$. To create the function `P` that computes this probability, we define a function, `pdist`, that takes as input a `Counter` (that is, a bag of words) and returns a function that acts as a probability distribution over all possible words. In a probability distribution the probability of each word is between 0 and 1, and the sum of the probabilities is 1." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def pdist(counter):\n", + " \"Make a probability distribution, given evidence from a Counter.\"\n", + " N = sum(counter.values())\n", + " return lambda x: counter[x]/N\n", + "\n", + "Pword = pdist(COUNTS)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0724106075672 the\n", + "0.00884356018896 is\n", + "0.000821562579453 most\n", + "0.000259678921039 common\n", + "0.000269631771671 word\n", + "0.0199482270806 in\n", + "0.000190913771217 english\n" + ] + } + ], + "source": [ + "# Print probabilities of some words\n", + "for w in tokens('\"The\" is most common word in English'):\n", + " print Pword(w), w" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, what is the probability of a *sequence* of words? Use the definition of a joint probability:\n", + "\n", + "$P(w_1 \\ldots w_n) = P(w_1) \\times P(w_2 \\mid w_1) \\times P(w_3 \\mid w_1 w_2) \\ldots \\times \\ldots P(w_n \\mid w_1 \\ldots w_{n-1})$\n", + "\n", + "In the bag of words model, each word is drawn from the bag *independently* of the others. So $P(w_2 \\mid w_1) = P(w_2)$, and we have:\n", + " \n", + "$P(w_1 \\ldots w_n) = P(w_1) \\times P(w_2) \\times P(w_3) \\ldots \\times \\ldots P(w_n)$\n", + "\n", + " \n", + " \n", + "\n", + "Now clearly this model is wrong; the probability of a sequence depends on the order of the words. But, as the statistician George Box said, *All models are wrong, but some are useful.* The bag of words model, wrong as it is, has many useful applications.\n", + " \n", + "How can we compute $P(w_1 \\ldots w_n)$? We'll use a different function name, `Pwords`, rather than `P`, and we compute the product of the individual probabilities:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Pwords(words):\n", + " \"Probability of words, assuming each word is independent of others.\"\n", + " return product(Pword(w) for w in words)\n", + "\n", + "def product(nums):\n", + " \"Multiply the numbers together. (Like `sum`, but with multiplication.)\"\n", + " result = 1\n", + " for x in nums:\n", + " result *= x\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.98419543271e-11 this is a test\n", + "8.64036404331e-16 this is a unusual test\n", + "0.0 this is a neverbeforeseen test\n" + ] + } + ], + "source": [ + "tests = ['this is a test', \n", + " 'this is a unusual test',\n", + " 'this is a neverbeforeseen test']\n", + "\n", + "for test in tests:\n", + " print Pwords(tokens(test)), test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Yikes—it seems wrong to give a probability of 0 to the last one; it should just be very small. We'll come back to that later. The other probabilities seem reasonable." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(5) Task: Word Segmentation\n", + "====\n", + "\n", + "**Task**: *given a sequence of characters with no spaces separating words, recover the sequence of words.*\n", + " \n", + "\n", + "Why? Languages with no word delimiters: [不带空格的词](http://translate.google.com/#auto/en/%E4%B8%8D%E5%B8%A6%E7%A9%BA%E6%A0%BC%E7%9A%84%E8%AF%8D)\n", + "\n", + "In English, sub-genres with no word delimiters ([spelling errors](https://www.google.com/search?q=wordstogether), [URLs](http://speedofart.com)).\n", + "\n", + "**Approach 1:** Enumerate all candidate segementations and choose the one with highest Pwords\n", + "\n", + "Problem: how many segmentations are there for an *n*-character text?\n", + "\n", + "**Approach 2:** Make one segmentation, into a first word and remaining characters. If we assume words are independent \n", + "then we can maximize the probability of the first word adjoined to the best segmentation of the remaining characters.\n", + " \n", + " assert segment('choosespain') == ['choose', 'spain']\n", + "\n", + " segment('choosespain') ==\n", + " max(Pwords(['c'] + segment('hoosespain')),\n", + " Pwords(['ch'] + segment('oosespain')),\n", + " Pwords(['cho'] + segment('osespain')),\n", + " Pwords(['choo'] + segment('sespain')),\n", + " ...\n", + " Pwords(['choosespain'] + segment('')))\n", + " \n", + " \n", + " \n", + "To make this somewhat efficient, we need to avoid re-computing the segmentations of the remaining characters. This can be done explicitly by *dynamic programming* or implicitly with *memoization*. Also, we shouldn't consider all possible lengths for the first word; we can impose a maximum length. What should it be? A little more than the longest word seen so far." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def memo(f):\n", + " \"Memoize function f, whose args must all be hashable.\"\n", + " cache = {}\n", + " def fmemo(*args):\n", + " if args not in cache:\n", + " cache[args] = f(*args)\n", + " return cache[args]\n", + " fmemo.cache = cache\n", + " return fmemo" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "18" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(len(w) for w in COUNTS)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def splits(text, start=0, L=20):\n", + " \"Return a list of all (first, rest) pairs; start <= len(first) <= L.\"\n", + " return [(text[:i], text[i:]) \n", + " for i in range(start, min(len(text), L)+1)]" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[('', 'word'), ('w', 'ord'), ('wo', 'rd'), ('wor', 'd'), ('word', '')]\n", + "[('r', 'eallylongtext'), ('re', 'allylongtext'), ('rea', 'llylongtext'), ('real', 'lylongtext')]\n" + ] + } + ], + "source": [ + "print splits('word')\n", + "print splits('reallylongtext', 1, 4)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@memo\n", + "def segment(text):\n", + " \"Return a list of words that is the most probable segmentation of text.\"\n", + " if not text: \n", + " return []\n", + " else:\n", + " candidates = ([first] + segment(rest) \n", + " for (first, rest) in splits(text, 1))\n", + " return max(candidates, key=Pwords)" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['choose', 'spain']" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment('choosespain')" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['speed', 'of', 'art']" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment('speedofart')" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "decl = ('wheninthecourseofhumaneventsitbecomesnecessaryforonepeople' +\n", + " 'todissolvethepoliticalbandswhichhaveconnectedthemwithanother' +\n", + " 'andtoassumeamongthepowersoftheearththeseparateandequalstation' +\n", + " 'towhichthelawsofnatureandofnaturesgodentitlethem')" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "when in the course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth the separate and equal station to which the laws of nature and of natures god entitle them\n" + ] + } + ], + "source": [ + "print(' '.join(segment(decl)))" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3.613815636889254e-141" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Pwords(segment(decl))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.305966345742529e-281" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Pwords(segment(decl+decl))" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Pwords(segment(decl+decl+decl))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a problem. We'll come back to it later." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['small', 'and', 'insignificant']" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment('smallandinsignificant')" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['large', 'and', 'insignificant']" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment('largeandinsignificant')" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4.1121373609e-10\n", + "1.06638804821e-11\n" + ] + } + ], + "source": [ + "print(Pwords(['large', 'and', 'insignificant']))\n", + "print(Pwords(['large', 'and', 'in', 'significant']))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Summary:\n", + " \n", + "- Looks pretty good!\n", + "- The bag-of-words assumption is a limitation.\n", + "- Recomputing Pwords on each recursive call is somewhat inefficient.\n", + "- Numeric underflow for texts longer than 100 or so words; we'll need to use logarithms, or other tricks.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# (6) Data: Mo' Data, Mo' Better" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's move up from millions to *billions and billions* of words. Once we have that amount of data, we can start to look at two word sequences, without them being too sparse. I happen to have data files available in the format of `\"word \\t count\"`, and bigram data in the form of `\"word1 word2 \\t count\"`. Let's arrange to read them in:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def load_counts(filename, sep='\\t'):\n", + " \"\"\"Return a Counter initialized from key-value pairs, \n", + " one on each line of filename.\"\"\"\n", + " C = Counter()\n", + " for line in open(filename):\n", + " key, count = line.split(sep)\n", + " C[key] = int(count)\n", + " return C" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "COUNTS1 = load_counts('count_1w.txt')\n", + "COUNTS2 = load_counts('count_2w.txt')\n", + "\n", + "P1w = pdist(COUNTS1)\n", + "P2w = pdist(COUNTS2)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "333333 588.124220187\n", + "286358 225.955251755\n" + ] + } + ], + "source": [ + "print len(COUNTS1), sum(COUNTS1.values())/1e9\n", + "print len(COUNTS2), sum(COUNTS2.values())/1e9" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('of the', 2766332391),\n", + " ('in the', 1628795324),\n", + " ('to the', 1139248999),\n", + " ('on the', 800328815),\n", + " ('for the', 692874802),\n", + " ('and the', 629726893),\n", + " ('to be', 505148997),\n", + " ('is a', 476718990),\n", + " ('with the', 461331348),\n", + " ('from the', 428303219),\n", + " ('by the', 417106045),\n", + " ('at the', 416201497),\n", + " ('of a', 387060526),\n", + " ('in a', 364730082),\n", + " ('will be', 356175009),\n", + " ('that the', 333393891),\n", + " ('do not', 326267941),\n", + " ('is the', 306482559),\n", + " ('to a', 279146624),\n", + " ('is not', 276753375),\n", + " ('for a', 274112498),\n", + " ('with a', 271525283),\n", + " ('as a', 270401798),\n", + " (' and', 261891475),\n", + " ('of this', 258707741),\n", + " (' the', 258483382),\n", + " ('it is', 245002494),\n", + " ('can be', 230215143),\n", + " ('If you', 210252670),\n", + " ('has been', 196769958)]" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "COUNTS2.most_common(30)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(7) Theory and Practice: Segmentation With Bigram Data\n", + "===\n", + "\n", + "A less-wrong approximation:\n", + " \n", + "$P(w_1 \\ldots w_n) = P(w_1 \\mid start) \\times P(w_2 \\mid w_1) \\times P(w_3 \\mid w_2) \\ldots \\times \\ldots P(w_n \\mid w_{n-1})$\n", + "\n", + "This is called the *bigram* model, and is equivalent to taking a text, cutting it up into slips of paper with two words on them, and having multiple bags, and putting each slip into a bag labeled with the first word on the slip. Then, to generate language, we choose the first word from the original single bag of words, and chose all subsequent words from the bag with the label of the previously-chosen word. To determine the probability of a word sequence, we multiply together the conditional probabilities of each word given the previous word. We'll do this with a function, `cPword` for \"conditional probability of a word.\"\n", + "\n", + "$P(w_n \\mid w_{n-1}) = P(w_{n-1}w_n) / P(w_{n-1}) $" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Pwords2(words, prev=''):\n", + " \"The probability of a sequence of words, using bigram data, given prev word.\"\n", + " return product(cPword(w, (prev if (i == 0) else words[i-1]) )\n", + " for (i, w) in enumerate(words))\n", + "\n", + "P = P1w # Use the big dictionary for the probability of a word\n", + "\n", + "def cPword(word, prev):\n", + " \"Conditional probability of word, given previous word.\"\n", + " bigram = prev + ' ' + word\n", + " if P2w(bigram) > 0 and P(prev) > 0:\n", + " return P2w(bigram) / P(prev)\n", + " else: # Average the back-off value and zero.\n", + " return P(word) / 2" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.98419543271e-11\n", + "6.41367629438e-08\n", + "1.18028600367e-11\n" + ] + } + ], + "source": [ + "print Pwords(tokens('this is a test'))\n", + "print Pwords2(tokens('this is a test'))\n", + "print Pwords2(tokens('is test a this'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To make `segment2`, we copy `segment`, and make sure to pass around the previous token, and to evaluate probabilities with `Pwords2` instead of `Pwords`." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@memo \n", + "def segment2(text, prev=''): \n", + " \"Return best segmentation of text; use bigram data.\" \n", + " if not text: \n", + " return []\n", + " else:\n", + " candidates = ([first] + segment2(rest, first) \n", + " for (first, rest) in splits(text, 1))\n", + " return max(candidates, key=lambda words: Pwords2(words, prev))" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['choose', 'spain']\n", + "['speed', 'of', 'art']\n", + "['small', 'and', 'in', 'significant']\n", + "['large', 'and', 'in', 'significant']\n" + ] + } + ], + "source": [ + "print segment2('choosespain')\n", + "print segment2('speedofart')\n", + "print segment2('smallandinsignificant')\n", + "print segment2('largeandinsignificant')" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['far', 'out', 'in', 'the', 'un', 'chart', 'ed', 'back', 'waters', 'of', 'the', 'un', 'fashionable', 'end', 'of', 'the', 'western', 'spiral', 'arm', 'of', 'the', 'galaxy', 'lies', 'a', 'small', 'un', 'regarded', 'yellow', 'sun']\n", + "['far', 'out', 'in', 'the', 'uncharted', 'backwaters', 'of', 'the', 'unfashionable', 'end', 'of', 'the', 'western', 'spiral', 'arm', 'of', 'the', 'galaxy', 'lies', 'a', 'small', 'un', 'regarded', 'yellow', 'sun']\n" + ] + } + ], + "source": [ + "adams = ('faroutintheunchartedbackwatersoftheunfashionableendofthewesternspiral' +\n", + " 'armofthegalaxyliesasmallunregardedyellowsun')\n", + "print segment(adams)\n", + "print segment2(adams)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P1w('unregarded')" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['a', 'dry', 'bare', 'sandy', 'hole', 'with', 'nothing', 'in', 'it', 'to', 'sit', 'down', 'on', 'or', 'to', 'eat']\n", + "['a', 'dry', 'bare', 'sandy', 'hole', 'with', 'nothing', 'in', 'it', 'to', 'sit', 'down', 'on', 'or', 'to', 'eat']\n" + ] + } + ], + "source": [ + "tolkien = 'adrybaresandyholewithnothinginittositdownonortoeat'\n", + "print segment(tolkien)\n", + "print segment2(tolkien)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Conclusion? Bigram model is a little better, but not much. Hundreds of billions of words still not enough. (Why not trillions?) Could be made more efficient." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(8) Theory: Evaluation\n", + "===\n", + "\n", + "So far, we've got an intuitive feel for how this all works. But we don't have any solid metrics that quantify the results. Without metrics, we can't say if we are doing well, nor if a change is an improvement. In general,\n", + "when developing a program that relies on data to help make\n", + "predictions, it is good practice to divide your data into three sets:\n", + "
    \n", + "
  1. Training set: the data used to create our spelling\n", + " model; this was the big.txt file.\n", + "
  2. Development set: a set of input/output pairs that we can\n", + " use to rank the performance of our program as we are developing it.\n", + "
  3. Test set: another set of input/output pairs that we use\n", + " to rank our program after we are done developing it. The\n", + " development set can't be used for this purpose—once the\n", + " programmer has looked at the development test it is tainted, because\n", + " the programmer might modify the program just to pass the development\n", + " test. That's why we need a separate test set that is only looked at\n", + " after development is done.\n", + "
\n", + "\n", + "For this program, the training data is the word frequency counts, the development set is the examples like `\"choosespain\"` that we have been playing with, and now we need a test set." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def test_segmenter(segmenter, tests):\n", + " \"Try segmenter on tests; report failures; return fraction correct.\"\n", + " return sum([test_one_segment(segmenter, test) \n", + " for test in tests]), len(tests)\n", + "\n", + "def test_one_segment(segmenter, test):\n", + " words = tokens(test)\n", + " result = segmenter(cat(words))\n", + " correct = (result == words)\n", + " if not correct:\n", + " print 'expected', words\n", + " print ' got', result\n", + " return correct\n", + "\n", + "cat = ''.join\n", + "\n", + "proverbs = (\"\"\"A little knowledge is a dangerous thing\n", + " A man who is his own lawyer has a fool for his client\n", + " All work and no play makes Jack a dull boy\n", + " Better to remain silent and be thought a fool that to speak and remove all doubt;\n", + " Do unto others as you would have them do to you\n", + " Early to bed and early to rise, makes a man healthy, wealthy and wise\n", + " Fools rush in where angels fear to tread\n", + " Genius is one percent inspiration, ninety-nine percent perspiration\n", + " If you lie down with dogs, you will get up with fleas\n", + " Lightning never strikes twice in the same place\n", + " Power corrupts; absolute power corrupts absolutely\n", + " Here today, gone tomorrow\n", + " See no evil, hear no evil, speak no evil\n", + " Sticks and stones may break my bones, but words will never hurt me\n", + " Take care of the pence and the pounds will take care of themselves\n", + " Take care of the sense and the sounds will take care of themselves\n", + " The bigger they are, the harder they fall\n", + " The grass is always greener on the other side of the fence\n", + " The more things change, the more they stay the same\n", + " Those who do not learn from history are doomed to repeat it\"\"\"\n", + " .splitlines())" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "expected ['power', 'corrupts', 'absolute', 'power', 'corrupts', 'absolutely']\n", + " got ['power', 'corrupt', 's', 'absolute', 'power', 'corrupt', 's', 'absolutely']\n", + "expected ['the', 'grass', 'is', 'always', 'greener', 'on', 'the', 'other', 'side', 'of', 'the', 'fence']\n", + " got ['the', 'grass', 'is', 'always', 'green', 'er', 'on', 'the', 'other', 'side', 'of', 'the', 'fence']\n" + ] + }, + { + "data": { + "text/plain": [ + "(18, 20)" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "test_segmenter(segment, proverbs)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(20, 20)" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "test_segmenter(segment2, proverbs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This confirms that both segmenters are very good, and that `segment2` is slightly better. There is much more that can be done in terms of the variety of tests, and in measuring statistical significance." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(9) Theory and Practice: Smoothing\n", + "======\n", + "\n", + "Let's go back to a test we did before, and add some more test cases:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2.98419543271e-11 this is a test\n", + "8.64036404331e-16 this is a unusual test\n", + "0.0 this is a nongovernmental test\n", + "0.0 this is a neverbeforeseen test\n", + "0.0 this is a zqbhjhsyefvvjqc test\n" + ] + } + ], + "source": [ + "tests = ['this is a test', \n", + " 'this is a unusual test',\n", + " 'this is a nongovernmental test',\n", + " 'this is a neverbeforeseen test',\n", + " 'this is a zqbhjhsyefvvjqc test']\n", + "\n", + "for test in tests:\n", + " print Pwords(tokens(test)), test" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The issue here is the finality of a probability of zero. Out of the three 15-letter words, it turns out that \"nongovernmental\" is in the dictionary, but if it hadn't been, if somehow our corpus of words had missed it, then the probability of that whole phrase would have been zero. It seems that is too strict; there must be some \"real\" words that are not in our dictionary, so we shouldn't give them probability zero. There is also a question of likelihood of being a \"real\" word. It does seem that \"neverbeforeseen\" is more English-like than \"zqbhjhsyefvvjqc\", and so perhaps should have a higher probability.\n", + "\n", + "We can address this by assigning a non-zero probability to words that are not in the dictionary. This is even more important when it comes to multi-word phrases (such as bigrams), because it is more likely that a legitimate one will appear that has not been observed before.\n", + "\n", + "We can think of our model as being overly spiky; it has a spike of probability mass wherever a word or phrase occurs in the corpus. What we would like to do is *smooth* over those spikes so that we get a model that does not depend on the details of our corpus. The process of \"fixing\" the model is called *smoothing*.\n", + "\n", + "For example, Laplace was asked what's the probability of the sun rising tomorrow. From data that it has risen $n/n$ times for the last *n* days, the maximum liklihood estimator is 1. But Laplace wanted to balance the data with the possibility that tomorrow, either it will rise or it won't, so he came up with $(n + 1) / (n + 2)$.\n", + "\n", + "\n", + " \n", + " \n", + "\n", + "
What we know is little, and what we are ignorant of is immense.
— Pierre Simon Laplace, 1749-1827" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def pdist_additive_smoothed(counter, c=1):\n", + " \"\"\"The probability of word, given evidence from the counter.\n", + " Add c to the count for each item, plus the 'unknown' item.\"\"\"\n", + " N = sum(counter.values()) # Amount of evidence\n", + " Nplus = N + c * (len(counter) + 1) # Evidence plus fake observations\n", + " return lambda word: (counter[word] + c) / Nplus \n", + "\n", + "P1w = pdist_additive_smoothed(COUNTS1)" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.7003201005861308e-12" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P1w('neverbeforeseen')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But now there's a problem ... we now have previously-unseen words with non-zero probabilities. And maybe 10-12 is about right for words that are observed in text: that is, if I'm *reading* a new text, the probability that the next word is unknown might be around 10-12. But if I'm *manufacturing* 20-letter sequences at random, the probability that one will be a word is much, much lower than 10-12. \n", + "\n", + "Look what happens:" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['this',\n", + " 'is',\n", + " 'a',\n", + " 'test',\n", + " 'of',\n", + " 'segment',\n", + " 'at',\n", + " 'i',\n", + " 'on',\n", + " 'of',\n", + " 'along',\n", + " 'sequence',\n", + " 'of',\n", + " 'words']" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment.cache.clear()\n", + "segment('thisisatestofsegmentationofalongsequenceofwords')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are two problems:\n", + " \n", + "First, we don't have a clear model of the unknown words. We just say \"unknown\" but\n", + "we don't distinguish likely unknown from unlikely unknown. For example, is a 8-character unknown more likely than a 20-character unknown?\n", + "\n", + "Second, we don't take into account evidence from *parts* of the unknown. For example, \n", + "\"unglobulate\" versus \"zxfkogultae\".\n", + "\n", + "For our next approach, *Good - Turing* smoothing re-estimates the probability of zero-count words, based on the probability of one-count words (and can also re-estimate for higher-number counts, but that is less interesting).\n", + "\n", + "\n", + "\n", + "
I. J. Good (1916 - 2009)             Alan Turing (1812 - 1954)\n", + "\n", + "So, how many one-count words are there in `COUNTS`? (There aren't any in `COUNTS1`.) And what are the word lengths of them? Let's find out:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(7, 1357),\n", + " (8, 1356),\n", + " (9, 1176),\n", + " (6, 1113),\n", + " (10, 938),\n", + " (5, 747),\n", + " (11, 627),\n", + " (12, 398),\n", + " (4, 367),\n", + " (13, 215),\n", + " (3, 161),\n", + " (14, 112),\n", + " (2, 51),\n", + " (15, 37),\n", + " (16, 10),\n", + " (17, 7)]" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "singletons = (w for w in COUNTS if COUNTS[w] == 1)\n", + "\n", + "lengths = map(len, singletons)\n", + "\n", + "Counter(lengths).most_common()" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0012278198461651215" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1357 / sum(COUNTS.values())" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist(lengths, bins=len(set(lengths)));" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def pdist_good_turing_hack(counter, onecounter, base=1/26., prior=1e-8):\n", + " \"\"\"The probability of word, given evidence from the counter.\n", + " For unknown words, look at the one-counts from onecounter, based on length.\n", + " This gets ideas from Good-Turing, but doesn't implement all of it.\n", + " prior is an additional factor to make unknowns less likely.\n", + " base is how much we attenuate probability for each letter beyond longest.\"\"\"\n", + " N = sum(counter.values())\n", + " N2 = sum(onecounter.values())\n", + " lengths = map(len, [w for w in onecounter if onecounter[w] == 1])\n", + " ones = Counter(lengths)\n", + " longest = max(ones)\n", + " return (lambda word: \n", + " counter[word] / N if (word in counter) \n", + " else prior * (ones[len(word)] / N2 or \n", + " ones[longest] / N2 * base ** (len(word)-longest)))\n", + "\n", + "# Redefine P1w\n", + "P1w = pdist_good_turing_hack(COUNTS1, COUNTS)" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['this',\n", + " 'is',\n", + " 'a',\n", + " 'test',\n", + " 'of',\n", + " 'segment',\n", + " 'at',\n", + " 'i',\n", + " 'on',\n", + " 'of',\n", + " 'a',\n", + " 'very',\n", + " 'long',\n", + " 'sequence',\n", + " 'of',\n", + " 'words']" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "segment.cache.clear()\n", + "segment('thisisatestofsegmentationofaverylongsequenceofwords')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was somewhat unsatisfactory. We really had to crank up the prior, specifically because the process of running `segment` generates so many non-word candidates (and also because there will be fewer unknowns with respect to the billion-word `WORDS1` than with respect to the million-word `WORDS`). It would be better to separate out the prior from the word distribution, so that the same distribution could be used for multiple tasks, not just for this one.\n", + "\n", + "Now let's think for a short while about smoothing **bigram** counts. Specifically, what if we haven't seen a bigram sequence, but we've seen both words individually? For example, to evaluate P(\"Greenland\") in the phrase \"turn left at Greenland\", we might have three pieces of evidence:\n", + "\n", + " P(\"Greenland\")\n", + " P(\"Greenland\" | \"at\")\n", + " P(\"Greenland\" | \"left\", \"at\")\n", + " \n", + "Presumably, the first would have a relatively large count, and thus large reliability, while the second and third would have decreasing counts and reliability. With *interpolation smoothing* we combine all three pieces of evidence, with a linear combination:\n", + " \n", + "$P(w_3 \\mid w_1w_2) = c_1 P(w_3) + c_2 P(w_3 \\mid w_2) + c_3 P(w_3 \\mid w_1w_2)$\n", + "\n", + "How do we choose $c_1, c_2, c_3$? By experiment: train on training data, maximize $c$ values on development data, then evaluate on test data.\n", + " \n", + "However, when we do this, we are saying, with probability $c_1$, that a word can appear anywhere, regardless of previous words. But some words are more free to do that than other words. Consider two words with similar probability:" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "7.73314623661e-05\n", + "7.72494966889e-05\n" + ] + } + ], + "source": [ + "print P1w('francisco')\n", + "print P1w('individuals')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "They have similar unigram probabilities but differ in their freedom to be the second word of a bigram:" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['San francisco', 'san francisco']\n" + ] + } + ], + "source": [ + "print [bigram for bigram in COUNTS2 if bigram.endswith('francisco')]" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['are individuals', 'other individuals', 'on individuals', 'infected individuals', 'in individuals', 'where individuals', 'or individuals', 'which individuals', 'to individuals', 'both individuals', 'help individuals', 'more individuals', 'interested individuals', 'from individuals', ' individuals', 'income individuals', 'these individuals', 'about individuals', 'the individuals', 'among individuals', 'some individuals', 'those individuals', 'by individuals', 'minded individuals', 'These individuals', 'qualified individuals', 'certain individuals', 'different individuals', 'For individuals', 'few individuals', 'and individuals', 'two individuals', 'for individuals', 'between individuals', 'affected individuals', 'healthy individuals', 'private individuals', 'with individuals', 'following individuals', 'as individuals', 'such individuals', 'that individuals', 'all individuals', 'of individuals', 'many individuals']\n" + ] + } + ], + "source": [ + "print [bigram for bigram in COUNTS2 if bigram.endswith('individuals')]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Intuitively, words that appear in many bigrams before are more likely to appear in a new, previously unseen bigram. In *Kneser-Ney* smoothing (Reinhard Kneser, Hermann Ney) we multiply the bigram counts by this ratio. But I won't implement that here, because The Count never covered it.\n", + "\n", + "(10) One More Task: Secret Codes\n", + "===\n", + "\n", + "Let's tackle one more task: decoding secret codes. We'll start with the simplest of codes, a rotation cipher, sometimes called a shift cipher or a Caesar cipher (because this was state-of-the-art crypotgraphy in 100 BC). First, a method to encode:" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def rot(msg, n=13): \n", + " \"Encode a message with a rotation (Caesar) cipher.\" \n", + " return encode(msg, alphabet[n:]+alphabet[:n])\n", + "\n", + "def encode(msg, key): \n", + " \"Encode a message with a substitution cipher.\" \n", + " table = string.maketrans(upperlower(alphabet), upperlower(key))\n", + " return msg.translate(table) \n", + "\n", + "def upperlower(text): return text.upper() + text.lower() " + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Uijt jt b tfdsfu nfttbhf.'" + ] + }, + "execution_count": 97, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rot('This is a secret message.', 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'Guvf vf n frperg zrffntr.'" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rot('This is a secret message.', 13)" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'This is a secret message.'" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rot(rot('This is a secret message.'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now decoding is easy: try all 26 candidates, and find the one with the maximum Pwords:" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def decode_rot(secret):\n", + " \"Decode a secret message that has been encoded with a rotation cipher.\"\n", + " candidates = [rot(secret, i) for i in range(len(alphabet))]\n", + " return max(candidates, key=lambda msg: Pwords(tokens(msg)))" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nyf befnj kyv rejnvi?\n", + "Who knows the answer?\n" + ] + } + ], + "source": [ + "msg = 'Who knows the answer?'\n", + "secret = rot(msg, 17)\n", + "\n", + "print(secret)\n", + "print(decode_rot(secret))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make it a tiny bit harder. When the secret message contains separate words, it is too easy to decode by guessing that the one-letter words are most likely \"I\" or \"a\". So what if the encode routine mushed all the letters together:" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def encode(msg, key): \n", + " \"Encode a message with a substitution cipher; remove non-letters.\" \n", + " msg = cat(tokens(msg)) ## Change here\n", + " table = string.maketrans(upperlower(alphabet), upperlower(key))\n", + " return msg.translate(table) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can decode by segmenting. We change candidates to be a list of segmentations, and still choose the candidate with the best Pwords: " + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def decode_rot(secret):\n", + " \"\"\"Decode a secret message that has been encoded with a rotation cipher,\n", + " and which has had all the non-letters squeezed out.\"\"\"\n", + " candidates = [segment(rot(secret, i)) for i in range(len(alphabet))]\n", + " return max(candidates, key=lambda msg: Pwords(msg))" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "pahdghplmaxtglpxkmablmbfxtgrhgxunxeexk\n", + "['who', 'knows', 'the', 'answer', 'this', 'time', 'anyone', 'bu', 'e', 'll', 'er']\n" + ] + } + ], + "source": [ + "msg = 'Who knows the answer this time? Anyone? Bueller?'\n", + "secret = rot(msg, 19)\n", + "\n", + "print(secret)\n", + "print(decode_rot(secret))" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-123 p ah d g h p l max t g l p x km a bl mb f x t gr h g x un x e ex k\n", + "-133 q b i eh i q m n by u hm q y l n b cm n c g y u h s i h y vo y ff y l\n", + "-128 r c j f i jr no c z v in r z mo c d nod h z v it j i z w p z g g z m\n", + "-115 sd k g j k so p da w j os an p de op e i a w j u k j ax q ah h an\n", + "-144 t el h k l t p q e b x k p t b o q e f p q f j b x k v l k by r b ii b o\n", + "-145 u f m il m u q r f cy l qu c p r f g q r g k cy l wm l c z s c j j c p\n", + "-141 v g n j m n v r sg d z mr v d q sg h r s h l d z m x nm dat d k k d q\n", + "-39 who knows the answer this time anyone bu e ll er\n", + "-119 xi p l op x tu if b o t x f s u i j tu j n f b oz p of c v f mm f s\n", + "-151 y j q m p q y u v j g c p u y g t v j ku v k o g c pa q pg d w g n n g t\n", + "-151 z k r n q r z v w k h d q v z h u w k l v w l p h d q br q he x ho oh u\n", + "-97 also r saw x lie r w a iv x l m w x m q i er c s r if y i pp iv\n", + "-146 b mt p st b x y m j f s x b j w y m n x y n r j f sd t s j g z j q q j w\n", + "-137 c n u q tu cy z n k g ty c k x z no y z os k g t eut k ha k r r k x\n", + "-124 do v r u v d z a o l h u z d ly a op z apt l h u f v u li bl s sly\n", + "-121 e p w s v we ab pm iv a em z b p q ab qu m iv g w v m j cm t tm z\n", + "-142 f q x t w x f bc q n j w b fn a c q r bc r v n j wh x w n k d n u un a\n", + "-119 gr y u x y g c dr ok x c go b dr s c d s w ok xi y x o leo v vo b\n", + "-119 h s z vy z h des ply d h p c est de t x ply j z y pm f p w w p c\n", + "-137 it a w z a i e ft q m ze i q d f tu e f u y q m z ka z q n g q xx q d\n", + "-130 j u b x ab j f g u r na f jr eg u v f g v z r n alba r oh r y y re\n", + "-125 k v cy bc k g h v sob g k s f h v w g h was o b m c b s p is z z s f\n", + "-130 l w d z c d l hi w t p ch l t g i w x h ix b t p c nd c t q j t a at g\n", + "-123 m x e a dem i j x u q dim u h j x y i j y c u q doe du r ku b bu h\n", + "-124 ny f be fn j k y v re j n vi k y z j k z d v rep fe vs l v c c vi\n", + "-134 oz g cf go k l z w s f k o w j l z ak la e w s f q g f w tm w d d w j\n" + ] + } + ], + "source": [ + "candidates = [segment(rot(secret, i)) for i in range(len(alphabet))]\n", + "\n", + "for c in candidates:\n", + " print int(log10(Pwords(c))), ' '.join(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What about a general substitution cipher? The problem is that there are 26! substitution ciphers, and we can't enumerate all of them. We would need to search through this space. Initially make some guess at a substitution, then swap two letters; if that looks better keep going, if not try something else. This approach solves most substitution cipher problems, although it can take a few minutes on a message of length 100 words or so.\n", + "\n", + "(∞ and beyond) Where To Go Next\n", + "===\n", + "\n", + "What to do next? Here are some options:\n", + " \n", + "- **Spelling correction**: Use bigram or trigram context; make a model of spelling errors/edit distance; go beyond edit distance 2; make it more efficient\n", + "- **Evaluation**: Make a serious test suite; search for best parameters (e.g. $c_1, c_2, c_3$)\n", + "- **Smoothing**: Implement Kneser-Ney and/or Interpolation; do letter *n*-gram-based smoothing\n", + "- **Secret Codes**: Implement a search over substitution ciphers\n", + "- **Classification**: Given a corpus of texts, each with a classification label, write a classifier that will take a new text and return a label. Examples: spam/no-spam; favorable/unfavorable; what author am I most like; reading level.\n", + "- **Clustering**: Group data by similarity. Find synonyms/related words.\n", + "- **Parsing**: Representing nested structures rather than linear sequences of words. relations between parts of the structure. Implicit missing bits. Inducing a grammar.\n", + "- **Meaning**: What semantic relations are meant by the syntactic relations?\n", + "- **Translation**: Using examples to transform one language into another.\n", + "- **Question Answering**: Using examples to transfer a question into an answer, either by retrieving a passage, or by synthesizing one.\n", + "- **Speech**: Dealing with analog audio signals rather than discrete sequences of characters." + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'congratulations'" + ] + }, + "execution_count": 110, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "correct('cpgratulations')" + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Life.ipynb b/pytudes/ipynb/Life.ipynb new file mode 100644 index 0000000..060437f --- /dev/null +++ b/pytudes/ipynb/Life.ipynb @@ -0,0 +1,836 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# John Conway's Game of Life\n", + "\n", + "The cellular automata game *Life*, invented by the mathematician [John Conway](https://en.wikipedia.org/wiki/John_Horton_Conway), makes a fun programming exercise. Let's review the [rules](http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life):\n", + "\n", + "The *world* of the Game of Life is an infinite two-dimensional orthogonal grid of *cells*, each of which is in one of two possible states, *live* or *empty*. Each cell has eight *neighbors*, the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following rules are applied to create the next *generation*:\n", + "\n", + "+ Any live cell with two or three live neighbors lives on to the next generation.\n", + "+ Any empty cell with exactly three live neighbors becomes a live cell in the next generation.\n", + "+ All other cells are empty in the next generation.\n", + "\n", + "For example, in the diagram below, \"`@`\" cells are live. In the transition from Generation 0 to 1, the cell marked \"`,`\" becomes empty (dies off) because it has zero live neighbors. In the next transition, a fourth `@` becomes live, because it has 3 live neighbors. All other cells stay the same. \n", + "\n", + " . . . . . . . . . . . . . . .\n", + " . . . @ . . . . , . . . . . .\n", + " . @ . . . . @ . . . . @ @ . .\n", + " . @ @ . . . @ @ . . . @ @ . .\n", + " . . . . . . . . . . . . . . .\n", + " Gen 0 Gen 1 Gen 2\n", + " \n", + "\n", + "\n", + "The world continues to evolve by these rules for as long as you care to observe. \n", + "\n", + "# Developing a Life Program\n", + "\n", + "\n", + "To create a program to play Life, start with the vocabulary of concepts:\n", + "\n", + "+ **World**\n", + "+ **Cell**\n", + "+ **Live/Empty**\n", + "+ **Neighbors**\n", + "+ **Next Generation**\n", + "+ **Display**\n", + "+ **Live Neighbor Counts**\n", + "\n", + "and consider how to implement them:\n", + "\n", + "+ **World**: The state of the world must represent which cells are empty and which are live. The tricky part is that the number of cells is infinite, and we can't store an infinite array in a finite computer. I can think of three ways to deal with this problem:\n", + " 1. **Change the rules**; make the world finite instead of infinite. (Cells at the edge of the world have fewer neighbors, or perhaps they wrap around to the other side of the world.)\n", + " 2. Use a **finite rectangular window** that covers all the live cells in the infinite grid. As the world\n", + " evolves, this window may have to grow or shift.\n", + "
Example: `world = [[0, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 1, 1, 0, 0], [0, 0, 0, 0, 0]]` \n", + "\n", + " 3. Represent a world as a **set of live cells.** This set will grow and shrink in size from one generation to the next, but we don't have to worry about overflowing the edges of an array.\n", + "
Example: `world = {(3, 1), (1, 2), (1, 3), (2, 3)}` \n", + "
I will go with this choice.\n", + "\n", + "\n", + "+ **Cell**: Each cell will be represented as an (x, y) pair of integer coordinates.
Example: `cell = (1, 2)`.\n", + "+ **Live/Empty**: \n", + "A cell is live if it is a member of the set of live cells. \n", + "
Example: \"`cell in world`\" is True, given the definition of `cell` and `world` above, so `cell` is live.\n", + "+ **Neighbors**: The cell `(x, y)` has eight neighbors, formed by adding or subtracting 1 from `x` or `y` or both. We can define\n", + "a function `neighbors(cell)` to return this set.\n", + "
Example: `neighbors((8, 8)) == [(7, 7), (8, 7), (9, 7), (7, 8), (9, 8), (7, 9), (8, 9), (9, 9)]`\n", + "\n", + "+ **Display**: We will need some way to display the state of the world. Let's defer that for now.\n", + "\n", + "+ **Next Generation**: We can define a function, `next_generation(world)`, that takes a world as input and returns\n", + "a new world with the new set of live cells according to the rules.\n", + "Example: `next_generation({(3, 1), (1, 2), (1, 3), (2, 3)}) == {(1, 2), (1, 3), (2, 3)}`\n", + "\n", + "+ **Live Neighbor Counts**: I need to know how many live neighbors each cell has. A good way to represent this is a dict of `{(x, y): count}`. But which cells need to be the keys of this dict? We can start with the live cells, and also add any cells neighboring the live cells. An easy way to generate this dict is to create a `Counter` and pass it every neighbor of every live cell. This may feel like we're doing the counting \"backwards.\" Instead of asking \"for each cell, how many live neighbors does it have?\" we are saying \"for each live cell, increment the count of each of its neighbors.\" The two amount to the same thing because *neighbor* is symmetric—if P is a neighbor of Q, then Q is a neighbor of P. Below we see the neighbor counts for each of the three generations; in each generation the top diagram gives the neighbor counts for the empty cells, and the bottom diagram gives the counts for the live cells. This is just to make the diagram easier to read; in the code these are combined into one `Counter`. Here are the counts:\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + " . . 1 1 1 . . . . . . . . . .\n", + " 1 1 2 @ 1 1 1 1 , . 1 2 2 1 .\n", + " 2 @ 4 2 1 2 @ 3 1 . 2 @ @ 2 .\n", + " 2 @ @ 1 . 2 @ @ 1 . 2 @ @ 2 .\n", + " 1 2 2 1 . 1 2 2 1 . 1 2 2 1 .\n", + " Gen 0 Gen 1 Gen 2\n", + " . . . . . . . . . . . . . . .\n", + " . . . 0 . . . . , . . . . . .\n", + " . 2 . . . . 2 . . . . 3 3 . .\n", + " . 2 2 . . . 2 2 . . . 3 3 . .\n", + " . . . . . . . . . . . . . . .\n", + " \n", + "\n", + "Here is the implementation. Note that in `next_generation` the `neighbor_counts` is used two ways so I decided to use two different names for clarity: `possible_cells` is used to iterate over all cells that might be live, and `counts` is used to check if a cell has the right number of neighbors." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from collections import Counter\n", + "\n", + "def next_generation(world):\n", + " \"The set of live cells in the next generation.\"\n", + " possible_cells = counts = neighbor_counts(world)\n", + " return {cell for cell in possible_cells\n", + " if (counts[cell] == 3) \n", + " or (counts[cell] == 2 and cell in world)}\n", + "\n", + "def neighbor_counts(world):\n", + " \"A {cell: int} counter of the number of live neighbors for each cell that has neighbors.\"\n", + " return Counter(nb for cell in world \n", + " for nb in neighbors(cell))\n", + "\n", + "def neighbors(cell):\n", + " \"All 8 adjacent neighbors of cell.\"\n", + " (x, y) = cell\n", + " return [(x-1, y-1), (x, y-1), (x+1, y-1), \n", + " (x-1, y), (x+1, y), \n", + " (x-1, y+1), (x, y+1), (x+1, y+1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see how this works:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2), (1, 3), (2, 3)}" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "world = {(3, 1), (1, 2), (1, 3), (2, 3)}\n", + "next_generation(world)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2), (1, 3), (2, 2), (2, 3)}" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "next_generation(next_generation(world))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 3), (2, 3), (3, 3), (1, 4), (3, 4), (1, 5), (2, 5), (3, 5)]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "neighbors((2, 4))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({(0, 1): 1,\n", + " (0, 2): 2,\n", + " (0, 3): 2,\n", + " (0, 4): 1,\n", + " (1, 1): 1,\n", + " (1, 2): 2,\n", + " (1, 3): 2,\n", + " (1, 4): 2,\n", + " (2, 0): 1,\n", + " (2, 1): 2,\n", + " (2, 2): 4,\n", + " (2, 3): 2,\n", + " (2, 4): 2,\n", + " (3, 0): 1,\n", + " (3, 2): 2,\n", + " (3, 3): 1,\n", + " (3, 4): 1,\n", + " (4, 0): 1,\n", + " (4, 1): 1,\n", + " (4, 2): 1})" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "neighbor_counts(world)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`run` is a function to play n generations of Life:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def run(world, n):\n", + " \"Run the world for n generations. No display; just return the nth generation.\"\n", + " for g in range(n):\n", + " world = next_generation(world)\n", + " return world" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2), (1, 3), (2, 2), (2, 3)}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "run(world, 100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Display\n", + "\n", + "Now let's see how to display worlds. We'll consider a rectangular window on the infinite plane, specified as ranges of `Xs` and `Ys` coordinates. The function `picture` turns a world into a string showing what the world looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "from IPython.display import clear_output, display_html\n", + "\n", + "LIVE = '@'\n", + "EMPTY = '.'\n", + "PAD = ' '\n", + " \n", + "def picture(world, Xs, Ys):\n", + " \"Return a picture: a grid of characters representing the cells in this window.\"\n", + " def row(y): return PAD.join(LIVE if (x, y) in world else EMPTY for x in Xs)\n", + " return '\\n'.join(row(y) for y in Ys)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ". . . . .\n", + ". . . @ .\n", + ". @ . . .\n", + ". @ @ . .\n", + ". . . . .\n" + ] + } + ], + "source": [ + "print(picture(world, range(5), range(5)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `display_run` runs the world for `n` steps, displaying the picture at each step:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def display_run(world, n=10, Xs=range(10), Ys=range(10), pause=0.2):\n", + " \"Step and display the world for the given number of generations.\"\n", + " for g in range(n + 1):\n", + " html = ('Generation {}, Population {}\\n{}'\n", + " .format(g, len(world), pre(picture(world, Xs, Ys))))\n", + " clear_output()\n", + " display_html(html, raw=True)\n", + " time.sleep(pause)\n", + " world = next_generation(world)\n", + " \n", + "def pre(text): return '
' + text + '
'" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 5, Population 4\n", + "
. . . . .\n",
+       ". . . . .\n",
+       ". @ @ . .\n",
+       ". @ @ . .\n",
+       ". . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(world, 5, range(5), range(5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Interesting Worlds\n", + "\n", + "Now let's take a look at some initial worlds that *Life* enthusiasts have discovered. It would be tedious to enumerate these with an explicit set of `(x, y)` coordinates, so we will define the function `shape` that takes a picture as input and returns a world; `shape` and `picture` are more-or-less inverses. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def shape(picture, offset=(3, 3)):\n", + " \"Convert a graphical picture (e.g. '@ @ .\\n. @ @') into a world (set of cells).\"\n", + " cells = {(x, y) \n", + " for (y, row) in enumerate(picture.splitlines())\n", + " for (x, c) in enumerate(row.replace(PAD, ''))\n", + " if c == LIVE}\n", + " return move(cells, offset)\n", + "\n", + "def move(cells, offset):\n", + " \"Move/Translate/slide a set of cells by a (dx, dy) displacement/offset.\"\n", + " (dx, dy) = offset\n", + " return {(x+dx, y+dy) for (x, y) in cells}\n", + "\n", + "blinker = shape(\"@@@\")\n", + "block = shape(\"@@\\n@@\")\n", + "beacon = block | move(block, (2, 2))\n", + "toad = shape(\".@@@\\n@@@.\")\n", + "glider = shape(\".@.\\n..@\\n@@@\")\n", + "rpentomino = shape(\".@@\\n@@.\\n.@.\", (36, 20))\n", + "line = shape(\".@@@@@@@@.@@@@@...@@@......@@@@@@@.@@@@@\", (10, 10))\n", + "growth = shape(\"@@@.@\\n@\\n...@@\\n.@@.@\\n@.@.@\", (10, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is how `shape` and `move` work:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(3, 3), (4, 3), (4, 4), (5, 4)}" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "shape(\"\"\"@ @ .\n", + " . @ @\"\"\")" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(3, 3), (3, 4), (4, 3), (4, 4)}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "block" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{(103, 203), (103, 204), (104, 203), (104, 204)}" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "move(block, (100, 200))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's run some examples. If you are viewing a static notebook, you will only see the last generation; rerun each cell to see all the generations." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 10, Population 3\n", + "
. . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . @ @ @ . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(blinker)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 10, Population 8\n", + "
. . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . @ @ . . . . .\n",
+       ". . . @ @ . . . . .\n",
+       ". . . . . @ @ . . .\n",
+       ". . . . . @ @ . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(beacon)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 10, Population 6\n", + "
. . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . @ @ @ . . .\n",
+       ". . . @ @ @ . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .\n",
+       ". . . . . . . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(toad)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 15, Population 5\n", + "
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+       ". . . . . . . @ @ .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(glider, 15)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 130, Population 178\n", + "
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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(rpentomino, 130, range(48), range(40))" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 160, Population 111\n", + "
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+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "zoo = (move(blinker, (5, 25)) | move(glider, (8, 13)) | move(blinker, (20, 25)) |\n", + " move(beacon, (24, 25)) | move(toad, (30, 25)) | move(block, (13, 25)) | move(block, (17, 33)))\n", + "\n", + "display_run(zoo, 160, range(48), range(40))" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "Generation 100, Population 72\n", + "
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+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n",
+       ". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display_run(growth, 100, range(40), range(40))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Outside of IPython\n", + "\n", + "If you want to run this code in your terminal, outside of an Ipython/Jupyter notebook, you can remove the line:\n", + "\n", + " from IPython.display import clear_output, display_html\n", + " \n", + "and add these lines:\n", + "\n", + " def clear_output(): print(\"\\033[;H\\033[2J\") # ANSI terminal home and clear\n", + " \n", + " def display_html(text, raw=False): print(text)\n", + " \n", + " def pre(text): return text\n", + " \n", + "# Coding Kata\n", + "\n", + "I once attended a [code kata](https://en.wikipedia.org/wiki/Kata_(programming%29) in which one of the exercises was to write the Game of Life without using any conditional (e.g. `if`) statements. I did it by using roughly the program shown here, but changing the lone `if` to a `filter` in `next_generation`:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "def next_generation(world):\n", + " \"The set of live cells in the next generation.\"\n", + " possible_cells = counts = neighbor_counts(world)\n", + " def good(cell): return counts[cell] == 3 or (counts[cell] == 2 and cell in world)\n", + " return set(filter(good, possible_cells))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Mean Misanthrope Density.ipynb b/pytudes/ipynb/Mean Misanthrope Density.ipynb new file mode 100644 index 0000000..73a1b44 --- /dev/null +++ b/pytudes/ipynb/Mean Misanthrope Density.ipynb @@ -0,0 +1,1075 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Puzzle of the Misanthropic Neighbors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider [this puzzle](http://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/) from [The Riddler](http://fivethirtyeight.com/tag/the-riddler/):\n", + " \n", + "> *The misanthropes are coming. Suppose there is a row of some number, N, of houses in a new, initially empty development. Misanthropes are moving into the development one at a time and selecting a house at random from those that have nobody in them and nobody living next door. They keep on coming until no acceptable houses remain. At most, one out of two houses will be occupied; at least one out of three houses will be. But what’s the expected fraction of occupied houses as the development gets larger, that is, as N goes to infinity?*\n", + "\n", + "# Consider *N*=4 Houses\n", + "\n", + "![N houses](http://www.publicdomainpictures.net/pictures/180000/nahled/street-doodle.jpg)\n", + "\n", + "To make sure we understand the problem, let's try a simple example, with *N*=4 houses. We will represent the originally empty row of four houses by four dots:\n", + "\n", + " ....\n", + " \n", + "Now the first person chooses one of the four houses (which are all acceptable). We'll indicate an occupied house by a `1`, so the four equiprobable choices are:\n", + "\n", + " Choice 0: 1...\n", + " Choice 1: .1..\n", + " Choice 2: ..1.\n", + " Choice 3: ...1\n", + " \n", + "When a house is occupied, any adjacent houses become unacceptable. We'll indicate that with a `0`:\n", + "\n", + " Choice 0: 10..\n", + " Choice 1: 010.\n", + " Choice 2: .010\n", + " Choice 3: ..01\n", + " \n", + "In all four cases, a second occupant has a place to move in, but then there is no place for a third occupant. \n", + "The occupancy is 2 in all cases, and thus the *expected occpancy* is 2. The occupancy fraction, or *density*, is 2/*N* = 2/4 = 1/2.\n", + " \n", + "\n", + "# Consider *N*=7 Houses\n", + "\n", + "With *N*=7 houses, there are 7 equiprobable choices for the first occupant:\n", + "\n", + " Choice 0: 10.....\n", + " Choice 1: 010....\n", + " Choice 2: .010...\n", + " Choice 3: ..010..\n", + " Choice 4: ...010.\n", + " Choice 5: ....010\n", + " Choice 6: .....01\n", + " \n", + "Now we'll add something new: the lengths of the **runs** of consecutive acceptable houses to the left and right of the chosen house:\n", + "\n", + " Choice 0: 10..... runs = (0, 5)\n", + " Choice 1: 010.... runs = (0, 4)\n", + " Choice 2: .010... runs = (1, 3) \n", + " Choice 3: ..010.. runs = (2, 2) \n", + " Choice 4: ...010. runs = (3, 1) \n", + " Choice 5: ....010 runs = (4, 0) \n", + " Choice 6: .....01 runs = (5, 0) \n", + " \n", + "# Defining `occ(n)`\n", + "\n", + "This gives me a key hint as to how to analyze the problem. I'll define `occ(n)` to be the expected number of occupied houses in a row of `n` houses. So:\n", + "\n", + " Choice 0: 10..... runs = (0, 5); occupancy = occ(0) + 1 + occ(5)\n", + " Choice 1: 010.... runs = (0, 4); occupancy = occ(0) + 1 + occ(4)\n", + " Choice 2: .010... runs = (1, 3); occupancy = occ(1) + 1 + occ(3)\n", + " Choice 3: ..010.. runs = (2, 2); occupancy = occ(2) + 1 + occ(2)\n", + " Choice 4: ...010. runs = (3, 1); occupancy = occ(3) + 1 + occ(1)\n", + " Choice 5: ....010 runs = (4, 0); occupancy = occ(4) + 1 + occ(0)\n", + " Choice 6: .....01 runs = (5, 0); occupancy = occ(5) + 1 + occ(0) \n", + " \n", + "So we can say that `occ(n)` is:\n", + "\n", + "- 0 when `n` is 0 (because no houses means no occupants),\n", + "- 1 when `n` is 1 (because one isolated acceptable house has one occupant),\n", + "- else the mean, over the `n` choices for the first occupied house,\n", + "of the sum of that house plus the occupancy of the runs to the left and right.\n", + "\n", + "We can implement that:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from statistics import mean\n", + "\n", + "def occ(n):\n", + " \"The expected occupancy for a row of n houses (under misanthrope rules).\"\n", + " return (0 if n == 0 else\n", + " 1 if n == 1 else\n", + " mean(occ(L) + 1 + occ(R)\n", + " for (L, R) in runs(n)))\n", + "\n", + "def runs(n):\n", + " \"\"\"A list [(L, R), ...] where the i-th tuple contains the lengths of the runs\n", + " of acceptable houses to the left and right of house i.\"\"\"\n", + " return [(max(0, i - 1), max(0, n - i - 2))\n", + " for i in range(n)]\n", + "\n", + "def density(n): return occ(n) / n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's check that `occ(4)` is 2, as we computed it should be, and for other small values, up to 7:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 0,\n", + " 1: 1,\n", + " 2: 1,\n", + " 3: 1.6666666666666667,\n", + " 4: 2,\n", + " 5: 2.466666666666667,\n", + " 6: 2.888888888888889,\n", + " 7: 3.323809523809524}" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{n: occ(n) for n in range(8)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks good, although I can't prove the value above 4 are ccorrect. Now check that `runs(7)` is what we described above:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0, 5), (0, 4), (1, 3), (2, 2), (3, 1), (4, 0), (5, 0)]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "runs(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Dynamic Programming Version of `occ`\n", + "\n", + "The computation of `occ(n)` makes multiple calls to `occ(n-1), occ(n-2),` etc. To avoid re-computing the same calls over and over, we will modify `occ` to save previous results using [dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming). I could implement that in one line with the decorator [`@functools.lru_cache`](https://docs.python.org/3/library/functools.html#functools.lru_cache), but then I would have to worry about the recursion limit. Instead I will explicitly manage a list, `cache`, such that `cache[n]` holds `occ(n)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def occ(n, cache=[0, 1]):\n", + " \"The expected occupancy for a row of n houses (under misanthrope rules).\"\n", + " # Store occ(i) in cache[i] for all as-yet-uncomputed values of i up to n:\n", + " for i in range(len(cache), n+1):\n", + " cache.append(mean(cache[L] + 1 + cache[R]\n", + " for (L, R) in runs(i)))\n", + " return cache[n]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make sure this new version gets the same results as the old version:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "occ(4) == 2" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.323809523809524" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "occ(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's make sure the caching makes computation pretty fast the first time, and *very* fast the second time:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2.68 s, sys: 13.5 ms, total: 2.7 s\n", + "Wall time: 2.71 s\n" + ] + }, + { + "data": { + "text/plain": [ + "864.9617138385324" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time occ(2000)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 4 µs, sys: 0 ns, total: 4 µs\n", + "Wall time: 5.01 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "864.9617138385324" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time occ(2000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Plotting `density(n)`\n", + "\n", + "To get a feel for the limit of `density(n)`, start by drawing a plot over some small values of `n`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('fivethirtyeight')\n", + "\n", + "def plot_density(ns):\n", + " \"Plot density(n) for each n in the list of numbers ns.\"\n", + " plt.xlabel('n houses'); plt.ylabel('density(n)')\n", + " plt.plot(ns, [density(n) for n in ns], 's-')\n", + " return density(ns[-1])" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4353323288377046" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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OwbKXLl2Co6Ojxo+TkxNOnz5t8vX0vYfYxUEEx3Yi9Oqi2UPkc0QiImGw+uTe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\nwqnLzMxESEiIdSplQxYvXqw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_density(range(1, 100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is something funny going on with the first few values of `n`. Let's separately look at the first few:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.46203174603174607" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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RE7PpJ/jatWubqw6Hp1YpTQLwhEaLv7TzkLAiIiK6GZwJpokspkRjT1AiIqfWYAB+8803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\nzZs3W7yHSqXCsmXLjNtlZWV44YUXEBM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HHntMeP3EiRPCQyXozo22ZhgTEfUHBoXx4sWL8e6778LNzQ1PPPEEUlNTYWpq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\nTIZhw4YhNjZWCHgAqKqqwl/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_density(range(100, 4000, 50))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The density is going down, and the curve is almost but not quite flat. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "# lim n → ∞ density(n)\n", + "\n", + "[The puzzle](http://fivethirtyeight.com/features/can-you-solve-the-puzzle-of-your-misanthropic-neighbors/)\n", + "is to figure out the limit of `density(n)` as `n` goes to infinity. The plot above makes it look like 0.432+something, but we can't answer the question just by plotting; we'll need to switch modes from *computational* thinking to *mathematical* thinking.\n", + "\n", + "At this point I started playing around with `density(n)`, looking at various values, differences of values, ratios of values, and ratios of differences of values, hoping to achieve some mathematical insight. Mostly I got dead ends.\n", + "But eventually I hit on something promising. I looked at the difference between density values (using the function `diff`), and particularly the difference as you double `n`:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0014849853757253895" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def diff(n, m): return density(n) - density(m)\n", + "\n", + "diff(100, 200)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And compared that to the difference when you double `n` again:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.0007424926878626947" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(200, 400)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Hmm—I noticed that the first difference is just about twice as much as the second. Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.0" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(100, 200) / diff(200, 400)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wow—not only is it *close* to twice as much, it is *exactly* twice as much (to the precision of floating point numbers). Let's try other starting values for `n`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.0" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n = 250; diff(n, 2*n) / diff(2*n, 4*n)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "2.0" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n = 500; diff(n, 2*n) / diff(2*n, 4*n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "OK, I'm convinced this is real! \n", + "\n", + "Now, what mathematical function behaves like this? I figured out that *f*(*n*) = (1 / *n*) does. The ratio of the differences would be:\n", + "\n", + "$$\\frac{f(n) - f(2n)}{f(2n) - f(4n)} = \\frac{1/n - 1/(2n)}{1/(2n) - 1 / (4n)}\\;\\;$$\n", + "\n", + "Multiplying top and bottom by *n* you get:\n", + "\n", + "\n", + "$$\\frac{1 - 1/2}{1/2 - 1 /4} = \\frac{1/2}{1/4} = 2\\;\\;$$\n", + "\n", + "If the function (1 / *n*) fits the pattern, then so does any *affine transformation* of (1 / *n*), because we are taking the ratio of differences. So that means a density function of the form\n", + "\n", + " density(n) = A + B / n \n", + " \n", + "would fit the patterm. I can try a `scipy.optimize.curve_fit` to estimate the parameters *A* and *B*:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 4.70916321e-33, -1.30373854e-30],\n", + " [ -1.30373854e-30, 1.44885627e-27]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from scipy.optimize import curve_fit\n", + "\n", + "Ns = list(range(100, 5001, 100))\n", + "\n", + "def f(n, A, B): return A + B / n\n", + "\n", + "((A, B), covariance) = curve_fit(f=f, xdata=Ns, ydata=[density(n) for n in Ns])\n", + "\n", + "covariance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `curve_fit` function returns a sequence of parameter values, and a covariance matrix. The fact that all the numbers in the covariance matrix are really small indicates that the parameters are a really good fit. Here are the parameters, `A` and `B`:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.43233235838169332, 0.29699707514503415)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A, B" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can plug them into a function that estimates the density:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "def estimated_density(n): return A + B / n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can test how close this function is to the true `density` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "6.106226635438361e-16" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(abs(density(n) - estimated_density(n))\n", + " for n in range(200, 4000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That says that, for all values of `n` from 200 to 4,000, `density(n)` and `estimated_density(n)` agree at least through the first 15 decimal places!\n", + "\n", + "We now have a plausible answer to the puzzle:\n", + "\n", + "> lim n→∞ density(n) ≅ A = 0.43233235838169" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Why?\n", + "\n", + "Theis answer is empirically strong (15 decimal places of accuracy) but theoretically weak: we don't have a **proof**, and we don't have an explanation for **why** the density function has this form. We need some more mathematical thinking. \n", + "\n", + "I didn't have any ideas, so I looked to see if anyone else had written something about the number 0.432332358169 I tried several searches and found two interesting formulas:\n", + "\n", + "- Search: [`[0.4323323]`](https://www.google.com/search?q=0.4323323) Formula: `sinh(1) / exp(1)` [(Page)](http://arxiv.org/pdf/1310.4360.pdf)\n", + "- Search: [`[0.432332358]`](https://www.google.com/search?q=0.432332358) Formula: `0.5(1-e^(-2))` [(Page)](http://www.actuarialoutpost.com/actuarial_discussion_forum/archive/index.php/t-52095.html)\n", + "\n", + "I can verify that the two formulas are equivalent, and that they are indeed equal to `A` to at least 15 decimal places:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.43233235838169365, 0.43233235838169365, 0.43233235838169332)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from math import sinh, exp, e\n", + "\n", + "S = sinh(1) / exp(1)\n", + "E = 0.5 * (1 - e ** (-2))\n", + "\n", + "S, E, A" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So I now have a suspicion that\n", + "\n", + "> lim n → ∞ density(n) = (1 - e-2) / 2\n", + "\n", + "but I still have no proof, nor any intuition as to why this is so." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# John Lamping to the Rescue\n", + "\n", + "I reported my results to Anne Paulson and John Lamping, who had originally related the problem to me, and the next day John wrote back with the following:\n", + "\n", + "
\n", + "I got a derivation of the formula!\n", + "\n", + "

Suppose that each house has a different \"attractiveness\", and that when it is a misanthrope's turn to pick a house, they consider the houses in order, from most attractive to least, and pick the first house not next to any other house. If the attractiveness are chosen independently, this process gives the same probabilities as each misanthrope picking from the available houses randomly.\n", + "\n", + "

To be more concrete, let the attractivenesses range from 0 to 1 with uniform probability, with lower numbers being being considered earlier, and hence more attractive. (This makes the math come out easier.)\n", + "\n", + "

Given the attractiveness, a, of a house, we can compute the chance that it will end up getting picked. It will get picked if and only if neither house on either side gets considered earlier and gets picked. Lets consider one side, and assume the houses, and their attractivenesses, are labeled a, b, c, d, e, f, g, ... with the house we are considering being a. There are an infinite number of cases where b won't get considered before a and picked. Here are the first few:\n", + "\n", + "

a < b (a is considered before b)\n", + "

a > b > c < d (Someone considered c first among these 4 and picked it. A later person considered b before a, but rejected it because c had already been chosen.)\n", + "

a > b > c > d > e < f (Someone considered e first among these 6, and picked it. A later person considered d, but rejected it because e was chosen, then considered c, which they picked. Still later, someone considered b, which they rejected because c had been chosen.)\n", + "\n", + "

We can write down the probabilities of these cases as a function of the attractiveness of a:\n", + "\n", + "

a < b: The chance that b is greater than a: 1 - a.\n", + "

a > b > c < d: Let y = a - c, so y is between 0 and a. The probability is the integral over the possible y of the chance that b is between a and c, times the chance that d is greater than c, or integral from 0 to a of y * (1 - a + y) dy.\n", + "

a > b > c > d > e < f: Let y = a - e. The probability is the integral of (the chance that b, c, and d are all between a and e, and ordered right, which is y^3 / 3!, times the chance that f is greater than e, which is (1 - a + y))\n", + "\n", + "

If you work out the definite integrals, you get\n", + "\n", + "

a < b: 1 - a\n", + "

a > b > c < d: a^2 / 2 - a^3 / 3!\n", + "

a > b > c > d > e < f: a^4 / 4! - a^5 / 5!\n", + "\n", + "

Add them all up, and you have 1 - a + a^2 / 2 - a^3 / 3! + a ^4 / 4! ... the Taylor expansion for e^-a. \n", + "\n", + "

Now, there will be a house at a if both adjacent houses are not picked earlier, so the chance is the square of the chance for one side: e^(-2a). Integrate that from 0 to 1, and you get 1/2 (1 - e^-2).\n", + "

\n", + "\n", + "You can compare John Lamping's solution to the solutions by [Jim Ferry](http://fivethirtyeight.com/features/the-perplexing-puzzle-of-the-proud-partygoers/) and [Andrew Mascioli](http://andrewmascioli.com/index.php/2016/04/24/the-misanthropic-neighborhood/). \n", + "\n", + "# Styles of Thinking\n", + "\n", + "It is clear that different write-ups of this problem display different styles of thinking. I'll attempt to name and describe them:\n", + "\n", + "- **Mathematical Publication Style**: This style uses sophisticated mathematics (e.g. generating functions, differentiation, asymptotic analysis, and manipulation of summations). It defines new abstractions without\n", + "necessarily trying to motivate them first, it is terse and formal, and it gets us to the conclusion in a way that is\n", + "clearly correct, but does not describe all the steps of how the author came up with the ideas. (Ferry and Mascioli)\n", + "- **Mathematical Exploration Style**: Like the Mathematical Publication Style, but with more explanatory prose. (Lamping)\n", + "- **Computational Thinking**: A more concrete style; tends to use programs with specific values of `n` rather than \n", + "creating a proof for all values of `n`; produces tables or plots to help guide intuition; verifies results\n", + "with tests or alternative implementations. (Norvig)\n", + "\n", + "In this specific puzzle, my steps were:\n", + "- Analyze the problem and implement code to solve it for small values of `n`.\n", + "- Plot results and examine them for insight.\n", + "- Play with the results and get a guess at a partial solution density(n) ≅ A + B / n.\n", + "- Solve numerically for `A` and `B`.\n", + "- Do a search with the numeric value of `A` to find a formula with that value.\n", + "- Given that formula, let Lamping figure out how it corresponds to the problem.\n", + "\n", + "This is mostly computational thinking, with a little mathematical thrown in. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Validation by Anticipating Objections\n", + "\n", + "Is our implementation of `occ(n)` correct? I think it is, but I can anticipate some objections and answer them:\n", + "\n", + "- *In `occ(n)`, is it ok to start from all empty houses, rather than considering layouts of partially-occupied houses?* Yes, because the problem states that initially all houses are empty, and each choice of a house breaks the street up into runs of acceptable houses, flanked by unacceptable houses. If we get the computation right for a run of `n` acceptable houses, then we can get the whole answer right. A key point is that the chosen first house breaks the row of houses into 2 runs of *acceptable* houses, not 2 runs of *unoccupied* houses. If it were unoccupied houses, then we would have to also keep track of whether there were occupied houses to the right and/or left of the runs. By considering runs of acceptable houses, eveything is clean and simple.\n", + "\n", + "- *In `occ(7)`, if the first house chosen is 2, that breaks the street up into runs of 1 and 3 acceptable houses. There is only one way to occupy the 1 house, but there are several ways to occupy the 3 houses. Shouldn't the average give more weight to the 3 houses, since there are more possibilities there?* No. We are calculating occupancy, and there is a specific number (5/3) which is the expected occupancy of 3 houses; it doesn't matter if there is one combination or a million combinations that contribute to that expected value, all that matters is what the expected value is.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Validation by Simulation\n", + "\n", + "\n", + "A simulation can add credence to our implementation of `density(n)`, for two reasons:\n", + "- The code for the simulation can have a more direct correspondance to the problem statement.\n", + "- When two very different implementations get the same result, that is evidence supporting both of them.\n", + "\n", + "\n", + "The simulation will start with an empty set of occupied houses. We then go through the houses in random order, occupying just the ones that have no neighbor. (Note that `random.sample(range(n), n)` gives a random ordering of `range(n)`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "\n", + "def simulate(n):\n", + " \"Simulate moving in to houses, and return a sorted tuple of occupied houses.\"\n", + " occupied = set()\n", + " for house in random.sample(range(n), n):\n", + " if (house - 1) not in occupied and (house + 1) not in occupied:\n", + " occupied.add(house)\n", + " return sorted(occupied)\n", + "\n", + "def simulated_density(n, repeat=10000):\n", + " \"Estimate density by simulation, repeated `repeat` times.\"\n", + " return mean(len(simulate(n)) / n \n", + " for _ in range(repeat))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see if the simulation returns results that match the actual `density` function and the `estimated_density` function:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " n simulate density estimated\n", + " 10 0.4621 0.4620 0.4620\n", + " 25 0.4442 0.4442 0.4442\n", + " 50 0.4383 0.4383 0.4383\n", + " 100 0.4354 0.4353 0.4353\n", + " 200 0.4339 0.4338 0.4338\n", + " 400 0.4331 0.4331 0.4331\n" + ] + } + ], + "source": [ + "print(' n simulate density estimated')\n", + "for n in (10, 25, 50, 100, 200, 400):\n", + " print('{:4d} {:.4f} {:.4f} {:.4f}'\n", + " .format(n, simulated_density(n), density(n), estimated_density(n)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We get good agreement (at least to 3 decimal places), suggesting that either our three implementations are all correct, or we've made mistakes in all three. \n", + "\n", + "The `simulate` function can also give us insights when we look at the results it produces:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 2, 4, 6]" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simulate(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's repeat that multiple times, and store the results in a `Counter`, which tracks how many times it has seen each result:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({(0, 2, 4, 6): 3220,\n", + " (0, 2, 5): 1214,\n", + " (0, 3, 5): 1029,\n", + " (0, 3, 6): 827,\n", + " (1, 3, 5): 1417,\n", + " (1, 3, 6): 976,\n", + " (1, 4, 6): 1317})" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from collections import Counter\n", + "\n", + "Counter(tuple(simulate(7)) for _ in range(10000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That says that about 1/3 of the time, things work out so that the 4 even-numbered houses are occupied. But if anybody ever chooses an odd-numbered house, then we are destined to have 3 houses occupied (in one of 6 different ways, of which (1, 3 5) is the most common, probably because it is the only one that has three chances of getting started with an odd-numbered house)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Verification by Test\n", + "\n", + "Another way to gain more confidence in the code is to run a test suite:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test():\n", + " assert occ(0) == 0\n", + " assert occ(1) == occ(2) == 1\n", + " assert occ(3) == 5/3\n", + " assert density(3) == occ(3) / 3\n", + " assert density(100) == occ(100) / 100\n", + " assert runs(3) == [(0, 1), (0, 0), (1, 0)]\n", + " assert runs(7) == [(0, 5), (0, 4), (1, 3), (2, 2), (3, 1), (4, 0), (5, 0)]\n", + " for n in (3, 7, 10, 20, 100, 101, 200, 201):\n", + " for repeat in range(500):\n", + " assert_valid(simulate(n), n) \n", + " return 'ok'\n", + "\n", + "def assert_valid(occupied, n):\n", + " \"\"\"Assert that, in this collection of occupied houses, no house is adjacent to an\n", + " occupied house, and every unoccupied position is adjacent to an occupied house.\"\"\"\n", + " occupied = set(occupied) # coerce to set\n", + " for house in range(n):\n", + " if house in occupied:\n", + " assert not ((house - 1) in occupied or (house + 1) in occupied)\n", + " else:\n", + " assert (house - 1) in occupied or (house + 1) in occupied\n", + "\n", + "test()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Conclusion\n", + "\n", + "I'm happy with my result:\n", + "\n", + "> lim n → ∞ density(n) = (1 - e-2) / 2 ≅ 0.43233235838169365 \n", + "\n", + "I got the fun of working on the puzzle, the satisfaction of seeing John Lamping work out a proof, and the awe of seeing the mathematically sophisticated solutions of Jim Ferry and Andrew Mascioli, solutions that I know I could never come up with, but that I could get near to by coming at the problem with a different style of thinking." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Palindrome.ipynb b/pytudes/ipynb/Palindrome.ipynb new file mode 100644 index 0000000..985ca0b --- /dev/null +++ b/pytudes/ipynb/Palindrome.ipynb @@ -0,0 +1,534 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Panama Palindrome\n", + "\n", + "## Utilities" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import random, re, bisect, time\n", + "\n", + "def is_palindrome(s):\n", + " \"Test if a string is a palindrome (only considering letters a-z).\"\n", + " s1 = canonical(s)\n", + " return s1 == reversestr(s1)\n", + "\n", + "def is_unique_palindrome(s):\n", + " \"Test if string s is a palindrome where each comma-separated phrase is unique.\"\n", + " return is_palindrome(s) and is_unique(phrases(s))\n", + "\n", + "def canonical(word, sub=re.compile('[^a-z]').sub):\n", + " \"The canonical form for comparing: only lowercase a-z.\"\n", + " return sub('', word.lower())\n", + "\n", + "def phrases(s):\n", + " \"Break a string s into comma-separated phrases.\"\n", + " return [phrase.strip() for phrase in s.split(',')]\n", + "\n", + "def reversestr(s):\n", + " \"Reverse a string.\"\n", + " return s[::-1]\n", + "\n", + "def is_unique(collection):\n", + " \"Return true if collection has no duplicate elements.\"\n", + " return len(collection) == len(set(collection))" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'test_utils passes'" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_utils():\n", + " assert is_unique_palindrome('A man, a plan, a canal, Panama!')\n", + " assert is_unique_palindrome('''A (man), a PLAN... a ``canal?'' -- Panama!''')\n", + " assert not is_unique_palindrome('A man, a plan, a radar, a canal, Panama.')\n", + " \n", + " assert is_palindrome('A man, a plan, a canal, Panama.')\n", + " assert is_palindrome('Radar. Radar? Radar!')\n", + " assert not is_palindrome('radars')\n", + "\n", + " assert phrases('A man, a plan, Panama') == ['A man', 'a plan', 'Panama']\n", + " assert canonical('A man, a plan, a canal, Panama') == 'amanaplanacanalpanama'\n", + " assert reversestr('foo') == 'oof'\n", + " assert is_unique([1, 2, 3])\n", + " assert not is_unique([1, 2, 2])\n", + " return 'test_utils passes'\n", + "\n", + "test_utils()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Dictionary" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "! [ -e npdict.txt ] || curl -O http://norvig.com/npdict.txt" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 126144 204928 1383045 npdict.txt\r\n" + ] + } + ], + "source": [ + "! wc npdict.txt" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "################ Reading in a dictionary\n", + "\n", + "class PalDict:\n", + " \"\"\"A dictionary with the following fields:\n", + " words: a sorted list of words: ['ant', 'bee', 'sea']\n", + " rwords: a sorted list of reversed words: ['aes', 'eeb', 'tna']\n", + " truename: a dict of {canonical:true} pairs, e.g. {'anelk': 'an elk', 'anneelk': 'Anne Elk'}\n", + " k:\n", + " and the followng methods:\n", + " \"\"\"\n", + " \n", + " def __init__(self, k=100, filename='npdict.txt'):\n", + " words, rwords, truename = [], [], {'': '', 'panama': 'Panama!'}\n", + " for tword in open(filename, 'r', encoding='ascii', errors='ignore').read().splitlines():\n", + " word = canonical(tword)\n", + " words.append(word)\n", + " rwords.append(reversestr(word))\n", + " truename[word] = tword\n", + " words.sort()\n", + " rwords.sort()\n", + " self.k = k\n", + " self.words = words\n", + " self.rwords = rwords\n", + " self.truename = truename\n", + " self.rangek = range(k)\n", + " self.tryharder = False\n", + "\n", + " def startswith(self, prefix):\n", + " \"\"\"Return up to k canonical words that start with prefix.\n", + " If there are more than k, choose from them at random.\"\"\"\n", + " return self._k_startingwith(self.words, prefix)\n", + "\n", + " def endswith(self, rsuffix):\n", + " \"\"\"Return up to k canonical words that end with the reversed suffix.\n", + " If you want words ending in 'ing', ask for d.endswith('gni').\n", + " If there are more than k, choose from them at random.\"\"\"\n", + " return [reversestr(s) for s in self._k_startingwith(self.rwords, rsuffix)]\n", + "\n", + " def __contains__(self, word):\n", + " return word in self.truename\n", + "\n", + " def _k_startingwith(self, words, prefix):\n", + " start = bisect.bisect_left(words, prefix)\n", + " end = bisect.bisect(words, prefix + 'zzzz')\n", + " n = end - start\n", + " if self.k >= n: # get all the words that start with prefix\n", + " results = words[start:end]\n", + " else: # sample from words starting with prefix \n", + " indexes = random.sample(range(start, end), self.k)\n", + " results = [words[i] for i in indexes]\n", + " random.shuffle(results)\n", + " ## Consider words that are prefixes of the prefix.\n", + " ## This is very slow, so don't use it until late in the game.\n", + " if self.tryharder:\n", + " for i in range(3, len(prefix)):\n", + " w = prefix[0:i]\n", + " if ((words == self.words and w in self.truename) or\n", + " (words == self.rwords and reversestr(w) in self.truename)):\n", + " results.append(w)\n", + " return results\n", + "\n", + "paldict = PalDict() \n", + "\n", + "def anpdictshort():\n", + " \"Find the words that are valid when every phrase must start with 'a'\"\n", + " def segment(word): return [s for s in word.split('a') if s]\n", + " def valid(word): return all(reversestr(s) in segments for s in segment(word))\n", + " words = [canonical(w) for w in open('anpdict.txt')]\n", + " segments = set(s for w in words for s in segment(w))\n", + " valid_words = [paldict.truename[w] for w in words if valid(w)]\n", + " file('anpdict-short2.txt', 'w').write('\\n'.join(valid_words))\n", + "\n", + "################ Search for a palindrome\n", + "\n", + "class Panama:\n", + " def __init__(self, L='A man, a plan', R='a canal, Panama', dict=paldict):\n", + " ## .left and .right hold lists of canonical words\n", + " ## .diff holds the number of characters that are not matched,\n", + " ## positive for words on left, negative for right.\n", + " ## .stack holds (action, side, arg) tuples\n", + " self.left = []\n", + " self.right = []\n", + " self.best = 0\n", + " self.seen = {}\n", + " self.diff = 0\n", + " self.stack = []\n", + " self.starttime = time.clock()\n", + " self.dict = dict\n", + " self.steps = 0\n", + " for word in L.split(','):\n", + " self.add('left', canonical(word))\n", + " for rword in reversestr(R).split(','):\n", + " self.add('right', canonical(reversestr(rword)))\n", + " self.consider_candidates()\n", + " \n", + " def search(self, steps=10*1000*1000):\n", + " \"Search for palindromes.\"\n", + " for self.steps in range(steps):\n", + " if not self.stack:\n", + " return 'done'\n", + " action, dir, substr, arg = self.stack[-1]\n", + " if action == 'added': # undo the last word added\n", + " self.remove(dir, arg)\n", + " elif action == 'trying' and arg: # try the next word if there is one\n", + " self.add(dir, arg.pop()) and self.consider_candidates()\n", + " elif action == 'trying' and not arg: # otherwise backtrack\n", + " self.stack.pop()\n", + " else:\n", + " raise ValueError(action)\n", + " self.report()\n", + " return self\n", + "\n", + " def add(self, dir, word):\n", + " \"add a word\"\n", + " if word in self.seen:\n", + " return False\n", + " else:\n", + " getattr(self, dir).append(word)\n", + " self.diff += factor[dir] * len(word)\n", + " self.seen[word] = True\n", + " self.stack.append(('added', dir, '?', word))\n", + " return True\n", + "\n", + " def remove(self, dir, word):\n", + " \"remove a word\"\n", + " oldword = getattr(self, dir).pop()\n", + " assert word == oldword\n", + " self.diff -= factor[dir] * len(word)\n", + " del self.seen[word]\n", + " self.stack.pop()\n", + " \n", + " def consider_candidates(self):\n", + " \"\"\"Push a new state with a set of candidate words onto stack.\"\"\"\n", + " if self.diff > 0: # Left is longer, consider adding on right\n", + " dir = 'right'\n", + " substr = self.left[-1][-self.diff:]\n", + " candidates = self.dict.endswith(substr)\n", + " elif self.diff < 0: # Right is longer, consider adding on left\n", + " dir = 'left'\n", + " substr = reversestr(self.right[-1][0:-self.diff])\n", + " candidates = self.dict.startswith(substr)\n", + " else: # Both sides are same size\n", + " dir = 'left'\n", + " substr = ''\n", + " candidates = self.dict.startswith('')\n", + " if substr == reversestr(substr):\n", + " self.report()\n", + " self.stack.append(('trying', dir, substr, candidates))\n", + " \n", + " def report(self):\n", + " \"Report a new palindrome to log file (if it is sufficiently big).\"\n", + " N = len(self)\n", + " if N > 13333:\n", + " self.dict.tryharder = True\n", + " if N > self.best and (N > 13000 or N > self.best+1000):\n", + " self.best = len(self)\n", + " self.bestphrase = str(self)\n", + " print('%5d phrases (%5d words) in %3d seconds (%6d steps)' % (\n", + " self.best, self.bestphrase.count(' ')+1, time.clock() - self.starttime,\n", + " self.steps))\n", + " assert is_unique_palindrome(self.bestphrase)\n", + "\n", + " def __len__(self):\n", + " return len(self.left) + len(self.right)\n", + "\n", + " def __str__(self):\n", + " truename = self.dict.truename\n", + " lefts = [truename[w] for w in self.left]\n", + " rights = [truename[w] for w in self.right]\n", + " return ', '.join(lefts + rights[::-1])\n", + " \n", + " def __repr__(self):\n", + " return ''.format(len(self))\n", + "\n", + "factor = {'left': +1, 'right': -1}\n", + "\n", + "# Note that we only allow one truename per canonical name. Occasionally\n", + "# this means we miss a good word (as in \"a node\" vs. \"an ode\"), but there\n", + "# are only 665 of these truename collisions, and most of them are of the\n", + "# form \"a mark-up\" vs. \"a markup\" so it seemed better to disallow them.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "126144" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(paldict.words)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "all tests pass\n", + " 1005 phrases ( 1239 words) in 0 seconds ( 18582 steps)\n", + " 2012 phrases ( 2478 words) in 0 seconds ( 41886 steps)\n", + " 3017 phrases ( 3710 words) in 0 seconds ( 64444 steps)\n", + " 4020 phrases ( 4957 words) in 0 seconds ( 92989 steps)\n", + " 5022 phrases ( 6184 words) in 1 seconds (128986 steps)\n", + " 6024 phrases ( 7408 words) in 1 seconds (162634 steps)\n", + " 7027 phrases ( 8607 words) in 1 seconds (204639 steps)\n", + " 8036 phrases ( 9846 words) in 2 seconds (254992 steps)\n", + " 9037 phrases (11050 words) in 2 seconds (320001 steps)\n", + "10039 phrases (12257 words) in 2 seconds (417723 steps)\n", + "11040 phrases (13481 words) in 3 seconds (565050 steps)\n", + "12043 phrases (14711 words) in 4 seconds (887405 steps)\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "################ Unit Tests\n", + " \n", + "def test2(p=PalDict()):\n", + " d = p.dict\n", + " def sameset(a, b): return set(a) == set(b)\n", + " assert 'panama' in d\n", + " assert d.words[0] in d\n", + " assert d.words[-1] in d\n", + " assert sameset(d.startswith('aword'), ['awording', 'awordbreak',\n", + " 'awordiness', 'awordage', 'awordplay', 'awordlore', 'awordbook',\n", + " 'awordlessness', 'aword', 'awordsmith'])\n", + " assert sameset(d.endswith('ytisob'), ['aglobosity', 'averbosity',\n", + " 'asubglobosity', 'anonverbosity', 'agibbosity'])\n", + " d.tryharder = True\n", + " assert sameset(d.startswith('oklahoma'), ['oklahoma', 'okla'])\n", + " d.tryharder = False\n", + " assert d.startswith('oklahoma') == ['oklahoma']\n", + " assert d.startswith('fsfdsfdsfds') == []\n", + " print('all tests pass')\n", + " return p\n", + "\n", + "p = Panama()\n", + "test2(p)\n", + "p.search().report()\n", + "p" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + "100 847k 100 847k 0 0 1037k 0 --:--:-- --:--:-- --:--:-- 1037k\n" + ] + } + ], + "source": [ + "! [ -e anpdict.txt ] || curl -O http://norvig.com/anpdict.txt" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "anpdictshort()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 4527 9055 39467 anpdict-short.txt\r\n", + " 4527 9055 39467 anpdict-short2.txt\r\n", + " 69241 138489 867706 anpdict.txt\r\n", + " 126144 204928 1383045 npdict.txt\r\n", + " 204439 361527 2329685 total\r\n" + ] + } + ], + "source": [ + "! wc *npd*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Letter-By-Letter Approach\n", + "\n", + "Can we go letter-by-letter instead of word-by-word? Advantages: \n", + "\n", + "* We can (if need be) be exhaustive at each decision point, trying all 26 possibilities.\n", + "* We can try the most likely letters first.\n", + "\n", + "Process\n", + "\n", + "* Keep left- nad right- partial phrase lists; and the current state:\n", + "\n", + " {left: ['aman', 'aplan'], right: ['acanal', panama'],\n", + " left_word: True, right_word: True, extra_chars: +3, palindrome: True}\n", + " \n", + "* Now consider all ways of extending:\n", + "\n", + " - Add the letter `'a'` to the left, either as a new word or a continuation of the old word (perhaps going for `'a planaria'`).\n", + " - Add a letter, any letter, to the right, either as a new word or a continuation of \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import namedtuple\n", + "\n", + "\n", + "def do(state, action, side, L): action(state, side, L)\n", + "def add(state, side, L): getattr(state, side)[-1] += L\n", + "def new(state, side, L): getattr(state, side).append(L)\n", + "def undo(action, letter):\n", + " if action == add:\n", + " elif action == new:\n", + " else:\n", + " raise ValueError()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Probability.ipynb b/pytudes/ipynb/Probability.ipynb new file mode 100644 index 0000000..ee8c703 --- /dev/null +++ b/pytudes/ipynb/Probability.ipynb @@ -0,0 +1,3322 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "
Peter Norvig, 12 Feb 2016
\n", + "\n", + "# A Concrete Introduction to Probability (using Python)\n", + "\n", + "\n", + "\n", + "\n", + "This notebook covers the basics of probability theory, with Python 3 implementations. (You should have some background in [probability](http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html) and [Python](https://www.python.org/about/gettingstarted/).) \n", + "\n", + "\n", + "In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n", + "\n", + ">*Probability ... is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n", + "\n", + "![Laplace](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG/180px-AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG)\n", + "
Pierre-Simon Laplace
1814
\n", + "\n", + "\n", + "Laplace really nailed it, way back then! If you want to untangle a probability problem, all you have to do is be methodical about defining exactly what the cases are, and then careful in counting the number of favorable and total cases. We'll start being methodical by defining some vocabulary:\n", + "\n", + "\n", + "- **[Experiment](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n", + " An occurrence with an uncertain outcome that we can observe.\n", + "
*For example, rolling a die.*\n", + "- **[Outcome](https://en.wikipedia.org/wiki/Outcome_(probability%29):**\n", + " The result of an experiment; one particular state of the world. What Laplace calls a \"case.\"\n", + "
*For example:* `4`.\n", + "- **[Sample Space](https://en.wikipedia.org/wiki/Sample_space):**\n", + " The set of all possible outcomes for the experiment. \n", + "
*For example,* `{1, 2, 3, 4, 5, 6}`.\n", + "- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n", + " A subset of possible outcomes that together have some property we are interested in.\n", + "
*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`. \n", + "- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n", + " As Laplace said, the probability of an event with respect to a sample space is the number of favorable cases (outcomes from the sample space that are in the event) divided by the total number of cases in the sample space. (This assumes that all outcomes in the sample space are equally likely.) Since it is a ratio, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n", + "
*For example, the probability of an even die roll is 3/6 = 1/2.*\n", + "\n", + "This notebook will develop all these concepts; I also have a [second part](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers paradoxes in Probability Theory." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Code for `P` \n", + "\n", + "`P` is the traditional name for the Probability function:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from fractions import Fraction\n", + "\n", + "def P(event, space): \n", + " \"The probability of an event, given a sample space of equiprobable outcomes.\"\n", + " return Fraction(len(event & space), \n", + " len(space))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Read this as implementing Laplace's quote directly: *\"Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.\"* \n", + " \n", + "\n", + "# Warm-up Problem: Die Roll" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "What's the probability of rolling an even number with a single six-sided fair die? \n", + "\n", + "We can define the sample space `D` and the event `even`, and compute the probability:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D = {1, 2, 3, 4, 5, 6}\n", + "even = { 2, 4, 6}\n", + "\n", + "P(even, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "It is good to confirm what we already knew.\n", + "\n", + "You may ask: Why does the definition of `P` use `len(event & space)` rather than `len(event)`? Because I don't want to count outcomes that were specified in `event` but aren't actually in the sample space. Consider:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "even = {2, 4, 6, 8, 10, 12}\n", + "\n", + "P(even, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here, `len(event)` and `len(space)` are both 6, so if just divided, then `P` would be 1, which is not right.\n", + "The favorable cases are the *intersection* of the event and the space, which in Python is `(event & space)`.\n", + "Also note that I use `Fraction` rather than regular division because I want exact answers like 1/3, not 0.3333333333333333." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "# Urn Problems\n", + "\n", + "Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=probability%20ball%20urn). (You'd think the urns would be empty by now.) \n", + "\n", + "![Jacob Bernoulli](http://www2.stetson.edu/~efriedma/periodictable/jpg/Bernoulli-Jacob.jpg)\n", + "
Jacob Bernoulli
1700
\n", + "\n", + "For example, here is a three-part problem [adapted](http://mathforum.org/library/drmath/view/69151.html) from mathforum.org:\n", + "\n", + "> An urn contains 23 balls: 8 white, 6 blue, and 9 red. We select six balls at random (each possible selection is equally likely). What is the probability of each of these possible outcomes:\n", + "\n", + "> 1. all balls are red\n", + "2. 3 are blue, 2 are white, and 1 is red\n", + "3. exactly 4 balls are white\n", + "\n", + "So, an outcome is a set of 6 balls, and the sample space is the set of all possible 6 ball combinations. We'll solve each of the 3 parts using our `P` function, and also using basic arithmetic; that is, *counting*. Counting is a bit tricky because:\n", + "- We have multiple balls of the same color. \n", + "- An outcome is a *set* of balls, where order doesn't matter, not a *sequence*, where order matters.\n", + "\n", + "To account for the first issue, I'll have 8 different white balls labeled `'W1'` through `'W8'`, rather than having eight balls all labeled `'W'`. That makes it clear that selecting `'W1'` is different from selecting `'W2'`.\n", + "\n", + "The second issue is handled automatically by the `P` function, but if I want to do calculations by hand, I will sometimes first count the number of *permutations* of balls, then get the number of *combinations* by dividing the number of permutations by *c*!, where *c* is the number of balls in a combination. For example, if I want to choose 2 white balls from the 8 available, there are 8 ways to choose a first white ball and 7 ways to choose a second, and therefore 8 × 7 = 56 permutations of two white balls. But there are only 56 / 2 = 28 combinations, because `(W1, W2)` is the same combination as `(W2, W1)`.\n", + "\n", + "We'll start by defining the contents of the urn:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'B1',\n", + " 'B2',\n", + " 'B3',\n", + " 'B4',\n", + " 'B5',\n", + " 'B6',\n", + " 'R1',\n", + " 'R2',\n", + " 'R3',\n", + " 'R4',\n", + " 'R5',\n", + " 'R6',\n", + " 'R7',\n", + " 'R8',\n", + " 'R9',\n", + " 'W1',\n", + " 'W2',\n", + " 'W3',\n", + " 'W4',\n", + " 'W5',\n", + " 'W6',\n", + " 'W7',\n", + " 'W8'}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def cross(A, B):\n", + " \"The set of ways of concatenating one item from collection A with one from B.\"\n", + " return {a + b \n", + " for a in A for b in B}\n", + "\n", + "urn = cross('W', '12345678') | cross('B', '123456') | cross('R', '123456789') \n", + "\n", + "urn" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "23" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(urn)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can define the sample space, `U6`, as the set of all 6-ball combinations. We use `itertools.combinations` to generate the combinations, and then join each combination into a string:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "100947" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import itertools\n", + "\n", + "def combos(items, n):\n", + " \"All combinations of n items; each combo as a concatenated str.\"\n", + " return {' '.join(combo) \n", + " for combo in itertools.combinations(items, n)}\n", + "\n", + "U6 = combos(urn, 6)\n", + "\n", + "len(U6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I don't want to print all 100,947 members of the sample space; let's just peek at a random sample of them:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['B5 R2 W8 B1 R9 W5',\n", + " 'B5 W2 B6 W8 R5 B3',\n", + " 'B4 R8 B6 B1 R7 W5',\n", + " 'B5 B2 W7 R2 R4 W6',\n", + " 'B2 B4 B6 W8 R6 R5',\n", + " 'R2 R4 R9 W4 B3 W5',\n", + " 'R1 R6 R5 R9 R7 W5',\n", + " 'B5 R8 W7 B6 B3 W5',\n", + " 'B2 R8 W7 R5 W4 B3',\n", + " 'R1 W2 R3 W1 R7 W5']" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import random\n", + "\n", + "random.sample(U6, 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Is 100,947 really the right number of ways of choosing 6 out of 23 items, or \"23 choose 6\", as mathematicians [call it](https://en.wikipedia.org/wiki/Combination)? Well, we can choose any of 23 for the first item, any of 22 for the second, and so on down to 18 for the sixth. But we don't care about the ordering of the six items, so we divide the product by 6! (the number of permutations of 6 things) giving us:\n", + "\n", + "$$23 ~\\mbox{choose}~ 6 = \\frac{23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18}{6!} = 100947$$\n", + "\n", + "Note that $23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18 = 23! \\;/\\; 17!$, so, generalizing, we can write:\n", + "\n", + "$$n ~\\mbox{choose}~ c = \\frac{n!}{(n - c)! \\cdot c!}$$\n", + "\n", + "And we can translate that to code and verify that 23 choose 6 is 100,947:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from math import factorial\n", + "\n", + "def choose(n, c):\n", + " \"Number of ways to choose c items from a list of n items.\"\n", + " return factorial(n) // (factorial(n - c) * factorial(c))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "100947" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "choose(23, 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we're ready to answer the 4 problems: \n", + "\n", + "### Urn Problem 1: what's the probability of selecting 6 red balls? " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(4, 4807)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "red6 = {s for s in U6 if s.count('R') == 6}\n", + "\n", + "P(red6, U6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's investigate a bit more. How many ways of getting 6 red balls are there?" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "84" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(red6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Why are there 84 ways? Because there are 9 red balls in the urn, and we are asking how many ways we can choose 6 of them:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "84" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "choose(9, 6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So the probability of 6 red balls is then just 9 choose 6 divided by the size of the sample space:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(red6, U6) == Fraction(choose(9, 6), \n", + " len(U6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "### Urn Problem 2: what is the probability of 3 blue, 2 white, and 1 red?" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(240, 4807)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b3w2r1 = {s for s in U6 if\n", + " s.count('B') == 3 and s.count('W') == 2 and s.count('R') == 1}\n", + "\n", + "P(b3w2r1, U6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can get the same answer by counting how many ways we can choose 3 out of 6 blues, 2 out of 8 whites, and 1 out of 9 reds, and dividing by the number of possible selections:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(b3w2r1, U6) == Fraction(choose(6, 3) * choose(8, 2) * choose(9, 1), \n", + " len(U6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here we don't need to divide by any factorials, because `choose` has already accounted for that. \n", + "\n", + "We can get the same answer by figuring: \"there are 6 ways to pick the first blue, 5 ways to pick the second blue, and 4 ways to pick the third; then 8 ways to pick the first white and 7 to pick the second; then 9 ways to pick a red. But the order `'B1, B2, B3'` should count as the same as `'B2, B3, B1'` and all the other orderings; so divide by 3! to account for the permutations of blues, by 2! to account for the permutations of whites, and by 100947 to get a probability:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + " P(b3w2r1, U6) == Fraction((6 * 5 * 4) * (8 * 7) * 9, \n", + " factorial(3) * factorial(2) * len(U6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "### Urn Problem 3: What is the probability of exactly 4 white balls?\n", + "\n", + "We can interpret this as choosing 4 out of the 8 white balls, and 2 out of the 15 non-white balls. Then we can solve it the same three ways:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(350, 4807)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "w4 = {s for s in U6 if\n", + " s.count('W') == 4}\n", + "\n", + "P(w4, U6)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(w4, U6) == Fraction(choose(8, 4) * choose(15, 2),\n", + " len(U6))" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(w4, U6) == Fraction((8 * 7 * 6 * 5) * (15 * 14),\n", + " factorial(4) * factorial(2) * len(U6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Revised Version of `P`, with more general events\n", + "\n", + "To calculate the probability of an even die roll, I originally said\n", + "\n", + " even = {2, 4, 6}\n", + " \n", + "But that's inelegant—I had to explicitly enumerate all the even numbers from one to six. If I ever wanted to deal with a twelve or twenty-sided die, I would have to go back and change `even`. I would prefer to define `even` once and for all like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def even(n): return n % 2 == 0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now in order to make `P(even, D)` work, I'll have to modify `P` to accept an event as either\n", + "a *set* of outcomes (as before), or a *predicate* over outcomes—a function that returns true for an outcome that is in the event:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def P(event, space): \n", + " \"\"\"The probability of an event, given a sample space of equiprobable outcomes.\n", + " event can be either a set of outcomes, or a predicate (true for outcomes in the event).\"\"\"\n", + " if is_predicate(event):\n", + " event = such_that(event, space)\n", + " return Fraction(len(event & space), len(space))\n", + "\n", + "is_predicate = callable\n", + "\n", + "def such_that(predicate, collection): \n", + " \"The subset of elements in the collection for which the predicate is true.\"\n", + " return {e for e in collection if predicate(e)}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here we see how `such_that`, the new `even` predicate, and the new `P` work:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2, 4, 6}" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "such_that(even, D)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(even, D)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2, 4, 6, 8, 10, 12}" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D12 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}\n", + "\n", + "such_that(even, D12)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(even, D12)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Note: `such_that` is just like the built-in function `filter`, except `such_that` returns a set.\n", + "\n", + "We can now define more interesting events using predicates; for example we can determine the probability that the sum of a three-dice roll is prime (using a definition of `is_prime` that is efficient enough for small `n`):" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(73, 216)" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D3 = {(d1, d2, d3) for d1 in D for d2 in D for d3 in D}\n", + "\n", + "def prime_sum(outcome): return is_prime(sum(outcome))\n", + "\n", + "def is_prime(n): return n > 1 and not any(n % i == 0 for i in range(2, n))\n", + "\n", + "P(prime_sum, D3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Card Problems\n", + "\n", + "Consider dealing a hand of five playing cards. We can define `deck` as a set of 52 cards, and `Hands` as the sample space of all combinations of 5 cards:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "52" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "suits = 'SHDC'\n", + "ranks = 'A23456789TJQK'\n", + "deck = cross(ranks, suits)\n", + "len(deck)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['4H 7D QS 4D 9D',\n", + " 'QC 2D TS 9S 3D',\n", + " 'QC 3S KC 4C JC',\n", + " '9H 7C TS 7H JH',\n", + " 'QC JD AS JH 8H']" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Hands = combos(deck, 5)\n", + "\n", + "assert len(Hands) == choose(52, 5)\n", + "\n", + "random.sample(Hands, 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can answer questions like the probability of being dealt a flush (5 cards of the same suit):" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(33, 16660)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def flush(hand):\n", + " return any(hand.count(suit) == 5 for suit in suits)\n", + "\n", + "P(flush, Hands)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Or the probability of four of a kind:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 4165)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def four_kind(hand):\n", + " return any(hand.count(rank) == 4 for rank in ranks)\n", + "\n", + "P(four_kind, Hands)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Fermat and Pascal: Gambling, Triangles, and the Birth of Probability\n", + "\n", + "\n", + "
Pierre de Fermat
1654\n", + "
Blaise Pascal]
1654\n", + "
\n", + "\n", + "Consider a gambling game consisting of tossing a coin. Player H wins the game if 10 heads come up, and T wins if 10 tails come up. If the game is interrupted when H has 8 heads and T has 7 tails, how should the pot of money (which happens to be 100 Francs) be split?\n", + "In 1654, Blaise Pascal and Pierre de Fermat corresponded on this problem, with Fermat [writing](http://mathforum.org/isaac/problems/prob1.html):\n", + "\n", + ">Dearest Blaise,\n", + "\n", + ">As to the problem of how to divide the 100 Francs, I think I have found a solution that you will find to be fair. Seeing as I needed only two points to win the game, and you needed 3, I think we can establish that after four more tosses of the coin, the game would have been over. For, in those four tosses, if you did not get the necessary 3 points for your victory, this would imply that I had in fact gained the necessary 2 points for my victory. In a similar manner, if I had not achieved the necessary 2 points for my victory, this would imply that you had in fact achieved at least 3 points and had therefore won the game. Thus, I believe the following list of possible endings to the game is exhaustive. I have denoted 'heads' by an 'h', and tails by a 't.' I have starred the outcomes that indicate a win for myself.\n", + "\n", + " h h h h * h h h t * h h t h * h h t t *\n", + " h t h h * h t h t * h t t h * h t t t\n", + " t h h h * t h h t * t h t h * t h t t\n", + " t t h h * t t h t t t t h t t t t\n", + "\n", + ">I think you will agree that all of these outcomes are equally likely. Thus I believe that we should divide the stakes by the ration 11:5 in my favor, that is, I should receive (11/16)*100 = 68.75 Francs, while you should receive 31.25 Francs.\n", + "\n", + ">I hope all is well in Paris,\n", + "\n", + ">Your friend and colleague,\n", + "\n", + ">Pierre\n", + "\n", + "Pascal agreed with this solution, and [replied](http://mathforum.org/isaac/problems/prob2.html) with a generalization that made use of his previous invention, Pascal's Triangle. There's even [a book](https://smile.amazon.com/Unfinished-Game-Pascal-Fermat-Seventeenth-Century/dp/0465018963?sa-no-redirect=1) about it.\n", + "\n", + "We can solve the problem with the tools we have:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def win_unfinished_game(Hneeds, Tneeds):\n", + " \"The probability that H will win the unfinished game, given the number of points needed by H and T to win.\"\n", + " def Hwins(outcome): return outcome.count('h') >= Hneeds\n", + " return P(Hwins, continuations(Hneeds, Tneeds))\n", + "\n", + "def continuations(Hneeds, Tneeds):\n", + " \"All continuations of a game where H needs `Hneeds` points to win and T needs `Tneeds`.\"\n", + " rounds = ['ht' for _ in range(Hneeds + Tneeds - 1)]\n", + " return set(itertools.product(*rounds))" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{('h', 'h', 'h', 'h'),\n", + " ('h', 'h', 'h', 't'),\n", + " ('h', 'h', 't', 'h'),\n", + " ('h', 'h', 't', 't'),\n", + " ('h', 't', 'h', 'h'),\n", + " ('h', 't', 'h', 't'),\n", + " ('h', 't', 't', 'h'),\n", + " ('h', 't', 't', 't'),\n", + " ('t', 'h', 'h', 'h'),\n", + " ('t', 'h', 'h', 't'),\n", + " ('t', 'h', 't', 'h'),\n", + " ('t', 'h', 't', 't'),\n", + " ('t', 't', 'h', 'h'),\n", + " ('t', 't', 'h', 't'),\n", + " ('t', 't', 't', 'h'),\n", + " ('t', 't', 't', 't')}" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "continuations(2, 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(11, 16)" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "win_unfinished_game(2, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our answer agrees with Pascal and Fermat; we're in good company!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Non-Equiprobable Outcomes: Probability Distributions\n", + "\n", + "So far, we have made the assumption that every outcome in a sample space is equally likely. In real life, we often get outcomes that are not equiprobable. For example, the probability of a child being a girl is not exactly 1/2, and the probability is slightly different for a second child. An [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark, where `GB` means a family where the first child is a girl and the second a boy:\n", + "\n", + " GG: 121801 GB: 126840\n", + " BG: 127123 BB: 135138\n", + " \n", + "We will introduce three more definitions:\n", + "\n", + "* [Frequency](https://en.wikipedia.org/wiki/Frequency_%28statistics%29): a number describing how often an outcome occurs. Can be a count like 121801, or a ratio like 0.515.\n", + "\n", + "* [Distribution](http://mathworld.wolfram.com/StatisticalDistribution.html): A mapping from outcome to frequency for each outcome in a sample space. \n", + "\n", + "* [Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution): A distribution that has been *normalized* so that the sum of the frequencies is 1.\n", + "\n", + "We define `ProbDist` to take the same kinds of arguments that `dict` does: either a mapping or an iterable of `(key, val)` pairs, and/or optional keyword arguments. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "class ProbDist(dict):\n", + " \"A Probability Distribution; an {outcome: probability} mapping.\"\n", + " def __init__(self, mapping=(), **kwargs):\n", + " self.update(mapping, **kwargs)\n", + " # Make probabilities sum to 1.0; assert no negative probabilities\n", + " total = sum(self.values())\n", + " for outcome in self:\n", + " self[outcome] = self[outcome] / total\n", + " assert self[outcome] >= 0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We also need to modify the functions `P` and `such_that` to accept either a sample space or a probability distribution as the second argument." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def P(event, space): \n", + " \"\"\"The probability of an event, given a sample space of equiprobable outcomes. \n", + " event: a collection of outcomes, or a predicate that is true of outcomes in the event. \n", + " space: a set of outcomes or a probability distribution of {outcome: frequency} pairs.\"\"\"\n", + " if is_predicate(event):\n", + " event = such_that(event, space)\n", + " if isinstance(space, ProbDist):\n", + " return sum(space[o] for o in space if o in event)\n", + " else:\n", + " return Fraction(len(event & space), len(space))\n", + " \n", + "def such_that(predicate, space): \n", + " \"\"\"The outcomes in the sample pace for which the predicate is true.\n", + " If space is a set, return a subset {outcome,...};\n", + " if space is a ProbDist, return a ProbDist {outcome: frequency,...};\n", + " in both cases only with outcomes where predicate(element) is true.\"\"\"\n", + " if isinstance(space, ProbDist):\n", + " return ProbDist({o:space[o] for o in space if predicate(o)})\n", + " else:\n", + " return {o for o in space if predicate(o)}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here is the probability distribution for Danish two-child families:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BB': 0.2645086533229465,\n", + " 'BG': 0.24882071317004043,\n", + " 'GB': 0.24826679089140383,\n", + " 'GG': 0.23840384261560926}" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "DK = ProbDist(GG=121801, GB=126840,\n", + " BG=127123, BB=135138)\n", + "DK" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And here are some predicates that will allow us to answer some questions:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def first_girl(outcome): return outcome[0] == 'G'\n", + "def first_boy(outcome): return outcome[0] == 'B'\n", + "def second_girl(outcome): return outcome[1] == 'G'\n", + "def second_boy(outcome): return outcome[1] == 'B'\n", + "def two_girls(outcome): return outcome == 'GG'" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4866706335070131" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(first_girl, DK)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4872245557856497" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(second_girl, DK)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The above says that the probability of a girl is somewhere between 48% and 49%, but that it is slightly different between the first or second child." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.4898669165584115, 0.48471942072973107)" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(second_girl, such_that(first_girl, DK)), P(second_girl, such_that(first_boy, DK))" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.5101330834415885, 0.5152805792702689)" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(second_boy, such_that(first_girl, DK)), P(second_boy, such_that(first_boy, DK))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The above says that the sex of the second child is more likely to be the same as the first child, by about 1/2 a percentage point." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# More Urn Problems: M&Ms and Bayes\n", + "\n", + "Here's another urn problem (or \"bag\" problem) [from](http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html) prolific Python/Probability author [Allen Downey ](http://allendowney.blogspot.com/):\n", + "\n", + "> The blue M&M was introduced in 1995. Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan). Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown). \n", + "A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996. He won't tell me which is which, but he gives me one M&M from each bag. One is yellow and one is green. What is the probability that the yellow M&M came from the 1994 bag?\n", + "\n", + "To solve this problem, we'll first represent probability distributions for each bag: `bag94` and `bag96`:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "bag94 = ProbDist(brown=30, yellow=20, red=20, green=10, orange=10, tan=10)\n", + "bag96 = ProbDist(blue=24, green=20, orange=16, yellow=14, red=13, brown=13)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Next, define `MM` as the joint distribution—the sample space for picking one M&M from each bag. The outcome `'yellow green'` means that a yellow M&M was selected from the 1994 bag and a green one from the 1996 bag." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'brown blue': 0.07199999999999998,\n", + " 'brown brown': 0.03899999999999999,\n", + " 'brown green': 0.059999999999999984,\n", + " 'brown orange': 0.04799999999999999,\n", + " 'brown red': 0.03899999999999999,\n", + " 'brown yellow': 0.041999999999999996,\n", + " 'green blue': 0.023999999999999994,\n", + " 'green brown': 0.012999999999999998,\n", + " 'green green': 0.02,\n", + " 'green orange': 0.015999999999999997,\n", + " 'green red': 0.012999999999999998,\n", + " 'green yellow': 0.013999999999999999,\n", + " 'orange blue': 0.023999999999999994,\n", + " 'orange brown': 0.012999999999999998,\n", + " 'orange green': 0.02,\n", + " 'orange orange': 0.015999999999999997,\n", + " 'orange red': 0.012999999999999998,\n", + " 'orange yellow': 0.013999999999999999,\n", + " 'red blue': 0.04799999999999999,\n", + " 'red brown': 0.025999999999999995,\n", + " 'red green': 0.04,\n", + " 'red orange': 0.031999999999999994,\n", + " 'red red': 0.025999999999999995,\n", + " 'red yellow': 0.027999999999999997,\n", + " 'tan blue': 0.023999999999999994,\n", + " 'tan brown': 0.012999999999999998,\n", + " 'tan green': 0.02,\n", + " 'tan orange': 0.015999999999999997,\n", + " 'tan red': 0.012999999999999998,\n", + " 'tan yellow': 0.013999999999999999,\n", + " 'yellow blue': 0.04799999999999999,\n", + " 'yellow brown': 0.025999999999999995,\n", + " 'yellow green': 0.04,\n", + " 'yellow orange': 0.031999999999999994,\n", + " 'yellow red': 0.025999999999999995,\n", + " 'yellow yellow': 0.027999999999999997}" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def joint(A, B, sep=''):\n", + " \"\"\"The joint distribution of two independent probability distributions. \n", + " Result is all entries of the form {a+sep+b: P(a)*P(b)}\"\"\"\n", + " return ProbDist({a + sep + b: A[a] * B[b]\n", + " for a in A\n", + " for b in B})\n", + "\n", + "MM = joint(bag94, bag96, ' ')\n", + "MM" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "First we'll look at the \"One is yellow and one is green\" part:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'green yellow': 0.25925925925925924, 'yellow green': 0.7407407407407408}" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def yellow_and_green(outcome): return 'yellow' in outcome and 'green' in outcome\n", + "\n", + "such_that(yellow_and_green, MM)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can answer the question: given that we got a yellow and a green (but don't know which comes from which bag), what is the probability that the yellow came from the 1994 bag?" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7407407407407408" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def yellow94(outcome): return outcome.startswith('yellow')\n", + "\n", + "P(yellow94, such_that(yellow_and_green, MM))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So there is a 74% chance that the yellow comes from the 1994 bag.\n", + "\n", + "Answering this question was straightforward: just like all the other probability problems, we simply create a sample space, and use `P` to pick out the probability of the event in question, given what we know about the outcome.\n", + "But in a sense it is curious that we were able to solve this problem with the same methodology as the others: this problem comes from a section titled **My favorite Bayes's Theorem Problems**, so one would expect that we'd need to invoke Bayes Theorem to solve it. The computation above shows that that is not necessary. \n", + "\n", + "![Bayes](http://img1.ph.126.net/xKZAzeOv_mI8a4Lwq7PHmw==/2547911489202312541.jpg)\n", + "
Rev. Thomas Bayes
1701-1761\n", + "
\n", + "\n", + "Of course, we *could* solve it using Bayes Theorem. Why is Bayes Theorem recommended? Because we are asked about the probability of an event given the evidence, which is not immediately available; however the probability of the evidence given the event is. \n", + "\n", + "Before we see the colors of the M&Ms, there are two hypotheses, `A` and `B`, both with equal probability:\n", + "\n", + " A: first M&M from 94 bag, second from 96 bag\n", + " B: first M&M from 96 bag, second from 94 bag\n", + " P(A) = P(B) = 0.5\n", + " \n", + "Then we get some evidence:\n", + " \n", + " E: first M&M yellow, second green\n", + " \n", + "We want to know the probability of hypothesis `A`, given the evidence:\n", + " \n", + " P(A | E)\n", + " \n", + "That's not easy to calculate (except by enumerating the sample space). But Bayes Theorem says:\n", + " \n", + " P(A | E) = P(E | A) * P(A) / P(E)\n", + " \n", + "The quantities on the right-hand-side are easier to calculate:\n", + " \n", + " P(E | A) = 0.20 * 0.20 = 0.04\n", + " P(E | B) = 0.10 * 0.14 = 0.014\n", + " P(A) = 0.5\n", + " P(B) = 0.5\n", + " P(E) = P(E | A) * P(A) + P(E | B) * P(B) \n", + " = 0.04 * 0.5 + 0.014 * 0.5 = 0.027\n", + " \n", + "And we can get a final answer:\n", + " \n", + " P(A | E) = P(E | A) * P(A) / P(E) \n", + " = 0.04 * 0.5 / 0.027 \n", + " = 0.7407407407\n", + " \n", + "You have a choice: Bayes Theorem allows you to do less calculation at the cost of more algebra; that is a great trade-off if you are working with pencil and paper. Enumerating the state space allows you to do less algebra at the cost of more calculation; often a good trade-off if you have a computer. But regardless of the approach you use, it is important to understand Bayes theorem and how it works.\n", + "\n", + "There is one important question that Allen Downey does not address: *would you eat twenty-year-old M&Ms*?\n", + "😨" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Newton's Answer to a Problem by Pepys\n", + "\n", + "\n", + "
Isaac Newton
1693
\n", + "
Samuel Pepys
1693
\n", + "
\n", + "\n", + "[This paper](http://fermatslibrary.com/s/isaac-newton-as-a-probabilist) explains how Samuel Pepys wrote to Isaac Newton in 1693 to pose the problem:\n", + "\n", + "> Which of the following three propositions has the greatest chance of success? \n", + " 1. Six fair dice are tossed independently and at least one “6” appears. \n", + " 2. Twelve fair dice are tossed independently and at least two “6”s appear. \n", + " 3. Eighteen fair dice are tossed independently and at least three “6”s appear.\n", + " \n", + "Newton was able to answer the question correctly (although his reasoning was not quite right); let's see how we can do. Since we're only interested in whether a die comes up as \"6\" or not, we can define a single die and the joint distribution over *n* dice as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "die = ProbDist({'6':1/6, '-':5/6})\n", + "\n", + "def dice(n, die):\n", + " \"Joint probability from tossing n dice.\"\n", + " if n == 1:\n", + " return die\n", + " else:\n", + " return joint(die, dice(n - 1, die))" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'---': 0.5787037037037037,\n", + " '--6': 0.11574074074074073,\n", + " '-6-': 0.11574074074074073,\n", + " '-66': 0.023148148148148143,\n", + " '6--': 0.11574074074074073,\n", + " '6-6': 0.023148148148148143,\n", + " '66-': 0.023148148148148143,\n", + " '666': 0.0046296296296296285}" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dice(3, die)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we are ready to determine which proposition is more likely to have the required number of sixes:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def at_least(k, result): return lambda s: s.count(result) >= k" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6651020233196158" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(1, '6'), dice(6, die))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6186673737322984" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(2, '6'), dice(12, die))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5973456859478073" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(3, '6'), dice(18, die))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We reach the same conclusion Newton did, that the best chance is rolling six dice." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "
\n", + "\n", + "# Simulation\n", + "\n", + "Sometimes it is inconvenient to explicitly define a sample space. Perhaps the sample space is infinite, or perhaps it is just very large and complicated, and we feel more confident in writing a program to *simulate* one pass through all the complications, rather than try to *enumerate* the complete sample space. *Random sampling* from the simulation\n", + "can give an accurate estimate of the probability.\n", + "\n", + "# Simulating Monopoly\n", + "\n", + "![](http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg)
[Mr. Monopoly](https://en.wikipedia.org/wiki/Rich_Uncle_Pennybags)
1940—\n", + "\n", + "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board. To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about buying or selling properties or exchanging money or winning or losing the game, because these don't change a player's location. We will assume that a player in jail will always pay to get out of jail immediately. \n", + "\n", + "A game of Monopoly can go on forever, so the sample space is infinite. But even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls (and even more possibilities when we consider drawing cards). So it is infeasible to explicitly represent the sample space.\n", + "\n", + "But it is fairly straightforward to implement a simulation and run it for, say, 400,000 rolls (so the average square will be landed on 10,000 times). Here is the code for a simulation:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from collections import deque\n", + "import random\n", + "\n", + "# The board: as specified by https://projecteuler.net/problem=84\n", + "(GO, A1, CC1, A2, T1, R1, B1, CH1, B2, B3,\n", + " JAIL, C1, U1, C2, C3, R2, D1, CC2, D2, D3, \n", + " FP, E1, CH2, E2, E3, R3, F1, F2, U2, F3, \n", + " G2J, G1, G2, CC3, G3, R4, CH3, H1, T2, H2) = board = range(40)\n", + "\n", + "Deck = deque\n", + "\n", + "CC_deck = Deck([GO, JAIL] + 14 * [None])\n", + "CH_deck = Deck([GO, JAIL, C1, E3, H2, R1, {R1, R2, R3, R4}, {R1, R2, R3, R4}, {U1, U2}, -3] + 6 * [None])\n", + "\n", + "def monopoly(steps):\n", + " \"\"\"Simulate given number of steps of a Monopoly game, \n", + " and return the counts of how often each square is visited.\"\"\"\n", + " counts = [0] * len(board)\n", + " doubles = 0\n", + " random.shuffle(CC_deck)\n", + " random.shuffle(CH_deck)\n", + " goto(GO)\n", + " for _ in range(steps):\n", + " d1, d2 = random.randint(1, 6), random.randint(1, 6)\n", + " doubles = (doubles + 1 if d1 == d2 else 0)\n", + " goto(here + d1 + d2)\n", + " if here == G2J or doubles == 3:\n", + " goto(JAIL)\n", + " doubles = 0\n", + " elif here in (CC1, CC2, CC3):\n", + " do_card(CC_deck)\n", + " elif here in (CH1, CH2, CH3):\n", + " do_card(CH_deck)\n", + " counts[here] += 1\n", + " return counts\n", + "\n", + "def goto(square):\n", + " \"Update 'here' to be this square (and handle passing GO).\"\n", + " global here\n", + " here = square % len(board) \n", + "\n", + "def do_card(deck):\n", + " \"Take the top card from deck and do what it says.\"\n", + " card = deck[0] # The top card\n", + " deck.rotate(-1) # Move top card to bottom of deck\n", + " if card == None: # Don't move\n", + " pass\n", + " elif card == -3: # Go back 3 spaces\n", + " goto(here - 3)\n", + " elif isinstance(card, set): # Advance to next railroad or utility\n", + " goto(min({place for place in card if place > here} or card))\n", + " else: # Go to destination named on card\n", + " goto(card)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "counts = monopoly(400000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I'll show a histogram of the squares, with a dotted red line at the average:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline \n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.hist(list(range(40)), bins=40, weights=counts, normed=True)\n", + "plt.plot([0, 39], [1/40, 1/40], 'r--');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "There is one square far above average: `JAIL`, at a little over 6%. There are four squares far below average: the three chance squares, `CH1`, `CH2`, and `CH3`, at around 1% (because 10 of the 16 chance cards send the player away from the square), and the \"Go to Jail\" square, square number 30 on the plot, which has a frequency of 0 because you can't end a turn there. The other squares are around 2% to 3% each, which you would expect, because 100% / 40 = 2.5%." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Central Limit Theorem / Strength in Numbers Theorem\n", + "\n", + "So far, we have talked of an *outcome* as being a single state of the world. But it can be useful to break that state of the world down into components. We call these components **random variables**. For example, when we consider an experiment in which we roll two dice and observe their sum, we could model the situation with two random variables, one for each die. (Our representation of outcomes has been doing that implicitly all along, when we concatenate two parts of a string, but the concept of a random variable makes it official.)\n", + "\n", + "The **Central Limit Theorem** states that if you have a collection of random variables and sum them up, then the larger the collection, the closer the sum will be to a *normal distribution* (also called a *Gaussian distribution* or a *bell-shaped curve*). The theorem applies in all but a few pathological cases. \n", + "\n", + "As an example, let's take 5 random variables reprsenting the per-game scores of 5 basketball players, and then sum them together to form the team score. Each random variable/player is represented as a function; calling the function returns a single sample from the distribution:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from random import gauss, triangular, choice, vonmisesvariate, uniform\n", + "\n", + "def SC(): return posint(gauss(15.1, 3) + 3 * triangular(1, 4, 13)) # 30.1\n", + "def KT(): return posint(uniform(5.2, 15.2) + 3 * triangular(1, 3.5, 9)) # 22.1\n", + "def DG(): return posint(vonmisesvariate(30, 2) * 3.08) # 14.0\n", + "def HB(): return posint(gauss(6.7, 1.5) if choice((True, False)) else gauss(16.7, 2.5)) # 11.7\n", + "def OT(): return posint(triangular(0, 12, 20) + uniform(0, 40) + gauss(6, 3)) # 37.0\n", + "\n", + "def posint(x): \"Positive integer\"; return max(0, int(round(x)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here is a function to sample a random variable *k* times, show a histogram of the results, and return the mean:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from statistics import mean\n", + "\n", + "def repeated_hist(rv, bins=10, k=200000):\n", + " \"Repeat rv() k times and make a histogram of the results.\"\n", + " samples = [rv() for _ in range(k)]\n", + " plt.hist(samples, bins=bins)\n", + " return mean(samples)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The two top-scoring players have scoring distributions that are slightly skewed from normal:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "30.12574" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "repeated_hist(OT, bins=range(0, 70, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we define the team score to be the sum of the five players, and look at the distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "114.30268" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def GSW(): return SC() + KT() + DG() + HB() + OT()\n", + "\n", + "repeated_hist(GSW, bins=range(70, 160, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sure enough, this looks very much like a normal distribution. The Central Limit Theorem appears to hold in this case. But I have to say \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Conclusion\n", + "\n", + "We've had an interesting tour and met some giants of the field: Laplace, Bernoulli, Fermat, Pascal, Bayes, Newton, ... even Mr. Monopoly and The Count.\n", + "\n", + "![The Count](http://img2.oncoloring.com/count-dracula-number-thir_518b77b54ba6c-p.gif)\n", + "
The Count
1972—
\n", + "\n", + "The conclusion is: be explicit about what the problem says, and then methodical about defining the sample space, and finally be careful in counting the number of outcomes in the numerator and denominator. Easy as 1-2-3. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "\n", + "# Appendix: Continuous Sample Spaces\n", + "\n", + "Everything up to here has been about discrete, finite sample spaces, where we can *enumerate* all the possible outcomes. \n", + "\n", + "But I was asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n", + "Here we will cover a simple example, which we first solve approximately by simulation, and then exactly by calculation.\n", + "\n", + "## The Hot New Game Show Problem: Simulation\n", + "\n", + "Oliver Roeder posed [this problem](http://fivethirtyeight.com/features/can-you-win-this-hot-new-game-show/) in the 538 *Riddler* blog:\n", + "\n", + ">Two players go on a hot new game show called *Higher Number Wins.* The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?\n", + "\n", + "We'll use this notation:\n", + "- **A**, **B**: the two players.\n", + "- *A*, *B*: the cutoff values they choose: the lower bound of the range of first numbers they will accept.\n", + "- *a*, *b*: the actual random numbers that appear on the screen.\n", + "\n", + "For example, if player **A** chooses a cutoff of *A* = 0.6, that means that **A** would accept any first number greater than 0.6, and reject any number below that cutoff. The question is: What cutoff, *A*, should player **A** choose to maximize the chance of winning, that is, maximize P(*a* > *b*)?\n", + "\n", + "First, simulate the number that a player with a given cutoff gets (note that `random.random()` returns a float sampled uniformly from the interval [0..1]):" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def number(cutoff):\n", + " \"Play the game with given cutoff, returning the first or second random number.\"\n", + " first = random.random()\n", + " return first if first > cutoff else random.random()" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6118974990212028" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "number(.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now compare the numbers returned with a cutoff of *A* versus a cutoff of *B*, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff *A* is better than cutoff *B*:" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Pwin(A, B, trials=30000):\n", + " \"The probability that cutoff A wins against cutoff B.\"\n", + " Awins = sum(number(A) > number(B) \n", + " for _ in range(trials))\n", + " return Awins / trials" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5018" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Pwin(.5, .6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: " + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import Counter\n", + "\n", + "def top(N, cutoffs):\n", + " \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n", + " winners = Counter(A if Pwin(A, B) > 0.5 else B\n", + " for (A, B) in itertools.combinations(cutoffs, 2))\n", + " return winners.most_common(N)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 19.8 s, sys: 72.1 ms, total: 19.9 s\n", + "Wall time: 20 s\n" + ] + }, + { + "data": { + "text/plain": [ + "[(0.60000000000000009, 46),\n", + " (0.58000000000000007, 43),\n", + " (0.59000000000000008, 43),\n", + " (0.64000000000000012, 42),\n", + " (0.65000000000000013, 41)]" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from numpy import arange\n", + "\n", + "%time top(5, arange(0.50, 0.99, 0.01))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We get a good idea of the top cutoffs, but they are close to each other, so we can't quite be sure which is best, only that the best is somewhere around 0.60. We could get a better estimate by increasing the number of trials, but that would consume more time.\n", + "\n", + "## The Hot New Game Show Problem: Exact Calculation\n", + "\n", + "More promising is the possibility of making `Pwin(A, B)` an exact calculation. But before we get to `Pwin(A, B)`, let's solve a simpler problem: assume that both players **A** and **B** have chosen a cutoff, and have each received a number above the cutoff. What is the probability that **A** gets the higher number? We'll call this `Phigher(A, B)`. We can think of this as a two-dimensional sample space of points in the (*a*, *b*) plane, where *a* ranges from the cutoff *A* to 1 and *b* ranges from the cutoff B to 1. Here is a diagram of that two-dimensional sample space, with the cutoffs *A*=0.5 and *B*=0.6:\n", + "\n", + "\n", + "\n", + "The total area of the sample space is 0.5 × 0.4 = 0.20, and in general it is (1 - *A*) · (1 - *B*). What about the favorable cases, where **A** beats **B**? That corresponds to the shaded triangle below:\n", + "\n", + "\n", + "\n", + "The area of a triangle is 1/2 the base times the height, or in this case, 0.42 / 2 = 0.08, and in general, (1 - *B*)2 / 2. So in general we have:\n", + "\n", + " Phigher(A, B) = favorable / total\n", + " favorable = ((1 - B) ** 2) / 2 \n", + " total = (1 - A) * (1 - B)\n", + " Phigher(A, B) = (((1 - B) ** 2) / 2) / ((1 - A) * (1 - B))\n", + " Phigher(A, B) = (1 - B) / (2 * (1 - A))\n", + " \n", + "And in this specific case we have:\n", + "\n", + " A = 0.5; B = 0.6\n", + " favorable = 0.4 ** 2 / 2 = 0.08\n", + " total = 0.5 * 0.4 = 0.20\n", + " Phigher(0.5, 0.6) = 0.08 / 0.20 = 0.4\n", + "\n", + "But note that this only works when the cutoff *A* ≤ *B*; when *A* > *B*, we need to reverse things. That gives us the code:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Phigher(A, B):\n", + " \"Probability that a sample from [A..1] is higher than one from [B..1].\"\n", + " if A <= B:\n", + " return (1 - B) / (2 * (1 - A))\n", + " else:\n", + " return 1 - Phigher(B, A)" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Phigher(0.5, 0.6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We're now ready to tackle the full game. There are four cases to consider, depending on whether **A** and **B** gets a first number that is above or below their cutoff choices:\n", + "\n", + "| first *a* | first *b* | P(*a*, *b*) | P(A wins | *a*, *b*) | Comment |\n", + "|:-----:|:-----:| ----------- | ------------- | ------------ |\n", + "| *a* > *A* | *b* > *B* | (1 - *A*) · (1 - *B*) | Phigher(*A*, *B*) | Both above cutoff; both keep first numbers |\n", + "| *a* < *A* | *b* < *B* | *A* · *B* | Phigher(0, 0) | Both below cutoff, both get new numbers from [0..1] |\n", + "| *a* > *A* | *b* < *B* | (1 - *A*) · *B* | Phigher(*A*, 0) | **A** keeps number; **B** gets new number from [0..1] |\n", + "| *a* < *A* | *b* > *B* | *A* · (1 - *B*) | Phigher(0, *B*) | **A** gets new number from [0..1]; **B** keeps number |\n", + "\n", + "For example, the first row of this table says that the event of both first numbers being above their respective cutoffs has probability (1 - *A*) · (1 - *B*), and if this does occur, then the probability of **A** winning is Phigher(*A*, *B*).\n", + "We're ready to replace the old simulation-based `Pwin` with a new calculation-based version:" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def Pwin(A, B):\n", + " \"With what probability does cutoff A win against cutoff B?\"\n", + " return ((1-A) * (1-B) * Phigher(A, B) # both above cutoff\n", + " + A * B * Phigher(0, 0) # both below cutoff\n", + " + (1-A) * B * Phigher(A, 0) # A above, B below\n", + " + A * (1-B) * Phigher(0, B)) # A below, B above" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That was a lot of algebra. Let's define a few tests to check for obvious errors:" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test():\n", + " assert Phigher(0.5, 0.5) == Phigher(0.7, 0.7) == Phigher(0, 0) == 0.5\n", + " assert Pwin(0.5, 0.5) == Pwin(0.7, 0.7) == 0.5\n", + " assert Phigher(.6, .5) == 0.6\n", + " assert Phigher(.5, .6) == 0.4\n", + " return 'ok'\n", + "\n", + "test()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's repeat the calculation with our new, exact `Pwin`:" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0.62000000000000011, 48),\n", + " (0.6100000000000001, 47),\n", + " (0.60000000000000009, 46),\n", + " (0.59000000000000008, 45),\n", + " (0.63000000000000012, 44)]" + ] + }, + "execution_count": 80, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top(5, arange(0.50, 0.99, 0.01))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is good to see that the simulation and the exact calculation are in rough agreement; that gives me more confidence in both of them. We see here that 0.62 defeats all the other cutoffs, and 0.61 defeats all cutoffs except 0.62. The great thing about the exact calculation code is that it runs fast, regardless of how much accuracy we want. We can zero in on the range around 0.6:" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0.6180000000000001, 199),\n", + " (0.6170000000000001, 198),\n", + " (0.6160000000000001, 197),\n", + " (0.61900000000000011, 196),\n", + " (0.6150000000000001, 195),\n", + " (0.6140000000000001, 194),\n", + " (0.6130000000000001, 193),\n", + " (0.62000000000000011, 192),\n", + " (0.6120000000000001, 191),\n", + " (0.6110000000000001, 190)]" + ] + }, + "execution_count": 81, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top(10, arange(0.500, 0.700, 0.001))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This says 0.618 is best, better than 0.620. We can get even more accuracy:" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0.61802999999999531, 200),\n", + " (0.61801999999999535, 199),\n", + " (0.61803999999999526, 198),\n", + " (0.6180099999999954, 197),\n", + " (0.61799999999999544, 196)]" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top(5, arange(0.61700, 0.61900, 0.00001))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So 0.61803 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can you prove that it is what I think it is?\n", + "\n", + "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of *A* and *B* between 0 and 1:" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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ZTAbP8wJ/n6ph0aJF7L77Ptx33zYkk/cRdrEDL6J1AtgtaEN8QOF5bwAfKfP3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\nXv7yl1vw+58j0VGVi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AyjH3Bfhc7/EiNG/B/bb799Uu+os6LhcDiZMXdSFjhdhqdmOpib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\nC3jsIh6PJ7uxhBD88MMP9O7dOxnwZOvEqhmjJXBCFiPdBllJx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u0s/GvMMAz0er3pPavV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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", + "\n", + "def map2(fn, A, B):\n", + " \"Map fn to corresponding elements of 2D arrays A and B.\"\n", + " return [list(map(fn, Arow, Brow))\n", + " for (Arow, Brow) in zip(A, B)]\n", + "\n", + "cutoffs = arange(0.00, 1.00, 0.02)\n", + "A, B = np.meshgrid(cutoffs, cutoffs)\n", + "\n", + "fig = plt.figure(figsize=(10,10))\n", + "ax = fig.add_subplot(1, 1, 1, projection='3d')\n", + "ax.set_xlabel('A')\n", + "ax.set_ylabel('B')\n", + "ax.set_zlabel('Pwin(A, B)')\n", + "ax.plot_surface(A, B, map2(Pwin, A, B));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does this [Pringle of Probability](http://fivethirtyeight.com/features/should-you-shoot-free-throws-underhand/) show us? The highest win percentage for **A**, the peak of the surface, occurs when *A* is around 0.5 and *B* is 0 or 1. We can confirm that, finding the maximum `Pwin(A, B)` for many different cutoff values of `A` and `B`:" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "cutoffs = (set(arange(0.00, 1.00, 0.01)) | \n", + " set(arange(0.500, 0.700, 0.001)) | \n", + " set(arange(0.61700, 0.61900, 0.00001)))" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.625, 0.5, 0.0]" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max([Pwin(A, B), A, B]\n", + " for A in cutoffs for B in cutoffs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? " + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.5, 0.61802999999999531, 0.61802999999999531]" + ] + }, + "execution_count": 86, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(min([Pwin(A, B), A, B] for B in cutoffs)\n", + " for A in cutoffs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And what if we run it the other way around, where **B** chooses a cutoff first, and then **A** responds?" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.5, 0.61802999999999531, 0.61802999999999531]" + ] + }, + "execution_count": 87, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "min(max([Pwin(A, B), A, B] for A in cutoffs)\n", + " for B in cutoffs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In both cases, the rational choice for both players in a cutoff of 0.61803, which corresponds to the \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing *B* = 0.61803, and notice that if *A* changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix *A* = 0.61803, then if *B* changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n", + "\n", + "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your space; count/measure carefully, and let your code take care of the rest." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/ProbabilityParadox.ipynb b/pytudes/ipynb/ProbabilityParadox.ipynb new file mode 100644 index 0000000..56ed36c --- /dev/null +++ b/pytudes/ipynb/ProbabilityParadox.ipynb @@ -0,0 +1,3102 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "
Peter Norvig, 3 Oct 2015, revised Oct-Feb 2016
\n", + "\n", + "# Probability, Paradox, and the Reasonable Person Principle\n", + "\n", + "In [another notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb), I introduced the basics of probability theory. I'll duplicate the code we developed there:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from fractions import Fraction\n", + "\n", + "class ProbDist(dict):\n", + " \"A Probability Distribution; an {outcome: probability} mapping.\"\n", + " def __init__(self, mapping=(), **kwargs):\n", + " self.update(mapping, **kwargs)\n", + " # Make probabilities sum to 1.0; assert no negative probabilities\n", + " total = sum(self.values())\n", + " for outcome in self:\n", + " self[outcome] = self[outcome] / total\n", + " assert self[outcome] >= 0\n", + " \n", + "def P(event, space): \n", + " \"\"\"The probability of an event, given a sample space of equiprobable outcomes. \n", + " event: a collection of outcomes, or a predicate that is true of outcomes in the event. \n", + " space: a set of outcomes or a probability distribution of {outcome: frequency}.\"\"\"\n", + " if is_predicate(event):\n", + " event = such_that(event, space)\n", + " if isinstance(space, ProbDist):\n", + " return sum(space[o] for o in space if o in event)\n", + " else:\n", + " return Fraction(len(event & space), len(space))\n", + " \n", + "def such_that(predicate, space): \n", + " \"\"\"The outcomes in the sample space for which the predicate is true.\n", + " If space is a set, return a subset {outcome,...};\n", + " if space is a ProbDist, return a ProbDist {outcome: frequency,...};\n", + " in both cases only with outcomes where predicate(element) is true.\"\"\"\n", + " if isinstance(space, ProbDist):\n", + " return ProbDist({o:space[o] for o in space if predicate(o)})\n", + " else:\n", + " return {o for o in space if predicate(o)}\n", + " \n", + "is_predicate = callable\n", + "\n", + "def cross(A, B):\n", + " \"The set of ways of concatenating one item from collection A with one from B.\"\n", + " return {a + b \n", + " for a in A for b in B}\n", + "\n", + "def joint(A, B, sep=''):\n", + " \"\"\"The joint distribution of two independent probability distributions. \n", + " Result is all entries of the form {a+sep+b: P(a)*P(b)}\"\"\"\n", + " return ProbDist({a + sep + b: A[a] * B[b]\n", + " for a in A\n", + " for b in B})" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "In this notebook we use this code to show how to solve some particularly perplexing paradoxical probability problems.\n", + "\n", + "# Child Paradoxes\n", + "\n", + "In 1959, [Martin Gardner]() [posed](https://en.wikipedia.org/wiki/Boy_or_Girl_paradox) these two problems:\n", + "\n", + "- **Child Problem 1.** Mr. Jones has two children. The older child is a boy. What is the\n", + "probability that both children are boys?\n", + "\n", + "- **Child Problem 2.** Mr. Smith has two children. At least one of them is a boy. What is\n", + "the probability that both children are boys? \n", + "\n", + "Then in 2006, Mike & Tom Starbird came up with a variant, which Gary Foshee introduced to Gardner fans in 2010:\n", + "\n", + "- **Child Problem 3.** I have two children. At least one of them is a boy born on Tuesday. What is\n", + "the probability that both children are boys? \n", + "\n", + "Problems 2 and 3 are considered *paradoxes* because they have surprising answers that people\n", + "argue about. \n", + "\n", + "(Assume the probability of a boy is exactly 1/2, and is independent of any siblings.)\n", + "\n", + "![Martin Gardner](https://upload.wikimedia.org/wikipedia/commons/0/04/Martin_Gardner.jpeg)\n", + "
Martin Gardner
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "### Child Problem 1: Older child is a boy. What is the probability both are boys?\n", + "\n", + "We use `'BG'` to denote the outcome in which the older child is a boy and the younger a girl. The sample space, `S`, of equi-probable outcomes is:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "S = {'BG', 'BB', 'GB', 'GG'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's define predicates for the conditions of having two boys, and of the older child being a boy:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def two_boys(outcome): return outcome.count('B') == 2\n", + "\n", + "def older_is_a_boy(outcome): return outcome.startswith('B')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can answer Problem 1:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(older_is_a_boy, S))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "You're probably thinking that was a lot of mechanism just to get the obvious answer. But in the next problems, what is obvious becomes less obvious.\n", + "\n", + "### Child Problem 2: At least one is a boy. What is the probability both are boys? \n", + "\n", + "Implementing this problem and finding the answer is easy:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def at_least_one_boy(outcome): return 'B' in outcome" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(at_least_one_boy, S))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Understanding the answer is tougher. Some people think the answer should be 1/2. Can we justify the answer 1/3? We can see there are three equiprobable outcomes in which there is at least one boy:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BB', 'BG', 'GB'}" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "such_that(at_least_one_boy, S)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Of those three outcomes, only one has two boys, so the answer of 1/3 is indeed justified. \n", + "\n", + "But some people *still* think the answer should be 1/2.\n", + "Their reasoning is *\"If one child is a boy, then there are two equiprobable outcomes for the other child, so the probability that the other child is a boy, and thus that there are two boys, is 1/2.\"* \n", + "\n", + "When two methods of reasoning give two different answers, we have a [paradox](https://en.wikipedia.org/wiki/Paradox). Here are three responses to a paradox:\n", + "\n", + "1. The very fundamentals of mathematics must be incomplete, and this problem reveals it!!!\n", + "2. I'm right, and anyone who disagrees with me is an idiot!!!\n", + "3. I have the right answer for one interpretation of the problem, and you have the right answer\n", + "for a different interpretation of the problem.\n", + "\n", + "If you're [Bertrand Russell](https://en.wikipedia.org/wiki/Russell%27s_paradox) or [Georg Cantor](https://en.wikipedia.org/wiki/Cantor%27s_paradox), you might very well uncover a fundamental flaw in mathematics; for the rest of us, I recommend Response 3. When I believe the answer is 1/3, and I hear someone say the answer is 1/2, my response is not *\"You're wrong!\"*, rather it is *\"How interesting! You must have a different interpretation of the problem; I should try to discover what your interpretation is, and why your answer is correct for your interpretation.\"* The first step is to be more precise in *my* wording of the experiment:\n", + "\n", + "- **Child Experiment 2a.** Mr. Smith is chosen at random from families with two children. He is asked if at least one of his children is a boy. He replies \"yes.\"\n", + "\n", + "The next step is to envision another possible interpretation of the experiment:\n", + "\n", + "- **Child Experiment 2b.** Mr. Smith is chosen at random from families with two children. He is observed at a time when he is accompanied by one of his children, chosen at random. The child is observed to be a boy. \n", + "\n", + "Experiment 2b needs a different sample space, which we will call `S2b`. It consists of 8 outcomes, not just 4; for each of the 4 outcomes in `S`, we have a choice of observing either the older child or the younger child. We will use the notation `'GB/g?'` to mean that the older child is a girl, the younger a boy, the older child was observed to be a girl, and the younger was not observed. The sample space is therefore:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "S2b = {'BB/b?', 'BB/?b', \n", + " 'BG/b?', 'BG/?g', \n", + " 'GB/g?', 'GB/?b', \n", + " 'GG/g?', 'GG/?g'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can figure out the subset of this sample space in which we observe Mr. Smith with a boy:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BB/?b', 'BB/b?', 'BG/b?', 'GB/?b'}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def observed_boy(outcome): return 'b' in outcome\n", + "\n", + "such_that(observed_boy, S2b)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And finally we can determine the probability that he has two boys, given that we observed him with a boy:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(observed_boy, S2b))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The paradox is resolved. Two reasonable people can have different interpretations of the problem, and can each reason flawlessly to reach different conclusions, 1/3 or 1/2. \n", + "\n", + "Which interpretation of the problem is \"better?\" We could debate that, or we could just agree to use unambiguous wording (that is, use the language of Experiment 2a or Experiment 2b, not the ambiguous language of Problem 2). \n", + "\n", + "## The Reasonable Person Principle\n", + "\n", + "It is an unfortunate fact of human nature that we often assume the other person is an idiot. As [George Carlin puts it](https://www.youtube.com/watch?v=XWPCE2tTLZQ) *\"Have you ever noticed when you're driving that anybody driving slower than you is an idiot, and anyone going faster than you is a maniac?\"*\n", + "\n", + "\n", + "
George Carlin
\n", + "\n", + "The opposite assumption—that other people are more likely to be **reasonable** rather than **idiots** is known as the **[reasonable person principle](http://www.cs.cmu.edu/~weigand/staff/)**. It is a guiding principle at Carnegie Mellon University's School of Computer Science, and is a principle I try to live by as well.\n", + "\n", + "Now let's return to an even more paradoxical problem.\n", + "\n", + "### Child Problem 3. One is a boy born on Tuesday. What's the probability both are boys?\n", + "\n", + "Most people can not imagine how the boy's birth-day-of-week could be relevant, and feel the answer should be the same as Problem 2. But to be sure, we need to clearly describe the experiment, define the sample space, and calculate. First:\n", + "\n", + "- **Child Experiment 3a.** A parent is chosen at random from families with two children. She is asked if at least one of her children is a boy born on Tuesday. She replies \"yes.\"\n", + "\n", + "Next we'll define a sample space. We'll use the notation \"`G1B3`\" to mean the older child is a girl born on the first day of the week (Sunday) and the younger a boy born on the third day of the week (Tuesday). We'll call the resulting sample space `S3`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "196" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sexesdays = cross('BG', '1234567')\n", + "S3 = cross(sexesdays, sexesdays)\n", + "len(S3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "That's too many to print, but we can sample them:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['G2G3', 'G6B7', 'B1G7', 'B4B7', 'B4G6', 'G5G5', 'B5G4', 'G4B4']" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import random\n", + "random.sample(S3, 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We determine below that the probability of having at least one boy is 3/4, both in `S3` (where we keep track of the birth day of week) and in `S` (where we don't):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(3, 4)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least_one_boy, S3)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(3, 4)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least_one_boy, S)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The probability of two boys is 1/4 in either sample space:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 4)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, S3)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 4)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, S)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And the probability of two boys given at least one boy is 1/3 in either sample space:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(at_least_one_boy, S3))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(at_least_one_boy, S))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We will define a predicate for the event of at least one boy born on Tuesday: " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def at_least_one_boy_tues(outcome): return 'B3' in outcome" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We are now ready to answer Problem 3:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(13, 27)" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(at_least_one_boy_tues, S3))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "13/27? \n", + "\n", + "How many saw that coming? 13/27 is quite different from 1/3, but rather close to 1/2. So \"at least one boy born on Tuesday\" is quite different from \"at least one boy.\" Are you surprised? Do you accept the answer, or do you think we did something wrong? Are there other interpretations of the experiment that lead to other answers?\n", + "\n", + "Here is one alternative interpretation:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "- **Child Experiment 3b.** A parent is chosen at random from families with two children. She is observed at a time when she is accompanied by one of her children, chosen at random. The child is observed to be a boy who reports that his birth day is Tuesday.\n", + "\n", + "We can represent outcomes in this sample space with the notation `G1B3/??b3`, meaning the older child is a girl born on Sunday, the younger a boy born on Tuesday, the older was not observed, and the younger was." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def observed_boy_tues(outcome): return 'b3' in outcome\n", + "\n", + "S3b = {children + '/' + observation\n", + " for children in S3\n", + " for observation in (children[:2].lower()+'??', '??'+children[-2:].lower())} " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['G4G5/??g5', 'B1B5/b1??', 'G6G4/g6??', 'B1G2/??g2', 'G5G6/g5??']" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(S3b, 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can answer this version of Child Problem 3:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(two_boys, such_that(observed_boy_tues, S3b))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So with the wording of Child Experiment 3b, the answer is the same as 2b.\n", + "\n", + "Still confused? Let's build a visualization tool to make things more concrete.\n", + "\n", + "# Visualization\n", + "\n", + "We'll display the results as a two dimensional grid of outcomes. An outcome will be colored white if it does not satisfy the condition stated in the problem; green if the outcome contains two boys; and yellow if it does satisfy the condition, but does not have two boys. Every cell in a row has the same older child, and every cell in a column has the same younger child. Here's the code to display a table:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from IPython.display import HTML\n", + "\n", + "def Pgrid(space, n, event, condition):\n", + " \"\"\"Display sample space in a grid, color-coded: green if event and condition is true; \n", + " yellow if only condition is true; white otherwise.\"\"\"\n", + " # n is the number of characters that make up the older child.\n", + " olders = sorted(set(outcome[:n] for outcome in space))\n", + " return HTML('' +\n", + " cat(row(older, space, event, condition) for older in olders) +\n", + " '
' + \n", + " 'P({} | {}) = {}'.format(\n", + " event.__name__, condition.__name__, \n", + " P(event, such_that(condition, space))))\n", + "\n", + "def row(older, space, event, condition):\n", + " \"Display a row where an older child is paired with each of the possible younger children.\"\n", + " thisrow = sorted(outcome for outcome in space if outcome.startswith(older))\n", + " return '' + cat(cell(outcome, event, condition) for outcome in thisrow) + ''\n", + "\n", + "def cell(outcome, event, condition): \n", + " \"Display outcome in appropriate color.\"\n", + " color = ('lightgreen' if event(outcome) and condition(outcome) else\n", + " 'yellow' if condition(outcome) else\n", + " 'white')\n", + " return '{}'.format(color, outcome) \n", + "\n", + "cat = ''.join" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can use this visualization tool to see that in Child Problem 1, there is one outcome with two boys (green) out of a total of two outcomes where the older is a boy (green and yellow) so the probability of two boys given that the older is a boy is 1/2." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
BBBG
GBGG
P(two_boys | older_is_a_boy) = 1/2" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 1\n", + "Pgrid(S, 1, two_boys, older_is_a_boy)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "For Child Problem 2, we see the probability of two boys (green) given at least one boy (green and yellow) is 1/3. " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
BBBG
GBGG
P(two_boys | at_least_one_boy) = 1/3" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 2\n", + "Pgrid(S, 1, two_boys, at_least_one_boy)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The answer is still 1/3 when we consider the day of the week of each birth. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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P(two_boys | at_least_one_boy) = 1/3" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 2, with days of week enumerated\n", + "Pgrid(S3, 2, two_boys, at_least_one_boy)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "Now for the paradox of Child Problem 3:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
B1B1B1B2B1B3B1B4B1B5B1B6B1B7B1G1B1G2B1G3B1G4B1G5B1G6B1G7
B2B1B2B2B2B3B2B4B2B5B2B6B2B7B2G1B2G2B2G3B2G4B2G5B2G6B2G7
B3B1B3B2B3B3B3B4B3B5B3B6B3B7B3G1B3G2B3G3B3G4B3G5B3G6B3G7
B4B1B4B2B4B3B4B4B4B5B4B6B4B7B4G1B4G2B4G3B4G4B4G5B4G6B4G7
B5B1B5B2B5B3B5B4B5B5B5B6B5B7B5G1B5G2B5G3B5G4B5G5B5G6B5G7
B6B1B6B2B6B3B6B4B6B5B6B6B6B7B6G1B6G2B6G3B6G4B6G5B6G6B6G7
B7B1B7B2B7B3B7B4B7B5B7B6B7B7B7G1B7G2B7G3B7G4B7G5B7G6B7G7
G1B1G1B2G1B3G1B4G1B5G1B6G1B7G1G1G1G2G1G3G1G4G1G5G1G6G1G7
G2B1G2B2G2B3G2B4G2B5G2B6G2B7G2G1G2G2G2G3G2G4G2G5G2G6G2G7
G3B1G3B2G3B3G3B4G3B5G3B6G3B7G3G1G3G2G3G3G3G4G3G5G3G6G3G7
G4B1G4B2G4B3G4B4G4B5G4B6G4B7G4G1G4G2G4G3G4G4G4G5G4G6G4G7
G5B1G5B2G5B3G5B4G5B5G5B6G5B7G5G1G5G2G5G3G5G4G5G5G5G6G5G7
G6B1G6B2G6B3G6B4G6B5G6B6G6B7G6G1G6G2G6G3G6G4G6G5G6G6G6G7
G7B1G7B2G7B3G7B4G7B5G7B6G7B7G7G1G7G2G7G3G7G4G7G5G7G6G7G7
P(two_boys | at_least_one_boy_tues) = 13/27" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 3\n", + "Pgrid(S3, 2, two_boys, at_least_one_boy_tues)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see there are 27 relevant outcomes, of which 13 are green. So 13/27 really does seem to be the right answer. This picture also gives us a way to think about why the answer is not 1/3. Think of the yellow-plus-green area as a horizontal stripe and a vertical stripe, with an overlap. Each stripe is half yellow and half green, so if there were no overlap at all, the probability of green would be 1/2. When each stripe takes up half the sample space and the overlap is maximal, the probability is 1/3. And in the Problem 3 table, where the overlap is small, the probability is close to 1/2 (but slightly smaller).\n", + "\n", + "One way to look at it is that if I tell you very specific information (such as a boy born on Tuesday), it is unlikely that this applies to both children, so we have smaller overlap and a probability closer to 1/2, but if I give you broad information (a boy), this is more likely to apply to either child, resulting in a larger overlap, and a probability closer to 1/3.\n", + "\n", + "You can read some more discussions of the problem by (in alphabetical order) \n", + "[Alex Bellos](https://www.newscientist.com/article/dn18950-magic-numbers-a-meeting-of-mathemagical-tricksters?full=true),\n", + "[Alexander Bogomolny](http://www.cut-the-knot.org/Probability/BearBornOnTuesday.shtml),\n", + "[Andrew Gelman](http://andrewgelman.com/2010/05/27/hype_about_cond/),\n", + "[David Bigelow](https://web.viu.ca/bigelow2/Problem%201127%20Solution.pdf),\n", + "[Julie Rehmeyer](https://www.sciencenews.org/article/when-intuition-and-math-probably-look-wrong),\n", + "[Keith Devlin](https://www.maa.org/external_archive/devlin/devlin_05_10.html),\n", + "[Peter Lynch](http://mathsci.ucd.ie/~plynch/Publications/BIMS-TwoChildParadox.pdf),\n", + "[Tanya Khovanova](http://arxiv.org/pdf/1102.0173v1.pdf),\n", + "and\n", + "[Wendy Taylor & Kaye Stacey](http://www.aamt.edu.au/Journals/Sample-articles/amt70_2_taylor.pdf)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Sleeping Beauty Paradox\n", + "\n", + "The [Sleeping Beauty Paradox](https://en.wikipedia.org/wiki/Sleeping_Beauty_problem) is another tricky one:\n", + "\n", + ">Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Then a fair coin will be tossed,\n", + "to determine which experimental procedure to undertake:\n", + "- Heads: Beauty will be awakened and interviewed on Monday only.\n", + "- Tails: Beauty will be awakened and interviewed on Monday and Tuesday only.\n", + "\n", + ">In all cases she is put back to sleep with an amnesia-inducing drug that makes her forget that awakening and sleep until the next one. In any case, she will be awakened on Wednesday without interview and the experiment ends. Any time Beauty is awakened and interviewed, she is asked, \"What is your belief now for the proposition that the coin landed heads?\"\n", + "\n", + "What should Sleeping Beauty say when she is interviewed? First, she should define the sample space. She could use the notation `'heads/Monday/interviewed'` to mean the outcome where the coin flip was heads, it is Monday, and she is interviewed. So there are 4 equiprobable outcomes:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "B = {'heads/Monday/interviewed', 'heads/Tuesday/sleep',\n", + " 'tails/Monday/interviewed', 'tails/Tuesday/interviewed'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "At this point, you're probably expecting me to define predicates, like this:\n", + "\n", + " def heads(outcome): return 'heads' in outcome\n", + " def interviewed(outcome): return 'interviewed' in outcome\n", + " \n", + "We've seen a lot of predicates like this. I think it is time to heed the \"[don't repeat yourself](https://en.wikipedia.org/wiki/Don%27t_repeat_yourself)\" principle, so I will define a predicate-defining function, `T`. Think of \"`T`\" for \"it is true that\":" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def T(property):\n", + " \"Return a predicate that is true of all outcomes that have 'property' as a substring.\"\n", + " return lambda outcome: property in outcome" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can get the answer:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "heads = T(\"heads\")\n", + "interviewed = T(\"interviewed\")\n", + "\n", + "P(heads, such_that(interviewed, B))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Note: I could have done that in one line: `P(T(\"heads\"), such_that(T(\"interviewed\"), B))`\n", + "\n", + "This problem is considered a paradox because there are people who argue that the answer should be 1/2, not 1/3. I admit I'm having difficulty coming up with a sample space that supports the \"halfer\" position. \n", + "\n", + "I do know of a question that has the answer 1/2:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(heads, B) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "But that seems like the wrong question; we want the probability of heads given that Sleeping Beauty was interviewed, not the unconditional probability of heads.\n", + "\n", + "The \"halfers\" argue that before Sleeping Beauty goes to sleep, her unconditional probability for heads should be 1/2. When she is interviewed, she doesn't know anything more than before she went to sleep, so nothing has changed, so the probability of heads should still be 1/2. I find two flaws with this argument. First, if you want to convince me, show me a sample space; don't just make philosophical arguments. (Although a philosophical argument can be employed to help you define the right sample space.) Second, while I agree that before she goes to sleep, Beauty's *unconditional* probability for heads should be 1/2, I would say that both before she goes to sleep and when she is awakened, her *conditional* probability of heads *given that she is being interviewed* should be 1/3, as shown by the sample space." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Monty Hall Paradox\n", + "\n", + "[This](https://en.wikipedia.org/wiki/Monty_Hall_problem) is one of the most famous probability paradoxes. It can be stated as follows:\n", + "\n", + "> Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, \"Do you want to switch your choice to door No. 2?\" Is it to your advantage to switch your choice?\n", + "\n", + "\n", + "
Monty Hall
\n", + "\n", + "Much has been written about this problem, but to solve it all we have to do is be careful about how we understand the problem, and about defining our sample space. I will define outcomes of the form `'Car1/Lo/Pick1/Open2'`, which means:\n", + "* `Car1`: The producers of the show randomly placed the car behind door 1.\n", + "* `Lo`: The host randomly commits to the strategy of opening the lowest-numbered allowable door. A door is allowable if it does not contain the car and was not picked by the contestant. Alternatively, the host could have chosen to open the highest-numbered allowable door (`Hi`).\n", + "* `Pick1`: The contestant picks door 1. Our sample space will only consider cases where the contestant picks door 1, but by symmetry, the same arguments could be used if the contestant picked door 2 or 3.\n", + "* `Open2`: After hearing the contestant's choice, and following the strategy, the host opens a door; in this case door 2.\n", + "\n", + "We can see that the sample space has 6 equiprobable outcomes involving `Pick1`:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "M = {'Car1/Lo/Pick1/Open2', 'Car1/Hi/Pick1/Open3',\n", + " 'Car2/Lo/Pick1/Open3', 'Car2/Hi/Pick1/Open3',\n", + " 'Car3/Lo/Pick1/Open2', 'Car3/Hi/Pick1/Open2'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now, assuming the contestant picks door 1 and the host opens door 3, we can ask:\n", + "- What are the possible outcomes remaining?\n", + "- What is the probability that the car is behind door 1? \n", + "- Or door 2?" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Car1/Hi/Pick1/Open3', 'Car2/Hi/Pick1/Open3', 'Car2/Lo/Pick1/Open3'}" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "such_that(T(\"Open3\"), M)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(T(\"Car1\"), such_that(T(\"Open3\"), M))" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(2, 3)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(T(\"Car2\"), such_that(T(\"Open3\"), M))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see that the strategy of **switching** from door 1 to door 2 will win the car 2/3 of the time, whereas the strategy of **sticking** with the original pick wins the car only 1/3 of the time. So if you like cars more than goats, you should switch. But don't feel bad if you got this one wrong; it turns out that Monty Hall himself, who opened many doors while hosting *Let's Make a Deal* for 13 years, didn't know the answer either, as revealed in this letter from Monty to Prof. Lawrence Denenberg, when Denenberg asked for permission to use the problem in his textbook:\n", + "\n", + "\n", + "If you were Denenberg, how would you answer Monty, in non-mathematical terms? I would try something like this:\n", + "\n", + "> When the contestant makes her initial pick, she has 1/3 chance of picking the car, and there is a 2/3 chance the car is behind one of the other doors. That's still true after you open a door, but now the 2/3 chance for *either* other door becomes concentrated as 2/3 behind *one* other door, so the contestant should switch.\n", + "\n", + "But that type of argument was not persuasive to everyone. [Marilyn vos Savant](http://marilynvossavant.com/game-show-problem/) reports that many of her readers (including, she is pleased to point out, many Ph.D.s) still insist the answer is that it doesn't matter if the contestant switches; the odds are 1/2 either way. Let's try to discover what problem and what sample space those people are dealing with. Perhaps they are reasoning like this:\n", + "\n", + "They define outcomes of the form `'Car1/Pick1/Open2/Goat'`, which means:\n", + "* `Car1`: First the car is randomly placed behind door 1.\n", + "* `Pick1`: The contestant picks door 1. \n", + "* `Open2`: The host opens one of the two other doors at random (so the host might open the door with the car).\n", + "* `Goat`: We observe there is a goat behind the opened door.\n", + "\n", + "Under this interpretation, the sample space of all outcomes involving `Pick1` is:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "M2 = {'Car1/Pick1/Open2/Goat', 'Car1/Pick1/Open3/Goat',\n", + " 'Car2/Pick1/Open2/Car', 'Car2/Pick1/Open3/Goat',\n", + " 'Car3/Pick1/Open2/Goat', 'Car3/Pick1/Open3/Car'}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And we can calculate the probability of the car being behind each door, given that the contestant picks door 1 and the host opens door 3 to reveal a goat:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(T(\"Car1\"), such_that(T(\"Open3/Goat\"), M2))" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(T(\"Car2\"), such_that(T(\"Open3/Goat\"), M2))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(0, 1)" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(T(\"Car3\"), such_that(T(\"Open3/Goat\"), M2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So we see that under this interpretation it doesn't matter if you switch or not. \n", + "\n", + "Is this a valid interpretation? I agree that the wording of the problem can be seen as being ambiguous. However, this interpretation has a serious problem: in all the history of *Let's Make a Deal*, it was never the case that the host opened up a door with the grand prize. This strongly suggests (but does not prove) that `M` is the correct sample space, not `M2`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "# Simulating the Monty Hall Problem\n", + "\n", + "Some people might be more convinced by a simulation than by a probability argument. Here is code for a simulation:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "import random\n", + "\n", + "\n", + "def monty(strategy):\n", + " \"\"\"Simulate this sequence of events:\n", + " 1. The host randomly chooses a door for the 'car'\n", + " 2. The contestant randomly makes a 'pick' of one of the doors\n", + " 3. The host randomly selects a non-car, non-pick door to be 'opened.' \n", + " 4. If strategy == 'switch', contestant changes 'pick' to the other unopened door\n", + " 5. Return true if the pick is the door with the car.\"\"\"\n", + " doors = (1, 2, 3)\n", + " car = random.choice(doors)\n", + " pick = random.choice(doors)\n", + " opened = random.choice([d for d in doors if d != car and d != pick])\n", + " if strategy == 'switch':\n", + " pick = next(d for d in doors if d != pick and d != opened)\n", + " return (pick == car)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can confirm that the contestant wins about 2/3 of the time with the `switch` strategy, and only wins about 1/3 of the time with the `stick` strategy:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({False: 33110, True: 66890})" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from collections import Counter\n", + "\n", + "Counter(monty('switch') for _ in range(10 ** 5))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({False: 66738, True: 33262})" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(monty('stick') for _ in range(10 ** 5))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Reasoning with Probability Distributions\n", + "\n", + "So far, we have made the assumption that every outcome in a sample space is equally likely. In real life, the probability of a child being a girl is not exactly 1/2. As mentioned in the [previous notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb), an [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark:\n", + "\n", + " GG: 121801 GB: 126840\n", + " BG: 127123 BB: 135138\n", + "\n", + "Let's implement that:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BB': 0.2645086533229465,\n", + " 'BG': 0.24882071317004043,\n", + " 'GB': 0.24826679089140383,\n", + " 'GG': 0.23840384261560926}" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "DK = ProbDist(GG=121801, GB=126840,\n", + " BG=127123, BB=135138)\n", + "DK" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now let's try the first two Child Problems with the probability distribution `DK`. Since boys are slightly more probable than girls, we expect a little over 1/2 for Problem 1, and a little over 1/3 for problem 2:" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5152805792702689" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 1 in DK\n", + "P(two_boys, such_that(older_is_a_boy, DK))" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.3473082824253857" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 2 in DK\n", + "P(two_boys, such_that(at_least_one_boy, DK))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "It all looks good. Now let's leave Denmark behind and try a new problem:\n", + "\n", + "### Child Problem 4. One is a boy born on Feb. 29. What is the probability both are boys?\n", + "\n", + "* **Child Problem 4.** I have two children. At least one of them is a boy born on leap day, February 29. What is the probability that both children are boys? Assume that 51.5% of births are boys and that birth days are distributed evenly across the 4×365 + 1 days in a 4-year cycle.\n", + "\n", + "We will use the notation `GLBN` to mean an older girl born on leap day (`L`) and a younger boy born on a non-leap day (`N`). " + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "sexes = ProbDist(B=51.5, G=48.5) # Probability distribution over sexes\n", + "days = ProbDist(L=1, N=4*365) # Probability distribution over Leap days and Non-leap days\n", + "child = joint(sexes, days) # Probability distribution for one child family\n", + "S4 = joint(child, child) # Probability distribution for two-child family" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's check out these last two probability distributions:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BL': 0.00035249828884325804,\n", + " 'BN': 0.5146475017111568,\n", + " 'GL': 0.0003319644079397673,\n", + " 'GN': 0.48466803559206023}" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "child" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'BLBL': 1.2425504363742495e-07,\n", + " 'BLBN': 0.00018141236371064045,\n", + " 'BLGL': 1.170168857556332e-07,\n", + " 'BLGN': 0.0001708446532032245,\n", + " 'BNBL': 0.00018141236371064045,\n", + " 'BNBN': 0.26486205101753507,\n", + " 'BNGL': 0.00017084465320322452,\n", + " 'BNGN': 0.24943319367670777,\n", + " 'GLBL': 1.170168857556332e-07,\n", + " 'GLBN': 0.00017084465320322452,\n", + " 'GLGL': 1.102003681388002e-07,\n", + " 'GLGN': 0.0001608925374826483,\n", + " 'GNBL': 0.0001708446532032245,\n", + " 'GNBN': 0.24943319367670777,\n", + " 'GNGL': 0.0001608925374826483,\n", + " 'GNGN': 0.2349031047246665}" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "S4" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can solve the problem. Since \"boy born on a leap day\" applies to so few children, we expect the probability of two boys to be just ever so slightly below the baseline rate for boys, 51.5%." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5149145040963757" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Child Problem 4\n", + "boy_born_on_leap_day = T(\"BL\")\n", + "\n", + "P(two_boys, such_that(boy_born_on_leap_day, S4))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The St. Petersburg Paradox\n", + "\n", + "The [St. Petersburg paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox) from 1713, named for the home town of the [Bernoullis](http://www.storyofmathematics.com/18th_bernoulli.html), and introduced by [Daniel Bernoulli](), the nephew of Jacob Bernoulli (the urn guy):\n", + "\n", + "> *A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The pot starts at 2 dollars and is doubled every time a head appears. The first time a tail appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if a tail appears on the first toss, 4 dollars if a head appears on the first toss and a tail on the second, etc. What is the expected value of this game to the player?*\n", + "\n", + "To calculate the expected value, we see there is a 1/2 chance of a tail on the first toss (yielding a pot of $2) and if not that, a 1/2 × 1/2 = 1/4 chance of a tail on the second toss (yielding a pot of $4), and so on. So in total, the expected value is:\n", + "\n", + " 2 * (1/2) + 4 * (1/4) + 8 * (1/8) + ... = 1 + 1 + 1 + ... = ∞\n", + "\n", + "The expected value is infinite! But anyone playing the game would not expect to win an infinite amount; thus the paradox.\n", + "\n", + "## Response 1: Limited Resources\n", + "\n", + "The first major response to the paradox is that the casino's resources are limited. Once you break their bank, they can't pay out any more, and thus the expected return is finite. Let's consider the case where the bank has a limit to their resources, and create a probability distribution for the problem. We keep doubling the pot and halving the probability of winning the amount in the pot (half because you get the pot on a tail but not a head), until we reach the limit." + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def st_pete(limit):\n", + " \"Return the probability distribution for the St. Petersburg Paradox with a limited bank.\"\n", + " P = {} # The probability distribution\n", + " pot = 2 # Amount of money in the pot\n", + " pr = 1/2. # Probability that you end up with the amount in pot\n", + " while pot < limit:\n", + " P[pot] = pr\n", + " pot = pot * 2\n", + " pr = pr / 2\n", + " P[limit] = pr * 2 # pr * 2 because you get limit for heads or tails\n", + " return ProbDist(P)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's try with the casino limited to 100 million dollars:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2: 0.5,\n", + " 4: 0.25,\n", + " 8: 0.125,\n", + " 16: 0.0625,\n", + " 32: 0.03125,\n", + " 64: 0.015625,\n", + " 128: 0.0078125,\n", + " 256: 0.00390625,\n", + " 512: 0.001953125,\n", + " 1024: 0.0009765625,\n", + " 2048: 0.00048828125,\n", + " 4096: 0.000244140625,\n", + " 8192: 0.0001220703125,\n", + " 16384: 6.103515625e-05,\n", + " 32768: 3.0517578125e-05,\n", + " 65536: 1.52587890625e-05,\n", + " 131072: 7.62939453125e-06,\n", + " 262144: 3.814697265625e-06,\n", + " 524288: 1.9073486328125e-06,\n", + " 1048576: 9.5367431640625e-07,\n", + " 2097152: 4.76837158203125e-07,\n", + " 4194304: 2.384185791015625e-07,\n", + " 8388608: 1.1920928955078125e-07,\n", + " 16777216: 5.960464477539063e-08,\n", + " 33554432: 2.9802322387695312e-08,\n", + " 67108864: 1.4901161193847656e-08,\n", + " 100000000: 1.4901161193847656e-08}" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "StP = st_pete(limit=10**8)\n", + "StP" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we define the function `EV` to compute the [expected value](https://en.wikipedia.org/wiki/Expected_value) of a probability distribution: " + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def EV(P):\n", + " \"The expected value of a probability distribution.\"\n", + " return sum(P[v] * v \n", + " for v in P)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "27.490116119384766" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "EV(StP)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This says that for a casino with a bankroll of 100 million dollars, if you want to maximize your expected value, you should be willing to pay up to $27.49 to play the game. Would you pay that much? I wouldn't, and neither would Daniel Bernoulli. \n", + "\n", + "## Response 2: Value of Money\n", + "\n", + "Daniel Bernoulli came up with a second response to the paradox based on the idea that if you have a lot of money, then additional money becomes less valuable to you. If I had nothing, and I won $1000, I would be very happy. But if I already had a million dollars and I won $1000, it would be less valuable. How much less valuable? Bernoulli proposed, and [experiments confirm](https://books.google.com/books?id=1oEa-BiARWUC&pg=PA205&lpg=PA205&dq=mr+beard+oil+wildcatter+value+of+money+utility&source=bl&ots=cBDIX-rkTz&sig=GHB8-inorWrU39vA8JYV_sCtqB8&hl=en&sa=X&ved=0CCAQ6AEwAGoVChMI5fu-p8qlyAIViKWICh0XAAz5#v=onepage&q=mr%20beard%20oil%20wildcatter%20value%20of%20money%20utility&f=false), that *the value of money is roughly logarithmic.* That is, rational bettors don't try to maximize their expected monetary value, they try to maximize their *expected utility*: the amount of \"happiness\" that the money is worth.\n", + "I'll write the function `util` to describe what a dollar amount is worth to a hypothetical gambler. `util` says that a dollar is worth a dollar, until the amount is \"enough\" money. After that point, each additional dollar is worth half as much (only brings half as much happiness). Value keeps accumulating at this rate until we reach the next threshold of \"enough,\" when the utility of additional dollars is halfed again. The exact details of `util` are not critical; what matters is that overall money becomes less valuable after we have won a lot of it." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def util(dollars, enough=1000): \n", + " \"The value of money: only half as valuable after you already have enough.\"\n", + " if dollars < enough:\n", + " return dollars\n", + " else:\n", + " additional = dollars-enough\n", + " return enough + util(additional / 2, enough * 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "A table and a plot will give a feel for the `util` function. Notice the characteristics concave-down shape of the plot." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 100 $ = 100 util\n", + " 1,000 $ = 1,000 util\n", + " 10,000 $ = 4,250 util\n", + " 100,000 $ = 15,937 util\n", + " 1,000,000 $ = 51,593 util\n", + " 10,000,000 $ = 162,460 util\n", + " 100,000,000 $ = 535,646 util\n", + " 1,000,000,000 $ = 1,658,229 util\n" + ] + } + ], + "source": [ + "for d in range(2, 10):\n", + " m = 10 ** d\n", + " print('{:15,d} $ = {:10,d} util'.format(m, int(util(m))))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Y axis is util(x); x axis is in thousands of dollars.\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline \n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.plot([util(x) for x in range(1000, 10000000, 1000)])\n", + "print('Y axis is util(x); x axis is in thousands of dollars.')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now I will define the function `EU`, which computes the [expected utility](http://wiki.lesswrong.com/wiki/Expected_utility) of the game:" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def EU(P, U):\n", + " \"The expected utility of a probability distribution, given a utility function.\"\n", + " return sum(P[e] * U(e) \n", + " for e in P)" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "13.096907431492582" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "EU(StP, util)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "That says we should pay up to $13.10 to play the game, which sounds more reasonable than $27.49.\n", + "\n", + "# Understanding St. Petersburg through Simulation\n", + "\n", + "Before I plunk down my $13, I'd like to understand the game better. I'll write a simulation of the game:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "button": false, + "collapsed": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def flip(): return random.choice(('head', 'tail'))\n", + "\n", + "def simulate_st_pete(limit=10**9):\n", + " \"Simulate one round of the St. Petersburg game, and return the payoff.\"\n", + " pot = 2\n", + " while flip() == 'head':\n", + " pot = pot * 2\n", + " if pot > limit:\n", + " return limit\n", + " return pot" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I will run the simulation 100,000 times (with a random seed specified for reproducability) and make the results into a probability distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2: 0.49755,\n", + " 4: 0.2506,\n", + " 8: 0.1259,\n", + " 16: 0.06322,\n", + " 32: 0.03151,\n", + " 64: 0.01607,\n", + " 128: 0.00751,\n", + " 256: 0.0037,\n", + " 512: 0.00191,\n", + " 1024: 0.00106,\n", + " 2048: 0.00045,\n", + " 4096: 0.00029,\n", + " 8192: 0.0001,\n", + " 16384: 6e-05,\n", + " 32768: 5e-05,\n", + " 65536: 1e-05,\n", + " 1048576: 1e-05}" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.seed(123456)\n", + "\n", + "results = ProbDist(Counter(simulate_st_pete() for _ in range(100000)))\n", + "results" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The results are about what you would expect: about half the pots are 2, a quarter are 4, an eighth are 8, and higher pots are more and more unlikely. Let's check expected utility and expected value:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(13.2477575, 26.71606)" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "EU(results, util), EV(results)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "These are not too far off from the theoretial values.\n", + "\n", + "To see better how things unfold, I will define a function to plot the running average of repeated rounds:" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def running_averages(iterable):\n", + " \"For each element in the iterable, yield the mean of all elements seen so far.\" \n", + " total, n = 0, 0\n", + " for x in iterable:\n", + " total, n = total + x, n + 1\n", + " yield total / n\n", + "\n", + "def plot_running_averages(fn, n):\n", + " \"Plot the running average of calling the function n times.\"\n", + " plt.plot(list(running_averages(fn() for _ in range(n))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's do ten repetitions of plotting the running averages of 100,000 rounds:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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Ly+uEz6KHe6+yktdKKngyPHtP4NixQ3Xu27xZ3YKD1dcxLGzPx05GhkpZpaSo\nlFdgoPoaHO77KIRAStnl39oeW3MAsBqtPLH0Ca4b7Z/Fefr3V+eI+HigKZaJA2P5538ruGVWDNdc\nA//978H33bDhUmprv2HUqKWEhPSRRu3OFB6uGrHbGrKLilRAuOACddL9/e9Vnf6rr1SbxogRe/eN\niVEpF+Chh6B2bRFjd35MdIKkPuE8Uj75grhlORRdGUi6bxsbx19N0MzTSLhqKkRF4XQepLuj2ay6\nBZ155t5tFRUqKPzwgzpjpqSo+b4vu0z9g4wcqWbpa25WAWPqVJW38Fd6KiZGTUF7zjl7t3k8KjVX\nUqKuBpYsgR9/VHOV5+YigKjoaKa63UwdMUIF4wez8QwbhWNANmu3WFm1StUmsrLUn2rBAhWrGxvV\nWx86VNU4srJ++ac6XhhMKogmJ6uYvq+2St7OnSo+5+erP8f8+eoCtrBQZQ3tdlVJbUtbhYWpc8/g\nwSqrmpGhtnWXHl1z+L7we2774jY+vfRTv9Qc9iUlpI7eQsHKgXu2XXaZulg9ULV748araW5eT0PD\ncgBGjlxCaOgBkp1d4ShqDr19hO6wYSqWbNmiTlClpaot/FcX+PjTmSsoePFr1hcG03/Nl5zQkkuZ\nNYXPHVMoSojEcrKJYWcmcWqajehLb0fmb0VKJ0bjEXTJ9Xph/Xp1hvz+e3VlHhiortKXLVOX05Mn\nqwE0kyapKujRVNGOtebQEW1T0a5apd7bypXqLBYXp85OI0eqCJGdraoOre0+1dXqbW/YoHZbtUrd\nPB6V+RsyRL3EiBHqfkxM972l7vBeZSVvVFTwXnb2Me3v9arMaViYqjzvW/tYt06ltbZsUX8Kkwlq\na3XNgRPiTyC/Jp/qliOftuHRR1Uvg84mBOzMG8g1f/2CD1d+x8d//jVnTcjEalVVwgNF9Li4mwgM\nzCIvbxwrV04gJeUvJCXdjcHQoz/2XiUqCv7v/1TzQBsV8AwIMZZ+08cyGoAbKdjmZtvLKxi7/J+c\nW/I+Ue83UPduED96RjPG4OJPsx5ixIhvGDmyhn79hhARMZ2wsJOx2dLaj5g3GlVkGjZMdd3dl8ej\n8inffgtvvKEa3+12dTV/0kkqVTZsmGrf6EliY9Vt36S706nSdps2qTP+O++ohTQKClSCftAgIg0G\nTomM5JRRo+DCwXDfIJaX9OfqawTXXqsCxuLFKoO4fr06wbU1iGdl7R0pHRd3fLRv7M9oVBVpUPNN\nRUSo1N0lx1p5AAAgAElEQVT+pFSBuLsqpT36LGU2mpmYOJGfin864n3uvlv97Kpu9i/eO50pqys5\n++MT+Pv8F3j8NxcwfLi6UE9Pb//8kJCx5ORIHI5i1q6dQVHR44wZs4qAgJSuKeAR6u01hkM52AV6\n8gAzyX8ZT0HBV3i9KQSnPkTwhg1Eff4VW9YOx+O5nFdfvYN777UxeHARw4atw+X6gpNP/orx48OI\nippEWNiUw//tTKa9w3zvuEN92Pn5akTb99/DvHnq8fDh6iwwfrwKFqmpPW8godW6t2/ovqkqp1NV\nzTduVIGwbTTa22/Dpk2MbGrhf3IQ2R9nc15WFsxSEUCmD6C4wsz69SpQLF2qat9bt6qrZ59PVZgG\nDtybpgoIUCfMxMTO7aTW2wjRNRe+B9OjgwOoAPGnb/50xM8//3x1hdKVq3VdOfxKzEYzl753IX94\n8nbsPz7CgAEmvvtOZRAOxGZLYMyYVRQV/Z28vHG43ZVYrQmMGPGd3wPFcUsIyMrCmpXFUOC11s2N\njbB0aSq5uaksXix55pnfcNttRtLTC0lP/5bMzOcZPVqQnr6S/v3PoqLiZUJDJxESMp6QkAlYrXHt\njzNggLq11TIaG1XDcV6eWij78svV9thYFTCsVpWM7qms1r2DAma273K+Lnc3T1y3kZfGr1O5ka+/\nhi1bEEVFJCYlkThwINMHDYJJQ+Ba9ToNxjA2b1bNPJs3w+qlLXz8XD1L8qMxGAWNjSpAZGaqRt22\nHH9iovoZE3N81jy6So8PDg+d8hDjnh9HqDWUGa/P4IwBZ3DLCbcc9PlGI9xyC/zzn2qlsH3WE+pU\nl2Rfwqj+o8h8OpPMqE959d0fOOmkSIzGvb08XnttIIsXw8svq7y4EAaSku4gPHwKa9acjsUSz4oV\nYwgPP5WUlAcJDOy+yez6cs2ho4KCVJuV6t0qABuNjbBmTTorVqTx88+1zJ7tYceOEDIyShgwwMjE\nibGkpn5JRMTNBASYCA4eQ1DQaIKDRxMYmI3VmoAQAo+nDqMxGBEUpHJh++bDXC51Nb5+vUoyT5jg\np0+g47wh4awJmgjXTfzlLxwO9R63bFERIDdXTZa0cSPBVitjvF5ISuLMceOgpADyFqlqQ1YW3oxB\nVIemUmhIZZtMZ+22NJb8GEFhkaCgQHU/T09X37XMzL2NuCkpKniEhPjjk+i9enxwyI7OxuFxYDaY\nmb9tPvO3zT9kcAD1TxEernpFnnmmSvF2hYGRA/Hd72POd3O4e/lwPl3xIf9+YAzR0XDRRVfx9tvq\ni9Gvn+pc8/e/q2pxcPAoTjyxEoCWlu38/HM2lZVvExPzawYMeBKzObxrCqwds6CgttlVBaD+Ps3N\nkJeXxvLlaSxfDi+8cDabNz8NwNChu8nM3Ep6+lIGDHiKtLSVhIam0NDwEwZDAEFBwzEagwgNnYTV\nmkBQ0CgCA7MwDBrUt2e8tdlUvmjIkF9u9/lUT4LychU8ysvVhz5njmrbWL8e4+bNRO/YQfSOPMbk\n53NJfr7KRUVEQFoa7qQ0ao39KAgZyqamVHasSuO5BcnkF1koKFDfveRkNYI8IUHVPiIiVCBJSlIZ\nPXUR55+Ppqfp8cFBCME5meewaPsiTko6ie8Kv2Nn7U5SwlIOuV9YmKrtjhunJg+dM6frynfvyfcy\nLGYYV300ndBpoTz366+59qJTAGhogE8/VWnmcePUZGr7DusPCEjj5JObaWkpYtOmK/nhhwji4m4i\nNfUhzOau7bemvwQdY7erNOK+qUSXS+XPt28P58cfx1FVNY4vvriVLVskAwfWM2ZMDRMnxjJ48Boi\nIz/E7d5Nbe33FBQ8hMtVgcUSQ0jIeGy2dGy2FIKChhEYmI3RaPffG+0OBoMaONE2eGJ/MTFqLMq+\npFQRur4eCgow5+cTlZdHVP0KxpS9q7r7FBdDTAxyTBrOuDRqQlKosCRQ4opmy6pYFpYk8I/qGLbv\nEDQ3q9iVkKCCRVvaqu2WkqJ+d7y0e/T44ABw09ib+GzLZ3tGKP/tx7/xzxn/POx+zz2nTswPP6z6\nF//rX11XxrMzz+bba74l619ZXLs7hf/MH0h4y8MEBc3kkkvUSmFvvglnn62e/+KLaqEhIdTiJ+ee\nmwjk8v77mzCbT6W09Bksljiysz8kJKTzqz46rdQ1LBbViJqVtfdvDdDSIli5MpQlS0JZuBDmzDmB\n/PwTsFpV225aGmRne8jOLiUtbSVxcd8TGvokQjTidle0BoqReDx1NDQsx+3ehc2WRnDwaMCA11tP\nYOBQgoKGExg4FLt9IAZDD+sN1dmEUJf7gYF758Voa7tp4/FAURFi+3Zs+fnEFRYSV/wtIysrVb/n\noiJoaVFn/pgYPKGRtNS72BU7jDJnHI3fNlLUHMnHjUmsrE6ioMJGS3gcsQmmPTWQ2mGwMwnmF6lx\nCXFxqkbS29s/ekVwyI7KRiLZVLWJi7Iu4umfn2butLkEmA+9YrkQqna6ZIlKCZx+Opx7bteVc0jU\nEOQDklpHLe9+O5aPG2+gaVUDVw6/EoMwcNllKkjceadql3z8cTVV8003qf1//3u48spBGAwl3H57\nDRMnXseaNdOx2wcRG/trYmNnYTB03mWLrjl0n4CAvYv+tKmrU2n3tlz42rUmVqxI4v33k9i48VzK\nyx8jIgLGjvWRnFxFfPw2YmN/JCUlgSFDpmM0BtDUtA6XqxSjcRA+n4Oqqg/ZufPPOJ0FWK3JBAZm\nExiYjd0+sDVoZGIwHEezyO07qmzf9p19NTSoVFZBAab6eoI3bCDYaiK9dBXYiiHQCLYGqFgPvkpk\nvRl3aRRNLQm0bLaxcVUC62KC2bZlGAsbo1hdFU+JI4LA2BBsyTH0TzASELC35hEXt/cWHd1zJ0Ls\nFcFBCIHVaGVNxRrumXQPb69/m9m5s3l02qNHtP+ECardKydHdZu7oouXaQizhXFi4okkRUdw8Zf/\nj6d/fprrR1/P+ITxOD1OrrjDwGOPjeTVV/d2Xvn2W9UF/rHH1MywV18dwezZ73LHHW6uvTaXysq5\nFBbOJSHhNgIDswgJmdD3Uw19XGjoLxe1GTRIrdHUpqlJdWYqKzOQnx/Npk3RfPjhRDZu3HctiOkM\nHqz2bbsZjeDzuWhu3kJT01qamtbvCRoOxw6s1gTs9kzs9kwCAjKxWvsTFDSitdH8yM9UnkYPnhoP\n5mgzRlsPPcPto6LidQoLHyUoaAQWSxxWazxWawIWSwymAeFYhpyIyRRx2FUghduNpbwcS1ER4du3\nU7ljB7FlZVzcf42a+ra0FFldja+2HrFiN44tUdQHxVHxQzw1tngKvAn81BLPpoZ4NjfG44iMJzwh\nkLgEw57aSGKiqgxFRamMWr9+3V8T6RXBAcBmstHiaQHgm6u+4Xef/Y6Hpz6MQRzZJzZ5smp7uPJK\n1b186NCuLK0yNGYY1XdW8+baN7nig19GpEuzL2XOuXPweFL49FM1uSaoL/Z556k0WEkJ/PnPZjIz\npwHTmDmzgssvP4eIiGUABAePIzX1IcLDT0Uc4efQRqeVer7AQHXBsD8pVXfPjRv33r74Qo1Tq6pS\nPWZDQizEx2eTnJy9Zx6ftDTo39+Nx7Od5ubNNDdvpqFhOSUlS/F4qnG5ygGwWhMxm6MIDZ2E3T6w\n9QQah9WaiMUSs+fkuf3O7ZQ+W4qwCIxBRiwxFixxFmwpNkrNIbhroqj6qA5LnAVrghVzlBmDqftz\nLS07W2j4uYHqmJ8xWWIwbBiDK6wCh30tjsbP8Vqq8YrdOJvLQfgwNsdhcsRj8vTHao7DGhhPQHgS\n9n79sccmERAah0hMVGfwiRPZVlnJ2xUVXLzPCGkBGAFcLuzl5dhLS4ktKVFf6pISKFkPJSXI4hLY\nno+o8OFdbcFrtOARZpxY2W4bQpEvmm9dcRS442kOi1NdnbtJrwkOFqOqChfWFXJx1sVYjVYW5i/k\n9AGnH2bPvebMUaMyzz5bdTHvjmH8BmHg8mGXc+nQS2l0NbKzdidhtjBeWvUSo/8zmlkjZnH31LsJ\nCGg/iVt8vGrIvu8+1V7y448xXHPNT5x1lo9Zs8oIDn6U/Pw7aGpaQ0zMFSQm/pGgoPaNeV6vg507\n/0Rk5FmEhk7ac3Wo00rdQ3olGOi0dcmF2DuY+ZRTfvm7pibVS3T5chVAjEb1v/7aa6p9tqLCTP/+\nmSQnZ5KergJJ2xi3rCwXAQH1NDdvpLl5M15vHU1N66iuno/LVYrTWYTP58BmS8duz6BhnIOwU+OJ\nHDcIoyMKX70JUR2HLLDjW+rDW++h9LlSXGUuWra04G30YulvwRJjwRRhwhpnVYEjzootxYY1yYo1\nwYowCNxVbqwJVgw2A8LYsc+t7LkyCucUYnmgDk9xGnUvDCPslDBcZS7MMWaEU+Jc14Rw+0h+tB8y\ntBSXLMblK8XZWExTzbd4yirwWauRwVUQUg8mL9RGYdqdTES/Iq6qS+GnpUmYff2xBvTHFpSAyROL\npb+NgOh+2IdmYznAXOECVLT3ejHW1WHctQtLdTV2k4nRDQ17aiKegkIcO5biLS7nmQ59Gkeu1wQH\nIQSvnv8q4xPGI4TghjE3MP316bTc24LNdOSLxl52mfrynHmmGrAacOhmi05jEAZCrCEMi1En7/sn\n389vR/2Wvyz+C5lPZ3Ld6Ou4YPAFjI5rP24+MVE1qoOqUTzxTCPX3hCFxfgUEyZI0tK2M23ah1RU\nDAdgojuQ+qrPCU+6GqMxELe7gqKix6mp+RKnsxiPZzcguOCCx2lqmo7dPrjTTlzaXo5iB8YAI2vP\nWkv90nrCp4YTODwQ+yA79oF2LDEWjEFG3NVupEdiH2zHGNCx9ExgoJoCaeTIA//e5VIdeNoWvdm6\nVc3woXpYWbDZ+pGefhJpaSftWTGt7WdCAvh8tTgc+TQ3b6WlfikypB6HIx+HIxevsU5dkdt2skuM\nxvfDPORf/0iwLZkoWxpWcwLGpgSMtTHI2jDcpW6cpU5atrVQs7AGZ5ETZ5ETz27PL8ps7mfGXeXG\nEmshIDMAa38r5hjznuBiDDRiCjOpmktr4Nn//zn1oVS8l8ZiNIaQ/HzOYT7FrIP+RkqJ1+GiZVc5\nztpqmoIL2Fi+geJSG0m2JtyU0WRZQV3953isJfhaimFNOOysAYcdURuNsSUaT0kA1IVAXTgB4bE4\n19qRFVHYo5KwBsVgibRhjorCEjsIS7wF8zAzpnATlmgzpHZPOrnXBAfgF2s6XzX8Kn732e946qen\nuPPEO4/qdR54QK2bkpmp+jV/9ZXqXdDd4oLjePasZ7lj4h3c8NkNPPz9w7/4/V+n/JWzBp61J6CA\n6qL7Z08oXA4UTaT0u6dpeGkkD/7lNgICbuOWm2oZ7xtMZeVbrPvuVgyGAPr1U91mxo5dg9NZQm3t\nd3i9guTkRaxd+098Pif9+p1LdPSlrTWLXt7NogfwtnhZmrgUU7gJT62HofOHgg8a1zRS/0M95S+W\nU/9j/S/2EVaBJUqlZox2I9YkK8YgI8FjgwlIDcCWattzZX2sLBZ1ok9La1/rkFKlpdpWStu+XU1G\n+8or6n5lJcTFhZGaOprExNEYVp1GWIKJcVeEkJKiarmLF8PQoZKqKi8tLT4SEm7D4SjE4dhOY2Me\nDsdOWpz5+KxOAoakYR2ZiMUSTZAlnkhrPGZzJCZTP6zWWMzmaIyE4d7lQRgEPqcPx3YHjiIHnt0e\nXKUuGlc30rKtBXelG2EWuCpcSKfcEzys8VZa8luIuqBzJiQSQmAKsBKcnExwcjL9GMXyykl8VVHB\njYeYeM/n8+LYXUFTxQ6aqwpxxu7GGN+Iq6Uct7cA4/QKfIEVOD1lNMtaDN4IDK5gRHMY1IciN9ug\nLghfefdNy9qrgsO+AswBrLp+FSPmjWDm4JkMiBhwxPsKodaWHTxYzSU2YYJ6HBd3+H27QnpEOguv\nXIjX52VJ8RLeXv82NS015NfkM/zfw4kNiuWaEdcwa+SsPe9z661b2Vy1mdVXz2dD5d94ffWbeEpO\nY+4353BtuZ0Z196EafylXDOjhlMCfkCIp5ASLJZ4YmIuwe2GJ564mLlzobl5K5WV77J168243dVE\nRs4gImIG4eFTMJl64SolPYD0SgyBBibVTEJ65Z7USOSMg68B4XP7cJY4cRY68bl8OAuc1C2pY/fC\n3ZQVlOHYoU6KtjSbChZpNmypNgLSA7Bn2rEl2yh4qIDdX+0mcFggpmAT5n5mrAlWSv9diiHQgDXe\nStCwoD372lJsGCwGDBYDQqgG0KgoteTD/pxO1fOzbfjAqg0+CqpMlH6oJo9dtgz+/W+IiREUF5uI\njYXIyBkHfK8eTx0tLfk4nSW43btwOktpbFyJ212N212Fy1WB270Lr7cRs7kfFkscLS1b8RrrCcwa\nhsUSg9tdo3piAVJ6sFrjEcKARSQimiLx1djwVdoxVVdjH++lvGkdISH+GXVuMBixR8Zhj4wDTjzk\nc30+F253JW73bjwe9Xl4vU243dW4XBXQhV3y99VrgwPA8NjhDIsZRsY/M5APHF0Lq8WiFuPweNRM\nrqNGqYXI95+LvTsZDUYmJU1iUtLeUVXzzp7Hx5s/ZtH2RUx8YSJDY4ZiNpiJCYxhQMQAzhyo1h54\nbeZrSCn5tuBbwiY0cOmvm3nn25N46K5Y7q2+9xfHGTK2nBNHReDzWXC74aOPMsjMvIcxY+6hpWUz\nVVXzWb78PUpLH6C2dizDhuUzcOBpREScQVDQ8IPWLGpqFmGzJRIQMOCoer30dUeaMzeYDQSkBBCQ\nsjfX2f83v1x90NPowZHvoGVHi7qKznewe8Fumjc14yx2It2SxLsSsSXZcOx04Ch00LiqEUOggX7n\n9cNZ7KRpQxM1X9bg2OGgeZNaeNoSZ1HBIknl/tt+WuOtWKItWGItWK1izxRRAJt/qiZohJP4G44+\nzWEyhRIcPIrg4FGHfF7bidLpLKGlZRuBgdlI6cHlqsDh2IHBYMPlKsPl2oXJFIbbvYtax1dI6cYT\nXE+zcSO+6GZqmsJwOouJjr7sqMva3QwGS2tPqviDPOPIeml2VK8ODgC5V+USMTeCDzd9yHmDzjuq\nfYVQox3vu0+Nn7n4Ypg1C/76154zgMVkMDFz8ExmDp7JE6c/wYebPiQ1LPWAYzyEEExOmQy2UOZc\nl8Och1OREpbnecjd8jP5jmVsLCklv7iWl1aPxBcxGYtlMACx8U48Tgvjx2cSFpbJa6/tfd2goGbi\n4mrIzFzK5MkPMmTIQhISphIePgWLJY7Q0EkYjcGsWTMNmy0Fp7OUoKDhhIZOIizsFMLCJmMy6Ylt\nOoMpyETQ8CCChge1+530SlyVLiwxliNuQ5I+ifRJXKUuHDsdOIucOAocNK5ppPrTapwlTlwVLjy7\nPVj6W1Sw6G/B2t9Kw/IGgka0L0dn2vdEGRIy7vA7aJ2m1weH8IBwXj3/VW6dfyvnv3U+5xkagKP/\nh506Vc2mPHAgPPKIWlf3GNfu6DJWk5WLsy/m4uyLj3gfIWDsaBNjR08A9lapaxobiR6/iJyHHmBX\nmZXNprexNw+k2vEbKjeeTehpn2OZMI+zh53EySmTCK2exndfXMgbb5zNpk0GMjLqGTFiOZmZLxMa\n+l/S0oqx2WD8+B14vc00NPxMbe13FBc/yYYNlyCEGau1P6GhkwkJGUdw8DgCAwcjpRchTLqdoxMI\no8Aae3SjooVBIAwCW5KqNRyMz9ma8ipx4ipz4SpzYQgwEHZyNy5NpnWrXh8cAC4fejlvrH2Dovoi\nPhwSzEDPCuDQ1dUDychQI+mvv16ll+64A26/vW/OpRJoDsKw5TwWXd9W23qV4vpiFuQvYEH+vRQU\nLOaJ05+gtKGUT7Z9wOKC/4ctwcaEuydwTdzphNScQtHaaeTmns6CBRAY6CU1tYnx4yEry0509GQG\nDZpMTMx9DBvmorFxDS5XKQ7HTnbv/prCwkdoadm6pzyhoScTFDS89TYCuz0Lo/HIe6FpXctgNRCQ\nFkBAWjd179P8rk8EByEEb134Fk8ve5r/+/r/mFs3moTAHUDKUb+Wzaam2N65UwWJ//xHDUR68sm9\nqzX1VQkhCcwaOYtZI2f9YvsfJvwBn/SxoXIDn275lGW7FrOk+BG2ubcx6JxBnHtNJlOSptNQkE7z\nziGs3xjLvHlGNm1S+6elWdi1awyNjSpfPXSo6p47cmQ9YWE7GTYsiqKi7WzeXEp4+E/Y7fNwOjcT\nEhKHxRJPQMAA7PZMzOYI7PbBmExhWCwxGI0hSOmjdbjRAUkpkdLTqdOOaNrx4JiDgxAiAXgFiAF8\nwHNSyqeEEOHAW0AysBO4SEpZ1wllPaRgazD3nHQPeU/dQ+WYW1l8/kDGPTeCpNAknj3zWaICj64r\nW0qKGnX6v/+p6TZeeUW1Rdx5p5qupS84mqENBmEgOzqb7Oi9ubYWdwsbqzbyzY5vWFy8kPy6f+MM\ncVKYXEj27dlcHzuSQZFDiGw6kbqtWQxItSGlStmVl8Orr4bgdg9j40aoqupPUpKksHDv/BGZmQ4G\nDSonNXUtGRlFREevITr6WSyWSlyucny+ZmprF7F+/TyCglYTEJDROo9QJjZbClJ6WbNmGgB2+yBs\ntlQCAjJobt7cOmGdpmkH05HTnAf4g5RylRAiCFghhFgAXAMsklLOFULcBdwD3N0JZT1iFwY+xcoV\nJn42PsHPpT/z3sb3WPe7dWRFH3xwy4EIAZdeqm7LlsEf/6jmZnr0UTXKWgiYOxfuukvNkfTrX6tp\nOnrDeLLOmD4jwBzAqP6jGNV/FLdz+57tja5G8sryyCvLY3PVRvLKX2fd7nXEe+IZHjuczcGbKZJF\nnHXzWQyNHsqvTAHc+tnvKTR6ARgVNYFJiScR1XwS7BpKTcEZfPKJSQ3c2uHDYvURHWUgc2ALK1cG\n8pe/ZJKa+gMORyFSuqit/Ya6uu9wOHYCRsaOXY2UPtXHvmUrUroICzvlwG9K0zSgA8FBSlkOlLfe\nbxRCbAQSgHOBya1PexnIpZuDA0Dk8r+z/NnfER0YzYXvXEj2s9n8OOtHJiQeWz/ncePU5H1ffAFX\nX61GtU+dCosWwfTpaobNtkFFTz6pUlFhPbytrquCWJAliJOTT+bk5JP3bPP4PGyu2szK8pWUx5dj\nMVpocjVR0VjBxqqN9A+NZsGVC/D4PJQ3lpNXlsca52usNa4lPywfToSo06Jw1hXjbInA6UikuXEy\nseel8fyutazclEKQJYhB/YYSFTqdtKTHibJH0eBqwGYOxGgwEhTUDRNqaVof0SkJEiFECjACWArE\nSCkrQAUQIUR0ZxzjWGREZgCw8MqFfLL5Eyb+dyJvXfgWF2VddEyvJwSccYZaBjQvD55/XgWHu+5S\nDdhSwrvvqlUPy8pUAJk8Wc20aT/OJ1A1GUxkRWcdce1t+oDpe+67vW4K6gooqS+huL6YGRkzsJvt\nbKvZxtpda6lsMlDSUMI3O7/hzXVv4vQ4KaovoqalBlDzciWGJBJsDSYxJJFASyAJwQnEh8QTbgsn\nJSyFtPA04oLjMBr0+AxNg04IDq0ppXeB21prEPsnLLp0/s+1a88lImI68fG/O+hzfD43Zw2cwcrr\nVzJy3kgufvdinjv7OX4z8jfHNKeQwaBmUR0zRo0IbSOECgS/+pVaU33tWnjhBVXTmDZNpaIuuqh7\nJvw7nN40K6vZaGZAxIB2o+APF2zqHHUYhAGz0UxhXSHbarZR0ViB2WimpL6ETVWbqGquoqKpgu27\nt1PVXEV8cDyJoYkkhCRgN9lJDE0k3BZOfEg8sUGxfF/4PVajlbjgOJJCk0gKTSImKIaalhoCzYF7\nxp9UNVXh8Xn4ctuXxATFEBEQQUxgDFZTH1+A5zjW7G6morECicRmsu35fyhrKCPAHECwJRif9LG+\ncj1htrA9t7ZJRXuaDgUHIYQJFRhelVJ+1Lq5QggRI6WsEELEArsOtv/s2bP33M/JySEnJ0dNIfnF\nhzD8djW15BlnHLIM1dUfU139MS5XKSkpDwLt+8vv2HEfRUVzGT06j4o7Knhj7Rtc+8m1zPluDh9c\n/AHDY4cf7Vs/tPnzCS0oJuccyaWXQk2NqmF89hnceqt6SkKCWlf6wgvVxGYdIaWk0eslyGjE2+BF\n7vZQ+34lptFh2DPtGIONOLY7MEeZsfbfe3LqDW0jHRFq2zv1x8DIgQyMHHjI5zs8DorqiiiuL6ao\nvojtu7dT01JDRWMFX+/8muL6YgpqCxgbPxar0UpRfRGFdYXUOmpxeV17vuSB5kBa6lp43/M+f1/y\nd3Y17aK6uZqymJnI6KmY3TVYDIJA3AhTIB5DAP2EixizkQiTQU1z4qljefEPuL0uoi0W4m127DhJ\nD4knNjCK/oFRRNijiAuKJTIwmhZhI8QgCTAaaXI1sX33dsIDwokIiCDYEqxrRN0g/NFwXF4XdrMd\nq9GK2+em0dUIQJQ9inpnPU6vE4CMiAx2O3ZT66jFKIyEWEOwmqyEWEP2BI1gSzDBlmCqNlSxa/0u\njAYjJkP39Ybp6JH+C2yQUv5jn20fA1ejxnhfBXx0gP0AuO++2e17/vhUoyRTpqjL7127oLW7u9u9\nG7P5l/1Jg4JGEVWZTcBvHqKl/EnMWWXsPwjOYLAREDCA1aun4PHUMiXiTFz31vPi6jeZ9uo0clJy\n+Mf0f+xZhnR/NTULCAzM+sVwdim9gEHVPP7yF5VPuvxyNcT6pptI3LEDfvcVTPovERERXFRdzUWD\nBvHvN85iadh0dtXbWLxYrQyWnKxi4KmnqsdH2xvqsaIi7tq+nXCTidO3W/lvnYfl80uxzfMitjp/\n8VxrkhWfEYJHhzDFG0nd0gA1QVmi9bifmdVmspERmbEnHXmkmlxNNLmbiLJH0eRuorShlKbaJhqe\namDhlQv3PG/aqlWcHGInw+xmV/NuSlvqKHY00+JtwuCuo6TJyTZpoN5noEaasUecSGxgFC3Cys9e\nHyWvONsAACAASURBVLu9AgdmaAJLQwsugw8oVTdvMwgTSC+4G8BdhxUPHk8jPlctVukiWLixW0IJ\nsAQTaDQQYjQQbDQRarZS3bwLu8mOwRpJUkAgiQEhRJitmPEQawshOTiK6MAo7Oa9+VGf9B3xeirH\ng3BbOKtuWEVs0N41F2RrFV0IgZSSZnczVpN1z0leSonT66TeWU+zu5lGVyO1jlpqHbU0OBtocDXg\niHHQMqkFl9dFi6eFb176plveT0e6sp6Imht0rRBiJSp99H+ooPC2EGIWUAAcNMHf0HCAsQP2QPVz\n3Tr1Mzoa6ksB+OGHiNZjmxk58oc9aysn3LccYx5AI/8MCeY99yYgE2j74wiioy+nf/9rWLo0nd27\nF/LD9yEMBH684jPu+f5Fkp9M5rT007hp7E2ckXEGGys3MqjfIIQQrFmj1owwGoPxeht+UdyQkPEM\n/rYBa1gI8oVnMN51FwCbns8kKuJ8Iusy1dJuXi9s3EjABx9witsNDQ1cDDx96lR2xk5g8YYT+P6/\nhdy+60RswwaSPdzCxKpSUs4OJStLMv//t3fuYXIVZcL/1bn2vXsuPTOZTJLJ/SYJG+4IEm4KoqiI\nsJpFZOWTRfxWYT9uuqv7Lbqi7uLlU0FWRR8VNlnk7hIQQYEAQgi5EiCZkEySuc/0TE93nz7X+v44\nnclgAHEhDDDn9zzn6TrVdfpUvV2n3lNVb9W7MYG/pUiyp0zy0BStuk1zq8Cv+CzY8kvublA54qhT\nefYegTQEj16d5uakYKcFzb1AXkWPqyjbbZY9DbOHhjh63ghrl7uodliBlYSC9CTJQ5IYeQMloZA9\nLktqSYrEwgTGlNe+LcNEMep5JFUVpZZPX0ruHBjgpp4emnSdJsNgmmnSpOu0GAZTTJMGTSOmKMT+\nh/4ak0aSpBHW25SRYl7DPDzT4zEee0k6Q1FYlm3gjIZX3nzvz+HXGpsB12XY85gdi2EFAUpgIxB4\nQmfI8xh0XfpdF0dKBhybzsoIu61RdlcrjLpVhHSxfIfBwKfsSirCQJcaJSeFURmhjIOLhicMfMVB\nKiPgbUR4o2iBReCO4KtJVLeAIT3iQiICm6QqSCmQEJKEqmIqBqZm4mkZsrpBRlHI6jqaGmOYOHW6\nQZMZpzmWJK3FUaRD3kzSEk8zJZ5De5v3ePYphX3hffVk/PcxLfYXuR34Ol//84neAF6PtdIaXnn1\n0Smv5TeCYH/Y80YQQg8Hw6dMAbpDpwu/+Q1TMq3wrf0D9VK6rFt3JMnkuxBCwz9sMeq8JcjvfBvn\nfQv4zGUL6Kz/DrZ9Lo8/HvYG2touIxabwfLl4V7xAwN30d9/G3ueP4N/mn8GXzni+1y77g+8/+b9\nu0jOrpuNqZmUywofXnwhe4fXs6FnPZceejzvn3Mmhp6hVHqGknIjO4+r0nsqGF4dUza20de2ieYj\nT4W6k8JJh/EUCuHexnPmoDz9NLM2b2bWLRfB4CBfdKqwFoa2LyQYzlG4s43dHMU8clhMY4QE7q2C\nocBlqPZzZ/Ilyswgxpc5gQAFj6/Nn8/X2trG/1/sqFbZOq/MvLMTVKtwxLllvnhPmc3lMjv2jGLt\ntVlUNpjiS9q2WrT2CuLrHBKrukhudxGOJLkgQWJhArPNJHVoiuSiJLGZsdfth+DlqO6q4g65mFNN\n9Eb9z25Vvatapf2JJzCFYKppsqNaHfvuqHSaMxsa6HUcNpZK9LkuPY5Dj+PwYi1dTtNChWEYtBgG\nz1UqVHyfmfE4OU3DDQI0IViUTDLVNGk1DBp1nXpdp07TyGnamFI6WKi13282DJqNcBgrrSiMf5Qz\nuk77AY5KXmkTt9eGLyUF16WzMszuyggjgaSMSU5V6LaK9NslBuwSI65LRSqM+gHDfsBwIAhkANIj\nbY9gSRUbcGQV3esjCByqGDhCx5OAGiNQ4gRqHBQdfAs1sNADG026mATEREBCAV9NYigapqKSVlWy\nmkZGM8gZMUwthid0snqMOj1GVjdJqmG6lKqiCkFSVTGEIFG7Nq2q6EK8IS9AuWtzVL0qDYkGuka7\nMFQDgcD2bXRFJ2kkyZgZ0kY6/DTTJPTEmKKIa3EUoRDTYmTMDAOVAWzPflOHB4WcoJlJIYTs65Pk\na2vTfv/78A95YvM5DG/bzLX66aFfz+uuC124AQ//Icmxx3YDAR0dV9DdfSMAx/7ybIxlJ8JnP8vH\nPgaXpP4Xy3/2Y4oLYMtXILf0k0ybdhmp1IFzC543yq5dX2P37m9gGFOpb/wo3epJFBwf13e5ds21\n7B7agCfSjNhFpqankjbT9Jf7qXpVvnj8F/n899dinn4ywSfOxfdHKRb/SNnaxcwZl4/tGeRXfda/\nZz3Sk8TnxtEyGolFCaQvyRyZIbk4id5QW8VrWQxe9zCVe59l2uz1BHffg1IYQppxWHIIYv48aGlh\nJD+HtdsVlqy6nE8tW8u2nbOo9o9w2twOUssPZ+XK0PdsPh9uDXLEEaHf4sHB0Mz2U5+CSmW/LKq+\nz9ZKhd22jSclOyyLTeUy60rhuOlgr8XMTsGybo0FHQqxLo/mnQGJ7oAgq6BWJFpSxR90yZ2QQ6/X\nkVJSXFNEy2moGRXpSIQhMFoMtJxGbEaM2IxY6CGs5hWstL5E90+66V/VDwK0eg1/1EfLaKBA+rA0\nRouB3qCjN+noeR2j2eDFjMelxZ2sPvkw9noOQ65LSlVJewotlopWp6HGVLpu7KL4eJGen/VgTjfR\nMhpKXIEGDadRxWpUKNbDkBHQlI+hlySFvKCnXjKYClBSKrs0h27PZdB1GfI8hlyXchCQ13Uqvk/S\ngp982OfaNVkadJ2kqvLQ8DA3zJv3unoOkwnb9+i2huksDdFjlxl0LIbsCgNOhWHXps/1EF4J6Y0y\n4nmM+gFl36cSBFSDAM8t4fo2LhqBoqPpGTQ9hdCSIAxQNFAMpKLjCxNXGEihgPQRgYsIqgjpg19F\nBDYaHvg2VWeYpGaAniMWVPG0FHpgM/rMZSxvX05Mi3Hn83ey6wu7UISCpmjUxeooOSWEECT0BBW3\nQtEuUrSLjNqjFO0ilmdR9apjh+u7uIE7ls5QDWZkZ/C5oz6HlPKgd+EnVDn09Mgxy53bHplNvb+D\nnz/3IZq3buPa724ZS1v6/MWkvncDf3hA5bjlo6hq+FZUvfEa1ie/zBG/Ohn1zLPh7/6Oj30sNB/9\n/r9X2XDE+zH/66HQn+IXvgBXXQWXXRYqncbGl+RHSkmx+AQ7dlzJyMhjNDZ+kClTLiKXW85jj7Vw\n9NE70fX9Cxc6hjq49dlb2VHYwUlfvom7Z7o8dsJMLj78Yv710X9luDrMvIZ5nDH3DPKJPMvrl7Pn\nmD0kr0ySacmQ3ZMlWBNQ+G2BxMIE9h4bfzScb6k7pY7KCxXSh6d516/H7f5nWbB2LaUXXkD09LBz\nzRqmr1tHr2EwZ9MmyGYZHAzNbNetCx21nHsuFIuwZUvoRW7NGsa2sUgkQkdHrxUpJf2uy3bLYptl\nsce2sYMA1/EZ6bXp77PoHLZwRn2mojO3S6HV1dg5WzBtfpqcpdBu69QVYD0VghGfVJdPvlcS7w/Q\n+nxkt4M34JE5JkP+7Dwtn2pBr9cJ7IArH3+ObS8U6R2sMmdEo6Ws0FJUaBwRZAug9noovR6pEqHC\naDFwB13szv3zLmpGxS/6NK1oIr0sTeNZjfhFH3/Uxy24uH0uTk+4sVx1d5Xqi1UUU0FNq+HupIMe\nfsnHL/uhB7I6DSWmENgBalqFVh3yOpojKd46SDC0dExxOEHAOU1NZN8pS+z/BC/wOO/28+ge7SYb\nyxLX4mTMDFkzy6A1SKFaIGtmxyZgB6wB2tJtJI0kqlBJGSnSZjgJm9ATxPU4cS0+9pa9pnMNfeU+\nDNVAUzRMzQzTaXFMzcRUzZd8Or5DIANysRzrutext7gXCOvxsD3M3uJedFVHEQoSieu59JZ7MbU4\n03Lt9FUGGXXKJM0cmhYnEBoeKooaR9FilAPJrx+9nHS8iaQep6e4i5996GdkY1kSeoL3zn7vGybb\nLVu2MDQ0hJSSE0444Z2vHLq75Zi/7M///iN8hDu4uRP+wzuXh2atZPr0L9LQ8AEqSjsXfuldXHHm\nEMd/80SU+x8MFxJ873vhvhZdXfDRj8Ktt44ph+uuC71XsX07fPrT8PDD4Y1mzgyHdY47Du65J2w9\nzzsvdI21MNy+2vNK9PXdwq5d12DbuwE47rjhV3R8E6xYwQtHzGLjqYfw0IsP8aOnf8TdH7+bpJHk\nkV2PsHLLSvpL/fRZBxpumaqJL32OmnoUf5X4Kw7RD2HW4CwSDyWYe85cvFM87u+4n7SZZsga4rmB\n51jZX2DPSAckZnB861KSsUauW3gE07PTSeiJCZ8XsIOA3dUqva7LtkqFx4pFNCHosm1sKem2bTaU\ny5ydz1MNAkwh6HIcumybbsch7QoaUwZ506RO05ifSNBqGFzW0cG/zpzJsnSaBYkEvY7DHttmV7XK\nXtum13U5OpPh4qYpOL21nUPN0AdxbHYMxVTwhj2kLzEaX5/5oJQSf9THK3j4lo835BHYAYEV4PSF\nSkQGkumXT3+DpPrWZ7g6TN036rjpQzehKzq+9LFcixF7hIpbwQs8ZtXNIpABI9URdo3sojnZTNEO\nPeKVnBJlt8yoM0rFrVBxK1iuRckpUbSL7B3dyycO+QRpI40XeNi+PZbG9m1szx77dHwHX/ok9ATD\n1WE6Rzr5yIKPoCoqlmvhBi5SSubWz6XklrBcCy/wGLQGmVU3i8Z4I5ZnYXs2M3IzKDklSk6JilvB\n9m2qXhXLtZBIrj/j+rBXgPiLd2EAKJfLXHTRRTz33HM8/fTTtLe3E4vFCIKAWCxGuVymo6ODZcuW\nEY/HWbNmzTtfOezZI3lU7+Om7m7mFK7hbH7NzZ3wsPdX3DDrmbG0cw/dxuE/OZ5bDuvhhJNA/PXH\n4ZZbwi9PPz2cp1i9GoBrl/+ER885nt9c08YP79zMZ+bPR73ttnDJcnMzpFLhxj7XXgs//CFceGG4\nag3gsMNCu9PTTw/TL1mCOztPYeQhmprOCSdJFIXv7dnDvUNDdNs2J9XV8Q9XX03DBz5A7PzzAbi5\nt5dHR0ZYnstxbCbDVNPEHXB5atFTvLs/9AJV9aps7N0YPlC1Ludjux9jc/9m7nnhHkpOiVl1s9hR\n2IGhGpw+53Q6Ch3Ynk2vNKkTHh+ccyq7hnays28nJUp0lbuQhBV+dm42lmORMTI0ZhpJG2nq4/VM\nSU+hLdOG5Vr0lftYmF9IfbyelJGiJdXC3uJebtt6G0II6uP1ZM0sjYlGpmWnMTU99aCPeQZSUvA8\num2b3bbNdsui7Pt0Ow4vWBY3L1xI3Ttxm9x3AMPVYdq/087wVcMTnZW3FR0dHcyZM4ebbrqJ6dOn\nM2PGDKrVKoqi4DgOtm2zYMECMpnQJ0ptkvudrRwWrXmKZ2t2wJeJH7JLNvFC51qavQ4unzVCkQyN\nDALwre05Lm0fpvePX+UT//iPCAiHiZYvh1Wrwh7BP/0T4qGHoCsG/2cpC76+il3NzVixGJ/+zW/4\n+qZN5D/zGfwPfpCyEGQ0jQufew4hBJc0NZG54w6mfvazFA49lMb169HGTWjuXrSIac8+izzhBO6P\nx3mhvZ0HDj+c+MyZnPP1r3PbkUfy0BlnMDMWY02xSFZVOS6b5cnRUfpdl0Msk2+ucHjoqTY6LIsA\neG9dHXMTCd6VTNJsGAy5LhlV5XnLQkdijb5IoTrIovwimpJNPFQo8IXt29lYLrN6yRJ23XorF110\n0VgeY/EYTVOb6Cx1QgPQDFqDhjakkW/Ko+ZUurwutJxGJVkh4SWo0+qoBBXKbhnP8AhEQFzEWV6/\nHGlKXM2l5JfYXdzNYGVwrHeydWAruViOOfVz6Cn1sKOwg7n1c9k2tI2FjQtJGkmmZaYxPTudulgd\nDYkGWtOtFO0ig5VB8sk8Tckm8onaZzL/miw2vvvEd7l+7fXkYjnq4nU0JZvImTkkElM1SRkpUkYK\nQzVekqYuVkfKSGFqJnEtTkyLIWvrM8ebY5ad8tiQxZ/i+m7oQ7hmhvhM9zNYnkVdrI5cLEfKSKEI\nBS/wSJtpBK8+uekFHqpQX5Jm36rulJFCU7SDaipackps6NlAxsyQMTMkjWQoI/WlZs0/X/9z7t9x\nPzkzF1pm6UkSemIsvM9+3/EdvvTgl/5ir4xvNXzfR1GU1+4wSUpGR0fRdR3DMFBfxupt69at7Nix\ng0QiQSKRIB6PE4vFiMVibN68mQsuuIDe3t7XdL9JoRx48HdQq/yX8H16aOGeziJneb/gM7PgRB5i\nplbmp94HkDLcruLmm+H4Y47ht5dcgrliRfhjF1wA73kPXHAB9avWct7GInd+cy4v3t/B6kqFnzU3\ns85x2G6/1Ob/zCDgLkXhPdksL1gWPY4DwEcaG7lzYIAAaB4aYkFnJ5ePjrIG6CqXOe3JJzlz2zYS\nphl6Ygfc22/nqRNPZMB1ebJY5J/a2zFr7uSKnseznSOUjniWOx5vZmulwoJEgkoQcOfAAAXPwxQC\nW0oMIXCkJL9nD/3nnTeW11hTE04uR92iRZw0YwZbf/1rNu/Zw7nLl/PNK65g+oIFlDIZdnd1MbBp\nE0cefzzW6Ci5uXPpHxzk+e3b6d67Fz8IaMznWbduHYVCASEEXV1ddHV1cdoZp7GzfyfWgEVvVy+7\nd++ms7OTSqXCtGnTcKRDbkqCZMImnU6BrdFvlchMSaPF4rTKLNm2eupjedy4gKBIOSPpsoepYDHK\nKF12Fw3xBqZnp1NwCgxYA/SX++kr9xHTYjQmGsnFctTH68mYGVrTrST1JDEtRspIcc3D17DikBWc\nt/Q8ClaBvnLfmF14X7mPfDLPSHWEUWeUslumaBfpL/czXB2m7JbHhgPcwCWQwdhYNzBmR64pGqpQ\nSegJUkaKuB7HkAqbh8I9yE0R9lxs6XJUcj6FoMywX6ESVPFlgKpolN3ymMJKanFSRorO0T3hqlkt\njuVZlN0yhmpQH68nqScxNZNn+58la2YpOSV86WOoxpjCSxvpsXH5lJGiYBVoTjVjqubYOL0XeOiq\njqmajNgj5BN50mZ6TIYDlQEM1cBQDVY9u4oHdjzA4vxiinaRslum5JTwAo+kHiqKpJFkT3EPZ8w9\ng+Xty8fWdFTcyljY8qywnHqSfDLPV0/66kFpMw42Z512Grffdx8QNsCmYWCaJoZhjDXkpmli7vus\nHRs2bKC7uxvTNHEcJ7y29l08Hicej7Njxw7mzZvHlClTKJf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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "random.seed('running')\n", + "\n", + "for i in range(10):\n", + " plot_running_averages(simulate_st_pete, 100000);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "What can we see from this? Nine of the 10 repetitions have a final expected value payoff (after 100,000 rounds) between 10 and 35. So a price around $13 still seems reasonable. One outlier has an average payoff just over 100, so if you are feeling lucky you might be willing to pay more than $13.\n", + "\n", + "# The Ellsburg Paradox\n", + "\n", + "The [Ellsburg Paradox](https://en.wikipedia.org/wiki/Ellsberg_paradox) has it all: an urn problem; a paradox; a conclusion that can only be resolved through psychology, not mathematics alone; and a colorful history with an inventor, [Daniel Ellsburg](https://en.wikipedia.org/wiki/Daniel_Ellsberg), who went on to become the releaser of the [Pentagon Papers](https://en.wikipedia.org/wiki/Pentagon_Papers). The paradox is as follows:\n", + "\n", + "> An urn contains 33 red balls and 66 other balls that are either black or yellow. You don't know the mix of black and yellow, just that they total 66. A single ball is drawn at random. You are asked which of these two gambles you would prefer:\n", + "- **R**: Win 100 for a red ball.\n", + "- **B**: Win 100 for a black ball.\n", + "\n", + "> Separately, you are also asked which of these two gambles you prefer:\n", + "- **RY**: Win 100 for a red or yellow ball.\n", + "- **BY**: Win 100 for a black or yellow ball.\n", + "\n", + "Many people reason as follows: \n", + "- **R**: I win 1/3 of the time\n", + "- **B**: I win somewhere between 0 and 2/3 of the time, but I'm not sure of the probability. \n", + "- **RY**: I win at least 1/3 of the time and maybe up to 100% of the time; I'm not sure. \n", + "- **BY**: I win 2/3 of the time. \n", + "- Overall, I prefer the relative certainty of **R** over **B** and of **BY** over **RY**.\n", + "\n", + "The paradox is that, from an expected utility point of view, that reasoning is inconsistent, no matter what the mix of black and yellow balls is (or no matter what you believe the mix might be). **RY** and **BY** are just the same gambles as **R** and **B**, but with an additional 100 for a yellow ball. So if you prefer **R** over **B**, you should prefer **RY** over **BY** (and if you prefer **B** over **R** you should prefer **BY** over **RY**), for any possible mix of black and yellow balls.\n", + "\n", + "Let's demonstrate. For each possible number of black balls (on the *x* axis), we'll plot the expected value of each of the four gambles; **R** as a solid red line, **B** as a solid black line, **RY** as a dotted red line, and **BY** as a dotted black line:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def ellsburg():\n", + " show('R', 'r')\n", + " show('B', 'k')\n", + " show('RY', 'r:')\n", + " show('BY', 'k:')\n", + " plt.xlabel('Number of black balls')\n", + " plt.ylabel('Expected value of each gamble')\n", + " \n", + "blacks = list(range(67))\n", + "all_urns = [Counter(R=33, B=b, Y=66-b) for b in blacks]\n", + " \n", + "def show(colors, line):\n", + " scores = [score(colors, urn) for urn in all_urns]\n", + " plt.plot(blacks, scores, line)\n", + " \n", + "def score(colors, urn): return sum(urn[c] for c in colors)\n", + "\n", + "ellsburg()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "We see that for any number of black balls up to 33, the solid red line is above the solid black line, which means **R** is better than **B**. The two gambles are equal with 33 black balls, and from there on, **B** is better than **R**.\n", + "\n", + "Similarly, up to 33 black balls, the dashed red line is above the dashed black line, so **RY** is better than **BY**. They are equal at 33, and after that, **BY** is better than **RY**. So in summary, **R** > **B** if and only if **RY** > **BY**.\n", + "\n", + "It is pretty clear that this holds for every possible mix of black and yellow balls, taken one at a time. But what if you believe that the mix might be one of several possibilities? For example, if we assume that any number of black balls from 0 to 66 is equally likely, then we can use a function, `expected_score` to give the expected return for a gamble (as specified by the colors in the gamble), averaged over a collection of possible urns, each with a different black/yellow mix:" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "R 33.0\n", + "B 33.0\n", + "RY 66.0\n", + "BY 66.0\n" + ] + } + ], + "source": [ + "def expected_score(colors, urns): \n", + " return sum(score(colors, urn) for urn in urns) / len(urns)\n", + "\n", + "def compare(urns):\n", + " for colors in ('R', 'B', 'RY', 'BY'):\n", + " print(colors.ljust(2), expected_score(colors, urns))\n", + " \n", + "compare(all_urns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "This says that **B** and **R** have an equal expected return, as do **BY** and **RY**.\n", + "\n", + "Now imagine that you believe that any mix is possible, but that a majority of black balls is more likely, in particular that the urns in the second half of the list of `all_urns` are twice as likely as those in the first half. Then we will see that **B** > **R** and **BY** > **RY**:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "R 33.0\n", + "B 38.554455445544555\n", + "RY 60.445544554455445\n", + "BY 66.0\n" + ] + } + ], + "source": [ + "compare(all_urns[:33] + 2 * all_urns[33:])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "If we believe the first half of the list (with fewer black balls) is twice as likely, we get this:" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "R 33.0\n", + "B 27.39\n", + "RY 71.61\n", + "BY 66.0\n" + ] + } + ], + "source": [ + "compare(2 * all_urns[:33] + all_urns[33:])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "This time the preferences are reversed for both gambles, **R** > **B** and **RY** > **BY**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "So why do many people prefer **R** > **B** and **BY** > **RY**? One explanation is *risk aversion*; it feels safer to take a definite 1/3 chance of winning, rather than a gamble that might be as good as 2/3, but might be as bad as 0. This is irrational thinking (in the sense that those who follow this strategy will win less), but people are sometimes irrational." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "# Simpson's Paradox\n", + "\n", + "This has nothing to do with the TV show. D'oh! In 1951, statistician [Edward Simpson](https://en.wikipedia.org/wiki/Edward_H._Simpson) (who worked with Alan Turing at Bletchley Park during World War II), noted that it is possible to take a sample space in which **A** is better than **B**, and split it into two groups, such that **B** is better than **A** in both groups. \n", + "\n", + "For example, here is data from trials of two treatments for kidney stones, **A** and **B**, separated into two subgroups or cases: first, for small kidney stones, and second for large ones. In all cases we record the number of good and bad outcomes of the treatment:" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "# Good and bad outcomes for kidney stone treatments A and B,\n", + "# each in two cases: [small_stones, large_stones]\n", + "A = [Counter(good=81, bad=6), Counter(good=192, bad=71)]\n", + "B = [Counter(good=234, bad=36), Counter(good=55, bad=25)]\n", + "\n", + "def success(case): return ProbDist(case)['good']" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "Let's compare probabilities of success:" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.9310344827586207, 0.7300380228136882]" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[success(case) for case in A]" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.8666666666666667, 0.6875]" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[success(case) for case in B]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "We see that for small stones, **A** is better, 93% to 87%, and for large stones, **A** is also better, 75% to 69%. So **A** is better no matter what, right?\n", + "\n", + "Not so fast.\n", + "\n", + "We can add up `Counter`s to get the overall success rate for **A** and **B**, over all cases:" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.78" + ] + }, + "execution_count": 72, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "success(A[0] + A[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8257142857142857" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "success(B[0] + B[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "Overall, **B** is more successful, 83% to 78%, even though **A** is better in both cases. So if you had kidney stones, and you want the highest chance of success, which treatment would you prefer? If you knew you had small stones (or large stones), the evidence supports **A**. But if the size was unknown, does that mean you should prefer **B**? Analysts agree that the answer is no, you should stick with **A**. The only reason why **B** has a higher overall success rate is that doctors choose to do **B** more often on the easier, small stone cases, and reserve **A** for the harder, large stone cases. **A** is better, but it has a lower overall percentage because it is given the difficult patients.\n", + "\n", + "Here's another example, showing the batting averages for two baseball players, Derek Jeter and David Justice, for the years 1995 and 1996 (I should say that Justice is considered a very good player, but Jeter is considered even better, a sure-bet future Hall of Fame player):" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "run_control": {} + }, + "outputs": [], + "source": [ + "Jeter = [Counter(hit=12, out=36), Counter(hit=183, out=399)]\n", + "Justice = [Counter(hit=104, out=307), Counter(hit=45, out=95)]\n", + "\n", + "def BA(case): \"Batting average\"; return ProbDist(case)['hit']" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.25, 0.31443298969072164]" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[BA(year) for year in Jeter]" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.25304136253041365, 0.32142857142857145]" + ] + }, + "execution_count": 76, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[BA(year) for year in Justice]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "So Justice had a higher batting average than Jeter for both 1995 and 1996. Let's check overall:" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.30952380952380953" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "BA(Jeter[0] + Jeter[1])" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "run_control": {} + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.27041742286751363" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "BA(Justice[0] + Justice[1])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "Overall, Jeter had a significantly higher batting average. How did Jeter manage to do worse both years, then? Because in 1995, Jeter was injured for much of the year, and his low batting average was over a small number of at-bats. In 1996, Jeter was healthy, but Justice was injured for much of the year; however he managed a high average in his few at-bats.\n", + "\n", + "For the kidney stone data, we trust the individual cases, not the overall, because there are biases that lead to patients being assigned to one treatment or the other. For the batting average data, we trust the overall numbers, because there are no such biases, and because larger numbers lead to a closer approximation to a true value. The data alone can't tell you what to believe; you need the story (and the model) behind the data as well." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Conclusion\n", + "\n", + "We've seen how to manage probability paradoxes. Just be explicit about what the problem says, and then methodical about defining the sample space, and finally be careful in counting the number of outcomes in the numerator and denominator. But the bigger lesson is: treat those around you as reasonable people, and when they have different opinions, try to discover what problem they are solving.\n", + "\n", + "*Note*: Mohammed El-Beltagy created a very nice [translation of an earlier version of this page to Julia](http://nbviewer.ipython.org/gist/mbeltagy/3ba5f77da6382da192c3). \n", + "." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Project Euler Utils.ipynb b/pytudes/ipynb/Project Euler Utils.ipynb new file mode 100644 index 0000000..933288f --- /dev/null +++ b/pytudes/ipynb/Project Euler Utils.ipynb @@ -0,0 +1,1011 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "
Peter Norvig, 20 Jan 2017
\n", + "\n", + "# Python Utilities for Project Euler\n", + "\n", + "After showing my utilities for [Advent of Code](http://adventofcode.org), I got some feedback:\n", + "\n", + " 1. Some of these are recipes in the `itertools` module (with different names).\n", + " 2. What about utilities for [Project Euler](https://projecteuler.net/about)?\n", + " \n", + "My answers: \n", + "\n", + " 1. I agree! I have renamed some of my utilities to be consistent with the `itertools` recipes.\n", + " 2. Here you go." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Imports\n", + "\n", + "In Project Euler I am writing short programs for my own consumption, so brevity is important, and I use `\"from\"` imports more often than I normally would:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "from collections import defaultdict, deque, Counter, namedtuple, abc\n", + "from fractions import Fraction\n", + "from functools import lru_cache, wraps\n", + "from itertools import chain, cycle, islice, combinations, permutations, repeat, takewhile, zip_longest\n", + "from itertools import product as crossproduct, count as count_from\n", + "from math import ceil, floor, factorial, gcd, log, sqrt, inf\n", + "import random\n", + "import time" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Utilities\n", + "\n", + "Here are the general utility functions (and data objects) I define:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "million = 10 ** 6 # 1,000,000\n", + "Ø = frozenset() # Empty set\n", + "distinct = set # Function to return the distinct elements of a collection of hashables\n", + "identity = lambda x: x # The function that returns the argument\n", + "cat = ''.join # Concatenate strings\n", + "\n", + "def first(iterable, default=False):\n", + " \"Return the first element of an iterable, or default if it is empty.\"\n", + " return next(iter(iterable), default)\n", + "\n", + "def first_true(iterable, pred=None, default=None):\n", + " \"\"\"Returns the first true value in the iterable.\n", + " If no true value is found, returns *default*\n", + " If *pred* is not None, returns the first item\n", + " for which pred(item) is true.\"\"\"\n", + " # first_true([a,b,c], default=x) --> a or b or c or x\n", + " # first_true([a,b], fn, x) --> a if fn(a) else b if fn(b) else x\n", + " return next(filter(pred, iterable), default)\n", + "\n", + "def upto(iterable, maxval):\n", + " \"From a monotonically increasing iterable, generate all the values <= maxval.\"\n", + " # Why <= maxval rather than < maxval? In part because that's how Ruby's upto does it.\n", + " return takewhile(lambda x: x <= maxval, iterable)\n", + "\n", + "def multiply(numbers):\n", + " \"Multiply all the numbers together.\"\n", + " result = 1\n", + " for n in numbers:\n", + " result *= n\n", + " return result\n", + "\n", + "def transpose(matrix): return tuple(zip(*matrix))\n", + "\n", + "def isqrt(n):\n", + " \"Integer square root (rounds down).\"\n", + " return int(n ** 0.5)\n", + "\n", + "def ints(start, end):\n", + " \"The integers from start to end, inclusive. Equivalent to range(start, end+1)\"\n", + " return range(start, end+1)\n", + "\n", + "def groupby(iterable, key=identity):\n", + " \"Return a dict of {key(item): [items...]} grouping all items in iterable by keys.\"\n", + " groups = defaultdict(list)\n", + " for item in iterable:\n", + " groups[key(item)].append(item)\n", + " return groups\n", + "\n", + "def grouper(iterable, n, fillvalue=None):\n", + " \"\"\"Collect data into fixed-length chunks:\n", + " grouper('ABCDEFG', 3, 'x') --> ABC DEF Gxx\"\"\"\n", + " args = [iter(iterable)] * n\n", + " return zip_longest(*args, fillvalue=fillvalue)\n", + "\n", + "def overlapping(iterable, n):\n", + " \"\"\"Generate all (overlapping) n-element subsequences of iterable.\n", + " overlapping('ABCDEFG', 3) --> ABC BCD CDE DEF EFG\"\"\"\n", + " if isinstance(iterable, abc.Sequence):\n", + " yield from (iterable[i:i+n] for i in range(len(iterable) + 1 - n))\n", + " else:\n", + " result = deque(maxlen=n)\n", + " for x in iterable:\n", + " result.append(x)\n", + " if len(result) == n:\n", + " yield tuple(result)\n", + " \n", + "def pairwise(iterable):\n", + " \"s -> (s0,s1), (s1,s2), (s2, s3), ...\"\n", + " return overlapping(iterable, 2)\n", + " \n", + "def sequence(iterable, type=tuple):\n", + " \"Coerce iterable to sequence: leave it alone if it is already a sequence, else make it of type.\"\n", + " return iterable if isinstance(iterable, abc.Sequence) else type(iterable)\n", + "\n", + "def join(iterable, sep=''):\n", + " \"Join the itemsin iterable, converting each to a string first.\"\n", + " return sep.join(map(str, iterable))\n", + "\n", + "def grep(pattern, lines):\n", + " \"Print lines that match pattern.\"\n", + " for line in lines:\n", + " if re.search(pattern, line):\n", + " print(line)\n", + " \n", + "def nth(iterable, n, default=None):\n", + " \"Returns the nth item (or a default value).\"\n", + " return next(islice(iterable, n, None), default)\n", + "\n", + "def ilen(iterable):\n", + " \"Length of any iterable (consumes generators).\"\n", + " return sum(1 for _ in iterable)\n", + "\n", + "def quantify(iterable, pred=bool):\n", + " \"Count how many times the predicate is true.\"\n", + " return sum(map(pred, iterable))\n", + "\n", + "def powerset(iterable):\n", + " \"powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)\"\n", + " seq = sequence(iterable)\n", + " return flatten(combinations(seq, r) for r in range(len(seq) + 1))\n", + "\n", + "def shuffled(iterable):\n", + " \"Create a new list out of iterable, and shuffle it.\"\n", + " new = list(iterable)\n", + " random.shuffle(new)\n", + " return new\n", + " \n", + "flatten = chain.from_iterable\n", + "\n", + "def int_cache(f):\n", + " \"\"\"Like lru_cache, but designed for functions that take a non-negative integer as argument;\n", + " when you ask for f(n), this caches all lower values of n first. That way, even if f(n) \n", + " recursively calls f(n-1), you will never run into recursionlimit problems.\"\"\"\n", + " cache = [] # cache[i] holds the result of f(i)\n", + " @wraps(f)\n", + " def memof(n):\n", + " for i in ints(len(cache), n):\n", + " cache.append(f(i))\n", + " return cache[n]\n", + " memof._cache = cache\n", + " return memof" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Primes\n", + "\n", + "My class `Primes` does what I need for the many Project Euler problems that involve primes:\n", + "\n", + "* Iterate through the primes up to 2 million.\n", + "* Instantly check whether an integer up to 2 million is a prime.\n", + "* With a bit more computation, check if, say, a 12-digit integer is prime.\n", + "\n", + "I precompute the primes up to 2 million, using \n", + "a [Sieve of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes), and then cache\n", + "the primes as both a list (to iterate through) and a set (to check membership). If there are `n`\n", + "primes currently cached and you ask for `primes[n+1]` (either directly, or indirectly by iterating over `primes`), \n", + "then the cache will be automatically doubled in size. But if you just ask if, say, \"`123456789011 in primes`\",\n", + "then I use repeted trial division without extending the cache." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 144 ms, sys: 18.7 ms, total: 163 ms\n", + "Wall time: 190 ms\n" + ] + } + ], + "source": [ + "class Primes:\n", + " \"\"\"Given `primes = Primes(2 * million)`, we can do the following:\n", + " * for p in primes: # iterate over infinite sequence of primes\n", + " * 37 in primes => True # primality test\n", + " * primes[0] => 2, primes[1] => 3 # nth prime\n", + " * primes[:5] => [2, 3, 5, 7, 11] # first 5 primes\n", + " * primes[5:9] => [13, 17, 19, 23] # slice of primes \n", + " * primes.upto(10) => 2, 3, 5, 7 # generate primes less than or equal to given value\"\"\"\n", + "\n", + " def __init__(self, n):\n", + " \"Create an iterable generator of primes, with initial cache of all primes <= n.\"\n", + " # sieve keeps track of odd numbers: sieve[i] is True iff (2*i + 1) has no factors (yet) \n", + " N = n // 2 # length of sieve\n", + " sieve = [True] * N\n", + " for i in range(3, isqrt(n) + 1, 2):\n", + " if sieve[i // 2]: # i is prime\n", + " # Mark start, start + i, start + 2i, ... as non-prime\n", + " start = i ** 2 // 2\n", + " sieve[start::i] = repeat(False, len(range(start, N, i)))\n", + " self._list = [2] + [2*i+1 for i in range(1, N) if sieve[i]]\n", + " self._set = set(self._list)\n", + " self.maxn = n # We have tested for all primes < self.maxn\n", + "\n", + " def __contains__(self, n):\n", + " \"Is n a prime?\"\n", + " # If n is small, look in _set; otherwise try prime factors up to sqrt(n)\n", + " if n <= self.maxn:\n", + " return n in self._set\n", + " else:\n", + " return not any(n % p == 0 for p in self.upto(n ** 0.5))\n", + "\n", + " def __getitem__(self, index):\n", + " \"Return the ith prime, or a slice: primes[0] = 2; primes[1] = 3; primes[1:4] = [3, 5, 7].\"\n", + " stop = (index.stop if isinstance(index, slice) else index)\n", + " if stop is None or stop < 0:\n", + " raise IndexError('Number of primes is infinite: https://en.wikipedia.org/wiki/Euclid%27s_theorem')\n", + " while len(self._list) <= stop:\n", + " # If asked for the ith prime and we don't have it yet, we will expand the cache.\n", + " self.__init__(2 * self.maxn)\n", + " return self._list[index]\n", + " \n", + " def upto(self, n):\n", + " \"Yield all primes <= n.\"\n", + " if self.maxn < n:\n", + " self.__init__(max(n, 2 * self.maxn))\n", + " return upto(self._list, n)\n", + " \n", + "%time primes = Primes(2 * million)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are 148,933 primes under 2 million, which is a small enough number that I'm not concerned with the memory consumed by `._list` and `._set`. If I needed to store 100 million primes, I would make different tradeoffs. For example, instead of a list and a set, I would probably just keep `sieve`, and make it be an `array('B')`. This would take less space (but for \"small\" sizes like 2 million, the current implementation is both faster and simpler).\n", + "\n", + "\n", + "# Factors\n", + "\n", + "Project Euler also has probems about prime factors, and divisors. I need to:\n", + "\n", + "* Quickly find the prime factors of any integer up to a million.\n", + "* With a bit more computation, find the prime factors of a 12-digit integer.\n", + "* Find the complete factorization of a number.\n", + "* Compute Euler's totient function.\n", + "\n", + "I will cache the factors of all the integers up to a million. To be more precise, I don't actually keep a list of all the factors of each integer; I only keep the largest prime factor. From that, I can easily compute all the other factors by repeated division. If asked for the factors of a number greater than a million, I do trial division until I get it under a million. In addition, `Factors` provides `totient(n)` for computing [Euler's totient function](https://en.wikipedia.org/wiki/Euler's_totient_function), or Φ(n), and `ndivisors(n)` for the total [number of divisors](http://primes.utm.edu/glossary/xpage/tau.html) of `n`." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "class Factors:\n", + " \"\"\"Given `factors = Factors(million)`, we can do the following:\n", + " * factors(360) => [5, 3, 3, 2, 2, 2] # prime factorization\n", + " * factors.largest[360] => 5 # largest prime factor\n", + " * distinct(factors(360)) => {2, 3, 5} # distinct prime factors\n", + " * factors.ndivisors(28) => 6 # How many positive integers divide n?\n", + " * factors.totient(36) => 12 # How many integers below n are relatively prime to n?\"\"\"\n", + " def __init__(self, maxn):\n", + " \"Initialize largest[n] to be the largest prime factor of n, for n < maxn.\"\n", + " self.largest = [1] * maxn\n", + " for p in primes.upto(maxn):\n", + " self.largest[p::p] = repeat(p, len(range(p, maxn, p)))\n", + " \n", + " def ndivisors(self, n):\n", + " \"The number of divisors of n.\"\n", + " # If n = a**x * b**y * ..., then ndivisors(n) = (x+1) * (y+1) * ...\n", + " exponents = Counter(self(n)).values()\n", + " return multiply(x + 1 for x in exponents)\n", + " \n", + " def totient(self, n):\n", + " \"Euler's Totient function, Φ(n): number of integers < n that are relatively prime to n.\"\n", + " # totient(n) = n∏(1 - 1/p) for p ∈ distinct(factors(n))\n", + " return int(n * multiply(1 - Fraction(1, p) for p in distinct(self(n))))\n", + " \n", + " def __call__(self, n):\n", + " \"Return a list of the numbers in the prime factorization of n.\"\n", + " result = []\n", + " # Need to make n small enough so that it is in the self.largest table\n", + " if n >= len(self.largest):\n", + " for p in primes:\n", + " while n % p == 0:\n", + " result.append(p)\n", + " n = n // p\n", + " if n < len(self.largest):\n", + " break\n", + " # Now n is in the self.largest table; divide by largest[n] repeatedly:\n", + " while n > 1:\n", + " p = self.largest[n]\n", + " result.append(p)\n", + " n = n // p\n", + " return result\n", + " \n", + "factors = Factors(million)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "148933" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(primes._list)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Tests\n", + "\n", + "Here are some unit tests (which also serve as usage examples):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " global primes, factors\n", + " primes = Primes(2 * million)\n", + " factors = Factors(million)\n", + " \n", + " assert first('abc') == first(['a', 'b', 'c']) == 'a'\n", + " assert first(primes) == 2\n", + " assert cat(upto('abcdef', 'd')) == 'abcd'\n", + " assert multiply([1, 2, 3, 4]) == 24\n", + " assert transpose(((1, 2, 3), (4, 5, 6))) == ((1, 4), (2, 5), (3, 6))\n", + " assert isqrt(9) == 3 == isqrt(10)\n", + " assert ints(1, 100) == range(1, 101)\n", + " assert identity('anything') == 'anything'\n", + " assert groupby([-3, -2, -1, 1, 2], abs) == {1: [-1, 1], 2: [-2, 2], 3: [-3]}\n", + " assert sequence('seq') == 'seq'\n", + " assert sequence((i**2 for i in range(5))) == (0, 1, 4, 9, 16)\n", + " assert join(range(5)) == '01234'\n", + " assert join(range(5), ', ') == '0, 1, 2, 3, 4'\n", + " assert cat(['do', 'g']) == 'dog'\n", + " assert nth('abc', 1) == nth(iter('abc'), 1) == 'b'\n", + " assert quantify(['testing', 1, 2, 3, int, len], callable) == 2 # int and len are callable\n", + " assert quantify([0, False, None, '', [], (), {}, 42]) == 1 # Only 42 is truish\n", + " assert set(powerset({1, 2, 3})) == {(), (1,), (1, 2), (1, 2, 3), (1, 3), (2,), (2, 3), (3,)}\n", + " assert first_true([0, None, False, {}, 42, 43]) == 42\n", + " assert list(grouper(range(8), 3)) == [(0, 1, 2), (3, 4, 5), (6, 7, None)]\n", + " assert list(pairwise((0, 1, 2, 3, 4))) == [(0, 1), (1, 2), (2, 3), (3, 4)]\n", + " assert list(overlapping((0, 1, 2, 3, 4), 3)) == [(0, 1, 2), (1, 2, 3), (2, 3, 4)]\n", + " assert list(overlapping('abcdefg', 4)) == ['abcd', 'bcde', 'cdef', 'defg'] \n", + " @int_cache\n", + " def fib(n): return (n if n <= 1 else fib(n - 1) + fib(n - 2))\n", + " f = str(fib(10000))\n", + " assert len(f) == 2090 and f.startswith('33644') and f.endswith('66875')\n", + "\n", + " assert 37 in primes\n", + " assert primes[0] == 2 and primes[1] == 3 and primes[10] == 31\n", + " assert primes[:5] == [2, 3, 5, 7, 11]\n", + " assert primes[5:9] == [13, 17, 19, 23]\n", + " assert 42 not in primes\n", + " assert 1299721 in primes\n", + " assert million not in primes\n", + " assert (2 ** 13 - 1) in primes\n", + " assert (2 ** 31 - 1) in primes\n", + " assert list(primes.upto(33)) == [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]\n", + " assert primes.maxn == 2 * million # Make sure we didn't extend cache\n", + " assert len(primes._set) == len(primes._list) == 148933\n", + " \n", + " assert factors(720) == [5, 3, 3, 2, 2, 2, 2]\n", + " assert distinct(factors(720)) == {2, 3, 5}\n", + " assert factors(37) == [37]\n", + " assert distinct(factors(72990720)) == {2, 3, 5, 11}\n", + " assert factors.ndivisors(6) == 4\n", + " assert factors.ndivisors(28) == 6\n", + " assert factors.ndivisors(720) == 30\n", + " assert factors.largest[720] == 5\n", + " assert factors.totient(36) == 12\n", + " assert factors.totient(43) == 42\n", + " for n in (28, 36, 37, 99, 101): \n", + " assert list(primes.upto(n)) == list(upto(primes, n))\n", + " assert factors.totient(n) == quantify(gcd(n, d) == 1 for d in ints(1, n))\n", + " assert n == sum(factors.totient(d) for d in ints(1, n) if n % d == 0)\n", + "\n", + "\n", + "\n", + " return 'pass'\n", + "\n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Timing\n", + "\n", + "My implementation is fast enough to solve Project Euler problems, as you can see from the timing numbers below:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 130 ms, sys: 14.7 ms, total: 144 ms\n", + "Wall time: 151 ms\n", + "CPU times: user 166 ms, sys: 10.4 ms, total: 177 ms\n", + "Wall time: 178 ms\n" + ] + } + ], + "source": [ + "# Instantiate both primes and factors\n", + "%time primes = Primes(2 * million)\n", + "%time factors = Factors(million)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 5 µs, sys: 1e+03 ns, total: 6 µs\n", + "Wall time: 9.06 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Check primality for numbers in cache\n", + "%time 1000003 in primes" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 5 µs, sys: 0 ns, total: 5 µs\n", + "Wall time: 8.11 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time 1000001 in primes" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 100 µs, sys: 1 µs, total: 101 µs\n", + "Wall time: 103 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Check primality for numbers beyond the cache\n", + "%time 2000003 in primes" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 10 µs, sys: 1e+03 ns, total: 11 µs\n", + "Wall time: 16 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "[19753, 5]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Factor numbers in cache\n", + "%time factors(98765)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 9 µs, sys: 1 µs, total: 10 µs\n", + "Wall time: 11.9 µs\n" + ] + }, + { + "data": { + "text/plain": [ + "[5, 5, 5, 5, 3, 3, 3, 3, 2, 2, 2, 2]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time factors(810000)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 8.38 ms, sys: 247 µs, total: 8.63 ms\n", + "Wall time: 11.3 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "[74843, 74843]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Factor numbers beyond the cache\n", + "%time factors(74843 ** 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "31999727999744007303991249934683126567194480546211\n", + "CPU times: user 152 ms, sys: 2.27 ms, total: 155 ms\n", + "Wall time: 168 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "[1000003, 1000003, 1000003, 1999993, 1999993, 1999993, 1999993, 1999993]" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = 1000003 ** 3 * 1999993 ** 5\n", + "print(x)\n", + "%time factors(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15.5 ms, sys: 810 µs, total: 16.3 ms\n", + "Wall time: 19.1 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "37550402023" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time sum(primes.upto(million))" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 2.67 ms, sys: 152 µs, total: 2.82 ms\n", + "Wall time: 3.99 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "62260698721" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sum of the first 100,000 primes\n", + "%time sum(primes[:100000])" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 62.9 ms, sys: 1.78 ms, total: 64.6 ms\n", + "Wall time: 70.9 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "1000003" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# First prime greater than a million\n", + "%time first(p for p in primes if p > million)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 23 ms, sys: 941 µs, total: 23.9 ms\n", + "Wall time: 26.7 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "19186879" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sum of the integers up to 10,000 that have exactly 3 distinct factors\n", + "%time sum(n for n in range(1, 10000) if len(distinct(factors(n))) == 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 88.2 ms, sys: 2.42 ms, total: 90.6 ms\n", + "Wall time: 97.2 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "65796" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# sum of the integers up to 10,000 that have exactly 3 divisors\n", + "%time sum(n for n in range(1, 10000) if factors.ndivisors(n) == 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 326 ms, sys: 3.1 ms, total: 329 ms\n", + "Wall time: 337 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "30393486" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The sum of the totient function of the integers up to 1000 \n", + "%time sum(map(factors.totient, range(1, 10000)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Project Euler Regression Testing\n", + "\n", + "My strategy for managing solutions to problems, and doing regression tests on them:\n", + "* My solution to problem 1 is the function `problem_1()`, which returns the solution when called (and so on for other problems).\n", + "* Once I have verified the answer to a problem (checking it on the Project Euler site), I store it in a dict called `solutions`.\n", + "* Running `verify()` checks that all `problem_`*n* functions return the correct solution. \n", + "\n", + "Project Euler asks participants not to publish solutions to problems, so I will comply, and instead show the solution to three fake problems:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def problem_1(N=100):\n", + " \"Sum of integers: Find the sum of all the integers from 1 to 100 inclusive.\"\n", + " return sum(ints(1, N))\n", + "\n", + "def problem_2(): \n", + " \"Two plus two: how much is 2 + 2?\"\n", + " return int('2' + '2')\n", + "\n", + "def problem_42():\n", + " \"What is life?\"\n", + " return 6 * 7\n", + "\n", + "solutions = {1: 5050, 2: 4} " + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Num Time Status Answer Problem Description Expected\n", + "=== ========== ====== ================ ===================== ========\n", + " 1 0.00 sec ok 5050 Sum of integers \n", + " 2 0.00 sec WRONG! 22 Two plus two 4\n", + " 42 0.00 sec NEW! 42 What is life? \n" + ] + } + ], + "source": [ + "def verify(problem_numbers=range(1, 600)):\n", + " \"\"\"Main test harness function to verify problems. Pass in a collection of ints (problem numbers).\n", + " Prints a message giving execution time, and whether answer was expected.\"\"\"\n", + " print('Num Time Status Answer Problem Description Expected')\n", + " print('=== ========== ====== ================ ===================== ========')\n", + " for p in problem_numbers:\n", + " name = 'problem_{}'.format(p)\n", + " if name in globals():\n", + " fn = globals()[name]\n", + " t0 = time.time()\n", + " answer = fn()\n", + " t = time.time() - t0\n", + " desc = (fn.__doc__ or '??:').split(':')[0]\n", + " status = ('NEW!' if p not in solutions else \n", + " 'WRONG!' if answer != solutions[p] else\n", + " 'SLOW!' if t > 60 else\n", + " 'ok')\n", + " expected = (solutions[p] if status == 'WRONG!' else '')\n", + " print('{:3d} {:6.2f} sec {:>6} {:<16} {:<21} {}'\n", + " .format(p, t, status, answer, desc, expected))\n", + "\n", + "verify()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/PropositionalLogic.ipynb b/pytudes/ipynb/PropositionalLogic.ipynb new file mode 100644 index 0000000..5617c14 --- /dev/null +++ b/pytudes/ipynb/PropositionalLogic.ipynb @@ -0,0 +1,483 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Translating English Sentences into Propositional Logic Statements\n", + "\n", + "In a Logic course, one exercise is to turn an English sentence like this:\n", + "\n", + "> *Sieglinde will survive, and either her son will gain the Ring and Wotan’s plan will be fulfilled or else Valhalla will be destroyed.*\n", + "\n", + "Into a formal Propositional Logic statement: \n", + "\n", + " P ⋀ ((Q ⋀ R) ∨ S)\n", + " \n", + "along with definitions of the propositions:\n", + "\n", + " P: Sieglinde will survive\n", + " Q: Sieglinde’s son will gain the Ring\n", + " R: Wotan’s plan will be fulfilled\n", + " S: Valhalla will be destroyed\n", + "\n", + "For some sentences, it takes detailed knowledge to get a good translation. The following two sentences are ambiguous, with different preferred interpretations, and translating them correctly requires knowledge of eating habits:\n", + "\n", + " I will eat salad or I will eat bread and I will eat butter. P ∨ (Q ⋀ R)\n", + " I will eat salad or I will eat soup and I will eat ice cream. (P ∨ Q) ⋀ R\n", + "\n", + "But for many sentences, the translation process is automatic, with no special knowledge required. I will develop a program to handle these easy sentences. The program is based on the idea of a series of translation rules of the form:\n", + "\n", + " Rule('{P} ⇒ {Q}', 'if {P} then {Q}', 'if {P}, {Q}')\n", + " \n", + "which means that the logic translation will have the form `'P ⇒ Q'`, whenever the English sentence has either the form `'if P then Q'` or `'if P, Q'`, where `P` and `Q` can match any non-empty subsequence of characters. Whatever matches `P` and `Q` will be recursively processed by the rules. The rules are in order—top to bottom, left to right, and the first rule that matches in that order will be accepted, no matter what, so be sure you order your rules carefully. One guideline I have adhered to is to put all the rules that start with a keyword (like `'if'` or `'neither'`) before the rules that start with a variable (like `'{P}'`); that way you avoid accidentally having a keyword swallowed up inside a `'{P}'`.\n", + "\n", + "Consider the example sentence `\"If loving you is wrong, I don't want to be right.\"` This should match the pattern \n", + "`'if {P}, {Q}'` with the variable `P` equal to `\"loving you is wrong\"`. But I don't want the variable `Q` to be \n", + "`\"I don't want to be right\"`, rather, I want to have `～Q` equal to `\"I do want to be right\"`. So in addition to having a set of `Rule`s to handle the `'if {P}, {Q}'` patterns, I will also have a list of `negations` to handle `\"don't\"` and the like.\n", + "\n", + "Here is the code to process `Rule` definitions (using [regular expressions](https://docs.python.org/3.5/library/re.html), which can sometimes be confusing.)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import re\n", + "\n", + "def Rule(output, *patterns):\n", + " \"A rule that produces `output` if the entire input matches any one of the `patterns`.\" \n", + " return (output, [name_group(pat) + '$' for pat in patterns])\n", + "\n", + "def name_group(pat):\n", + " \"Replace '{Q}' with '(?P.+?)', which means 'match 1 or more characters, and call it Q'\"\n", + " return re.sub('{(.)}', r'(?P<\\1>.+?)', pat)\n", + " \n", + "def word(w):\n", + " \"Return a regex that matches w as a complete word (not letters inside a word).\"\n", + " return r'\\b' + w + r'\\b' # '\\b' matches at word boundary" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what a rule looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(('{P} ⇒ {Q}',\n", + " ['if (?P

.+?) then (?P.+?)$', 'if (?P

.+?), (?P.+?)$']),)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Rule('{P} ⇒ {Q}', 'if {P} then {Q}', 'if {P}, {Q}')," + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And now the actual rules. If your sentence is not translated correctly, you can attempt to augment these rules to handle your sentence." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "rules = [\n", + " Rule('{P} ⇒ {Q}', 'if {P} then {Q}', 'if {P}, {Q}'),\n", + " Rule('{P} ⋁ {Q}', 'either {P} or else {Q}', 'either {P} or {Q}'),\n", + " Rule('{P} ⋀ {Q}', 'both {P} and {Q}'),\n", + " Rule('～{P} ⋀ ～{Q}', 'neither {P} nor {Q}'),\n", + " Rule('～{A}{P} ⋀ ～{A}{Q}', '{A} neither {P} nor {Q}'), # The Kaiser neither ...\n", + " Rule('～{Q} ⇒ {P}', '{P} unless {Q}'),\n", + " Rule('{P} ⇒ {Q}', '{Q} provided that {P}', '{Q} whenever {P}', \n", + " '{P} implies {Q}', '{P} therefore {Q}', \n", + " '{Q}, if {P}', '{Q} if {P}', '{P} only if {Q}'),\n", + " Rule('{P} ⋀ {Q}', '{P} and {Q}', '{P} but {Q}'),\n", + " Rule('{P} ⋁ {Q}', '{P} or else {Q}', '{P} or {Q}'),\n", + " ]\n", + "\n", + "negations = [\n", + " (word(\"not\"), \"\"),\n", + " (word(\"cannot\"), \"can\"),\n", + " (word(\"can't\"), \"can\"),\n", + " (word(\"won't\"), \"will\"),\n", + " (word(\"ain't\"), \"is\"),\n", + " (\"n't\", \"\"), # matches as part of a word: didn't, couldn't, etc.\n", + " ]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now the mechanism to process these rules. The key function is `match_rule`, which matches an English sentence against a rule. The function returns two values, a string representing the translation of the English sentence into logic, and `defs`, a dictionary of `{Variable: \"value\"}` pairs. If `match_rule` finds that the rule matches, it recursively calls `match_rules` to match each of the subgroups of the regular expression (the `P` and `Q` in `if {P}, then {Q}`).\n", + "The function `match_literal` handles negations, and is where the `defs` dictionary actually gets updated." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def match_rules(sentence, rules, defs):\n", + " \"\"\"Match sentence against all the rules, accepting the first match; or else make it an atom.\n", + " Return two values: the Logic translation and a dict of {P: 'english'} definitions.\"\"\"\n", + " sentence = clean(sentence)\n", + " for rule in rules:\n", + " result = match_rule(sentence, rule, defs)\n", + " if result: \n", + " return result\n", + " return match_literal(sentence, negations, defs)\n", + " \n", + "def match_rule(sentence, rule, defs):\n", + " \"Match rule, returning the logic translation and the dict of definitions if the match succeeds.\"\n", + " output, patterns = rule\n", + " for pat in patterns:\n", + " match = re.match(pat, sentence, flags=re.I)\n", + " if match:\n", + " groups = match.groupdict()\n", + " for P in sorted(groups): # Recursively apply rules to each of the matching groups\n", + " groups[P] = match_rules(groups[P], rules, defs)[0]\n", + " return '(' + output.format(**groups) + ')', defs\n", + " \n", + "def match_literal(sentence, negations, defs):\n", + " \"No rule matched; sentence is an atom. Add new proposition to defs. Handle negation.\"\n", + " polarity = ''\n", + " for (neg, pos) in negations:\n", + " (sentence, n) = re.subn(neg, pos, sentence, flags=re.I)\n", + " polarity += n * '～'\n", + " sentence = clean(sentence)\n", + " P = proposition_name(sentence, defs)\n", + " defs[P] = sentence\n", + " return polarity + P, defs\n", + " \n", + "def proposition_name(sentence, defs, names='PQRSTUVWXYZBCDEFGHJKLMN'):\n", + " \"Return the old name for this sentence, if used before, or a new, unused name.\"\n", + " inverted = {defs[P]: P for P in defs}\n", + " if sentence in inverted:\n", + " return inverted[sentence] # Find previously-used name\n", + " else:\n", + " return next(P for P in names if P not in defs) # Use a new unused name\n", + " \n", + "def clean(text): \n", + " \"Remove redundant whitespace; handle curly apostrophe and trailing comma/period.\"\n", + " return ' '.join(text.split()).replace(\"’\", \"'\").rstrip('.').rstrip(',')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "('(P ⇒ ～Q)', {'P': 'loving you is wrong', 'Q': 'I do want to be right'})" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "match_rule(\"If loving you is wrong, I don't want to be right\",\n", + " Rule('{P} ⇒ {Q}', 'if {P}, {Q}'),\n", + " {})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some more test sentences and a top-level function to handle them:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "English: Polkadots and Moonbeams. \n", + "\n", + "Logic: (P ⋀ Q)\n", + "P: Polkadots\n", + "Q: Moonbeams\n", + "\n", + "English: If you liked it then you shoulda put a ring on it. \n", + "\n", + "Logic: (P ⇒ Q)\n", + "P: you liked it\n", + "Q: you shoulda put a ring on it\n", + "\n", + "English: If you build it, he will come. \n", + "\n", + "Logic: (P ⇒ Q)\n", + "P: you build it\n", + "Q: he will come\n", + "\n", + "English: It don't mean a thing, if it ain't got that swing. \n", + "\n", + "Logic: (～P ⇒ ～Q)\n", + "P: it is got that swing\n", + "Q: It do mean a thing\n", + "\n", + "English: If loving you is wrong, I don't want to be right. \n", + "\n", + "Logic: (P ⇒ ～Q)\n", + "P: loving you is wrong\n", + "Q: I do want to be right\n", + "\n", + "English: Should I stay or should I go. \n", + "\n", + "Logic: (P ⋁ Q)\n", + "P: Should I stay\n", + "Q: should I go\n", + "\n", + "English: I shouldn't go and I shouldn't not go. \n", + "\n", + "Logic: (～P ⋀ ～～P)\n", + "P: I should go\n", + "\n", + "English: If I fell in love with you, would you promise to be true and help me\n", + "understand. \n", + "\n", + "Logic: (P ⇒ (Q ⋀ R))\n", + "P: I fell in love with you\n", + "Q: would you promise to be true\n", + "R: help me understand\n", + "\n", + "English: I could while away the hours conferrin' with the flowers, consulting\n", + "with the rain and my head I'd be a scratchin' while my thoughts are busy\n", + "hatchin' if I only had a brain. \n", + "\n", + "Logic: (P ⇒ (Q ⋀ R))\n", + "P: I only had a brain\n", + "Q: I could while away the hours conferrin' with the flowers, consulting with the rain\n", + "R: my head I'd be a scratchin' while my thoughts are busy hatchin'\n", + "\n", + "English: There's a federal tax, and a state tax, and a city tax, and a street\n", + "tax, and a sewer tax. \n", + "\n", + "Logic: (P ⋀ (Q ⋀ (R ⋀ (S ⋀ T))))\n", + "P: There's a federal tax\n", + "Q: a state tax\n", + "R: a city tax\n", + "S: a street tax\n", + "T: a sewer tax\n", + "\n", + "English: A ham sandwich is better than nothing and nothing is better than\n", + "eternal happiness therefore a ham sandwich is better than eternal happiness. \n", + "\n", + "Logic: ((P ⋀ Q) ⇒ R)\n", + "P: A ham sandwich is better than nothing\n", + "Q: nothing is better than eternal happiness\n", + "R: a ham sandwich is better than eternal happiness\n", + "\n", + "English: If I were a carpenter and you were a lady, would you marry me anyway?\n", + "and would you have my baby. \n", + "\n", + "Logic: ((P ⋀ Q) ⇒ (R ⋀ S))\n", + "P: I were a carpenter\n", + "Q: you were a lady\n", + "R: would you marry me anyway?\n", + "S: would you have my baby\n", + "\n", + "English: Either Danny didn't come to the party or Virgil didn't come to the\n", + "party. \n", + "\n", + "Logic: (～P ⋁ ～Q)\n", + "P: Danny did come to the party\n", + "Q: Virgil did come to the party\n", + "\n", + "English: Either Wotan will triumph and Valhalla will be saved or else he won't\n", + "and Alberic will have the final word. \n", + "\n", + "Logic: ((P ⋀ Q) ⋁ (～R ⋀ S))\n", + "P: Wotan will triumph\n", + "Q: Valhalla will be saved\n", + "R: he will\n", + "S: Alberic will have the final word\n", + "\n", + "English: Sieglinde will survive, and either her son will gain the Ring and\n", + "Wotan's plan will be fulfilled or else Valhalla will be destroyed. \n", + "\n", + "Logic: (P ⋀ ((Q ⋀ R) ⋁ S))\n", + "P: Sieglinde will survive\n", + "Q: her son will gain the Ring\n", + "R: Wotan's plan will be fulfilled\n", + "S: Valhalla will be destroyed\n", + "\n", + "English: Wotan will intervene and cause Siegmund's death unless either Fricka\n", + "relents or Brunnhilde has her way. \n", + "\n", + "Logic: (～(R ⋁ S) ⇒ (P ⋀ Q))\n", + "P: Wotan will intervene\n", + "Q: cause Siegmund's death\n", + "R: Fricka relents\n", + "S: Brunnhilde has her way\n", + "\n", + "English: Figaro and Susanna will wed provided that either Antonio or Figaro pays\n", + "and Bartolo is satisfied or else Marcellina's contract is voided and the\n", + "Countess does not act rashly. \n", + "\n", + "Logic: ((((P ⋁ Q) ⋀ R) ⋁ (S ⋀ ～T)) ⇒ (U ⋀ V))\n", + "P: Antonio\n", + "Q: Figaro pays\n", + "R: Bartolo is satisfied\n", + "S: Marcellina's contract is voided\n", + "T: the Countess does act rashly\n", + "U: Figaro\n", + "V: Susanna will wed\n", + "\n", + "English: If the Kaiser neither prevents Bismarck from resigning nor supports the\n", + "Liberals, then the military will be in control and either Moltke's plan will be\n", + "executed or else the people will revolt and the Reich will not survive. \n", + "\n", + "Logic: ((～PQ ⋀ ～PR) ⇒ (S ⋀ (T ⋁ (U ⋀ ～V))))\n", + "P: the Kaiser\n", + "Q: prevents Bismarck from resigning\n", + "R: supports the Liberals\n", + "S: the military will be in control\n", + "T: Moltke's plan will be executed\n", + "U: the people will revolt\n", + "V: the Reich will survive\n" + ] + } + ], + "source": [ + "sentences = '''\n", + "Polkadots and Moonbeams.\n", + "If you liked it then you shoulda put a ring on it.\n", + "If you build it, he will come.\n", + "It don't mean a thing, if it ain't got that swing.\n", + "If loving you is wrong, I don't want to be right.\n", + "Should I stay or should I go.\n", + "I shouldn't go and I shouldn't not go.\n", + "If I fell in love with you,\n", + " would you promise to be true\n", + " and help me understand.\n", + "I could while away the hours\n", + " conferrin' with the flowers,\n", + " consulting with the rain\n", + " and my head I'd be a scratchin'\n", + " while my thoughts are busy hatchin'\n", + " if I only had a brain.\n", + "There's a federal tax, and a state tax, and a city tax, and a street tax, and a sewer tax.\n", + "A ham sandwich is better than nothing \n", + " and nothing is better than eternal happiness\n", + " therefore a ham sandwich is better than eternal happiness.\n", + "If I were a carpenter\n", + " and you were a lady,\n", + " would you marry me anyway?\n", + " and would you have my baby.\n", + "Either Danny didn't come to the party or Virgil didn't come to the party.\n", + "Either Wotan will triumph and Valhalla will be saved or else he won't and Alberic will have \n", + " the final word.\n", + "Sieglinde will survive, and either her son will gain the Ring and Wotan’s plan \n", + " will be fulfilled or else Valhalla will be destroyed.\n", + "Wotan will intervene and cause Siegmund's death unless either Fricka relents \n", + " or Brunnhilde has her way.\n", + "Figaro and Susanna will wed provided that either Antonio or Figaro pays and Bartolo is satisfied \n", + " or else Marcellina’s contract is voided and the Countess does not act rashly.\n", + "If the Kaiser neither prevents Bismarck from resigning nor supports the Liberals, \n", + " then the military will be in control and either Moltke's plan will be executed \n", + " or else the people will revolt and the Reich will not survive'''.split('.')\n", + "\n", + "import textwrap\n", + "\n", + "def logic(sentences, width=80): \n", + " \"Match the rules against each sentence in text, and print each result.\"\n", + " for s in map(clean, sentences):\n", + " logic, defs = match_rules(s, rules, {})\n", + " print('\\n' + textwrap.fill('English: ' + s +'.', width), '\\n\\nLogic:', logic)\n", + " for P in sorted(defs):\n", + " print('{}: {}'.format(P, defs[P]))\n", + "\n", + "logic(sentences)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks pretty good! But far from perfect. Here are some errors:\n", + "\n", + "* `Should I stay` *etc.*:
questions are not propositional statements.\n", + "\n", + "* `If I were a carpenter`:
doesn't handle modal logic.\n", + "\n", + "* `nothing is better`:
doesn't handle quantifiers.\n", + "\n", + "* `Either Wotan will triumph and Valhalla will be saved or else he won't`:
gets `'he will'` as one of the propositions, but better would be if that referred back to `'Wotan will triumph'`.\n", + "\n", + "* `Wotan will intervene and cause Siegmund's death`:
gets `\"cause Siegmund's death\"` as a proposition, but better would be `\"Wotan will cause Siegmund's death\"`.\n", + "\n", + "* `Figaro and Susanna will wed`:
gets `\"Figaro\"` and `\"Susanna will wed\"` as two separate propositions; this should really be one proposition. \n", + "\n", + "* `\"either Antonio or Figaro pays\"`:
gets `\"Antonio\"` as a proposition, but it should be `\"Antonio pays\"`.\n", + "\n", + "* `If the Kaiser neither prevents`:
uses the somewhat bogus propositions `PQ` and `PR`. This should be done in a cleaner way. The problem is the same as the previous problem with Antonio: I don't have a good way to attach the subject of a verb phrase to the multiple parts of the verb/object, when there are multiple parts.\n", + "\n", + "\n", + "\n", + "I'm sure more test sentences would reveal many more types of errors.\n", + "\n", + "There's also [a version](proplogic.py) of this program that is in Python 2 and uses only ASCII characters; if you have a Mac or Linux system you can download this as [`proplogic.py`](proplogic.py) and run it with the command `python proplogic.py`. Or you can run it [online](https://www.pythonanywhere.com/user/pnorvig/files/home/pnorvig/proplogic.py?edit)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/Riddler Battle Royale.ipynb b/pytudes/ipynb/Riddler Battle Royale.ipynb new file mode 100644 index 0000000..a10e594 --- /dev/null +++ b/pytudes/ipynb/Riddler Battle Royale.ipynb @@ -0,0 +1,868 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Riddler Battle Royale\n", + "\n", + "\n", + "\n", + "> [538's *The Riddler* Asks](http://fivethirtyeight.com/features/the-battle-for-riddler-nation-round-2/): *In a distant, war-torn land, there are 10 castles. There are two warlords: you and your archenemy, with whom you’re competing to collect the most victory points. Each castle has its own strategic value for a would-be conqueror. Specifically, the castles are worth 1, 2, 3, …, 9, and 10 victory points. You and your enemy each have 100 soldiers to distribute, any way you like, to fight at any of the 10 castles. Whoever sends more soldiers to a given castle conquers that castle and wins its victory points. If you each send the same number of troops, you split the points. You don’t know what distribution of forces your enemy has chosen until the battles begin. Whoever wins the most points wins the war. Submit a plan distributing your 100 soldiers among the 10 castles.*\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# Load some useful modules\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import csv\n", + "import random\n", + "from collections import Counter\n", + "from statistics import mean" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's play with this and see if we can find a good solution. Some implementation choices:\n", + "* A `Plan` will be a tuple of 10 soldier counts (one for each castle).\n", + "* `castles` will hold the indexes of the castles. Note that index 0 is castle 1 (worth 1 point) and index 9 is castle 10 (worth 10 points).\n", + "* `half` is half the total number of points; if you get more than this you win.\n", + "* `plans` will hold a set of plans that were submitted in the previous contest.\n", + "* `play(A, B)` gives the single game reward for Plan A against Plan B: 1 if A wins, 0 if A loses, and 1/2 for a tie.\n", + "* `reward(a, b, payoff)` returns payoff, payoff/2, or 0, depending on whether `a` is bigger than `b`." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "Plan = tuple \n", + "castles = range(10)\n", + "half = 55/2 \n", + "plans = {Plan(map(int, row[:10])) \n", + " for row in csv.reader(open('battle_royale.csv'))}\n", + "\n", + "def play(A, B): \n", + " \"Play Plan A against Plan B and return a reward (0, 1/2, or 1).\"\n", + " A_points = sum(reward(A[c], B[c], c + 1) for c in castles)\n", + " return reward(A_points, half) \n", + "\n", + "def reward(a, b, payoff=1): return (payoff if a > b else payoff / 2 if a == b else 0) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some tests:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "assert reward(6, 5, 9) == 9 # 6 soldiers defeat 5, winning all 9 of the castle's points\n", + "assert reward(6, 6, 8) == 4 # A tie on an 8-point castle is worth 4 points\n", + "assert reward(6, 7, 7) == 0 # No points for a loss\n", + "assert reward(30, 25) == 1 # 30 victory points beats 25\n", + "\n", + "assert len(plans) == 1202\n", + "\n", + "assert play((26, 5, 5, 5, 6, 7, 26, 0, 0, 0),\n", + " (25, 0, 0, 0, 0, 0, 0, 25, 25, 25)) == 1 # A wins game\n", + "\n", + "assert play((26, 5, 5, 5, 6, 7, 26, 0, 0, 0),\n", + " (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)) == 0 # B wins game\n", + "\n", + "assert play((25, 5, 5, 5, 6, 7, 26, 0, 0, 0),\n", + " (25, 0, 0, 0, 0, 0, 0, 25, 25, 25)) == 1/2 # Tie game" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's run a tournament, playing each plan against every other, and returning a list of `[(plan, mean_game_points),...]`. I will also define `show` to pretty-print these results and display a histogram:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def tournament(plans):\n", + " \"Play each plan against each other; return a sorted list of [(plan: mean_points)]\"\n", + " rankdict = {A: mean_points(A, plans) for A in plans}\n", + " return Counter(rankdict).most_common()\n", + "\n", + "def mean_points(A, opponents): \n", + " \"Mean points for A playing against all opponents (but not against itself).\"\n", + " return mean(play(A, B) for B in opponents if B is not A)\n", + "\n", + "def show(rankings, n=10): \n", + " \"Pretty-print the n best plans, and display a histogram of all plans.\"\n", + " print('Top', n, 'of', len(rankings), 'plans:')\n", + " for (plan, points) in rankings[:n]:\n", + " print(pplan(plan), pct(points))\n", + " plt.hist([s for (p, s) in rankings], bins=20)\n", + " \n", + "def pct(x): return '{:6.1%}'.format(x)\n", + "def pplan(plan): return '(' + ', '.join('{:2}'.format(c) for c in plan) + ')'" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[((0, 25, 0, 0, 0, 0, 0, 25, 25, 25), 1),\n", + " ((26, 5, 5, 5, 6, 7, 26, 0, 0, 0), 0.5),\n", + " ((25, 0, 0, 0, 0, 0, 0, 25, 25, 25), 0)]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# This is what the result of a tournament looks like:\n", + "tournament({(26, 5, 5, 5, 6, 7, 26, 0, 0, 0),\n", + " (25, 0, 0, 0, 0, 0, 0, 25, 25, 25),\n", + " (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)})" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Top 10 of 1202 plans:\n", + "( 0, 3, 4, 7, 16, 24, 4, 34, 4, 4) 85.6%\n", + "( 5, 7, 9, 11, 15, 21, 25, 2, 2, 3) 84.1%\n", + "( 3, 5, 8, 10, 13, 1, 26, 30, 2, 2) 83.3%\n", + "( 2, 2, 6, 12, 2, 18, 24, 30, 2, 2) 83.3%\n", + "( 2, 8, 2, 2, 10, 18, 26, 26, 3, 3) 83.2%\n", + "( 3, 6, 7, 9, 11, 2, 27, 31, 2, 2) 83.2%\n", + "( 1, 1, 1, 5, 11, 16, 28, 29, 3, 5) 82.8%\n", + "( 1, 3, 1, 1, 17, 20, 21, 30, 3, 3) 82.6%\n", + "( 3, 6, 10, 12, 16, 21, 26, 2, 2, 2) 82.4%\n", + "( 6, 6, 6, 11, 20, 21, 21, 3, 3, 3) 82.2%\n" + ] + }, + { + "data": { + "image/png": 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ZOqed9ksTtTt69C/43vemXIwkneRS1Wdq49PsNLkUWKyqy7vne4Gqqg+s2Gb6B5akBlTV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\n4m8ATnvjYfE5sOcAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# A tournament with all 1202 plans:\n", + "rankings = tournament(plans)\n", + "show(rankings)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks like there are a few really bad plans in there. Let's just keep the top 1000 plans (out of 1202), and re-run the rankings:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Top 10 of 1000 plans:\n", + "( 0, 3, 4, 7, 16, 24, 4, 34, 4, 4) 87.4%\n", + "( 5, 5, 5, 5, 5, 5, 27, 30, 6, 7) 84.8%\n", + "( 5, 5, 5, 5, 5, 5, 30, 30, 5, 5) 84.2%\n", + "( 3, 3, 5, 5, 7, 7, 30, 30, 5, 5) 84.1%\n", + "( 1, 2, 3, 4, 6, 16, 25, 33, 4, 6) 82.5%\n", + "( 2, 2, 2, 5, 5, 26, 26, 26, 3, 3) 82.4%\n", + "( 1, 1, 1, 5, 11, 16, 28, 29, 3, 5) 82.0%\n", + "( 0, 1, 3, 3, 11, 18, 25, 33, 3, 3) 82.0%\n", + "( 5, 7, 9, 11, 15, 21, 25, 2, 2, 3) 81.7%\n", + "( 0, 0, 5, 5, 25, 3, 25, 3, 31, 3) 81.5%\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plans = {A for (A, _) in rankings[:1000]}\n", + "rankings = tournament(plans)\n", + "show(rankings)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The top 10 plans are still winning over 80%, and the top plan remains `(0, 3, 4, 7, 16, 24, 4, 34, 4, 4)`. This is an interesting plan: it places most of the soldiers on castles 4+5+6+8, which totals only 23 points, so it needs to pick up 5 more points from the other castles (that have mostly 4 soldiers attacking each one). Is this a good strategy? Where should we optiomally allocate soldiers? \n", + "\n", + "To gain some insight, I'll create a plot with 10 curves, one for each castle. Each curve maps the number of soldiers sent to the castle (on the x-axis) to the expected points won (against the 1000 plans) on the y-axis:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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rfUIR+Mrf3R1c8RlEAeOAKcCrmqZFAjuEEFd5VbK2ZPdume8/MlL6CkJD21si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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plotter(plans, X=range(41)):\n", + " X = list(X)\n", + " def mean_reward(c, s): return mean(reward(s, p[c], c+1) for p in plans)\n", + " for c in range(10):\n", + " plt.plot(X, [mean_reward(c, s) for s in X], '.-')\n", + " plt.xlabel('Number of soldiers (on each of the ten castles)')\n", + " plt.ylabel('Expected points won')\n", + " plt.grid()\n", + " \n", + "plotter(plans)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example, this says that for castle 10 (the orange line at top), there is a big gain in expected return as we increase from 0 to 4 soldiers, and after that the gains are relatively less steep. This plot is interesting, but I can't see how to directly read off a best plan from it.\n", + "\n", + "## Hillclimbing\n", + "\n", + "Instead I'll see if I can improve the existing plans, using a simple *hillclimbing* strategy: Take a Plan A, and change it by randomly moving some soldiers from one castle to another. If that yields more `mean_points`, then keep the updated plan, otherwise discard it. Repeat." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def hillclimb(A, plans=plans, steps=1000):\n", + " \"Try to improve Plan A, repeat `steps` times; return new plan and total.\"\n", + " m = mean_points(A, plans)\n", + " for _ in range(steps):\n", + " B = mutate(A)\n", + " m, A = max((m, A), \n", + " (mean_points(B, plans), B))\n", + " return A, m\n", + "\n", + "def mutate(plan):\n", + " \"Return a new plan that is a slight mutation.\"\n", + " plan = list(plan) # So we can modify it.\n", + " i, j = random.sample(castles, 2)\n", + " plan[i], plan[j] = random_split(plan[i] + plan[j])\n", + " return Plan(plan)\n", + "\n", + "def random_split(n):\n", + " \"Split the integer n into two integers that sum to n.\"\n", + " r = random.randint(0, n)\n", + " return r, n - r" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see how well this works. Remember, the best plan so far had a score of `87.4%`. Can we improve on that?" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 3, 4, 15, 7, 21, 3, 31, 3, 13), 0.916)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((0, 3, 4, 7, 16, 24, 4, 34, 4, 4))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We got an improvement. Let's see what happens if we start with other plans:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 5, 5, 12, 7, 22, 3, 31, 3, 12), 0.912)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((10, 10, 10, 10, 10, 10, 10, 10, 10, 10))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((1, 3, 4, 14, 7, 21, 3, 31, 4, 12), 0.9105)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((0, 1, 2, 3, 4, 18, 18, 18, 18, 18))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 5, 5, 15, 7, 21, 3, 31, 6, 7), 0.9065)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((2, 3, 5, 5, 5, 20, 20, 20, 10, 10))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 2, 6, 7, 18, 1, 26, 2, 32, 6), 0.8855)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((0, 0, 5, 5, 25, 3, 25, 3, 31, 3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What if we hillclimb 20 times longer?" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((0, 5, 6, 14, 9, 21, 3, 31, 3, 8), 0.9065)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hillclimb((0, 3, 4, 7, 16, 24, 4, 34, 4, 4), steps=20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Opponent modeling\n", + "\n", + "To have a chance of winning the second round of this contest, we have to predict what the other entries will be like. Nobody knows for sure, but I can hypothesize that the entries will be slightly better than the first round, and try to approximate that by hillclimbing from each of the first-round plans for a small number of steps:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def hillclimbers(plans, steps=100):\n", + " \"Return a sorted list of [(improved_plan, mean_points), ...]\"\n", + " pairs = {hillclimb(plan, plans, steps) for plan in plans}\n", + " return sorted(pairs, key=lambda pair: pair[1], reverse=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[((29, 19, 2, 10, 6, 5, 3, 1, 25, 0), 1),\n", + " ((11, 9, 18, 3, 1, 11, 0, 27, 0, 0), 1),\n", + " ((0, 25, 0, 0, 0, 0, 0, 25, 25, 25), 1)]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# For example:\n", + "hillclimbers({(26, 5, 5, 5, 6, 7, 26, 0, 0, 0),\n", + " (25, 0, 0, 0, 0, 0, 0, 25, 25, 25),\n", + " (0, 25, 0, 0, 0, 0, 0, 25, 25, 25)})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will define `plans2` (and `rankings2`) to be my estimate of the entries for round 2:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 6min 11s, sys: 3.21 s, total: 6min 14s\n", + "Wall time: 6min 17s\n", + "Top 10 of 1000 plans:\n", + "( 1, 4, 5, 15, 6, 21, 3, 31, 3, 11) 90.8%\n", + "( 0, 3, 5, 14, 7, 21, 3, 30, 4, 13) 90.6%\n", + "( 0, 4, 6, 15, 9, 21, 4, 31, 5, 5) 90.2%\n", + "( 2, 4, 3, 13, 5, 22, 3, 32, 4, 12) 90.1%\n", + "( 0, 3, 5, 15, 8, 21, 4, 32, 6, 6) 90.0%\n", + "( 0, 3, 5, 15, 6, 24, 3, 31, 5, 8) 90.0%\n", + "( 0, 3, 6, 13, 6, 21, 5, 30, 4, 12) 90.0%\n", + "( 3, 4, 5, 15, 7, 21, 2, 31, 6, 6) 89.9%\n", + "( 2, 3, 3, 13, 6, 21, 3, 30, 5, 14) 89.8%\n", + "( 0, 2, 2, 12, 2, 23, 4, 31, 3, 21) 89.8%\n" + ] + }, + { + "data": { + "image/png": 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Agao6F7gb2Dd9MyVJQ5rmBu6PV9X93fL3gMPAbuAS4ObubTcDl07bSEnSsAaZ80+yB/gp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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%time rankings2 = hillclimbers(plans)\n", + "plans2 = {A for (A, _) in rankings2}\n", + "show(rankings2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though we only took 100 steps, the `plans2` plans are greatly improved: Almost all of them defeat 75% or more of the first-round `plans`. The top 10 plans are all very similar, targeting castles 4+6+8+10 (for 28 points), but reserving 20 or soldiers to spread among the other castles. Let's look more carefully at every 40th plan, plus the last one:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "( 1, 4, 5, 15, 6, 21, 3, 31, 3, 11) 90.8%\n", + "( 0, 6, 3, 13, 3, 22, 2, 32, 4, 15) 88.9%\n", + "( 1, 3, 6, 13, 9, 22, 1, 30, 4, 11) 88.3%\n", + "( 2, 2, 1, 13, 3, 21, 2, 32, 3, 21) 87.9%\n", + "( 0, 2, 5, 5, 15, 2, 28, 31, 5, 7) 87.6%\n", + "( 2, 2, 4, 14, 9, 1, 27, 30, 6, 5) 87.3%\n", + "( 3, 2, 3, 12, 3, 28, 3, 32, 6, 8) 87.0%\n", + "( 1, 3, 2, 5, 18, 3, 26, 3, 33, 6) 86.7%\n", + "( 0, 4, 4, 6, 15, 3, 29, 30, 5, 4) 86.5%\n", + "( 5, 5, 4, 5, 13, 22, 2, 29, 3, 12) 86.2%\n", + "( 5, 6, 5, 6, 16, 24, 26, 1, 5, 6) 85.9%\n", + "( 0, 2, 5, 15, 8, 3, 20, 36, 6, 5) 85.7%\n", + "( 5, 1, 6, 12, 2, 24, 5, 32, 4, 9) 85.4%\n", + "( 2, 5, 8, 16, 11, 3, 2, 36, 5, 12) 85.1%\n", + "( 2, 7, 3, 15, 14, 2, 3, 31, 9, 12) 84.8%\n", + "( 6, 5, 8, 6, 7, 22, 30, 3, 7, 6) 84.6%\n", + "( 5, 3, 3, 5, 3, 21, 26, 26, 3, 5) 84.4%\n", + "( 0, 2, 4, 13, 2, 22, 17, 33, 2, 5) 84.0%\n", + "( 0, 7, 12, 6, 8, 21, 2, 29, 12, 3) 83.5%\n", + "( 5, 5, 4, 13, 18, 2, 26, 2, 6, 19) 83.0%\n", + "( 5, 6, 3, 15, 17, 24, 4, 2, 5, 19) 82.5%\n", + "( 5, 6, 5, 9, 6, 22, 34, 1, 7, 5) 81.8%\n", + "( 4, 3, 7, 17, 17, 22, 3, 3, 5, 19) 81.0%\n", + "( 0, 1, 2, 11, 12, 13, 28, 27, 2, 4) 80.4%\n", + "( 5, 6, 13, 16, 15, 26, 2, 4, 7, 6) 78.9%\n", + "( 0, 0, 1, 13, 0, 1, 24, 21, 36, 4) 70.3%\n" + ] + } + ], + "source": [ + "for (p, m) in rankings2[::40] + [rankings2[-1]]:\n", + " print(pplan(p), pct(m))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see a wider variety in plans as we go farther down the rankings. Now for the plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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lZWXceuutrFixAgCj0Uhqamq9C7szpg9XmTtXS8+xbJkWeutsWVDm0dhEiqJE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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plotter(plans2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that many castles (e.g. 9 (green), 8 (blue), 7 (black), 6 (yellowish)) have two plateaus. Castle 7 (black) has a plateau at 3.5 points for 6 to 20 soldiers (suggesting that 6 soldiers is a good investment and 20 soldiers a bad investment), and then another plateau at 7 points for everything above 30 soldiers.\n", + "\n", + "Now that we have an estimate of the opponents, we can use `hillclimbers` to try to find a plan that does well against all the others:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 5min 40s, sys: 1 s, total: 5min 41s\n", + "Wall time: 5min 42s\n", + "Top 10 of 1000 plans:\n", + "( 3, 8, 10, 18, 21, 3, 5, 6, 10, 16) 99.9%\n", + "( 1, 9, 10, 17, 21, 6, 4, 6, 9, 17) 99.9%\n", + "( 1, 8, 10, 18, 21, 4, 4, 6, 11, 17) 99.9%\n", + "( 0, 10, 10, 17, 20, 4, 5, 6, 7, 21) 99.9%\n", + "( 2, 11, 1, 16, 18, 7, 6, 6, 8, 25) 99.8%\n", + "( 1, 8, 11, 19, 20, 4, 6, 5, 7, 19) 99.8%\n", + "( 0, 1, 11, 15, 18, 7, 6, 5, 13, 24) 99.8%\n", + "( 2, 10, 1, 17, 18, 9, 5, 6, 8, 24) 99.8%\n", + "( 1, 9, 10, 17, 19, 4, 6, 6, 9, 19) 99.8%\n", + "( 0, 2, 11, 18, 21, 4, 6, 8, 8, 22) 99.8%\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%time rankings3 = hillclimbers(plans2)\n", + "show(rankings3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can try even harder to improve the champ:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "((3, 9, 10, 17, 21, 3, 5, 6, 7, 19), 1)" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "champ, _ = rankings3[0]\n", + "hillclimb(champ, plans2, 10000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are some champion plans from previous runs of this notebook:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "champs = {\n", + " (0, 1, 3, 16, 20, 3, 4, 5, 32, 16),\n", + " (0, 1, 9, 16, 15, 24, 5, 5, 8, 17),\n", + " (0, 1, 9, 16, 16, 24, 5, 5, 7, 17),\n", + " (0, 2, 9, 16, 15, 24, 5, 5, 8, 16),\n", + " (0, 2, 9, 16, 15, 25, 5, 4, 7, 17),\n", + " (0, 3, 4, 7, 16, 24, 4, 34, 4, 4),\n", + " (0, 3, 5, 6, 20, 4, 4, 33, 8, 17),\n", + " (0, 4, 5, 7, 20, 4, 4, 33, 7, 16),\n", + " (0, 4, 6, 7, 19, 4, 4, 31, 8, 17),\n", + " (0, 4, 12, 18, 21, 7, 6, 4, 8, 20),\n", + " (0, 4, 12, 19, 25, 4, 5, 6, 8, 17),\n", + " (0, 5, 6, 7, 18, 4, 5, 32, 7, 16),\n", + " (0, 5, 7, 3, 18, 4, 4, 34, 8, 17),\n", + " (1, 2, 9, 16, 15, 24, 5, 4, 7, 17),\n", + " (1, 2, 9, 16, 15, 24, 5, 4, 8, 16),\n", + " (1, 2, 11, 16, 15, 24, 5, 4, 7, 15),\n", + " (1, 3, 14, 18, 24, 4, 5, 6, 8, 17),\n", + " (1, 6, 3, 16, 16, 24, 5, 5, 7, 17),\n", + " (2, 3, 7, 16, 16, 25, 5, 5, 8, 13),\n", + " (2, 3, 8, 16, 12, 25, 5, 4, 8, 17),\n", + " (2, 3, 8, 16, 15, 24, 5, 4, 7, 16),\n", + " (2, 3, 8, 16, 15, 25, 4, 5, 8, 14),\n", + " (2, 3, 8, 16, 16, 24, 5, 5, 8, 13),\n", + " (2, 3, 9, 15, 12, 25, 4, 5, 8, 17),\n", + " (2, 3, 9, 16, 12, 24, 5, 5, 8, 16),\n", + " (2, 4, 12, 18, 24, 4, 6, 5, 8, 17),\n", + " (3, 3, 7, 16, 16, 24, 5, 5, 8, 13),\n", + " (3, 3, 8, 16, 12, 25, 4, 4, 8, 17),\n", + " (3, 3, 8, 16, 15, 25, 5, 4, 7, 14),\n", + " (3, 4, 12, 18, 23, 4, 6, 5, 8, 17),\n", + " (3, 4, 15, 18, 23, 4, 5, 6, 8, 14),\n", + " (3, 5, 7, 16, 5, 4, 5, 34, 7, 14),\n", + " (3, 6, 13, 17, 23, 4, 6, 5, 8, 15),\n", + " (4, 3, 12, 18, 23, 4, 5, 6, 8, 17),\n", + " (4, 5, 3, 15, 11, 23, 5, 5, 10, 19),\n", + " (4, 6, 3, 16, 14, 25, 5, 5, 8, 14),\n", + " (4, 6, 3, 16, 16, 24, 5, 5, 7, 14),\n", + " (4, 6, 3, 16, 16, 24, 5, 5, 8, 13),\n", + " (5, 3, 12, 17, 23, 4, 5, 6, 8, 17),\n", + " (5, 5, 3, 16, 12, 25, 4, 5, 8, 17),\n", + " (5, 6, 3, 16, 16, 24, 5, 5, 7, 13),\n", + " (5, 6, 7, 3, 21, 4, 27, 5, 8, 14),\n", + " (5, 6, 8, 3, 18, 4, 27, 5, 8, 16),\n", + " (5, 6, 8, 3, 20, 4, 27, 5, 8, 14),\n", + " (5, 6, 8, 3, 21, 4, 27, 5, 8, 13)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can evaluate each of them against the original `plans`, against the improved `plans2`, against their fellow champs, and against all of those put together:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Plan plans plans2 champs all\n", + "( 0, 5, 7, 3, 18, 4, 4, 34, 8, 17) 85.5% 96.0% 68.5% 90.2%\n", + "( 0, 4, 6, 7, 19, 4, 4, 31, 8, 17) 84.7% 95.0% 63.0% 89.2%\n", + "( 0, 1, 3, 16, 20, 3, 4, 5, 32, 16) 85.6% 95.2% 31.5% 89.0%\n", + "( 0, 3, 5, 6, 20, 4, 4, 33, 8, 17) 84.1% 95.2% 60.9% 89.0%\n", + "( 0, 5, 6, 7, 18, 4, 5, 32, 7, 16) 84.3% 96.3% 28.3% 88.9%\n", + "( 3, 5, 7, 16, 5, 4, 5, 34, 7, 14) 85.2% 95.7% 18.5% 88.8%\n", + "( 5, 6, 8, 3, 18, 4, 27, 5, 8, 16) 81.8% 96.4% 64.1% 88.6%\n", + "( 0, 4, 5, 7, 20, 4, 4, 33, 7, 16) 84.7% 95.0% 18.5% 88.2%\n", + "( 5, 6, 8, 3, 20, 4, 27, 5, 8, 14) 82.0% 96.2% 48.9% 88.2%\n", + "( 0, 1, 9, 16, 15, 24, 5, 5, 8, 17) 78.2% 98.6% 72.8% 88.0%\n", + "( 5, 6, 7, 3, 21, 4, 27, 5, 8, 14) 81.8% 96.0% 51.1% 88.0%\n", + "( 0, 1, 9, 16, 16, 24, 5, 5, 7, 17) 79.1% 98.5% 46.7% 87.8%\n", + "( 5, 6, 8, 3, 21, 4, 27, 5, 8, 13) 82.0% 95.2% 45.7% 87.6%\n", + "( 2, 3, 9, 15, 12, 25, 4, 5, 8, 17) 78.5% 97.9% 58.7% 87.5%\n", + "( 4, 5, 3, 15, 11, 23, 5, 5, 10, 19) 76.8% 97.8% 97.8% 87.5%\n", + "( 2, 3, 8, 16, 12, 25, 5, 4, 8, 17) 78.2% 98.1% 57.6% 87.5%\n", + "( 2, 3, 8, 16, 15, 25, 4, 5, 8, 14) 79.7% 97.9% 31.5% 87.5%\n", + "( 0, 2, 9, 16, 15, 24, 5, 5, 8, 16) 78.5% 98.2% 50.0% 87.4%\n", + "( 2, 3, 7, 16, 16, 25, 5, 5, 8, 13) 79.3% 97.5% 44.6% 87.4%\n", + "( 4, 6, 3, 16, 14, 25, 5, 5, 8, 14) 79.0% 97.4% 48.9% 87.3%\n", + "( 5, 5, 3, 16, 12, 25, 4, 5, 8, 17) 78.1% 97.8% 60.9% 87.3%\n", + "( 4, 6, 3, 16, 16, 24, 5, 5, 7, 14) 80.3% 97.2% 21.7% 87.3%\n", + "( 2, 3, 8, 16, 15, 24, 5, 4, 7, 16) 80.2% 97.8% 10.9% 87.2%\n", + "( 1, 2, 9, 16, 15, 24, 5, 4, 7, 17) 79.8% 97.8% 19.6% 87.2%\n", + "( 0, 2, 9, 16, 15, 25, 5, 4, 7, 17) 79.1% 97.9% 31.5% 87.2%\n", + "( 2, 3, 8, 16, 16, 24, 5, 5, 8, 13) 79.5% 97.5% 29.3% 87.2%\n", + "( 2, 3, 9, 16, 12, 24, 5, 5, 8, 16) 78.0% 98.2% 45.7% 87.1%\n", + "( 3, 3, 8, 16, 15, 25, 5, 4, 7, 14) 80.3% 97.6% 6.5% 87.1%\n", + "( 1, 2, 9, 16, 15, 24, 5, 4, 8, 16) 79.2% 97.6% 27.2% 87.0%\n", + "( 3, 3, 7, 16, 16, 24, 5, 5, 8, 13) 79.8% 97.1% 26.1% 87.0%\n", + "( 4, 6, 3, 16, 16, 24, 5, 5, 8, 13) 80.0% 96.7% 28.3% 87.0%\n", + "( 3, 3, 8, 16, 12, 25, 4, 4, 8, 17) 78.8% 97.8% 28.3% 87.0%\n", + "( 5, 6, 3, 16, 16, 24, 5, 5, 7, 13) 80.9% 96.5% 8.7% 86.9%\n", + "( 1, 2, 11, 16, 15, 24, 5, 4, 7, 15) 79.9% 97.2% 6.5% 86.7%\n", + "( 1, 6, 3, 16, 16, 24, 5, 5, 7, 17) 75.2% 97.9% 41.3% 85.5%\n", + "( 5, 3, 12, 17, 23, 4, 5, 6, 8, 17) 64.3% 99.5% 84.8% 82.0%\n", + "( 4, 3, 12, 18, 23, 4, 5, 6, 8, 17) 64.0% 99.5% 88.0% 81.9%\n", + "( 3, 4, 12, 18, 23, 4, 6, 5, 8, 17) 63.2% 99.5% 88.0% 81.5%\n", + "( 2, 4, 12, 18, 24, 4, 6, 5, 8, 17) 63.0% 99.5% 91.3% 81.5%\n", + "( 3, 4, 15, 18, 23, 4, 5, 6, 8, 14) 63.4% 99.5% 76.1% 81.3%\n", + "( 3, 6, 13, 17, 23, 4, 6, 5, 8, 15) 63.2% 99.4% 78.3% 81.2%\n", + "( 1, 3, 14, 18, 24, 4, 5, 6, 8, 17) 62.4% 99.5% 93.5% 81.2%\n", + "( 0, 4, 12, 19, 25, 4, 5, 6, 8, 17) 62.1% 99.5% 95.7% 81.1%\n", + "( 1, 9, 11, 17, 21, 6, 5, 4, 10, 16) 62.1% 100.0% 76.1% 80.9%\n", + "( 0, 4, 12, 18, 21, 7, 6, 4, 8, 20) 61.4% 99.6% 100.0% 80.9%\n", + "( 1, 7, 13, 17, 23, 6, 6, 5, 8, 14) 62.4% 99.5% 78.3% 80.9%\n", + "( 0, 3, 4, 7, 16, 24, 4, 34, 4, 4) 87.4% 37.6% 0.0% 61.1%\n" + ] + } + ], + "source": [ + "def μ(plan, plans): return pct(mean_points(plan,plans))\n", + "all = plans | plans2 | champs\n", + "\n", + "print('Plan plans plans2 champs all')\n", + "for p in sorted(champs, key=lambda p: -mean_points(p, all)):\n", + " print(pplan(p), μ(p, plans), μ(p, plans2), μ(p, champs), μ(p, all))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Which plan is best? In the end, we don't know, because we don't know the pool we will be competing against." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/SET.ipynb b/pytudes/ipynb/SET.ipynb new file mode 100644 index 0000000..7534eae --- /dev/null +++ b/pytudes/ipynb/SET.ipynb @@ -0,0 +1,697 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# SET\n", + "\n", + "How many cards are there? There are four features (color, shape, shading, and number of figures) on each card, and each feature can take one of three values. So the number of cards is:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "81" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "3 ** 4" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "How many sets are there?" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1080.0" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "81 * 80 * 1 / 6" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "How many sets does each card participate in? We need to look at the number of sets (1080) and the number of cards in a set (3), divided by the number of cards (81):" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "40.0" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1080 * 3 / 81" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "Note that each *pair* of cards participates in exactly one set.\n", + "\n", + "How many layouts of 12 cards are there? The answer is (81 choose 12):" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "70724320184700.0" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from math import factorial as fact\n", + "\n", + "def C(n, k): \n", + " \"Number of ways of choosing k things from n things.\"\n", + " return fact(n) / fact(n-k) / fact(k)\n", + "\n", + "C(81, 12)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "That's a lot of digits; hard to read. This should help:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "70.7243201847" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M = 10 ** 6 # Million\n", + "T = 10 ** 12 # Trillion\n", + "\n", + "C(81, 12) / T" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "70 trillion layouts. Of those some will have 6 sets, some more, some less.\n", + "\n", + "In a layout of 12 cards, how many triples (that could potentially be a set) are there?" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "220.0" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "C(12, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": {} + }, + "source": [ + "So, what we're looking for is when exactly 6 of these are sets, and the other 214 are not." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2173.5413336637" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "C(1080, 6) / T" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "81" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from itertools import product\n", + "\n", + "feature = (1, 2, 3)\n", + "\n", + "Card = tuple\n", + "\n", + "cards = set(product(feature, feature, feature, feature))\n", + "len(cards)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def match(card1, card2):\n", + " return Card(match_feature(card1[i], card2[i]) \n", + " for i in (0, 1, 2, 3))\n", + "\n", + "def match_feature(f1, f2):\n", + " return f1 if f1 == f2 else 6 - f1 - f2" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(1, 3, 1, 3)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "match((1, 2, 3, 3),\n", + " (1, 1, 2, 3))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "2173 trillion; even worse.\n", + "\n", + "How many layouts are there where:\n", + "- The first six cards form no sets\n", + "- The last six cards each form a set?" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "246.7179" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "81 * 80 * (79 - 1) * (78 - 3) * (77 - 6) * (76 - 10) / fact(6) / M" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.091475" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "15 * 21 * 28 * 36 * 45 * 55 / fact(6) / M" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "All tests pass.\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for the instruction booklet\n", + "-----+--------+--------+----------------\n", + " 12 | 33 | 1 | 33:1\n", + " 15 | 2,500 | 1 | 2500:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for initial layout\n", + "-----+--------+--------+----------------\n", + " 12 | 96,844 | 3,156 | 31:1\n", + " 15 | 99,963 | 37 | 2702:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for game play\n", + "-----+--------+--------+----------------\n", + " 12 | 86,065 | 5,871 | 15:1\n", + " 15 | 5,595 | 64 | 87:1\n", + " 18 | 57 | 0 | inft:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for initial layout, but no sets before dealing last 3 cards\n", + "-----+--------+--------+----------------\n", + " 12 | 26,426 | 3,242 | 8:1\n", + " 15 | 3,207 | 35 | 92:1\n" + ] + } + ], + "source": [ + "import random\n", + "import collections \n", + "import itertools \n", + "\n", + "\"\"\"\n", + "Game of Set (Peter Norvig 2010-2015)\n", + "\n", + "How often do sets appear when we deal an array of cards?\n", + "How often in the course of playing out the game?\n", + "\n", + "Here are the data types we will use:\n", + "\n", + " card: A string, such as '3R=0', meaning \"three red striped ovals\".\n", + " deck: A list of cards, initially of length 81.\n", + " layout: A list of cards, initially of length 12.\n", + " set: A tuple of 3 cards.\n", + " Tallies: A dict: {12: {True: 33, False: 1}}} means a layout of size 12\n", + " tallied 33 sets and 1 non-set.\n", + "\"\"\"\n", + "\n", + "#### Cards, dealing cards, and defining the notion of sets.\n", + "\n", + "CARDS = [number + color + shade + symbol \n", + " for number in '123' \n", + " for color in 'RGP' \n", + " for shade in '@O=' \n", + " for symbol in '0SD']\n", + "\n", + "def deal(n, deck): \n", + " \"Deal n cards from the deck.\"\n", + " return [deck.pop() for _ in range(n)]\n", + "\n", + "def is_set(cards):\n", + " \"Are these 3 cards a set? No if any feature has 2 values.\"\n", + " for f in range(4):\n", + " values = {card[f] for card in cards}\n", + " if len(values) == 2: \n", + " return False\n", + " return True\n", + "\n", + "def find_set(layout):\n", + " \"Return a set found from this layout, if there is one.\"\n", + " for cards in itertools.combinations(layout, 3):\n", + " if is_set(cards):\n", + " return cards\n", + " return ()\n", + "\n", + "#### Tallying set:no-set ratio\n", + "\n", + "def Tallies(): \n", + " \"A data structure to keep track, for each size, the number of sets and no-sets.\"\n", + " return collections.defaultdict(lambda: {True: 0, False: 0})\n", + "\n", + "def tally(tallies, layout):\n", + " \"Record that a set was found or not found in a layout of given size; return the set.\"\n", + " s = find_set(layout)\n", + " tallies[len(layout)][bool(s)] += 1\n", + " return s\n", + " \n", + "#### Three experiments\n", + "\n", + "def tally_initial_layout(N, sizes=(12, 15)):\n", + " \"Record tallies for N initial deals.\"\n", + " tallies = Tallies()\n", + " deck = list(CARDS)\n", + " for deal in range(N):\n", + " random.shuffle(deck)\n", + " for size in sizes:\n", + " tally(tallies, deck[:size])\n", + " return tallies\n", + "\n", + "def tally_initial_layout_no_prior_sets(N, sizes=(12, 15)):\n", + " \"\"\"Simulate N initial deals for each size, keeping tallies for Sets and NoSets,\n", + " but only when there was no set with 3 fewer cards.\"\"\"\n", + " tallies = Tallies()\n", + " deck = list(CARDS)\n", + " for deal in range(N):\n", + " random.shuffle(deck)\n", + " for size in sizes:\n", + " if not find_set(deck[:size-3]):\n", + " tally(tallies, deck[:size])\n", + " return tallies\n", + "\n", + "def tally_game_play(N):\n", + " \"Record tallies for the play of N complete games.\"\n", + " tallies = Tallies()\n", + " for game in range(N):\n", + " deck = list(CARDS)\n", + " random.shuffle(deck)\n", + " layout = deal(12, deck)\n", + " while deck:\n", + " s = tally(tallies, layout)\n", + " # Pick up the cards in the set, if any\n", + " for card in s: layout.remove(card)\n", + " # Deal new cards\n", + " if len(layout) < 12 or not s:\n", + " layout += deal(3, deck) \n", + " return tallies\n", + "\n", + "def experiments(N):\n", + " show({12: [1, 33], 15: [1, 2500]}, \n", + " 'the instruction booklet')\n", + " show(tally_initial_layout(N), \n", + " 'initial layout')\n", + " show(tally_game_play(N // 25), \n", + " 'game play')\n", + " show(tally_initial_layout_no_prior_sets(N), \n", + " 'initial layout, but no sets before dealing last 3 cards')\n", + "\n", + "\n", + "def show(tallies, label):\n", + " \"Print out the counts.\"\n", + " print()\n", + " print('Size | Sets | NoSets | Set:NoSet ratio for', label)\n", + " print('-----+--------+--------+----------------')\n", + " for size in sorted(tallies):\n", + " y, n = tallies[size][True], tallies[size][False]\n", + " ratio = ('inft' if n==0 else int(round(float(y)/n)))\n", + " print('{:4d} |{:7,d} |{:7,d} | {:4}:1'\n", + " .format(size, y, n, ratio))\n", + "\n", + "def test():\n", + " assert len(CARDS) == 81 == len(set(CARDS))\n", + " assert is_set(('3R=O', '2R=S', '1R=D'))\n", + " assert not is_set(('3R=0', '2R=S', '1R@D'))\n", + " assert find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R=D']) == ('3R=0', '2R=S', '1R=D')\n", + " assert not find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R@D'])\n", + " photo = '2P=0 3P=D 2R=0 3GO0 2POD 3R@D 2RO0 2ROS 1P@S 2P@0 3ROS 2GOD 2P@D 1GOD 3GOS'.split()\n", + " assert not find_set(photo)\n", + " assert set(itertools.combinations([1, 2, 3, 4], 3)) == {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)}\n", + " print('All tests pass.')\n", + "\n", + "test()\n", + "experiments(100000)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for the instruction booklet\n", + "-----+--------+--------+----------------\n", + " 12 | 33 | 1 | 33:1\n", + " 15 | 2,500 | 1 | 2500:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for initial layout\n", + "-----+--------+--------+----------------\n", + " 12 | 9,696 | 304 | 32:1\n", + " 15 | 9,995 | 5 | 1999:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for game play\n", + "-----+--------+--------+----------------\n", + " 12 | 8,653 | 542 | 16:1\n", + " 15 | 513 | 5 | 103:1\n", + " 18 | 5 | 0 | inft:1\n", + "\n", + "Size | Sets | NoSets | Set:NoSet ratio for initial layout, but no sets before dealing last 3 cards\n", + "-----+--------+--------+----------------\n", + " 12 | 2,630 | 294 | 9:1\n", + " 15 | 293 | 1 | 293:1\n" + ] + } + ], + "source": [ + "experiments(10000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": {} + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Scrabble.ipynb b/pytudes/ipynb/Scrabble.ipynb new file mode 100644 index 0000000..7dbea70 --- /dev/null +++ b/pytudes/ipynb/Scrabble.ipynb @@ -0,0 +1,13389 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "

Peter Norvig
29 December 2015
\n", + "\n", + "# Refactoring a Crossword Game Program\n", + "\n", + "In my [CS 212 class](https://www.udacity.com/course/design-of-computer-programs--cs212) on Udacity, the [most complex lesson](https://www.udacity.com/course/viewer#!/c-cs212/l-48634860) involved a crossword game program (for games such as Scrabble® and Words with Friends®). The program was developed *incrementally*. First I asked \"what words can be made with a rack of seven letters, reagardless of the board?\", then I asked \"how can you place words onto a single row of the board?\", and finally, I, with the help of the students, developed a program to find the highest scoring play anywhere on the board. This approach made for a good sequence of exercises, each building on the previous one. But the code ended up being overly complicated—it accumlated [technical debt](https://en.wikipedia.org/wiki/Technical_debt)—because it kept around old ideas from each iteration.\n", + "\n", + "In this notebook I will refactor the program to pay off the technical debt.\n", + "\n", + "# Vocabulary\n", + "\n", + "Our program uses these concepts:\n", + "\n", + "* **Dictionary**: A set of all legal words. Each word has only the letters A-Z.\n", + "* **Word**: a string of uppercase letters. \n", + "* **Tile**: a letter (or a blank) that can be played on the board to form words. \n", + "* **Blank**: a tile with no letter on it; the player who places it on the board gets to choose which letter it will represent. \n", + "* **Rack**: a collection of up to seven tiles that a player uses to make words.\n", + "* **Board**: a grid of squares onto which players play tiles to make words. \n", + "* **Square**: a location on the board; a square can hold one tile. (In the code, the variable name `s` always stands for a square number, and `sq` for the contents of a square, which can be a tile or empty.)\n", + "* **Bonus**: some squares give you bonus scores: double or triple letter or word scores.\n", + "* **Play**: a play consists of placing some tiles on the board to form a continuous string of letters in one direction (across or down), such that only valid words are formed, and such that one of the letters is placed on an anchor square.\n", + "* **Anchor square**: Every play must place a letter on an anchor square: either the center start square or a square that is adjacent to a tile previously played on the board. \n", + "* **Direction:** Every play must be in either the across or down direction. (The variable `dir` always stands for a direction, and is `1` for across and `17` for down.)\n", + "* **Cross word**: a word formed in the *other* direction from a play. For example, a play forms a word in the across direction, and in doing so, places a letter that extends a word in the down direction. Any new extended *cross word* must be in the dictionary.\n", + "* **Score**: the points awarded for a play, consisting of the sum of the word scores for each word created (the main word and possibly any cross words), plus a *bingo* bonus if all seven letters are used. \n", + "* **Word score**: Each word scores the sum of the letter scores for each tile (either placed by the player or already on the board but part of the word) times the word bonus score. The word bonus score starts at 1, and is multiplied by 2 for each double word square and 3 for each triple word square covered by a tile on this play.\n", + "* **Letter score**: The letter score is the value on the letter tile (for example, 1 for `A` and 10 for `Q`) times the letter bonus score. The letter bonus is 2 when a tile is first placed on a double letter square (or the center star) and 3 when first placed on a triple letter square; it is 1 for a tile already on the board, or for a new tile played on a non-letter-bonus square. The letter score for a blank tile is always zero.\n", + "* **Bingo**: a bonus gained by using all seven tiles in one play. In Words with Friends® the bingo bonus is 35; in Scrabble® it is 50.\n", + "* **Game**: players take turns making plays until one player has no more tiles. After making a play, the player's\n", + "rack is replenished with tiles until the player has 7 tiles or until the bag of tiles is empty.\n", + "* **Prefix**: a string of zero or more letters that starts some word in the dictionary. Not a concept that has to do\n", + "with the *rules* of the game; it will be important in our *algorithm* that finds valid plays.\n", + "\n", + "This notebook uses these imports:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from __future__ import division, print_function\n", + "from collections import defaultdict, namedtuple\n", + "from IPython.display import HTML, display\n", + "import random" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "# Dictionary and Words\n", + "\n", + "We will represent the dictionary as a set of words. A word is an uppercase string of letters, like `'WORD'`. There are several standard dictionaries used by different communities of players; we will use the ENABLE dictionary—we can cache a local copy with this shell command:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "! [ -e enable1.txt ] || curl -O http://norvig.com/ngrams/enable1.txt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can define what words are, load the dictionary, and show how the dictionary works:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def Word(w) -> str: return w.strip().upper()\n", + "\n", + "def is_word(word) -> bool: \n", + " \"Is this a legal word in the dictionary?\"\n", + " return word.upper() in DICTIONARY" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "DICTIONARY = {Word(w) for w in open('enable1.txt')}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "172820" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(DICTIONARY)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['RATANY',\n", + " 'CONFERRING',\n", + " 'PHOTOTOXICITIES',\n", + " 'BESTIRS',\n", + " 'STRENGTH',\n", + " 'JACKSMELTS',\n", + " 'INVERSION',\n", + " 'PILEUP',\n", + " 'EYEBARS',\n", + " 'KNUCKLEHEADED']" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(DICTIONARY, 10)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "'HELLO' in DICTIONARY" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Tiles, Blanks, and Racks\n", + "\n", + "We'll represent a tile as a one-character string, like `'W'`. We'll represent a rack as a string of tiles, usually of length 7, such as `'EELRTTS'`. (I also considered a `collections.Counter` to represent a rack, but felt that `str` was simpler, and with the rack size limited to 7, efficiency was not a major issue.)\n", + "\n", + "The blank tile causes some complications. We'll represent a blank in a player's rack as the underscore character, `'_'`. But once the blank is played on the board, it must be used as if it was a specific letter. However, it doesn't score the points of the letter. I chose to use the lowercase version of the letter to represent this. That way, we know what letter the blank is standing for, and we can distinguish between scoring and non-scoring tiles. For example, `'EELRTT_'` is a rack that contains a blank; and `'LETTERs'` is a word played on the board that uses the blank to stand for the letter `S`. \n", + "\n", + "We'll define `letters` to give all the distinct letters that can be made by a rack, and `remove` to remove letters from a rack (after they have been played)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "BLANK = '_' # The blank tile (as it appears in the rack)\n", + "cat = ''.join # Function to concatenate strings\n", + "\n", + "def letters(rack) -> str:\n", + " \"All the distinct letters in a rack (including lowercase if there is a blank).\"\n", + " if BLANK in rack:\n", + " return cat(set(rack.replace(BLANK, ''))) + 'abcdefghijklmnopqrstuvwxyz'\n", + " else:\n", + " return cat(set(rack))\n", + " \n", + "def letters(rack) -> str:\n", + " \"All the distinct letters in a rack (including lowercase if there is a blank).\"\n", + " if BLANK in rack:\n", + " return letters(rack.replace(BLANK, '')) + 'abcdefghijklmnopqrstuvwxyz'\n", + " else:\n", + " return cat(set(rack))\n", + " \n", + "def remove(tiles, rack) -> str:\n", + " \"Return a copy of rack with the given tile(s) removed.\"\n", + " for tile in tiles:\n", + " if tile.islower(): tile = BLANK\n", + " rack = rack.replace(tile, '', 1)\n", + " return rack" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "is_word('LETTERs')" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ERLST'" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "letters('LETTERS')" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ERLTabcdefghijklmnopqrstuvwxyz'" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "letters('EELRTT_')" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'LTER'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "remove('SET', 'LETTERS')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'LE'" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "remove('TREaT', 'LETTER_') " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# The Board, Squares, Directions, and Bonus Squares\n", + "\n", + "In the [previous version](https://www.udacity.com/course/viewer#!/c-cs212/l-48634860) of this program, the board was a two-dimensional matrix, and a square on the board was denoted by a `(row, col)` pair of indexes. There's nothing wrong with that representation, but for this version we will choose a different representation that is simpler in most ways:\n", + "\n", + "* The board is represented as a one-dimensional list of squares.\n", + "* The default board is 15×15 squares, but\n", + "we will include a *border* around the outside, making the board size 17×17. \n", + "* Squares are denoted by integer indexes, from 0 to 288.\n", + "* To move in the `ACROSS` direction from one square to the next, increment the square index by 1.\n", + "* To move in the `DOWN` direction from one square to the next, increment the square index by 17.\n", + "* The border squares are filled with a symbol, `OFF`, indicating that they are off the board.\n", + "The advantage of the border is that the code never has to check if it is at the edge of the board; it can always\n", + "look at the neighboring square without fear of indexing off the end of the board.\n", + "* Each square on the board is initially filled by a symbol indicating the bonus value of the square. When a tile is placed on a square,\n", + "the tile replaces the bonus value.\n", + "\n", + "How will we implement this? We'll define `Board` as a subclass of `list` and give it two additional attributes: \n", + "\n", + "- `down`: the increment to move in the down direction; 17 for a standard board.\n", + "- `directions`: the four increments to move to any neighboring square; `(1, 17, -1, -17)` in a standard board.\n", + "\n", + "Jupyter/Ipython notebooks have a special convention for displaying objects in HTML. We will adopt it as a method of `Board`:\n", + "\n", + "- `_repr_html_`: return a string of HTML that displays the board as a table." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "ACROSS = 1 # The 'across' direction; 'down' depends on the size of the board\n", + "OFF = '#' # A square that is off the board\n", + "EMPTY = '.:;-=*'\n", + "SL, DL, TL, DW, TW, STAR = EMPTY # Single/double/triple letter; double/triple word; star\n", + "\n", + "Square = int # Squares are implemented as integer indexes.\n", + "Direction = int # Directions are implemented as integer increments\n", + "\n", + "class Board(list):\n", + " \"\"\"A Board is a (linear) list of squares, each a single character.\n", + " Note that board[s + down] is directly below board[s].\"\"\"\n", + "\n", + " def __init__(self, squares, bingo=None):\n", + " list.__init__(self, squares)\n", + " self.bingo = bingo or squares.bingo\n", + " down = int(len(squares)**0.5)\n", + " self.down = down\n", + " self.directions = (ACROSS, down, -ACROSS, -down)\n", + " \n", + " def _repr_html_(self) -> str: return board_html(self)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We'll define the standard boards for Words with Friends® and Scrabble®:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "WWF = Board(\"\"\"\n", + "# # # # # # # # # # # # # # # # #\n", + "# . . . = . . ; . ; . . = . . . #\n", + "# . . : . . - . . . - . . : . . #\n", + "# . : . . : . . . . . : . . : . #\n", + "# = . . ; . . . - . . . ; . . = #\n", + "# . . : . . . : . : . . . : . . #\n", + "# . - . . . ; . . . ; . . . - . #\n", + "# ; . . . : . . . . . : . . . ; #\n", + "# . . . - . . . * . . . - . . . #\n", + "# ; . . . : . . . . . : . . . ; #\n", + "# . - . . . ; . . . ; . . . - . #\n", + "# . . : . . . : . : . . . : . . #\n", + "# = . . ; . . . - . . . ; . . = #\n", + "# . : . . : . . . . . : . . : . #\n", + "# . . : . . - . . . - . . : . . #\n", + "# . . . = . . ; . ; . . = . . . #\n", + "# # # # # # # # # # # # # # # # #\n", + "\"\"\".split(), bingo=35)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "SCRABBLE = Board(\"\"\"\n", + "# # # # # # # # # # # # # # # # #\n", + "# = . . : . . . = . . . : . . = #\n", + "# . - . . . ; . . . ; . . . - . #\n", + "# . . - . . . : . : . . . - . . #\n", + "# : . . - . . . : . . . - . . : #\n", + "# . . . . - . . . . . - . . . . #\n", + "# . ; . . . ; . . . ; . . . ; . #\n", + "# . . : . . . : . : . . . : . . #\n", + "# = . . : . . . * . . . : . . = #\n", + "# . . : . . . : . : . . . : . . #\n", + "# . ; . . . ; . . . ; . . . ; . #\n", + "# . . . . - . . . . . - . . . . #\n", + "# : . . - . . . : . . . - . . : #\n", + "# . . - . . . : . : . . . - . . #\n", + "# . - . . . ; . . . ; . . . - . #\n", + "# = . . : . . . = . . . : . . = #\n", + "# # # # # # # # # # # # # # # # #\n", + "\"\"\".split(), bingo=50)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "assert len(WWF) == len(SCRABBLE) == 17 * 17\n", + "assert all(sq in EMPTY or sq == OFF for sq in WWF + SCRABBLE)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Displaying the Board in HTML\n", + "\n", + "I want to diaplay the board in HTML, as a table with different background colors for the bonus squares; and gold-colored letter tiles. I also want to display the point values for each letter on the tiles; I'll use a `defaultdict` of `{letter: int}` named `POINTS` for that." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def board_html(board) -> str:\n", + " \"An HTML representation of the board.\"\n", + " size = board.down - 2\n", + " squares = [square_html(sq) for sq in board if sq != OFF]\n", + " row = ('' + '{}' * size)\n", + " return ('' + row * size + '
').format(*squares)\n", + " \n", + "board_colors = {\n", + " DL: ('lightblue', 66, 'DL'),\n", + " TL: ('lightgreen', 66, 'TL'),\n", + " DW: ('lightcoral', 66, 'DW'),\n", + " TW: ('orange', 66, 'TW'),\n", + " SL: ('whitesmoke', 66, ''),\n", + " STAR: ('violet', 100, '✭')}\n", + "\n", + "def square_html(sq) -> str:\n", + " \"An HTML representation of a square.\"\n", + " color, size, text = board_colors.get(sq, ('gold', 120, sq))\n", + " if text.isupper(): \n", + " text = '{}{}'.format(text, POINTS.get(text, ''))\n", + " params = \"width:25px; height:25px; text-align:center; padding:0px;\"\n", + " style = \"background-color:{}; font-size:{}%\".format(color, size, text)\n", + " return '' + text\n", + "\n", + "POINTS = defaultdict(int, \n", + " A=1, B=3, C=3, D=2, E=1, F=4, G=2, H=4, I=1, J=8, K=5, L=1, M=3, \n", + " N=1, O=1, P=3, Q=10, R=1, S=1, T=1, U=1, V=4, W=4, X=8, Y=4, Z=10)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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We will implement `Play` as a named tuple of four components:\n", + "- `start`: the index number of the square that holds the first letter in the word.\n", + "- `dir`: the direction, with 1 indicating `ACROSS` and `board.down` (normally, 17) indicating `DOWN`.\n", + "- `letters`: the letters of the word, in order, as a `str`. Blanks are lowercase. Some letters are from the rack; some may have been on the board.\n", + "- `rack`: the letters that would remain in the player's rack after making this play. Not strictly necessary as part of the play, but useful information.\n", + "\n", + "The function `make_play` returns a new board with the play made on it. It does not do any checking to see if the play is legal." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "Play = namedtuple('Play', 'start, dir, letters, rack')\n", + "\n", + "def make_play(board, play) -> Board:\n", + " \"Make the play on a copy of board and return the copy.\"\n", + " copy = Board(board)\n", + " end = play.start + len(play.letters) * play.dir\n", + " copy[play.start:end:play.dir] = play.letters\n", + " return copy" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Example Board\n", + "\n", + "Let's test out what we've done so far. 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Find all *anchor squares* on the board. An anchor square is an empty square that is adjacent to a letter on the board—every legal move must place a letter on an anchor square. (One exception: on the game's first play, there are no letters on the board, and the `STAR` square in the center counts as the only anchor square.)\n", + "2. Using just the letters in the rack, find all *prefixes* of words in the dictionary. For example, with the rack `ABC`, we find that `B`, `BA`, and `BAC` are all prefixes of the word `BACK` (and the rack contains other prefixes of other words as well).\n", + "3. For each anchor square and for both directions (across and down):\n", + " - Try each prefix before the anchor (that is, to the left or above the anchor). Don't allow a prefix to extend to another anchor or off the board. That means we won't have to worry about *cross words* for the prefix. If there are already letters on the board before the anchor point, use them as the (only possible) prefix rather than using the prefixes from the rack. For each prefix that fits:\n", + " - Starting at the anchor, march forward (or down) one square at a time, trying to fill empty squares with each possible letter from the rack that forms a valid prefix of a word in the dictionary. If the march forward hits letters that are already on the board, make sure they form a valid prefix too. Also check that any cross words are valid words. When we make a complete word (with an empty or `OFF` square ahead), yield the play that made the word.\n", + " \n", + "So, each legal play will have zero or more prefix letters (which either all come from the rack or all were already on the board), followed by one letter from the rack covering an anchor square, followed by zero or more additional letters (which can be a mix of letters from the rack and letters already on the board), followed by an empty or `OFF` square." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Prefixes\n", + "\n", + "Here we define the set of all prefixes of all words in the dictionary, and investigate the set:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def dict_prefixes(dictionary) -> set:\n", + " \"The set of all prefixes of each word in a dictionary.\"\n", + " return {word[:i] for word in dictionary for i in range(len(word))}\n", + "\n", + "PREFIXES = dict_prefixes(DICTIONARY)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "276374" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(PREFIXES)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.5992014813100335" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(PREFIXES) / len(DICTIONARY)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['TOASTM',\n", + " 'SYNTAX',\n", + " 'BOOGEYM',\n", + " 'MASSAS',\n", + " 'TONS',\n", + " 'PYROT',\n", + " 'ETHNOCENTRICIT',\n", + " 'TROOPIA',\n", + " 'EVENTFULNES',\n", + " 'PENITENTIA']" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(PREFIXES, 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here are all the prefixes from a tiny dictionary of three words. Note that the empty string is a prefix, and we include `HELP` because it is a prefix of `HELPER`, but we don't include `HELPER`, because there is no letter we can add to `HELPER` to make a word in this dictionary:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'', 'H', 'HE', 'HEL', 'HELL', 'HELP', 'HELPE'}" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dict_prefixes({'HELLO', 'HELP', 'HELPER'})" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The function `rack_prefixes` gives the set of prefixes that can be made just from the letters in the rack. Most of the work is done by `extend_prefixes`, which accumulates a set of prefixes into `results`:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def rack_prefixes(rack) -> set: \n", + " \"All word prefixes that can be made by the rack.\"\n", + " return extend_prefixes('', rack, set())\n", + "\n", + "def extend_prefixes(prefix, rack, results) -> set:\n", + " if prefix.upper() in PREFIXES:\n", + " results.add(prefix)\n", + " for L in letters(rack):\n", + " extend_prefixes(prefix+L, remove(L, rack), results)\n", + " return results" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'', 'A', 'AB', 'AC', 'B', 'BA', 'BAC', 'C', 'CA', 'CAB'}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rack = 'ABC'\n", + "rack_prefixes(rack)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The number of prefixes in a rack is usually on the order of a hundred, unless there is a blank in the rack:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "155" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(rack_prefixes('LETTERS'))" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "120" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(rack_prefixes('HJRIPUM'))" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1590" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(rack_prefixes('LETTER_'))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Anchor Squares\n", + "\n", + "An anchor square is either the star in the middle of the board, or an empty square that is adjacent to a letter:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def is_anchor(board, s) -> bool:\n", + " \"Is this square next to a letter already on the board? (Or is it a '*')?\"\n", + " return (board[s] == STAR or\n", + " board[s] in EMPTY and any(board[s + d].isalpha() for d in board.directions))\n", + "\n", + "def all_anchors(board) -> list:\n", + " \"A list of all anchor squares on the board.\"\n", + " return [s for s in range(len(board)) if is_anchor(board, s)]" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[144]" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The only anchor on an empty board is the star in the middle\n", + "all_anchors(WWF) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Plays on Example Board\n", + "\n", + "Let's work through the process of finding plays on the example `board`. First, we'll find all the anchors:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "53" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "anchors = all_anchors(board)\n", + "len(anchors)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "To visualize these anchors, we'll make each one be a star, on a copy of `board`:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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"cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we'll define a rack, and find all the prefixes for the rack:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "88" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rack = 'ABCHKNQ'\n", + "\n", + "prefixes = rack_prefixes(rack)\n", + "len(prefixes)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "' BANQ BH KANB KAC HACK ACK QAN BAH CAB CHAB BAN HACKB NA CH KHAN CAH AH ANKH H BHA CHAK CANK BAC KAH NAK KBA CN ABH ANK QA HAN NACH Q CAN BA BAK K HAC A AQ HAK BHAK CA NAB NAC AB BHAN KNAC C AK CHA KA HANK HACKN ACQ HANC N B ANC BANK KN HA KAN BACH CHAQ BACKH AN ABN KAB KACH KB AHC CHAN CAK BANKC BACK ANH KH ACKN AC BANC KNA KHA HAB ANCH ACH ACN'" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "' '.join(prefixes)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We won't go through all the anchor/prefix combinations; we'll just pick one: the anchor above the `M` in `MUSES`:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ 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" + ], + "text/plain": [ + "['#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'B',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'T',\n", + " 'O',\n", + " 'U',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'G',\n", + " '.',\n", + " 'B',\n", + " 'A',\n", + " '.',\n", + " '.',\n", + " 'B',\n", + " 'E',\n", + " '.',\n", + " 'C',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " 'A',\n", + " '.',\n", + " '.',\n", + " 'M',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'N',\n", + " '.',\n", + " 'H',\n", + " 'E',\n", + " 'A',\n", + " 'R',\n", + " 'D',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'V',\n", + " 'I',\n", + " 'R',\n", + " 'U',\n", + " 'L',\n", + " 'e',\n", + " 'N',\n", + " 'T',\n", + " ';',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'L',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'E',\n", + " ':',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'E',\n", + " '.',\n", + " 'L',\n", + " 'Y',\n", + " 'T',\n", + " 'H',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " 'E',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'R',\n", + " 'E',\n", + " 'D',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'R',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'E',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " 'N',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#']" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "board3[141] = 'A'\n", + "assert 'BA' in PREFIXES and is_word('A' + 'MUSES')\n", + "board3" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can continue marching forward, trying letters from the rack that form valid prefixes. Let's try the combination `CK`:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "['#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'B',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'T',\n", + " 'O',\n", + " 'U',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'G',\n", + " '.',\n", + " 'B',\n", + " 'A',\n", + " 'C',\n", + " 'K',\n", + " 'B',\n", + " 'E',\n", + " '.',\n", + " 'C',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " 'A',\n", + " '.',\n", + " '.',\n", + " 'M',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'N',\n", + " '.',\n", + " 'H',\n", + " 'E',\n", + " 'A',\n", + " 'R',\n", + " 'D',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'V',\n", + " 'I',\n", + " 'R',\n", + " 'U',\n", + " 'L',\n", + " 'e',\n", + " 'N',\n", + " 'T',\n", + " ';',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'L',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'E',\n", + " ':',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'E',\n", + " '.',\n", + " 'L',\n", + " 'Y',\n", + " 'T',\n", + " 'H',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " 'E',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'R',\n", + " 'E',\n", + " 'D',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'R',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'E',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " 'N',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#']" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "board3[142:144] = 'CK'\n", + "assert 'BACK' in PREFIXES\n", + "board3" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We've spelled the word `BACK`, but we can't count it as a legal play, because there isn't an empty square to the right of `BACK`; there are two existing letters, `BE`. Fortunately, `BACKBE` is a valid prefix, so we can continue to the next empty square, where we can choose an `N`:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "['#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'B',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'T',\n", + " 'O',\n", + " 'U',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'G',\n", + " '.',\n", + " 'B',\n", + " 'A',\n", + " 'C',\n", + " 'K',\n", + " 'B',\n", + " 'E',\n", + " 'N',\n", + " 'C',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " 'A',\n", + " '.',\n", + " '.',\n", + " 'M',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'N',\n", + " '.',\n", + " 'H',\n", + " 'E',\n", + " 'A',\n", + " 'R',\n", + " 'D',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'V',\n", + " 'I',\n", + " 'R',\n", + " 'U',\n", + " 'L',\n", + " 'e',\n", + " 'N',\n", + " 'T',\n", + " ';',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'L',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'E',\n", + " ':',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'E',\n", + " '.',\n", + " 'L',\n", + " 'Y',\n", + " 'T',\n", + " 'H',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " 'E',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'R',\n", + " 'E',\n", + " 'D',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'R',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'E',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " 'N',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#']" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "board3[146] = 'N'\n", + "assert 'BACKBENC' in PREFIXES\n", + "board3" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We continue to the next square (a double word square), and place an `H`, which completes a word, `BACKBENCH` (with an empty square to the right), and simultaneously makes a cross word, `THE`:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "['#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'B',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'T',\n", + " 'O',\n", + " 'U',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'G',\n", + " '.',\n", + " 'B',\n", + " 'A',\n", + " 'C',\n", + " 'K',\n", + " 'B',\n", + " 'E',\n", + " 'N',\n", + " 'C',\n", + " 'H',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " 'A',\n", + " '.',\n", + " '.',\n", + " 'M',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'N',\n", + " '.',\n", + " 'H',\n", + " 'E',\n", + " 'A',\n", + " 'R',\n", + " 'D',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'V',\n", + " 'I',\n", + " 'R',\n", + " 'U',\n", + " 'L',\n", + " 'e',\n", + " 'N',\n", + " 'T',\n", + " ';',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'L',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'E',\n", + " ':',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'E',\n", + " '.',\n", + " 'L',\n", + " 'Y',\n", + " 'T',\n", + " 'H',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " 'E',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'R',\n", + " 'E',\n", + " 'D',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'S',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'R',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'E',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " ';',\n", + " '.',\n", + " 'N',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#']" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "board3[148] = 'H'\n", + "assert is_word('BACKBENCH') and is_word('THE')\n", + "board3" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We've found a valid play; we can now backtrack to consider other letters for this and other prefix/anchor combinations. Now let's code this up! \n", + "\n", + "# Code for Finding All Plays\n", + "\n", + "The function `all_plays` generates all legal plays by looking at every anchor square, trying all prefix plays, and then trying to extend each one, one letter at a time. (Note that it also generates the empty play, because a player always has the option of passing.)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def all_plays(board, rack):\n", + " \"\"\"Generate all plays that can be played on board with this rack.\n", + " Try placing every possible prefix before every anchor point; \n", + " then extend one letter at a time, looking for valid plays.\"\"\"\n", + " yield Play(0, ACROSS, '', rack) # The empty play (no letters, no points)\n", + " prefixes = rack_prefixes(rack)\n", + " for anchor in all_anchors(board):\n", + " for dir in (ACROSS, board.down):\n", + " for play in prefix_plays(prefixes, board, anchor, dir, rack):\n", + " yield from extend_play(board, play)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now for the function `prefix_plays`, which returns a list of all partial plays consisting of a prefix placed before the anchor. Note that these are not *legal* plays; they are *partial* plays, some of which will end up being extended into legal plays. \n", + "\n", + "There are two cases: if there are letters on the board immediately before the anchor, then those letters form the only allowable prefix. If not, we can use any prefix from the rack up to `maxlen`, which is the number of empty squares that do not run into another anchor, nor off the board." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def prefix_plays(prefixes, board, anchor, dir, rack):\n", + " \"Return all Plays of a prefix to the left/above anchor.\"\n", + " if board[anchor-dir].isalpha(): # Prefix already on the board; only 1 prefix\n", + " start = scan_letters(board, anchor, -dir)\n", + " yield Play(start, dir, cat(board[start:anchor:dir]), rack)\n", + " else: # Prefixes from rack fit in space before anchor\n", + " maxlen = (anchor - scan_to_anchor(board, anchor, -dir)) // dir\n", + " for prefix in prefixes:\n", + " if len(prefix) <= maxlen:\n", + " yield Play(anchor - len(prefix) * dir, dir, prefix, remove(prefix, rack))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now `extend_play` takes a partial play, determines the square, `s`, that is one square past the end of the play, and tries all possible letters there. If adding a letter forms a valid prefix (and also does not form an invalid cross word), then we continue on (by calling `extend_play` recursively). If adding the letter forms a valid word, we yield the play." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def extend_play(board, play):\n", + " \"Explore all ways of adding to end of play; return ones that form full words.\"\n", + " s = play.start + play.dir * len(play.letters)\n", + " if board[s] == OFF: return\n", + " cword = crossword(board, s, play.dir)\n", + " possible_letters = board[s].upper() if board[s].isalpha() else letters(play.rack)\n", + " for L in possible_letters:\n", + " prefix2 = play.letters + L\n", + " if prefix2.upper() in PREFIXES and valid_crossword(cword, L):\n", + " rack2 = play.rack if board[s].isalpha() else remove(L, play.rack)\n", + " play2 = Play(play.start, play.dir, prefix2, rack2)\n", + " if is_word(prefix2) and not board[s + play.dir].isalpha():\n", + " yield play2\n", + " yield from extend_play(board, play2)\n", + "\n", + "def scan_letters(board, s, dir) -> Square:\n", + " \"Return the last square number going from s in dir that is a letter.\"\n", + " while board[s + dir].isalpha():\n", + " s += dir\n", + " return s\n", + "\n", + "def scan_to_anchor(board, s, dir) -> Square:\n", + " \"Return the last square number going from s in dir that is not an anchor nor off board.\"\n", + " while board[s + dir] != OFF and not is_anchor(board, s + dir):\n", + " s += dir\n", + " return s" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Crosswords\n", + "\n", + "If adding a letter in, say, the `ACROSS` direction also adds on to a word in the `DOWN` direction, then we need to make sure that this *cross word* is also valid. The function `crossword` finds the cross word at square `s` and returns it with a `'.'` indicating the empty square where the new letter will be placed, so we would get `'.MUSES'` and `'T.E'` for the two crosswords in the `'BACKBENCH'` play." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def crossword(board, s, dir) -> str:\n", + " \"\"\"The word that intersects s in the other direction from dir.\n", + " Use '.' for the one square that is missing a letter.\"\"\"\n", + " def canonical(L): return L if L.isalpha() else '.'\n", + " d = other(dir, board)\n", + " start = scan_letters(board, s, -d)\n", + " end = scan_letters(board, s, d)\n", + " return cat(canonical(board[s]) for s in range(start, end+d, d))\n", + "\n", + "def valid_crossword(cword, L) -> bool:\n", + " \"Is placing letter L valid (with respective to the crossword)?\"\n", + " return len(cword) == 1 or cword.replace('.', L).upper() in DICTIONARY\n", + "\n", + "def other(dir, board) -> Direction:\n", + " \"The other direction (across/down) on the board.\"\n", + " return board.down if dir == ACROSS else ACROSS" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'.MUSES'" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "crossword(board, 141, ACROSS)" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'T.E'" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "crossword(board, 148, ACROSS)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The function `valid_crossword` checks if replacing the empty square with a specific letter will form a valid word:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "valid_crossword('.MUSES', 'A')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can now see all the prefix plays for the anchor at 141 (just above `MUSES`):" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{Play(start=140, dir=1, letters='A', rack='BCHKNQ'),\n", + " Play(start=140, dir=1, letters='B', rack='ACHKNQ'),\n", + " Play(start=140, dir=1, letters='C', rack='ABHKNQ'),\n", + " Play(start=140, dir=1, letters='H', rack='ABCKNQ'),\n", + " Play(start=140, dir=1, letters='K', rack='ABCHNQ'),\n", + " Play(start=140, dir=1, letters='N', rack='ABCHKQ'),\n", + " Play(start=140, dir=1, letters='Q', rack='ABCHKN'),\n", + " Play(start=141, dir=1, letters='', rack='ABCHKNQ')}" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(prefix_plays(rack_prefixes(rack), board, 141, 1, rack))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And we can see all the ways to extend the play of `'B'` there:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{Play(start=140, dir=1, letters='BA', rack='CHKNQ'),\n", + " Play(start=140, dir=1, letters='BACKBENCH', rack='Q'),\n", + " Play(start=140, dir=1, letters='BAH', rack='CKNQ'),\n", + " Play(start=140, dir=1, letters='BAN', rack='CHKQ')}" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "set(extend_play(board, Play(start=140, dir=1, letters='B', rack='ACHKNQ')))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Scoring\n", + "\n", + "Now we'll show how to count up the points made by a play. The score is the sum of the word score for the play, plus a bingo score if all seven letters are used, plus the sum of the word scores for any cross words. The word score is the sum of the letter scores (where each letter score may be doubled or tripled by a bonus square when the letter is first played on the square), all multiplied by any word bonus(es) encountered by the newly-placed letters." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def score(board, play) -> int:\n", + " \"The number of points scored by making this play on the board.\"\n", + " return (word_score(board, play) \n", + " + bingo(board, play) \n", + " + sum(word_score(board, cplay) \n", + " for cplay in cross_plays(board, play)))\n", + "\n", + "def word_score(board, play) -> int:\n", + " \"Points for a single word, counting word- and letter-bonuses.\"\n", + " total, word_bonus = 0, 1\n", + " for (s, L) in enumerate_play(play):\n", + " sq = board[s]\n", + " word_bonus *= (3 if sq == TW else 2 if sq == DW else 1)\n", + " total += POINTS[L] * (3 if sq == TL else 2 if sq == DL else 1)\n", + " return word_bonus * total\n", + "\n", + "def bingo(board, play) -> int:\n", + " \"A bonus for using 7 letters from the rack.\"\n", + " return (board.bingo if (play.rack == '' and letters_played(board, play) == 7) \n", + " else 0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here are the various helper functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def letters_played(board, play) -> int:\n", + " \"The number of letters played from the rack.\"\n", + " return sum(board[s] in EMPTY for (s, L) in enumerate_play(play))\n", + " \n", + "def enumerate_play(play) -> list:\n", + " \"List (square_number, letter) pairs for each tile in the play.\"\n", + " return [(play.start + i * play.dir, L) \n", + " for (i, L) in enumerate(play.letters)]\n", + " \n", + "def cross_plays(board, play):\n", + " \"Generate all plays for words that cross this play.\"\n", + " cross = other(play.dir, board)\n", + " for (s, L) in enumerate_play(play):\n", + " if board[s] in EMPTY and (board[s-cross].isalpha() or board[s+cross].isalpha()):\n", + " start, end = scan_letters(board, s, -cross), scan_letters(board, s, cross)\n", + " before, after = cat(board[start:s:cross]), cat(board[s+cross:end+cross:cross])\n", + " yield Play(start, cross, before + L + after, play.rack)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "What should the `BACKBENCH` play score? The word covers two double-word bonuses, but no letter bonuses. The sum of the letter point values is 3+1+3+5+3+1+1+3+4 = 24, and 24×2×2 = 96. The cross word `AMUSES` scores 8, and `THE` is on a double word bonus, so it scores 6×2 = 12. There is one letter remaining in the rack, so no bingo, just a total score of 96 + 8 + 12 = 116." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "116" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "score(board, Play(start=140, dir=1, letters='BACKBENCH', rack='Q'))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can find the highest scoring play by enumerating all plays and taking the one with the maximum score:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def highest_scoring_play(board, rack) -> Play: \n", + " \"Return the Play that gives the most points.\"\n", + " return max(all_plays(board, rack), key=lambda play: score(board, play))" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Play(start=140, dir=1, letters='BACKBENCH', rack='Q')" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "highest_scoring_play(board, rack)" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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We start with a bag of tiles with the official Scrabble® distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "100" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "BAG = 'AAAAAAAAABBCCDDDDEEEEEEEEEEEEFFGGGHHIIIIIIIIIJKLLLLMMNNNNNNOOOOOOOOPPQRRRRRRSSSSTTTTTTUUUUVVWWXYYZ__'\n", + "len(BAG)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Then the function `play_game` will take a list of *player strategies* as input, and play those strategies against each other over the course of a game. A strategy is a function that takes a board and a rack as input and returns a play. For example, `highest_scoring_play` is a strategy. If the optional argument `verbose` is true, then the board is displayed after each play." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def play_game(strategies=[highest_scoring_play, highest_scoring_play], \n", + " board=WWF, verbose=True) -> list:\n", + " \"A number of players play a game; return a list of their scores.\"\n", + " board = Board(board)\n", + " bag = list(BAG)\n", + " random.shuffle(bag)\n", + " scores = [0 for _ in strategies]\n", + " racks = [replenish('', bag) for _ in strategies]\n", + " while True:\n", + " old_board = board\n", + " for (p, strategy) in enumerate(strategies):\n", + " board = make_one_play(board, p, strategy, scores, racks, bag, verbose)\n", + " if racks[p] == '':\n", + " # Player p has gone out; game over\n", + " return subtract_remaining_tiles(racks, scores, p)\n", + " if old_board == board:\n", + " # No player has a move; game over\n", + " return scores\n", + "\n", + "def make_one_play(board, p, strategy, scores, racks, bag, verbose) -> Board:\n", + " \"\"\"One player, player p, chooses a move according to the strategy.\n", + " We make the move, replenish the rack, update scores, and return the new Board.\"\"\"\n", + " rack = racks[p]\n", + " play = strategy(board, racks[p])\n", + " racks[p] = replenish(play.rack, bag)\n", + " points = score(board, play)\n", + " scores[p] += points\n", + " board = make_play(board, play)\n", + " if verbose:\n", + " display(HTML('Player {} with rack {} makes {}
for {} points; draws: {}; scores: {}'\n", + " .format(p, rack, play, points, racks[p], scores)),\n", + " board)\n", + " return board\n", + "\n", + "def subtract_remaining_tiles(racks, scores, p) -> list:\n", + " \"Subtract point values from each player and give them to player p.\"\n", + " for i in range(len(racks)):\n", + " points = sum(POINTS[L] for L in racks[i])\n", + " scores[i] -= points\n", + " scores[p] += points\n", + " return scores\n", + "\n", + "def replenish(rack, bag) -> str:\n", + " \"Fill rack with 7 letters (as long as there are letters left in the bag).\"\n", + " while len(rack) < 7 and bag:\n", + " rack += bag.pop()\n", + " return rack" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "application/javascript": [ + "IPython.OutputArea.auto_scroll_threshold = 9999;" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "%%javascript\n", + "IPython.OutputArea.auto_scroll_threshold = 9999;" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "Player 0 with rack NIEUTBT makes Play(start=144, dir=1, letters='BUTTE', rack='NI')
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" + ], + "text/plain": [ + "['#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'A',\n", + " 'V',\n", + " 'o',\n", + " 'W',\n", + " 'E',\n", + " 'R',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'W',\n", + " 'O',\n", + " 'N',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " 'K',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'G',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'L',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'H',\n", + " 'I',\n", + " '.',\n", + " ':',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '=',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " 'U',\n", + " '.',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " 'N',\n", + " '.',\n", + " '.',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'T',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'C',\n", + " ':',\n", + " '.',\n", + " 'A',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '-',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'C',\n", + " 'A',\n", + " 'I',\n", + " 'R',\n", + " 'D',\n", + " 'S',\n", + " '#',\n", + " '#',\n", + " ';',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " 'N',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'D',\n", + " '.',\n", + " '.',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'J',\n", + " '.',\n", + " 'O',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'B',\n", + " 'U',\n", + " 'T',\n", + " 'T',\n", + " 'E',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " 'H',\n", + " 'E',\n", + " '.',\n", + " 'D',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " 'N',\n", + " '.',\n", + " '.',\n", + " ';',\n", + " '#',\n", + " '#',\n", + " 'E',\n", + " 'L',\n", + " '.',\n", + " 'I',\n", + " '.',\n", + " 'T',\n", + " '.',\n", + " 'O',\n", + " '.',\n", + " 'F',\n", + " 'E',\n", + " 'T',\n", + " 'U',\n", + " 'S',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " 'L',\n", + " ':',\n", + " 'Z',\n", + " '.',\n", + " 'A',\n", + " ':',\n", + " 'M',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " 'G',\n", + " 'Y',\n", + " 'R',\n", + " 'E',\n", + " 'N',\n", + " 'E',\n", + " '.',\n", + " 'E',\n", + " 'O',\n", + " 'L',\n", + " 'O',\n", + " 'P',\n", + " 'I',\n", + " 'l',\n", + " 'E',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " 'R',\n", + " 'U',\n", + " 'N',\n", + " '.',\n", + " '.',\n", + " 'F',\n", + " 'A',\n", + " 'X',\n", + " '.',\n", + " '.',\n", + " ':',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " 'M',\n", + " 'O',\n", + " 'B',\n", + " 'S',\n", + " '.',\n", + " 'I',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " 'T',\n", + " 'O',\n", + " 'A',\n", + " 'D',\n", + " 'Y',\n", + " '.',\n", + " '#',\n", + " '#',\n", + " '.',\n", + " '.',\n", + " '.',\n", + " '=',\n", + " '.',\n", + " 'A',\n", + " 'G',\n", + " 'A',\n", + " 'P',\n", + " 'E',\n", + " '.',\n", + " 'S',\n", + " 'O',\n", + " 'A',\n", + " 'R',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#',\n", + " '#']" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "[307, 422]" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "play_game()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "That was an exciting game, ranging to the four edges of the board, with three bingos: INCIDENT,\n", + "EOLOPILE and \n", + "VOLUTIN (yes, those are actual words). \n", + "\n", + "But that was just one game; Let's get statistics for both players over, say, 10 games:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "min: 278, median: 389, mean: 378.15, max: 447\n", + "CPU times: user 26.7 s, sys: 313 ms, total: 27 s\n", + "Wall time: 29.1 s\n" + ] + } + ], + "source": [ + "%%time\n", + "\n", + "games = 10\n", + "\n", + "scores = sorted(score for game in range(games) \n", + " for score in play_game(verbose=False))\n", + "\n", + "print('min: {}, median: {}, mean: {}, max: {}'.format(\n", + " min(scores), scores[games], sum(scores)/(2*games), max(scores)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Tests\n", + "\n", + "I *should* have a complete test suite. Instead, all I have this minimal suite, plus the confidence I gained from seeing the game play." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'ok'" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def sames(A, B): return sorted(A) == sorted(B)\n", + "\n", + "def test():\n", + " \"Unit tests.\"\n", + " assert is_word('WORD')\n", + " assert is_word('LETTERs')\n", + " assert is_word('ETHyLENEDIAMINETETRAACETATES')\n", + " assert not is_word('ALFABET')\n", + " \n", + " rack = 'ABCHKNQ'\n", + " \n", + " assert sames(letters(rack), rack)\n", + " assert sames(letters('ABAC_'), 'ABCabcdefghijklmnopqrstuvwxyz')\n", + " \n", + " assert dict_prefixes({'HELLO', 'HELP', 'HELPER'}) == {\n", + " '', 'H', 'HE', 'HEL', 'HELL', 'HELP', 'HELPE'}\n", + " \n", + " assert rack_prefixes('ABC') == {'', 'A', 'AB', 'AC', 'B', 'BA', 'BAC', 'C', 'CA', 'CAB'}\n", + " assert len(rack_prefixes('LETTERS')) == 155\n", + " assert len(rack_prefixes('LETTER_')) == 1590\n", + " \n", + " DOWN = WWF.down\n", + " plays = {\n", + " Play(145, DOWN, 'ENTER', ''),\n", + " Play(144, ACROSS, 'BE', ''),\n", + " Play(138, DOWN, 'GAVE', ''),\n", + " Play(158, DOWN, 'MUSES', ''),\n", + " Play(172, ACROSS, 'VIRULeNT', ''),\n", + " Play(213, ACROSS, 'RED', ''),\n", + " Play(198, ACROSS, 'LYTHE', ''),\n", + " Play(147, DOWN, 'CHILDREN', ''),\n", + " Play(164, ACROSS, 'HEARD', ''),\n", + " Play(117, DOWN, 'BRIDLES', ''),\n", + " Play(131, ACROSS, 'TOUR', '')}\n", + "\n", + " board = Board(WWF)\n", + " for play in plays:\n", + " board = make_play(board, play)\n", + " \n", + " assert len(WWF) == len(board) == 17 * 17\n", + " assert all_anchors(WWF) == [144]\n", + " assert all_anchors(board) == [\n", + " 100, 114, 115, 116, 121, 127, 128, 130, 137, 139, 141, 143, 146, 148, 149, 150, 154, 156, 157, 159, 160, \n", + " 161, 163, 171, 180, 182, 183, 184, 188, 190, 191, 193, 194, 195, 197, 206, 208, 210, 212, 216, 217, 218, \n", + " 225, 227, 230, 231, 233, 236, 243, 248, 250, 265, 267]\n", + " \n", + " assert crossword(board, 141, ACROSS) == '.MUSES'\n", + " assert crossword(board, 148, ACROSS) == 'T.E'\n", + " assert valid_crossword('.MUSES', 'A')\n", + " assert not valid_crossword('.MUSES', 'B')\n", + " \n", + " assert sames(prefix_plays(rack_prefixes(rack), board, 141, 1, rack),\n", + " [Play(start=141, dir=1, letters='', rack='ABCHKNQ'),\n", + " Play(start=140, dir=1, letters='C', rack='ABHKNQ'),\n", + " Play(start=140, dir=1, letters='K', rack='ABCHNQ'),\n", + " Play(start=140, dir=1, letters='B', rack='ACHKNQ'),\n", + " Play(start=140, dir=1, letters='A', rack='BCHKNQ'),\n", + " Play(start=140, dir=1, letters='H', rack='ABCKNQ'),\n", + " Play(start=140, dir=1, letters='N', rack='ABCHKQ'),\n", + " Play(start=140, dir=1, letters='Q', rack='ABCHKN')])\n", + " \n", + " assert sames(extend_play(board, Play(start=140, dir=1, letters='B', rack='ACHKNQ')),\n", + " {Play(start=140, dir=1, letters='BA', rack='CHKNQ'),\n", + " Play(start=140, dir=1, letters='BACKBENCH', rack='Q'),\n", + " Play(start=140, dir=1, letters='BAH', rack='CKNQ'),\n", + " Play(start=140, dir=1, letters='BAN', rack='CHKQ')})\n", + "\n", + " assert len(BAG) == 100\n", + " \n", + " assert replenish('RACK', ['X', 'B', 'A', 'G']) == 'RACKGAB'\n", + " assert replenish('RACK', []) == 'RACK'\n", + " assert replenish('RACK', ['A', 'B']) == 'RACKBA'\n", + " \n", + " assert score(WWF, Play(144, ACROSS, 'BE', '')) == (3 + 1)\n", + " assert score(board, Play(140, ACROSS, 'BACKBENCH', 'Q')) == 116\n", + " \n", + " return 'ok'\n", + "\n", + "test()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Conclusion: How Did We Do?\n", + "\n", + "We can break that into four questions:\n", + " \n", + "1. **Is the code easy to follow?** \n", + " - I'm biased, but I think this code is easy to understand, test, and modify.\n", + "2. **Does the strategy score well?** \n", + " - Yes: the mean and median are both well over 350, which is enough for [the elite club](https://www.facebook.com/WWF350Club) of high scorers. \n", + " - No: this is not quite world-champion caliber.\n", + "3. **Is the code fast enough?** \n", + " - It takes less than 3 seconds to play a complete game for both players; that's fast enough for me. If desired, the code could be made about 100 times faster, by using multiprocessing, by caching more information, by not building explicit lists for intermediate results (although those intermediate results make the code easier to test), by using PyPy or Cython, or by porting to another language.\n", + "4. **What's left to do?**\n", + " - We could give players the option of trading in tiles.\n", + " - We could explore better strategies. A better strategy might:\n", + " - Plan ahead to use high-scoring letters only with bonuses.\n", + " - Manage letters to increase the chance of a bingo.\n", + " - Use blank tiles strategically, not greedily.\n", + " - Play defensively to avoid giving the opponent good chances at high scores.\n", + " - Think ahead in the end game to go out before the opponent (or at least avoid being stuck with high-scoring letters in the rack).\n", + " - In the end game, know which tiles have not been played and thus which ones the opponent could have.\n", + " - The display could be prettier.\n", + " - The game could be interfaced to an online game server.\n", + " - More complete unit tests would be great.\n", + " - We could compare this program to those of the [giants](https://www.cs.cmu.edu/afs/cs/academic/class/15451-s06/www/lectures/scrabble.pdf) whose [shoulders](http://ericsink.com/downloads/faster-scrabble-gordon.pdf) we [stood](http://web.archive.org/web/20040116175427/http://www.math-info.univ-paris5.fr/~bouzy/ProjetUE3/Scrabble.pdf) [upon](http://www.gtoal.com/wordgames/scrabble.html).\n", + " \n", + "Thanks to Markus Dobler for correcting one bug and making another useful suggestion.\n", + "\n", + "
\n", + "*[Peter Norvig](http://norvig.com)*" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Sicherman Dice.ipynb b/pytudes/ipynb/Sicherman Dice.ipynb new file mode 100644 index 0000000..35ab0de --- /dev/null +++ b/pytudes/ipynb/Sicherman Dice.ipynb @@ -0,0 +1,2087 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Sicherman Dice\n", + "\n", + "*Note: This notebook takes the form of a conversation between two problem solvers. One speaks in* **bold**, *the other in* plain. *Also note, for those who are not native speakers of English: \"dice\" is the plural form; \"die\" is the singular.*\n", + "\n", + "Huh. This is interesting. You know how in many games, such as craps or Monopoly, you roll two regular dice and add them up. Only the sum matters, not what either of the individual dice shows.\n", + "\n", + "**Right.**\n", + "\n", + "And some of those sums, like 8, can be made multiple ways, while 2 and 12 can only be made one way. \n", + "\n", + "**Yeah. 8 can be made 5 ways, so it has a 5/36 probability of occurring.**\n", + "\n", + "The interesting thing is that people have been playing dice games for 7,000 years. But it wasn't until 1977 that Colonel George Sicherman asked whether is is possible to have a pair of dice that are not regular dice—that is, they don't have (1, 2, 3, 4, 5, 6) on the six sides—but have the same distribution of sums as a regular pair—so the pair of dice would also have to have 5 ways of making 8, but it could be different ways; maybe 7+1 could be one way. Sicherman assumes that each side bears a positive integer.\n", + "\n", + "**And what did he find?**\n", + "\n", + "Wouldn't it be more fun to figure it out for ourselves?\n", + "\n", + "**OK!**\n", + "\n", + "How could we proceed?\n", + "\n", + "**When in doubt, [use brute force](http://quotes.lifehack.org/quote/ken-thompson/when-in-doubt-use-brute-force/): we can write a program to enumerate the possibilities:**\n", + "\n", + "\n", + "- **Generate all dice that could possibly be part of a solution, such as (1, 2, 2, 4, 8, 9).**\n", + "- **Consider all pairs of these dice, such as ((1, 3, 4, 4, 5, 8), (1, 2, 2, 3, 3, 4))**\n", + "- **See if we find any pairs that are not the regular pair, but do have the same distribution of sums as the regular pair.**\n", + "\n", + "\n", + "That's great. I can code up your description almost verbatim. I'll also keep track of our TO DO list:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def sicherman():\n", + " \"\"\"The set of pairs of 6-sided dice that have the same\n", + " distribution of sums as a regular pair of dice.\"\"\"\n", + " return {pair for pair in pairs(all_dice())\n", + " if pair != regular_pair\n", + " and sums(pair) == regular_sums}\n", + "\n", + "# TODO: pairs, all_dice, regular_pair, sums, regular_sums" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Looks good to me.**\n", + "\n", + "Now we can tick off the items in the TO DO list. The function `pairs` is first, and it is easy:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def pairs(collection): \n", + " \"Return all pairs (A, B) from collection where A <= B.\"\n", + " return [(A, B) for A in collection for B in collection if A <= B]\n", + "\n", + "# TODO: all_dice, regular_pair, sums, regular_sums" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**That's good. We could have used the library function `itertools.combinations_with_replacement`, but let's just leave it as is. We should test to make sure it works:**" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('A', 'A'), ('A', 'B'), ('A', 'C'), ('B', 'B'), ('B', 'C'), ('C', 'C')]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pairs(['A', 'B', 'C'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# TO DO: `sums(pair)`\n", + "\n", + "\n", + "Now for `sums`: we need some way to represent all the 36 possible sums from a pair of dice. We want a representation that will be the same for two different pairs if all 36 sums are the same, but where the order or composition of the sums doesn't matter. \n", + "\n", + "**So we want a set of the sums?**\n", + "\n", + "Well, it can't be a set, because we need to know that 8 can be made 5 ways, not just that 8 is a member of the set. The technical term for a collection where order doesn't matter but where you can have repeated elements is a **bag**, or sometimes called a [**multiset**](https://en.wikipedia.org/wiki/Multiset). For example, the regular pair of dice makes two 11s with 5+6 and 6+5, and another pair could make two 11s with 7+4 and 3+8. Can you think of a representation that will do that?\n", + "\n", + "**Well the easiest is just a sorted list or tuple—if we don't want order to matter, sorting takes care of that. Another choice would be a dictionary of {sum: count} entries, like {2: 1, 3: 2, ... 11: 2, 12: 1}. There is even a library class, `collections.Counter`, that does exactly that.**\n", + "\n", + "How do we choose between the two representations?\n", + "\n", + "**I don't think it matters much. Since there are only 36 entries, I think the sorted list will be simpler, and probably more efficient. For 100-sided dice I'd probably go with the Counter.**\n", + "\n", + "OK, here's some code implementing `sums` as a sorted list, and definitions for regular die pair, and sums.\n", + "By the way, I could have used `range(1, 7)` to define a regular die, but `range` is zero-based, and regular dice are one-based, so I defined the function `ints` instead." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def sums(pair):\n", + " \"All possible sums of a side from one die plus a side from the other.\"\n", + " (A, B) = pair\n", + " return Bag(a + b for a in A for b in B)\n", + "\n", + "Bag = sorted # Implement a bag as a sorted list\n", + "\n", + "def ints(start, end): \n", + " \"A tuple of the integers from start to end, inclusive.\"\n", + " return tuple(range(start, end + 1))\n", + "\n", + "regular_die = ints(1, 6)\n", + "regular_pair = (regular_die, regular_die)\n", + "regular_sums = sums(regular_pair)\n", + "\n", + "# TODO: all_dice" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's check the `regular_sums`:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "36" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(regular_sums)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12]\n" + ] + } + ], + "source": [ + "print(regular_sums)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**And we can see what that would look like to a `Counter`:**" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 6, 8: 5, 9: 4, 10: 3, 11: 2, 12: 1})" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from collections import Counter\n", + "\n", + "Counter(regular_sums)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Looks good! Now only one more thing on our TODO list:**\n", + "\n", + "# TO DO: `all_dice()`\n", + "\n", + "\n", + "`all_dice` should generate all possible dice, where by \"possible\" I mean the dice that could feasibly be part of a pair that is a solution to the Sicherman problem. Do we know how many dice that will be? Is it a large enough number that efficiency will be a problem?\n", + "\n", + "**Let's see. A die has six sides each. If each side can be a number from, say, 1 to 10, that's 106 or a million possible dice; a million is a small number for a computer.**\n", + "\n", + "True, a million is a relatively small number for `all_dice()`, but how many `pairs(all_dice())` will there be?\n", + "\n", + "**Ah. A million squared is a trillion. That's a large number even for a computer. Just counting to a trillion takes hours in Python; checking a trillion pairs will take days.**\n", + "\n", + "So we need to get rid of most of the dice. What about permutations?\n", + "\n", + "**Good point. If I have the die (1, 2, 3, 4, 5, 6), then I don't need the 6! = 720 different permutations of this die— that is, dice like (2, 4, 6, 1, 3, 5).\n", + "Each die should be a bag (I learned a new word!) of sides. So we've already eliminated 719/720 = 99.9% of the work.**\n", + "\n", + "One other thing bothers me ... how do you know that the sides can range from 1 to 10? Are you sure that 11 can't be part of a solution? Or 12?\n", + "\n", + "**Every side on every die must be a positive integer, right?**\n", + "\n", + "Right. No zeroes, no negative numbers, no fractions.\n", + "\n", + "**Then I know for sure that 12 can't be on any die, because when you add 12 to whatever is on the other die, you would get at least 13, and 13 is not allowed in the regular distribution of sums.**\n", + "\n", + "Good. How about 11?\n", + "\n", + "**We can't have a sum that is bigger than 12. So if one die had an 11, the other would have to have all 1s. That wouldn't work, because then we'd have six 12s, but we only want one. So 10 is the biggest allowable number on a die.**\n", + "\n", + "What else can we say about the biggest number on a die?\n", + "\n", + "**There's one 12 in the sums. But there are several ways to make a 12: 6+6 or 7+5 or 8+4, and so on. So I can't say for sure what the biggest number on any one die will be. But I can say that whatever the biggest number on a die is, it will be involved in summing to 12, so there can be only one of them, because we only want to make one 12.**\n", + "\n", + "What about the smallest number on a die?\n", + "\n", + "**Well, there's only one 2 allowed in the sums. The only way to sum to 2 is 1+1: a 1 from each of the dice in the pair. If a die had no 1s, we wouldn't get a 2; if a die had more than one 1, we would get too many 2s. So every die has to have exactly one 1.**\n", + "\n", + "Good. So each die has exactly one 1, and exactly one of whatever the biggest number is, something in the range up to 10. Here's a picture of the six sides of any one die:\n", + "\n", + " 1  <\n", + "2-10 ≤\n", + "2-10 ≤\n", + "2-10 ≤\n", + "2-10 <\n", + "2-10\n", + "\n", + "The bag of sides is always listed in non-decreasing order; the first side, 1, is less than the next, and the last side, whatever it is, is greater than the one before it.\n", + "\n", + "**Wait a minute: you have [2-10] < [2-10]. But 2 is not less than 2, and 10 is not less than 10. I think it should be [2-9] < [3-10]. So the picture should be like this:**\n", + "\n", + "\n", + " 1  <\n", + "2-9 ≤\n", + "2-9 ≤\n", + "2-9 ≤\n", + "2-9 <\n", + "3-10\n", + "\n", + "Good! We're making progress in cutting down the range. But it bothers me because it says the range for the biggest number is 3 to 10. But if one die has a 3 and the other a 10, that adds to 13. So I'm thinking that it is not possible to have a 10 after all—because if one die had a 10, then the other would have to have a 2 as the biggest number, and that can't be. Therefore the biggest number is in the range of 3 to 9. But then the others have to be \n", + "less, so make them 2 to 8:\n", + "\n", + " 1  <\n", + "2-8 ≤\n", + "2-8 ≤\n", + "2-8 ≤\n", + "2-8 <\n", + "3-9\n", + "\n", + "**I can turn this picture into code:**" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def all_dice():\n", + " \"A list of all feasible 6-sided dice for the Sicherman problem.\"\n", + " return [(1, s2, s3, s4, s5, s6)\n", + " for s2 in ints(2, 8) \n", + " for s3 in ints(s2, 8)\n", + " for s4 in ints(s3, 8)\n", + " for s5 in ints(s4, 8) \n", + " for s6 in ints(s5+1, 9)]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I think we're ready to run `sicherman()`. Any bets on what we'll find out?\n", + "\n", + "**I bet that Sicherman is remembered because he discovered a pair of dice that works. If he just proved the non-existence of a pair, I don't think that would be noteworthy.**\n", + "\n", + "Makes sense. Here goes:\n", + "\n", + "# The Answer" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8))}" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sicherman()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Look at that!**\n", + "\n", + "It turns out you can buy a pair of dice with just these numbers.\n", + "\n", + "\n", + "\n", + "Here's a table I borrowed from [Wikipedia](https://en.wikipedia.org/wiki/Sicherman_dice) that shows both pairs of dice have the same sums. \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
23456789101112
Regular dice:\n", + "
(1, 2, 3, 4, 5, 6)\n", + "
(1, 2, 3, 4, 5, 6)		1+11+2
\n", + "2+1		1+3
\n", + "2+2
\n", + "3+1		1+4
\n", + "2+3
\n", + "3+2
\n", + "4+1		1+5
\n", + "2+4
\n", + "3+3
\n", + "4+2
\n", + "5+1		1+6
\n", + "2+5
\n", + "3+4
\n", + "4+3
\n", + "5+2
\n", + "6+1		2+6
\n", + "3+5
\n", + "4+4
\n", + "5+3
\n", + "6+2		3+6
\n", + "4+5
\n", + "5+4
\n", + "6+3		4+6
\n", + "5+5
\n", + "6+4		5+6
\n", + "6+5		6+6
Sicherman dice:\n", + "
(1, 2, 2, 3, 3, 4)\n", + "
(1, 3, 4, 5, 6, 8)		1+12+1
\n", + "2+1		3+1
\n", + "3+1
\n", + "1+3		1+4
\n", + "2+3
\n", + "2+3
\n", + "4+1		1+5
\n", + "2+4
\n", + "2+4
\n", + "3+3
\n", + "3+3		1+6
\n", + "2+5
\n", + "2+5
\n", + "3+4
\n", + "3+4
\n", + "4+3		2+6
\n", + "2+6
\n", + "3+5
\n", + "3+5
\n", + "4+4		1+8
\n", + "3+6
\n", + "3+6
\n", + "4+5		2+8
\n", + "2+8
\n", + "4+6
3+8
\n", + "3+8		4+8
\n", + "\n", + "We could stop here. Or we could try to solve it for *N*-sided dice.\n", + "\n", + "# Why stop now? Onward!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "OK. I know 4-, 12-, and 20-sided dice are common, but we'll try to handle any *N* > 1. My guess is we won't go too far before our program becomes too slow. So, before we try *N*-sided dice, let's analyze six-sided dice a little better, to see if we can eliminate some of the pairs before we start. The picture says that (1, 2, 2, 2, 2, 3) could be a valid die. Could it?\n", + "\n", + "**No! If a die had four 2s, then we know that since the other die has one 1, we could make 2 + 1 = 3 four ways. But the `regular_sums` has only two 3s. So that means that a die can have no more than two 2s. New picture:**\n", + "\n", + " 1  <\n", + "2-8 ≤\n", + "2-8 ≤\n", + "3-8 ≤\n", + "3-8 <\n", + "3-9\n", + "\n", + "Now we've got [3-8] < [3-9]; that's not right. If a die can only have one 1 and two 2s, then it must have at least one number that is a 3 or more, followed by the biggest number, which must be 4 or more, and we know a pair of biggest numbers must sum to 12, so the range of the biggest can't be [4-9], it must be [4-8]:\n", + "\n", + " 1  <\n", + "2-7 ≤\n", + "2-7 ≤\n", + "3-7 ≤\n", + "3-7 <\n", + "4-8" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def all_dice():\n", + " \"A list of all feasible 6-sided dice for the Sicherman problem.\"\n", + " return [(1, s2, s3, s4, s5, s6)\n", + " for s2 in ints(2, 7) \n", + " for s3 in ints(s2, 7)\n", + " for s4 in ints(max(s3, 3), 7)\n", + " for s5 in ints(s4, 7) \n", + " for s6 in ints(s5+1, 8)]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I'll count how many dice and how many pairs there are now:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "231" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(all_dice())" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "26796" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(pairs(all_dice()))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Nice—we got down from a trillion pairs to 26,000. I don't want to print `all_dice()`, but I can sample a few:**" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 5, 5, 5, 7, 8),\n", + " (1, 6, 6, 6, 7, 8),\n", + " (1, 3, 4, 6, 6, 7),\n", + " (1, 3, 3, 7, 7, 8),\n", + " (1, 3, 5, 5, 6, 8),\n", + " (1, 2, 2, 4, 4, 5),\n", + " (1, 2, 5, 6, 7, 8),\n", + " (1, 3, 4, 4, 4, 8),\n", + " (1, 2, 3, 5, 5, 6),\n", + " (1, 2, 2, 3, 3, 8)]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import random\n", + "\n", + "random.sample(all_dice(), 10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# `sicherman(N)`\n", + "\n", + "OK, I think we're ready to update `sicherman()` to `sicherman(N)`. \n", + "\n", + "**Sure, most of that will be easy, just parameterizing with `N`:**" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def sicherman(N=6):\n", + " \"\"\"The set of pairs of N-sided dice that have the same\n", + " distribution of sums as a regular pair of N-sided dice.\"\"\"\n", + " reg_sums = regular_sums(N)\n", + " reg_pair = regular_pair(N)\n", + " return {pair for pair in pairs(all_dice(N))\n", + " if pair != reg_pair\n", + " and sums(pair) == reg_sums}\n", + "\n", + "def regular_die(N): return ints(1, N)\n", + "def regular_pair(N): return (regular_die(N), regular_die(N))\n", + "def regular_sums(N): return sums(regular_pair(N))\n", + "\n", + "# TODO: all_dice(N)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Good. I think it would be helpful for me to look at a table of `regular_sums`:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N: 1 {2: 1}\n", + "N: 2 {2: 1, 3: 2, 4: 1}\n", + "N: 3 {2: 1, 3: 2, 4: 3, 5: 2, 6: 1}\n", + "N: 4 {2: 1, 3: 2, 4: 3, 5: 4, 6: 3, 7: 2, 8: 1}\n", + "N: 5 {2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 4, 8: 3, 9: 2, 10: 1}\n", + "N: 6 {2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 6, 8: 5, 9: 4, 10: 3, 11: 2, 12: 1}\n", + "N: 7 {2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 6, 8: 7, 9: 6, 10: 5, 11: 4, 12: 3, 13: 2, 14: 1}\n" + ] + } + ], + "source": [ + "for N in ints(1, 7):\n", + " print(\"N:\", N, dict(Counter(regular_sums(N))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**That is helpful. I can see that any `regular_sums` must have one 2 and two 3s, and three 4s, and so on, not just for `N=6` but for any `N` (except for trivially small `N`). And that means that any regular die can have at most two 2s, three 3s, four 4s, and so on. So we have this picture:**\n", + "\n", + " 1  <\n", + "2+ ≤\n", + "2+ ≤\n", + "3+ ≤\n", + "3+ ≤\n", + "3+ ≤\n", + "4+ ≤\n", + "4+ ≤\n", + "4+ ≤\n", + "4+ ≤ ...\n", + "\n", + "**where [2+] means the lower bound is 2, but we haven't figured out yet what the upper bound is.**\n", + "\n", + "Let's figure out upper bounds starting from the biggest number. What can the biggest number be?\n", + "\n", + "**For a pair of *N*-sided die, the biggest sides from each one must add up to 2*N*. Let's take *N*=10 as an example. The biggest numbers on two 10-sided Sicherman dice must sum to 20. According to the picture above, the lower bound on the biggest number would be 4, but because there can only be one of the biggest number, the lower bound is 5. So to add up to 20, the range must be [5-15]:**\n", + "\n", + "\n", + " 1  <\n", + "2+ ≤\n", + "2+ ≤\n", + "3+ ≤\n", + "3+ ≤\n", + "3+ ≤\n", + "4+ ≤\n", + "4+ ≤\n", + "4+ <\n", + "5-15 \n", + "\n", + "There's probably some tricky argument for the upper bounds of the other sides, but I'm just going to say the upper bound is one less than the upper bound of the biggest number:\n", + "\n", + " 1  <\n", + "2-14 ≤\n", + "2-14 ≤\n", + "3-14 ≤\n", + "3-14 ≤\n", + "3-14 ≤\n", + "4-14 ≤\n", + "4-14 ≤\n", + "4-14 <\n", + "5-15 \n", + "\n", + "\n", + "Let's start by coding up `lower_bounds(N)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def lower_bounds(N):\n", + " \"A list of lower bounds for respective sides of an N-sided die.\"\n", + " lowers = [1]\n", + " for _ in range(N-1):\n", + " m = lowers[-1] # The last number in lowers so far\n", + " lowers.append(m if (lowers.count(m) < m) else m + 1)\n", + " lowers[-1] = lowers[-2] + 1\n", + " return lowers" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2, 2, 3, 3, 4]" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lower_bounds(6)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 2, 2, 3, 3, 3, 4, 4, 4, 5]" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "lower_bounds(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And `upper_bounds(N)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def upper_bounds(N):\n", + " \"A list of upper bounds for respective sides of an N-sided die.\"\n", + " U = 2 * N - lower_bounds(N)[-1]\n", + " return [1] + (N - 2) * [U - 1] + [U]" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 7, 7, 7, 7, 8]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "upper_bounds(6)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[1, 14, 14, 14, 14, 14, 14, 14, 14, 15]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "upper_bounds(10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now, what do we have to do for `all_dice(N)`? When we knew we had six sides, we wrote six nested loops. We can't do that for *N*, so what do we do?\n", + "\n", + "**Here's an iterative approach: we keep track of a list of partially-formed dice, and on each iteration, we add a side to all the partially-formed dice in all possible ways, until the dice all have `N` sides. So for example, we'd start with:**\n", + "\n", + " dice = [(1,)]\n", + " \n", + "**and then on the next iteration (let's assume *N*=6, so the lower bound is 2 and the upper bound is 7), we'd get this:**\n", + "\n", + " dice = [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7)]\n", + " \n", + "**on the next iteration, we find all the ways of adding a third side, and so on. Like this:**" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def all_dice(N):\n", + " \"Return a list of all possible N-sided dice for the Sicherman problem.\"\n", + " lowers = lower_bounds(N)\n", + " uppers = upper_bounds(N)\n", + " def possibles(die, i):\n", + " \"The possible numbers for the ith side of an N-sided die.\"\n", + " return ints(max(lowers[i], die[-1] + int(i == N-1)),\n", + " uppers[i])\n", + " dice = [(1,)]\n", + " for i in range(1, N):\n", + " dice = [die + (side,)\n", + " for die in dice\n", + " for side in possibles(die, i)]\n", + " return dice" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**The tricky part was with the `max`: the actual lower bound at least `lowers[i]`, but it must be as big as the previous side, `die[-1]`. And just to make things complicated, the very last side has to be strictly bigger than the previous; `\" + int(i == N-1)\"` does that by adding 1 just in case we're on the last side, and 0 otherwise.**\n", + "\n", + "**Let's check it out:**" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "231" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(all_dice(6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Reassuring that we get the same number we got with the old version of `all_dice()`." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 2, 2, 3, 4, 6),\n", + " (1, 3, 5, 5, 6, 8),\n", + " (1, 3, 3, 6, 7, 8),\n", + " (1, 2, 3, 3, 3, 7),\n", + " (1, 3, 5, 5, 7, 8),\n", + " (1, 2, 4, 5, 6, 8),\n", + " (1, 3, 6, 6, 7, 8),\n", + " (1, 3, 4, 5, 5, 7)]" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(all_dice(6), 8)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Running `sicherman(N)` for small `N`\n", + "\n", + "Let's try `sicherman` for some small values of `N`:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2: set(),\n", + " 3: set(),\n", + " 4: {((1, 2, 2, 3), (1, 3, 3, 5))},\n", + " 5: set(),\n", + " 6: {((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8))}}" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{N: sicherman(N)\n", + " for N in ints(2, 6)}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Again, reassuring that we get the same result for `sicherman(6)`. And interesting that there is a result for `sicherman(4)` but not for the other *N*.\n", + "\n", + "Let's go onwards from *N*=6, but let's check the timing as we go:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 304 ms, sys: 2.73 ms, total: 307 ms\n", + "Wall time: 519 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "{((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8))}" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time sicherman(6)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 18.2 s, sys: 209 ms, total: 18.4 s\n", + "Wall time: 21.4 s\n" + ] + }, + { + "data": { + "text/plain": [ + "set()" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time sicherman(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Estimating run time of `sicherman(N)` for larger `N`\n", + "\n", + "OK, it takes 50 or 60 times longer to do 7, compared to 6. At this rate, *N*=8 will take 15 minutes, 9 will take 15 hours, and 10 will take a month.\n", + "\n", + "**Do we know it will continue to rise at the same rate? You're saying the run time is exponential in *N*? **\n", + "\n", + "I think so. The run time is proportional to the number of pairs. The number of pairs is proportional to the square of the number of dice. The number of dice is roughly exponential in *N*, because each time you increase *N* by 1, you have to try a number of new sides that is similar to the number for the previous side (but not quite the same). I should plot the number of pairs on a log scale and see if it looks like a straight line.\n", + "\n", + "I can count the number of pairs without explicitly generating the pairs. If there are *D* dice, then the number of pairs is what? Something like *D* × (*D* + 1) / 2? Or is it *D* × (*D* - 1) / 2?\n", + "\n", + "**Let's draw a picture. With *D* = 4, here are all the ways to pair one die with another to yield 10 distinct pairs:**\n", + " \n", + " 11 .. .. ..\n", + " 21 22 .. ..\n", + " 31 32 33 ..\n", + " 41 42 43 44\n", + " \n", + "**To figure out the formula, add a row to the top:**\n", + "\n", + " .. .. .. ..\n", + " 11 .. .. ..\n", + " 21 22 .. ..\n", + " 31 32 33 ..\n", + " 41 42 43 44\n", + " \n", + "**Now we have a *D* × (*D* + 1) rectangle, and we can see that half (10) of them are pairs, and half (the other 10) are not pairs (because they would be repetitions). So the formula is *D* × (*D* + 1)/2, and checking for *D*=4, (4 × 5) / 2 = 10, so we're good.**\n", + " \n", + "OK, let's try it. First some boilerplate for plotting:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import matplotlib\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def logplot(X, Y, *options):\n", + " \"Plot Y on a log scale vs X.\"\n", + " fig, ax = plt.subplots()\n", + " ax.set_yscale('log')\n", + " ax.plot(X, Y, *options)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can plot and display the number of pairs:" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2: 1,\n", + " 3: 1,\n", + " 4: 55,\n", + " 5: 496,\n", + " 6: 26796,\n", + " 7: 1274406,\n", + " 8: 17502486,\n", + " 9: 823794345,\n", + " 10: 37613250675,\n", + " 11: 1688821500366,\n", + " 12: 25925418283128}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_pairs(Ns):\n", + " \"Given a list of N values, plot the number of pairs and return a dict of them.\"\n", + " Ds = [len(all_dice(N)) for N in Ns]\n", + " Npairs = [D * (D + 1) // 2 for D in Ds]\n", + " logplot(Ns, Npairs, 'bo-')\n", + " return {Ns[i]: Npairs[i] for i in range(len(Ns))}\n", + "\n", + "plot_pairs(ints(2, 12))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "OK, we've learned two things. One, it *is* roughly a straight line, so the number of pairs is roughly exponential. Two, there are a *lot* of pairs. 1014, just for *N*=12. I don't want to even think about *N*=20.\n", + "\n", + "**So if we want to get much beyond *N*=8, we're either going to need a brand new approach, or we need to make far fewer pairs of dice.**\n", + "\n", + "\n", + "\n", + "# Making Fewer `pairs`\n", + "\n", + "Maybe we could tighten up the upper bounds, but I don't think that will help very much.\n", + "How about if we concentrate on making fewer pairs, without worrying about making fewer dice?\n", + "\n", + "**How could we do that? Isn't the number of pairs always (*D*2 + *D*)/2 ?**\n", + "\n", + "Remember, we're looking for *feasible* pairs. So if there was some way of knowing ahead of time that two dice were incompatible as a pair, we wouldn't even need to consider the pair.\n", + "\n", + "**By incompatible, you mean they can't form a pair that is a solution.**\n", + "\n", + "Right. Consider this: in any valid pair, the sum of the biggest number on each die must be 2*N*. For example, with *N* = 6:\n", + "\n", + " ((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8)) sum of biggests = 4 + 8 = 12\n", + " ((1, 2, 3, 4, 5, 6), (1, 2, 3, 4, 5, 6)) sum of biggests = 6 + 6 = 12\n", + " \n", + "So if we have a die with biggest number 7, what dice should we consider pairing it with?\n", + "\n", + "**Only ones with biggest number 5.**\n", + "\n", + "**I get it: we sort all the die into bins labeled with their biggest number. Then we look at each bin, and for the \"7\" bin, we pair them up with the dice in the \"5\" bin. In general, the *B* bin can only pair with the 2*N* - *B* bin.**\n", + "\n", + "Exactly. \n", + "\n", + "**Cool. I can see how that can cut the amount of work by a factor of 10 or so. But I was hoping for a factor of a million or so.**\n", + "\n", + "There are other properties of a feasible pair.\n", + "\n", + "**Like what?**\n", + "\n", + "Well, what about the number of 2s in a pair?\n", + "\n", + "**Let's see. We know that any `regular_sums` has to have two 3s, and the only way to make a 3 is 2+1. And each die has only one 1, so that means that each pair of dice has to have a total of exactly two 2s.**\n", + "\n", + "Does it have to be one 2 on each die?\n", + "\n", + "**No. It could be one each, or it could be two on one die and none on the other. So a die with *T* twos can only pair with dice that have 2 - *T* twos.**\n", + "\n", + "Great. Can you think of another property?\n", + "\n", + "**Give me a hint.**\n", + "\n", + "Let's look at the sums of 6-sided Sicherman and regular pairs:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "42" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum((1, 2, 2, 3, 3, 4) + (1, 3, 4, 5, 6, 8))" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "42" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sum((1, 2, 3, 4, 5, 6) + (1, 2, 3, 4, 5, 6))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**They're the same. Is that [the question](http://hitchhikers.wikia.com/wiki/42) that 42 is the answer to? But does a Sicherman pair always have to have the same sum as a regular pair? I guess it doea, because the sum of `sums(pair)` is just all the sides added up *N* times each, so two pairs have the same sum of `sums(pair)` if and only if they have the same sum.**\n", + "\n", + "So consider the die (1, 3, 3, 3, 4, 5). What do we know about the dice that it can possibly pair with?\n", + "\n", + "**OK, that die has a biggest side of 5, so it can only pair with dice that have a biggest side of 12 - 5 = 7. It has a sum of 19, so it can only pair with dice that have a sum of 42 - 19 = 23. And it has no 2s, so it can only pair with dice that have two 2s.**\n", + "\n", + "I wonder how many such dice there are, out of all 231 `all_dice(6)`?" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{(1, 2, 2, 5, 6, 7)}" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{die for die in all_dice(6) if max(die) == 12 - 5 and sum(die) == 42 - 19 and die.count(2) == 2}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**There's only 1. So, (1, 3, 3, 3, 4, 5) only has to try to pair with one die, rather than 230. Nice improvement!**\n", + "\n", + "In general, I wonder what the sum of the sides of a regular pair is?\n", + "\n", + "**Easy, that's `N * (N + 1)`. [Gauss](http://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/) knew that when he was in elementary school!**\n", + "\n", + "# More efficient `pairs(dice)`\n", + "\n", + "**OK, we can code this up easily enough**:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from collections import defaultdict\n", + "\n", + "def tabulate(dice):\n", + " \"\"\"Put all dice into bins in a hash table, keyed by bin_label(die).\n", + " Each bin holds a list of dice with that key.\"\"\"\n", + " # Example: {(21, 6, 1): [(1, 2, 3, 4, 5, 6), (1, 2, 3, 4, 4, 7), ...]\n", + " table = defaultdict(list)\n", + " for die in dice:\n", + " table[bin_label(die)].append(die)\n", + " return table\n", + "\n", + "def pairs(dice):\n", + " \"Return all pairs of dice that could possibly be a solution to the Sicherman problem.\"\n", + " table = tabulate(dice)\n", + " N = len(dice[0])\n", + " for bin1 in table:\n", + " bin2 = compatible_bin(bin1, N)\n", + " if bin2 in table and bin1 <= bin2:\n", + " for A in table[bin1]:\n", + " for B in table[bin2]:\n", + " yield (A, B)\n", + "\n", + "def bin_label(die): return sum(die), max(die), die.count(2)\n", + "\n", + "def compatible_bin(bin1, N): \n", + " \"Return a bin label that is compatible with bin1.\"\n", + " (S1, M1, T1) = bin1\n", + " return (N * (N + 1) - S1, 2 * N - M1, 2 - T1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Let's make sure it works:**" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{2: set(),\n", + " 3: set(),\n", + " 4: {((1, 2, 2, 3), (1, 3, 3, 5))},\n", + " 5: set(),\n", + " 6: {((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8))}}" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{N: sicherman(N)\n", + " for N in ints(2, 6)}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Good, those are the same answers as before. But how much faster is it?" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 24.9 ms, sys: 1.23 ms, total: 26.1 ms\n", + "Wall time: 153 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "set()" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time sicherman(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Wow, that's 1000 times faster than before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**I want to take a peek at what some of the bins look like:**" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(list,\n", + " {(12, 4, 2): [(1, 2, 2, 3, 4)],\n", + " (13, 4, 1): [(1, 2, 3, 3, 4)],\n", + " (13, 5, 2): [(1, 2, 2, 3, 5)],\n", + " (14, 4, 0): [(1, 3, 3, 3, 4)],\n", + " (14, 5, 1): [(1, 2, 3, 3, 5)],\n", + " (14, 5, 2): [(1, 2, 2, 4, 5)],\n", + " (14, 6, 2): [(1, 2, 2, 3, 6)],\n", + " (15, 5, 0): [(1, 3, 3, 3, 5)],\n", + " (15, 5, 1): [(1, 2, 3, 4, 5)],\n", + " (15, 6, 1): [(1, 2, 3, 3, 6)],\n", + " (15, 6, 2): [(1, 2, 2, 4, 6)],\n", + " (16, 5, 0): [(1, 3, 3, 4, 5)],\n", + " (16, 5, 1): [(1, 2, 4, 4, 5)],\n", + " (16, 6, 0): [(1, 3, 3, 3, 6)],\n", + " (16, 6, 1): [(1, 2, 3, 4, 6)],\n", + " (16, 6, 2): [(1, 2, 2, 5, 6)],\n", + " (17, 5, 0): [(1, 3, 4, 4, 5)],\n", + " (17, 6, 0): [(1, 3, 3, 4, 6)],\n", + " (17, 6, 1): [(1, 2, 3, 5, 6), (1, 2, 4, 4, 6)],\n", + " (18, 5, 0): [(1, 4, 4, 4, 5)],\n", + " (18, 6, 0): [(1, 3, 3, 5, 6), (1, 3, 4, 4, 6)],\n", + " (18, 6, 1): [(1, 2, 4, 5, 6)],\n", + " (19, 6, 0): [(1, 3, 4, 5, 6), (1, 4, 4, 4, 6)],\n", + " (19, 6, 1): [(1, 2, 5, 5, 6)],\n", + " (20, 6, 0): [(1, 3, 5, 5, 6), (1, 4, 4, 5, 6)],\n", + " (21, 6, 0): [(1, 4, 5, 5, 6)],\n", + " (22, 6, 0): [(1, 5, 5, 5, 6)]})" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tabulate(all_dice(5))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Pretty good: four of the bins have two dice, but the rest have only one die.**\n", + "\n", + "And let's see how many pairs we're producing now. We'll tabulate *N* (the number of sides); *D* (the number of *N*-sided dice), the number `pairs(dice)` using the new `pairs`, and the number using the old `pairs`:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " N: D #pairs(dice) D*(D-1)/2\n", + " 2: 1 1 0\n", + " 3: 1 1 0\n", + " 4: 10 3 45\n", + " 5: 31 9 465\n", + " 6: 231 71 26,565\n", + " 7: 1,596 670 1,272,810\n", + " 8: 5,916 6,614 17,496,570\n", + " 9: 40,590 76,215 823,753,755\n", + "10: 274,274 920,518 37,612,976,401\n", + "11: 1,837,836 11,506,826 1,688,819,662,530\n" + ] + } + ], + "source": [ + "print(' N: D #pairs(dice) D*(D-1)/2')\n", + "for N in ints(2, 11):\n", + " dice = list(all_dice(N))\n", + " D = len(dice)\n", + " print('{:2}: {:9,d} {:12,d} {:17,d}'.format(N, D, len(list(pairs(dice))), D*(D-1)//2))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "OK, we're doing 100,000 times better for *N*=11. But it would still take a long time to test 11 million pairs. Let's just get the answers up to *N*=10:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 26.2 s, sys: 129 ms, total: 26.3 s\n", + "Wall time: 26.6 s\n" + ] + }, + { + "data": { + "text/plain": [ + "{2: set(),\n", + " 3: set(),\n", + " 4: {((1, 2, 2, 3), (1, 3, 3, 5))},\n", + " 5: set(),\n", + " 6: {((1, 2, 2, 3, 3, 4), (1, 3, 4, 5, 6, 8))},\n", + " 7: set(),\n", + " 8: {((1, 2, 2, 3, 3, 4, 4, 5), (1, 3, 5, 5, 7, 7, 9, 11)),\n", + " ((1, 2, 2, 3, 5, 6, 6, 7), (1, 3, 3, 5, 5, 7, 7, 9)),\n", + " ((1, 2, 3, 3, 4, 4, 5, 6), (1, 2, 5, 5, 6, 6, 9, 10))},\n", + " 9: {((1, 2, 2, 3, 3, 3, 4, 4, 5), (1, 4, 4, 7, 7, 7, 10, 10, 13))},\n", + " 10: {((1, 2, 2, 3, 3, 4, 4, 5, 5, 6), (1, 3, 5, 6, 7, 8, 9, 10, 12, 14))}}" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%%time\n", + "{N: sicherman(N)\n", + " for N in ints(2, 10)}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Not bad; we solved it for all *N* up to 10 in just a few seconds more than it took for just *N*=7 with the old version. Interestingly, there are solutions for all composite *N* but no prime *N*. So I have some questions:\n", + "\n", + "- Do all composire *N* have solutions?\n", + "- Do no prime *N* have solutions?\n", + "- Do some *N* have more than the 3 solutions that 8 has?\n", + "- Could we handle larger *N* if we worked with [generating functions](https://en.wikipedia.org/wiki/Sicherman_dice)?\n", + "\n", + "\n", + "**Good questions, but I think this is a good place to stop for now.**\n", + "\n", + "Agreed!" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/Sierpinski.ipynb b/pytudes/ipynb/Sierpinski.ipynb new file mode 100644 index 0000000..d076716 --- /dev/null +++ b/pytudes/ipynb/Sierpinski.ipynb @@ -0,0 +1,335 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Chaos Game with Triangles\n", + "\n", + "John D. Cook [proposed](https://www.johndcook.com/blog/2017/07/08/the-chaos-game-and-the-sierpinski-triangle/) an interesting \"game\" from the book *[Chaos and Fractals](https://smile.amazon.com/Chaos-Fractals-New-Frontiers-Science/dp/0387202293)*: start at a vertex of an equilateral triangle. Then move to a new point halfway between the current point and one of the three vertexes of the triangle, chosen at random. Repeat to create *N* points, and plot them. What do you get? \n", + "\n", + "I'll refactor Cook's code a bit and then we'll see:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import random\n", + "\n", + "def random_walk(vertexes, N):\n", + " \"Walk halfway from current point towards a random vertex; repeat for N points.\"\n", + " points = [random.choice(vertexes)]\n", + " for _ in range(N-1):\n", + " points.append(midpoint(points[-1], random.choice(vertexes)))\n", + " return points\n", + "\n", + "def show_walk(vertexes, N=5000):\n", + " \"Walk halfway towards a random vertex for N points; show reults.\"\n", + " Xs, Ys = transpose(random_walk(vertexes, N))\n", + " Xv, Yv = transpose(vertexes)\n", + " plt.plot(Xs, Ys, 'r.')\n", + " plt.plot(Xv, Yv, 'bs')\n", + " plt.gca().set_aspect('equal')\n", + " plt.gcf().set_size_inches(9, 9)\n", + " plt.axis('off')\n", + " plt.show()\n", + " \n", + "def midpoint(p, q): return ((p[0] + q[0])/2, (p[1] + q[1])/2)\n", + "\n", + "def transpose(matrix): return zip(*matrix)\n", + "\n", + "triangle = ((0, 0), (0.5, (3**0.5)/2), (1, 0))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_walk(triangle, 20)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "OK, the first 20 points don't tell me much. What if I try 20,000 points?" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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PIft83RxYqNwgQhgSQISojZmYWSVNADyI5afYItU2GvhhWC1WtCfpQnpbAL/E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\nh7JEbvs3UG+CnT3Xt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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_walk(triangle, 20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Wow! The [Sierpinski Triangle](https://en.wikipedia.org/wiki/Sierpinski_triangle)! \n", + "What happens if we start with a different set of vertexes, like a square?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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m8Cac1po5aXRX/PlDFLKGBUs2tG6c655uPhxrPd3qVE6NPNKH5s18zuKML3yW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\nw+58yY4C5yDY2cYydoudNLc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GafOetvM1aDiv72PfO40Xn23f7MarPH1vF5AjupHfxUCl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K8sBM34nEt4tAQ9TuF8VSznbbRt4agA7SzJ/l3LeDiXTh3whY2D2mEx/5h4m4zsMvE7QNO2Tshy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\nSLeQtb+lFvB4cY2NPrYrw1q70TpIXP3Krixa2c65+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3PyQWUMNPKi4W2kUVwVwIxqiTJk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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "square = ((0, 0), (0, 1), (1, 0), (1, 1))\n", + "\n", + "show_walk(square)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There doesn't seem to be any structure there. Let's try again to make sure:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XwI289lF3g6zMkefnXvi8CQdtd7HFL2P0kmCBw4Ky8zKvDrvN4d8HsRiQXEf/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X3PDGfBePAw+iks96hL1zEnexYAEnS/tEEbW7IRJyf/HuMwKQhX/T6EO493rH222NxaPTDvhLeL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\naJzW5XQ4pYvzMTRDW8uyIhbBoLXrV/Jud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mDRsIQDBOpN0LANC6IO6DGY0BwCbn7jPAIR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2zvlh+XEMCAyHAg4X2uE10rbxT8w9bsLp2r7UnveMqwjDc321WL03s3YM9AEycE9N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/5luvghhrDV51khOkXVC0HnIejvm+3/s1jzOs7e4XkB3gQoVA+O10BNz3PVOzj+5ro0u/3X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\nfAt/KAc9Yh7v5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HSpNAy+WHNXu3cBNGg1z7e0ZuyVeSjr+FNkEO3788zAxUy5+3tZfqgH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\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OtKmfgU6lWyd/mJ86j6ezGgEkHV97r4qnF8g0lp+YhzUA340X5dtfR+5aegjPdy5pey0U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\n9OP/Aay0DeKUwjGKAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_walk(square, 20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I'm still not seeing anything but random points. How about a right triangle?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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gPXEf1mPTDCsxLY2HM/oQEa6nkl6+HgvsTJ/7Uxn79cRtps/rEOCxuF9PYPEr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\nAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "right_triangle = ((0, 0), (0, 1), (1, 0))\n", + "\n", + "show_walk(right_triangle, 20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We get a squished Serpinski triangle. How about a pentagon? (I'm lazy so I had Wolfram Alpha [compute the vertexes](https://www.wolframalpha.com/input/?i=vertexes+of+regular+pentagon).)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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s95TgrCVCqt3k4uYa53PKs3fA2Xll3Oar0be5t1yfai94JI8msBGDfwj3O+l1\n4O0T2DWQVfNBSd+PkqMR0NjButnHAlCWgJf5WNp9ZMrfjjswl6oOt5lDtOvyBHWUnK8WITVGg+Lm\nGudzxRuIOHc5ICen+SgWSvsMhGJx5YJvrdeH6z4HoQDgYxAL5D0OoTjgdwDgZ4a/nQDA3wGA/wih\neN3jw+8fAYBjAHgGQnE/q0+L4frHGt/hcrX9tP+XAGA3aTP+/gkAeG1oCwHgIQB8CEIxwdh2vP5H\nZt96vkV4520A+C0IRf3qFO65BaEg4iEA/A0A+E+zd7P7Vu6/dl349+sQvikMz38MtLFvfUbtuYEe\nb3ovJ6c1JgcoTk69gsG6PvxdFwxR+H4WQvXcqxAE+yeHK44A4MMQqv5+FUIF4E9BC+DofYcUCLw9\nPO8QAL6nvA/vc96P9JpHIAATBID75j31vj05tPM9A/wtAOAPIACnNwHg6cZ3/gcA8M8hggMCX/39\n7KGNjSsA8DsQxoee2wYm+57zKITK19+EUGn6LQD4EljjWG/LQY7TvDS3CsfZeRRH9Xmfg+tq+2P7\nGujmC5niHTE6ba42N0X009lFuzqxjATSk8vlPj/j+14fx0cxmJT4eNlJ72KbFFZMJjeZhbe9UOT4\nd+qL7Cn1I/fz0cK2eRTb6p1unZ0n5g/NDZCcnLopntq/A0Fl/h0A+O7w9/J9GxuXq9eNu+dxCFqE\nj0DQTDwJQbX/B8N//wyCaecYwsn5RwDwveG/xxA0GCdDW49A0J7chVWdXkO7h8NzNgb+NAQtDNEu\nhFM4Dn36VmEcDgHgFwDgGQgajd8b2Xc5jj8PAD8A+sZBQ3Cps83PD+0+AgAfhaBVeAaC5oR/Dzm3\n6nOqhcI4fGF45hcA8SeA+EfF8Sn1Q/+N3vHDEL7l/eHqRyCMI/+uNZLfoOdeJ6fJyAGK01kkvoF+\nDFo20jGCp++eXUgF3schCsXHIaj4L0FQ7z8LiH8uBNcnAeAXh3ZSobk62h2egwO/BQA/+gCUBfoq\nBL+SDQhgJh3jdIxegzH+E3mfaBzfBoBvQfDVoW+Mos9vAMD3O5/xFgS/FQ4aqM+rEc7he5dBSUql\nftT6iADwP0CcS+8O3EpyLq96Hjo5qeQ+KE7rSdIGzv8d6HUIJ/77EE6NNadK6Rj6LIRTv21jb3Em\nzftMjoqfB4DfheiT8QCiD4LdzlhHybE+A9Hn42MAcA+CYPq/IfqnAARhCBDGPvX36B2j9j5JB1wA\ngH0A+LlZNjC4AAAgAElEQVTh/58c/vv96vtGR1Xyy7B9VnqdpldFpX5ovwH8JwBwG4KG6BgAvggA\n/x4AfhssP5u6z9Q4h10np6lobhuTs3PGuQ1cht0umE/BbQyhmz2ZM8up3uM9MpNoqR5M6g+T5vnQ\nc21M5euwrM9Aer8s8kc+MroPyipDXNO29zBWde4fMyvvi/7MK7gOtWlK4c95iLbMzEsZckt+Nstl\n5LXXgfusOE/Cs3fA2Tnjet0c/m/E1myicVOvV8rV+1GrqJtmjU0To2l1ePZwCkfEtn4u0KrKm+fq\n4ABlvwo+9IRw0wiqfAzHZkyt33eazqGtY9R+nQQoyMDHuIzBel+uINW3mmvsnC8Mz94BZ+eM9agH\nnnWUhDtWQUZb++MTdNWyxtrt8v4/QICrI8aIa2vsftY0Qen9hxijenaxp5ZM2tb0gioHUuXoHf2+\n5QDp8vOaNG3TAqZwLUVkIcaoLP375XOwZc7y4pOliC/PZus8Cc/eAWdnlfOTM5l0aNPdwaDCHmda\nqGUPrV2XChvq22FTf3RQ8wCtwnx6n7RQXMscUK/KG+6/IQTc9ojvtjpBVROS+vUcECwPSJfrOzep\n2GMU+92m6Yv3XEGAqwjwCgazZzkEv69q9WVMQ+KPMTUZ2SDYTT/OI3n2Djg7V1kvYU/alNP3FUiF\nzU0MJ1eq61LvT356Jf6Xjfe+kAmucs6MVl8aWcCvTUOhj81q0q6nuWNK2hDNj2k8IF3NHNZML3Ju\nWUUdNQ0aNzO2+ln1AHUODg8ECNGBaYsWyAGMs8Gzd8DZucrpSa98+jyd/sgEZlxgPp9ttNoGHIoD\n/r8CoJSTauWCiJvAuFDTfAQ2MVRMtrU0UQjFAn6197DbWU2V3HbznJYYr08QTu9LI82UmmZO9vsG\nStCbC31ZBZrmUh3I9b/DNkbn23otoZpGzX1XnAs8ewecLxiPExJcNS6r/p7Ohmb7fOxiMO0gBjON\ntXHHaInUQfYdBPiPTLD0+EhcY/3i1YVPCn2oqfL1aJd1EiQtAEj3Y2rv/9Tvm5spS2YXKr54V31+\nPg+22LsScLW1L8u9h/Zsvi5kYcccuKRrKfcrco2K88Czd8D5AvGYTT/4mtzH9CSsC9Fx/SlvhNG2\nT6dfHu4qI4IQcxW39DfZx3ACpX9zDQxiKZrCPqXycX1Y6cMJhlO5pWrXv89ZdILkArPXwbbFlNQj\nSNsjwsiMguq3DNflJrv4rlEzU/ZLGhuuPSZcvxSJRT5c3DG73qbzheDZO+B8gbhXyIXNi7QTiDGq\nZPmTbbtt/IeYht4iAtxCMqOkGzY3uzw69PWl4Xq6VwKSfYwn3TtYc5S1hE74O6+Hc4AB3C2GvloR\nHlFIlb7Pqn1LVj/32h1sW67tBdst45c7oj5EzWxX/04toHvZvDnt4fppv/J7UjA4vWnK+czy7B1w\nvkCcq7lrUQYy+uQ6tjpJ1vvScqKVphPel2hG0U+vmwhwD6PpR54QyZ9GmnyWzYmywACI6HmHGBOw\nkSYKMY0m4e9RCldenW/J6cy/VgdbKTC1BHX9GqXa+OkalFvDnLG+U5hD8f6W8OVptGHt/kC8X7so\no+9yQNgWDed87nn2DjhfIE4BSl2Vm6uyN7H1FNzWl5owJtPO0cAoOHe+jPe9r1x/jNHGvoVRCyMF\nRu5o2/5eWsIuapeyxJLgs6Iu1heELOOf0KbFeHSYmzRuh6iZEtvb6utruOc6phl8Oagin49NzAFm\nG/CYUhvW5g+k+UhFYBXnLX/Pa2s7B51PjWfvgPMF4nQTkhuvtZkuhg37OQzmEh490x8Gm7ZdMpfw\nqJgb7LnUX835ch9jyLFMO66dGEmTRMLmCIPWZRnV+w3x7Hvs2ZsYQAoHiJo/y3o6KC5rmtC+uXzf\nWr4Pq628nfF91f08pM9HHs3WAzxSrd9l9R1W890sv5qzbUJ0XgnP3gHnC8K5GjcXkNoGqat/y5EQ\ny/dVnuZ4lAQBCDLPSCdYWcfmDgI8IYTBjriOwjYlCLIcKdN046m2h0d/HGAAJZqjKL2XFNbrEamj\nf5exZhVd6Grv2+OrUm5nOTNKDn40n488l0pJo6GDKEujmZtf62NZMtdKH6nzZ0J0npxn74DzBeE8\nd8gW5ptwLhx1x8H7TYKj3qcWQHST9U/WBKK+74n+keZlC1NhQO9nFeTjnEfz6H0jDQ7X2hxh9Ncp\nh3za30iafebXqvSesmuAq/y+W9iaBFAHftw8eBMDKL2C0Wk5z1VTm5/5+0efp/ax4yBKJubjoJw0\nbXz+WxFeUuPIHci19eUgxLmJZ++A8wXg9IQ/RjhyoayriNNn1YVpGRDpZqTUJ+YeUsRNmkhOz26b\nt/s+RqdBGheKAkrt82kbHMycYAqaODgiU5OsmVI7YWs5K9ZHq9Ij4GrJ2uz3bQMQ+rhxM8xNDInN\nKILq4TBvWiOJLKHfHzqsj4UEKOS8KgH0tnq/3jYBnbYQ5L7vPj9Idj5Vnr0Dzuec841WP5Xqp8PL\nGE+c2wPXVMT0LEvI2+GOej+sXCCIXMtRE5wp0EImEBbs3vKJOFwnHTh54joaX2lCavfVke9xdvOf\n0NyRcypNlpZr8cY5YcfcPDtivJ5HXUOGWPZv0YS+bnrJ5762NjiIluYsWps0//j8QQwO1TtYTrsv\ntXjjw4VtzdF6gGTnU+PZO+B8TlkHAscYTA+1hE7c8TTNphnV71o6d57UDTH4f8iiZRwslTbc5SvA\n5u93BfNQX4rKaLP564nrJKjQa+qMOYX2mlXm5lyYLdgYlWsN6Q6yW9UxK88rAkUysqpHg8K1hno4\neq6hi+ssAtv7GMCGXBNa9tcD0VcCdaUDBvcxaasjVP9+y/vzOJ9Znr0DzueQ8w1bSxLWGpaImAtj\nzTSzwDSpGzHXcvB2TzBoZPrs4a0VYG37u5U1UwNiUtDyhGv2OOYn4+VMNWfJb6AUsl0HKAtMQ7H1\nUPj8hG87H0dgdBWjCWV/mHstZkgu9PPIHX1upessgFq+JupVquM8l75NteSKmnOv5a/SZuo9ayDZ\neTKevQPO55D1gmdSc1DLOkkbkszOavmqyKRuqFyjAYR2gJH+VvID4BE12umRHDDtNPl69VsuLMph\n1qdlqlk334B07qQh2xpwy+8jJ+Zt1MyA+glfF6A6yKTvrptqyt9SmqykcNc0dE9hCM/nc+x6x1iW\nI29650B78UBtLM8GSHaejGfvgPMZ45bNKNcycDV3Xqrdfk7ul2FvYNyBlbP0E3kFa/4ZLdoGW0Oi\nRdToZoIyEOO/7WM0PaSJrlqFQ8sptBdsLKOVWe0cXWAw79EckCC1pYowzT1Z80bPRqtrC2Sb2xi1\nIHohwPp472AA/JZ/FfdRoj5z7aKeeK5tLbaZZHrnYa6RcjDiDIjoAMW5g9sFd+6oGv6ul2rX27AF\npS1kFhhs77uYpwHfHISWDFnuT2Num5mkYyP3SbBU2raDbDzBcrPOG2wM+yIl2gVNOVQ03jNN2YHp\n56k0Eaa+SOW5XdLWyW+h1ehZYNDmLUSbNzH160Asz6+aedAy71kAaoEhO+tyBTZ710ptHsb3Wm1u\nI+czybN3wPkMcX/9Gmknb7m//1ReO4GFzZnq4iCmTn9t4bbp76VTNE98Jc04/UJcr0TMnSHvs9/G\nZdYN/X4BU3B1MgjUtA5Mes80ZQf6+tmrLWrPzJvPG24S2kWAL6MMv03v3cGoqZBVhqU5j2f4bckp\nojnwltZP3V+jTRvaclgY7x9S8wtyvtA8eweczxC3mQlsJ9K2+1u0FxKM1LQ60j/lPawl4dJV9uRf\nwk/RMSoiBSjvY0jPX/YbsN4rHU9uZviH7N9UhBBRAwm8Tbt9Pn6HGACPTNOff4tSvpjp5lrfd87v\nzxPr1cY7b4O+J2Uw5uOyJfrG/T8QAa4Zc38PeYZfe/7L8OKeasylFPyX2bxs1Ybq5ph4nR5ZV//O\nDlCcTZ69A85njNvNBFYeksUgOHRVcwnE6Btmi1aGC/mYYK3/vaV/CSbCQo8+2sW2/Ca6sMgFlgQQ\nnKU2R4a+1tonfiDez9KgWM6MyznNjv3OrXOptXq0Pja59k2/7m42x2tzP+1bHj0TgUBrhlvNSZc7\nAtvmuVyrRiYuzbQ53hcp1VK5icc54dk74HyOeKzvRt5OjyNjm4p5GRu8bgJBxicI8CpGPxf5Wzll\nfNksxseMnzT5/+fl6XPTkC6MbOfi/4BaZtxcKzN9LZ8pQk1TTYHs4x57TxK8Je3SEUYn5jwXSHrd\nLgY/KAlOev23yLxmmRlbNEByHGXWYV0bk/aDO29byQ37wWPLene+8Dx7B5zXgKc49cZ2Sr4bU2xk\n04Qgtr6zvlnvYjDt0AZPGoe7Q5vc32UXozDXnQF19b9Uy/Nwzz/FtCp0ns8lbbOUNEs7/VOG2vYc\nFvqJe5zTrBY9k45D2ZRg9TPvIw7fUS+SF/jK8MwFxiy9WpLAqB2J9/GCjhbouly4hoej93wHejY3\nL9K8klrA3DyX9+Pa0K5uvrX/PpU2bfm9yflM8uwdcD5l1m3Spc2ub3NoMwGNc6irtd/XRttJ396s\nSVh+A1Phfg1jNFFMxpXb2q8iRXuE37nZQQ9BDQKGwM+D6jjysbK1UvybkA+Knh+mXC9JO3FPp0Hp\n+W5lDQz1kcDljzHVLtE3kGYx3QckAgK6dh8B3hTXLdg1NDabmJqZtGt0P5H2ulU3jee0VBWWEU26\n+bbt78us9eUc5p3PNM/eAedTZG3BLysM2p+rmwXmGYd2TU5dK6Sf9vN2JEC5l9xTyp4b25DOvl9r\nHsfSxh1+sx1Ka2Nhgbjl52ntObkWwro/d+olh1Zu6tgX13DgImvqBM2D7peE4jry96DILgKj/Dvv\nsWu3lT5ra1MbH9lH/bvW1qH83Y5ck6bELfNbrXKdxj57yPI54tk74HyK3GPbnyrz6GlvGi0nqF5N\nTl0rtIOa30F6HQcyEohcE306VMerFQzpzy47hbaOiTYWy2jGrO/V9hypYZDmGSvBH9eOcFPHNrvm\nLfGNnsc8Bwr3yZCO0zzKK41S0fO0yH+TqUi+L72fZlLaEX3cx7SY5DKaDD0Ds6614RqXKZ7b5kDr\nEUHnjmfvgPMpsg1GphE6+mn29DaNPtPNnKYiZGMSM3tGs9Eu2r4qKRjiicHsPsrTulVBd/yY9N4b\nhar+ri3P0csB1EAYN3nlpo54jTTd3R+u3UZykk3XyC7GWjt03TbmuVO4BoX7huyJ5+2J/nAwxgEW\nr3VF4OEqRm0QAZvxcz2fuwcftBX6dwPtvEDjwo/j/fnhxga1DlDOGc/eAedT5h5B0n+tZi8ft2lE\nAXalujHFe6bR+qR90MwHl9l/a1FL/EQvK8Tex5AZtuxMGdtKN+vUJ0UPn86Fy/5ogdEzTtZv8bvS\nu/Dx6BMouaDv//YpALjM/vsEpuHWpW+c+/mk6+EQI5jgQIP7bGwiwJ+Zz7Kjsk4wr7+Tm3VaNIvl\nMcpBbvqOue9RD4BvXc8lbWCvxqVnHjvPwrN3wPkMsi64pY3/FYyRBD1qWtIS8CgZyiXSGqY5Xq2c\nt8X9deTfFubz8ms3EeA2pgIPMU3GZavGc6C3jXlI8x2lD9zxch+tzLBTjpP9G42X5rPRB1DStnmE\nylgzExe01N8nEOBbw3fra1f3yyFtlwYeeA0dROmonM4LqTU5xNTEIudlfe3U34eDQct/7Rrae0L/\ngSFfCwtMQT75Bknw25YnpnUeO8/Gs3fA+YyxdYKJm6yWxKxNxaxv1NQOT/G+GjNF2o7cXJ9Hu7pt\nqsYOf5OCSIIJyWUHxhygvMLaT9tIgQkBw20MVW3HahksDYkthOp5OE4wAoJS2QFNnW/5U+kZVO33\nuiLmFh9LnpgsajvaxqXkL8NzqpCWUGahfTlrO32/HXbP0XB9LCKYXjuNZlEmmqsdCKY4MKTvwdcA\nYlrGYDkQNrX21XkSnr0DzmeIczOFFKpaMbTj5sWeb0DEpDGYRjvS/q70PC5ENZ8FqSkhAEeCiJsf\n6H042MidPGMfuIlIKxp4NNxf0lJQXR1dFd82DvrGr5me9DGUGidKeGaD1zbtTIv2ymqbO3dSbRwr\nMRnVQbLNF7o5iwtX7qfxMkY/kZsI8DabHw+G7yvb5vlNpNNqrSDlFEBBM+GWDwRTHRjy/YEALo1n\nPQqtfb27BmVNePYOOK8R106dOYDgznLS1wGxt4hc3j4JXh4ZcHohyuF5cuN7BdOTqjx5cU3JySCI\nuGDeR4AvDv+Vgpo7Qe5kQic9NdMGTeYN7bQsvwX18dpwj+1cG8dA04Jodn/d0VV+s55v2Objk2tM\n2sofXMbUBwaHb7cp2iQgkM5nPamaBVg0QLHPnkuAxRK+W+L+A/bsYwxO07X3XW7ttI3pan044vc4\nxgjKNPDbY4qThwDPaLtGPHsHnCfmsZtETdCEa3I/iPR+2iAOMEQS9NmC85o5T8y+YaTvdY8JCS2c\nUmpKEPOqtlzDwp0kuQCQNXdISGnmL2nW4cBGmtvomU9ga7iyrkmSvjF2TZflxn4h+plm2M37WPcN\nyuc7H6O8InRufjnBGMXDTWjS/McBC697c4y5SWlvWC/8u/4Y41rkY0x94P4gBIDGOYf2r4OSlma1\nPhw5KB0Hfk+zz86jefYOOE/Iyyy4lmibfFOWm1Rqo+7v/3ragcN7SR+SaLqKGyMJCr2qbbguj4ZI\nvx03zXDzjxRSxHvDc7VQ09vsb2QSOlbe5Vrl/TVNEnfu5Cf7cd++bT6QoJempLI/Svm9tsU4aWYq\n7lvF/ao4oN/ECKYOMYQXc8BpObGSBuyGeMaB0TZiyFS7g2m48+pzDZXGVNcorU6bspr5tR77jfMH\nPHsHnCfkZTYJPUrEOq2WUqa3gSNN09N2Sjv9TU/PYWIBNBIsFKIaw3/zdvaU9+e5OWJhusDcLIAI\n8P4gqHYw1wSQloa0WV/GVNNB1z9AgOfMMU3NFOm3yU1yMRqp99vr10mNmg6gx/oPxH7soKYFiu+4\ni7lG6xVMnVQ5wKCxoIR7PBncFmtb5jchDRXPaEttU//uI8AfY2pKmk/Q6vPDrp6djuu04e7j+u5+\nJ2vMs3fAeUJOF1x5k9Dvlfbddk1MHmYsVeXS1ltyflweAE07pjxUl1KRaw6tUjvyJ5jmLZHmoFJy\nNW0MFkx43cKgFTnBNFspYgAuUvMgT+cymkYTJAvM67hw9fpL4rn0vJbSAfXvmOf+KAGUPLw0FZ7y\nW+2wceDOz6SRKmm03sS8IKQEiXT9fUwdb2NfAstoLwpH1kKKEfOxpggyu7bO6vcbOT/0qsfpPqNr\nrJbriw5667+538ma8uwdcJ6Y44KzN4nV3atvPOlGdhNbQ4bT9k/fSS9VnVMdlUdRC7XOtSPvoSZQ\no5ak7/SYCtunMGg9ePtHmPrucCAk/RcoIor7qaQatxxwydM/3U9agkOsCUhdINtavhxwUw4Xa27J\niBcC2dx3hkwzXOAfDWPCv6lMY0+ajavDt0XG38DU5EOJ2aRjMteWHLD3IQATnHTttSj5gL1j1LZN\nu5fY68nW2No+QHq9oGXKaPDnWQce9zM5ozx7B5xXxMuoL8erzKXDJG1YcrOn/Bft7beZf6bdiDS/\nnPAcLVmU9Cu4Ku7dHtrMwU37u3MhK7PSpiaK1IQggeNieLdtTM1JXGsmBWMpgoWEby3clJsy5DPJ\nGdQ2KabvdNnoyw2MQEHT7siifzh8D8vJ9Qhj1A05Gctx4d9lC4M2hY+tBWK56YcA5t3hfgnAjjDN\nbHuEAaSOM+3UwUd9PZU1tjQfNO2V9JdaFPtS798+aia6cN185i/npXn2DjivkJdRX465196w6P+5\n0DjCEB7Zrkko9WkVG5EOUGrJorgwlcXlCJwgpgKTtDIvYDQv8E1dvht3WEUMER+6ij9qE64O400Z\nV2tqeR6Fwr+ZXWCy/N00U4YGXGtmn1LEzl3UTTL3WF8lYDsYxiQ3k9gaxQN2v9RAaWNLAlgDlseY\na2TuJ+MQ+qH5uHAQZZsM62OomcVqZhquadO1rrZ2S+bzyc3Jfdob6YRs+bW1j5HzWvDsHXBekvPN\nYjoTx/j+WAJPOoBSobhdXNZhLgdHyzvgRRNPNCuUk0XJPB1So8SdHREjuNnFYBbA4b+k+pf+EJaQ\npVOoVfCRmzm4BoALEktA828WN/hWAJtqjO4q7Uvgmof6pu3lQDS0I7PU0riS5mMfSTMR30vLP5Ob\nSfLx5061MtKqJKRvYhDI/LttYR6lQ/fzNO56DqJxGjkdzOd9zUGvBW400Kp/K2ni4bWE6Br7nXSz\nTu6EbM9Bqz03/awhz94B5yU431DKlWFPczFqtTtiH55CPfJkTASGFQUzjalHCuIUtMhkUaWonl1M\nT47vsc1bhiXzf+9helIt5x9JAas0KdC15OBJuUVoDu0iT0Knvwd3+C3PpXCN1BjFei3paZqusSKk\npGCyBCcBVNJ2aRoartHIa+PU5oH+LPl3TUjzIn+pMA3fgfyWHmL0Y5FgjvxXFsV50LZvyDGUgGIL\nc9CrXSO1KXx85XhIXzWtjpCcMxqA4ia1soNwGyBz/5Q15Nk74LwE55Ezdh6T01yM6bMOMD25Unih\nFvXQu8FqJ6J2U89YwBaBEKUdtyJuuClAZv8kHwVuJkAMfga3q2OiC8OS+YPMHFKDwrU6uplFD0Gv\nz6VSWHU0+2i5XVItiv5eVqQXBxEUIszHl2uR7rL/cu1UfU5YGiQd0NI3IMdYzRTHx+o+pqCDzIAW\nWO6PiNH6bwGX/D472q/lW8X1w53ljzGCHT5n7mHUIupgsqbNs9dKGzh1no1n74DzEpwuvH0sA5R2\nwb18v6R9mE7e0jnuFqaCKQqw+H55voRygbo2/4hlAFtqmriF3Kkx/r4n3o0EIwmqHQxOjlJ7coQx\noqTlHbjA0lTqXPtB/hb89P8G5gBBjqkEKDIKS4/ESb+FNA/R2PMTtDxN2+9V/jYETE4whFzLqBFN\nqySjbKbzV0hNDFLjwrUP0n/rCGX23nRNyFpB9WrQ3NepZU6V5z4H3dyE0/qtci1rYOmEvsWeWY8W\nq71XOv/6nPWdT5Vn74DzkpyqVUtZXltPR30aBe2e+CyZpIoLY9Ii0AYVQyxjG7WwZcu0UvePaN1I\n9feT/gAlgcp/38RUq8IFsuaf0eukrG34XFPFI5HIT+hE9JOffLnw5HOL+0zcxegz0/Yt8rG/jjH6\nxTJbaSfg0rxDTOcasnZpjOSYy/FIAfP4NZqbYXLQcmUYV4oIk341XFDTnLmN0XfpGAGeMObEjWFs\n5XfrB2D5t+PzbYExv0zPAUGCV+lcLufw9aW+S/49pNmxX6vqvBKevQPOE3Lb6ae/cmz5efw0xTcZ\nGcZKGpMUcFgObHq+BM3ePc5npUXopWMSHW/1qsv3Mc0TwgXJLYwCXzNpEFhbppgbH8c9jEKOa6m0\nBGc8JwiPatGiL7SChMc4zgciT81eAp72CZgLNwkMiU8wAGAuSJ8S/93B1LTW/j5t71rys+Ch9xwg\nSsdlXiyS30v/fw856Egz8SKGDLT8Xl6CoU0o6/WRtHD2A9EXubYk0CFgxs0utObrZTiW+x6PsndL\n19Ay3955aZ69A85rwrVMsPo9WmQBV5PT6YeACvmkbBc2Kn5q5hvJGxgjMsaod63IA03okYDgm6V0\nsiw7d+qnZgkI8vvGfTtpUqLnye9zK3tOuFembddO7ha44xFIbadyC6DIb9I2VxFTR2JpWuOgQPOF\n0PxU+Hxe1sk6X1d2PhRibj4hkxAHALKfnF9l3+kF8dt9TB2kCcTKeW+DFXu9yqKKx5hrwDRfFW7G\n0nyCNA3eMmtF3+f0uUNA3zUqM/HsHXBeIcdTS32RlU4W9j1aLRYZ7kmbrZVIqXZq3sI8e2ffydYO\nTbVOdFxAHGJeh4VOe1sYhHsemZGfNLl2iQOCY7RU1rYZQ4IFDqQQg7aATuCpc2vbdyeQyf0hLHBn\nhdba/V7WHyr0j6ea54KSm7n2kYPh/L2lGZIzD98eL6BsTR397TZGkwg3+fH5Jn07aN4cYZp2/wGm\nIGCBETzi8P9PIPnb6Gsj12a2vY8EeYeFZ3DgInP60DXXMJ8/y6ekt/YbO+KNxiM1QTufCs/eAecO\n7lPFSkcweXrJ2+kNWQztcCfLQ4zmAZkwywY+cfMhYRCFgn6ySVXZ7WPBVfzaie4m5gLiIQYwQSnd\n71Xu4/lSNH+KBaZ+KNQeNyHR/S0REqSJoFOnTBxHbeyrY1Y+UVI4eCnXS+vYWtFF/c6JpeigtO+t\nWhgZ5cPfV/qJ9AtIfX5zEyhpFv8njMCV+wNp6yAC27Dm/iXqIICbhWrfb09tw34fK0eL7EPtEMI1\nKUfDWDyXjHfpsBW1nZvZby39z/txj/VD5i1ys88p8uwdcG5ky0xhX2+dCHi2y9TOmi5Se0NOT8OW\nKYPnIyknUsrfjwMqrRZJK3iSmgbNh0KqqXnILdecyHDgkhCQzow8d4j0PeD/TyYPLevu85hrK66L\n/v2r7L1qdvW68Khr1Wpja2uwlslyzIVqLphqYD5tQ2r49jAX2HoIdt/8k/Nbti/Dza+Kd1pgjNaT\n2q7cNFL7vvn3KwPHuN5lVF29qnXpe8ffuBM5jQlpsTgQl1oi0lSmGqTWb6OPwxbqpr9rI+aqm4hG\n8uwdcG7kXrW4fjK5iaECbe30aSc7q5+GpfZjG4PvQy2BnDRT0HtuYRp2iFjzDaiBOVvNKwEaP+HK\njYrMKJoQ50DiGCn5Wf6OEqAgpsm86O+0KcvsnldFG6Tp4ep3CVQPMBcw8oSvqb1TcFne5DUTwDQ+\nBHmfN1F3Dq6DeVswL8TfJVhsXXtckMoIIWqL+q6ZmV5Vvok8EEh/odQ0kr5nK7Cy8ruUoup4bpRx\nRQt1J/KHGEyiuoYm97Mpf6P2uaEd8Poin+K42HtfaS05O0CZZBDhqV8HeO73c37q17vb69n4y21Q\nMncMVAgAACAASURBVDRysNvG6Feh2+/j/TYY0jNJXmHP0UwQPPeJ9V7k75HnOsjDDHNfCrv/utam\nvBHLZFj8NMXNMlLDQ06QEhzyUzPdewtj0q5bmKa654CMAxYaby1qgq5PwzB1rY11wi05MnIgR1lP\nSwBQSyhW3qhb10X8f9IOIeM91Pxi2tqXfaZn1LOVlteP1Kjx+b2JAcBSCnz+Lpp5lt5ZmtRa9gUC\nyX1miniAsKsQL6MRS9uQhxENoJQ0KOVxaE8vsMC4Jo8Q4Csjxq0efaRFMQ5z76Pw5P8ymVw5ozx7\nB84Dh0mDmPNzv9/VVtvJv2Zb1046ciMnp6+SKrfFZryLEfRIYU2nu3Jp9dwX4D7KU1jLCTwXYNoY\njD+lRKDyVczNOZY2RnMAJL6FMURTjhvPD2PVROEnaWmKkkn66PvbmoCyIyMX3AtMAe4JRg2RPr7j\n07Hz70nrolRZuPxNllmHfBxqJ958/UgQSyHlHNDfRIB/YcwVei+q1Jya69r2BS7I72Gec0iCP800\npSfSm5JDP99h701+bbaGJtxzHYPfCh2UrLnYdtCzah/J8SrPoS+Lb7itXLNvzN3jz8PWX0wiV84w\nz96B88ATAhR7I29VA+rhflJQ3sMoHGvqb2uRS9MLPynSSVme8i0HWc3nQgKZBVL0jN6fkkqdq9JT\nM1Tf9+GbPGKIoHhU7VvsA4ELLtSJ9zDXVFhJu0hTpQEwqvNTA3C2JqB949ZU6qQVsEyCuhaNn+ht\nQCIFvPQDIiBHmilu5snNVuPWocy/w0GF5sipARoNxEpQyHPWkDaAHDZlpWYd6Fn7RP7d7ijvQ6n4\n+TrSDhC6w3Uva33NtShkyqntR/yb6OZpbW/TAdllDGCHj9cJu6d2iKR1L81VEqBIELSPbK4/A89g\nvtQQHaA49w3iFABF38i5QGqxmy4wT3mvaVBIu9HuVJg/S9poKX27rFBMKnLdLp0ClAdDW6mtN71G\nAzn56T8VCnvi91Sl2joG+Sb/HtajViiPhXQAjH2Nz+a+PzJplyWwT5BCaTmIKc8zzZTxaPG3dI7J\nyrucS5oZPma8nbsYhLOliXsZ03BZYgIj0hdF+w5Su2WdsPkaonXIBV6pAKE0b3LBZ4FYbY6eIMAX\n2d/eQ716cslcKue21HzROpHfR4Y3U5tj/HByh9ramq5FaNX3omNs1dbl48W/oVyrVD3aNhHpY8XH\nVWo2tRpXH/TJAQo6QJlkEKcBKHKR8aRkdZt6mNjSjPMiphsknTa1sOM6AIrPucwW8xHGk5cMLa5H\nPdjRRqVaMFYhRM3MIp0gJVhpr2yqb/LSSVGLWqET+CYGe7qeCtweC/mMbUwFNkU6jP2GljagJOyu\nY/SbkH4V8lqewwaHb3AD9UUjTTRSc0ACOpo48rE7YWNuAVcLoMo19A3lW2oC+3nxfO4Ybn+bOEef\nwDSJ2g5rj4e+206oNf+KMP9S027+zjkAyrVv6djr86umOdXXdA7aWhP/cQ1km7+Qns2W/5vM1zJL\nttR2auCK9j/SLJa0x/Q7gdoFAmy5iQcdoEwyiNNpUCwhWrept5w8wjNaBCqvnirVn/LEIX0oaGHm\npy29PW4G0Qt3WQnHek7/8QTLi+WV1O2W8xzf5ClTbrpx6xsm14qQVkUKKl7HhGuTZJ9lRIg045X6\nz78hn2ekvqeNkkcc6YXoouAiu7+VW+J46BOy/m2jronhZi+Z9E8fu/isUsI5zWTBQctlTHO+IEaz\nkZbZlBynqU+yzhK1QU7LJeAgQRxf88esvWP1O+h7SN28kT6fDi/6+KbX1TS5lzGfn/Kd7UOH1sf8\nHaRmT5ptSuYgvmfw8ZLzJZ/T6by38hTxcdTbyPudgdhH4O991wHKGnTirPNkUTzpZE3Vn22LVj95\nlBel/JsMabXs0RJ48CgXHqFC98rNTZ7e+WKmkwT17Qqmp3XtVCrvsVS3+sbTsrmn1/INijtu8jGV\n4I1YUw1z4fp+Ns75BizNgVeHPpT7r2cOlWHNtzGe/viYb2JPFEj+LHl6X2DQ8u2inLc5eLWAySYC\n/CoGn4E8qZwOXDWhdMzel8aBg2wtsymtUZrvlmp/25xbuQYDMQVpvRFE5X1imftanZ1LGpS4j9Ae\np2sXyv3UTKqXG8dGu1fOj7KZU5/bulN5+/hn7U0aHXpGefYOXFguLap082uPn9dPR/VFGa/jJ9bc\nlmsJ8fB3zWGWC9Q98bt+4k/7y0GSTKYl7+fgR4smatUutEZq8A1FhgJbqfwtHxt54jxBWZVY7+sW\nBuHHwWHZgVEX0DdQF8ykVaH3Suu4tM3x1hOpBiJsjUm4bpONKSLAW9gizNPvLDWPnEv+HtZ9dA+F\nzJcPGHk7PL+Orh1s2UNWs1/Vk/bl81NG4/G9KDqCl9vhe5wU5FvYCljG55KyTHNtB5q291quvXPK\ns3fgQnJp4off6wup1kZPW3mb3DShgREJbuQmuyd+lyYJcqithc9Kwc/V0M9h9MO4h/qmZalu+09a\n8e/k+Mfb5GOV281z8FfToBxg8Ekob95x7Mvq9PgMXeCFdyEA+MeYAhTSytzBVBBfY21G7VX+TErp\n3pYmPtzDzUsEMDWA8nXRp/vIgXHfWjzCPA/PTbPvuubjIQZNHzlFtwhfriWSJkJ7bS+jSRjDLbmF\n+to4YnOuFHnGzZF8bGgty8NIDljydcad+Ht8VLQyAWO1Vdb+sny9oXPEs3fgQnLbxO/xOalpBXqF\nc92Waz9DMy9x4Uvq8Px0nF/7JqZmiwWmocxcBb8nrrsi2l5g9EGxhOll9l/NxKL5ONBvCyzZ5/ME\nW3LjvILBTEOOeXfVtvKTF4GLWih37SR4jAHo8XTi/B03MfqMHCLAPyz2NW2Xp3bXBXYqrPk9+jiE\ne6QG5Y3smrb1SKd9HoGmJR5MQUD4XQI3WdG7BWDIddByQJHXUO6c8oFF70d5PVj7iHZvCbSmbciU\n9pqPk37wSfeoBabRYNy52DoIEAht0VBPr9Xo1eRcYJ69AxeS2wBIGRz0LJ64AY8rdtb2PikgiL/J\nk9cN9u/U+dKOZNofNh4JHrgKngvSdKPWhaUlTHWNS0lTUTv1ayfB/DvSb7a/St5P/q4HaFfu1dTi\nGhjjz9RSpi8whPzewtzXQvbVMoHsKe3Se8lonQeYglBulqGx3USAb2NIoDc+N4c+RvKbyjw/Gkih\nb98LMNoqfOvX3EQtd0j7PlRbD/kJ39bg2OssbUNmh7acsKVpuJb12g4o0OfkQ4zZny2gNq1WY1XA\n5xzy7B24sDzFxC+1kZ5kdlA6cU77HiVzFT+1lJO35ZoYDkR4vglpDuGOlfmGpm9MUU1ta0y0dO1p\nv/NN+QilxqAsjDRQdoRaRJPudIpqu/o34uYoDYzpUVRpO9KsQd8HMZxKCUjyZ/aUViC/FxlWzPsq\nVf51f632eSzHiI9JLlTDfbS+jjAf0xaAYa2blqzRmiO2NLH2+WSM0+DIYpbleRm/G2mQrIOYrXnU\n9wyaE5bPDgFhPnfJibmusZx233RzToVn74DzhJyCElpwPDIBUZ6gx7dvm0Pye3YxprAnbUvJqVSG\n3clTtJXpU9+o003sLtogo3yiiZqokjr+N5Q+2AIrBz63MJh6dlBqpGwAF9+1/M20tPocjC2wtGnq\nSb3eZ99CAknSqskcH6WKyjKSJub90FX+9ZN43/zWxoj8bbTEWpaZpnZ44LWytAiX9vWpCen8t5J5\nTwLhVg2ONMftYvQLa6mL0wrCdjBoXp9ALYqsNfw5XcPczKznmaodvpxXzrN3wHkiTheTZiogPsD0\nBN27CUr1bfm0qOU7KG2A/MQSN5PUmdY+7drOqqlqWYtO0k1U7ePCNSdaxs4F2qn6pRMxL0ZonazJ\nvGO9qwSq2ti1bObcnMJPs/cwgM430PYJoudqjoypAA7PkrWbpAlQ05DJCKTxAEX/plxwLzD63diC\nTRu7+LcrmEZdaZo48o+4haSRautzLUrIOkDUI6v0593EVNt1gmnUV24mbHsPvv45eC9FwfX5dPD3\ny/1YFka7urP2mHdbdo5eEJ69AxeeWyZt2zVyMZEg4bksyJej30GrlPG1fFosZYysh0SXr9VOu+Uo\njlz45EJ83DeUfgd3mp+RC950fO13SH1aogC8iTlQlSfDlpOr5pdzjEFrwr/pFzEFZT9WvollYpLf\nNBfeab82MdXGPIEpaCh9916thBX6zE0JlgZCy2Mk/WwQyZepHLZcjzipf8eaNqRPcOq+YMsVE8zn\nnATunK91vWP7u2gaFH74qGmE9HF0bcwonr0DF5pbJq222ZXb4kKRTu7RLDF2MeeLte3+VBVcy52Q\nbxS1zXPM+6Snp/7TV9/4289IT4tcO3FXtCNP4tY4SQHIfVqkAO0FvByASR+Rb2AqPN5HXeulm5j0\nuR59i8r9IhB2B3mF3t51ll6b15CxTtM6kHkJc62hFOiWBkUTyNx0VjIZUfh72v/yAaJPcMa5I6O6\nXmHvp2cero85d6AnYFvXoNTeUe9/3dQVf5P5oSyH3tIhZJp95oLx7B240NzmjFauQ5Ne27NIl8k2\nWfZVqD3P3iR4Toh27cbY94n3TuNRb/VDc/TT7Ob5+Orvr/XZPoG/gzy6J31uahpK32MHowA6Gtrn\nwoLXGOFaDbqeksjdwNz8ZGkdbmAU0MfDv0tjafvhpOBP93mSYCQCpJoDdylCRXPClGZNyq/CDw1k\nktvCmDUZWV/0PSLvs67FsEDpuDxJmnaOly7gZpKWAwbvv1VWgHLLXENtzvatdevblUBcOUldPSpr\nB6N/TluiQ2cHKLNyi3DsAShngbVNIv1bdDacVrtR2yTHArYW85xmGpC+FGNCUXnIJzftyBDgPYyg\nSObtSJ1rdU0MYgAgVzEV9NHHIC9Ex0/Y0mdggdwfJ/x7H/N+WyCBxpL8cOj6Ywx1bziwu4m2z4cU\nOjsYfSioPTnmpYR7UksiK/VqQJ18UqQ5iADeNlrZccN1L6BtBjnGVLvW7iirz2XLjKz5GZWfm7Yp\nw/dfxFWkRBiXSbYMcmvjqK8n16A08uwduPBcE45xI62bSM4C6+aJFhtwn3YjPZVOb/uN36Vmequ9\nL2I5Asfa9GjjlOCOp75H9twtLPm5xDa1UFHiF0V/UvNTCppkteJr4p3oe2xiXu2YczQX6GMpwQ1F\nQnFzA9fK8LakYJTtlJLeWYCBa0lsp+uStkW/VgM2tC/wZHW5BmWqjKj5u3Mz5gIlIG3TEEuguMve\na1pfjdb9JB9fetfyetfG0c7bdLb38VPi2Tvg3MBjT/jryPom9xxaYajxNNl+oiqroq1NMvc7KD+j\nrNnKAZJUW9PfpJOrZvriBRQl4LJOrtsYKyPL6zjvYa5x0DQx9zBoGMrmp9jnN9m9pcgIqdHhZgr6\nN2VnXaCWHj28233RBr27LNnAx1GGd3Mg86I5F+rmgHo9J90BtJw0LJ3bWmHCEwxarhuYmvVOw4yp\ngcceQEBmHNtHabr9p8WJXmo88iR91prV26uDVueMZ++AcyNbC6HFzHBafem7n4TcTcxP+1pWzfaT\nR1kVrY1fexG0eF8pOkk7fVlRSJr5wjqZa4DrOpZNADLz5xEGsHGEQYh/GfPILhIW1O57GPwiuFmu\nZH7iY4MIcFV5F/ouHDS9h0GwLjD1R0EM2g1uqtkVY8czqT7E4LRJwp5MSptijJ/A4OD7RaxFD41b\nl5opk/Kf8OfxtOs58Es1ZpoZifw2tCR8XNO2ymzSC9TWWQ6we7U0cj5fbm5r3HtYGo9xJixtrTs3\n8+wdcG7g8ma3GnVoT1/i30unPmkKIHOCPEVKn4g+u3Hax1wVnV+rqfrriewisImmN/v0Vcrwqgke\nKfAtwMVr5tRPZqmw2MbotHeIQWBawsXKHWMJkh3xTbcL/cg1SfEa6V9S8g8h7coxRgde6Wgtwd09\n1tYx8u+/zFrQv5mMSOGRVttsTLX7+DP4mNF3p/ktheiect/4vaINjKXfMX6bveZnp/NDFuc8xpaQ\n3+XeJc9Ure8pshSC+5VMzLN3wNngsvCiTev0Ha/0vmgaA35y0zbYYwxmAKqeS2p2KaRkZE9ZdZ7e\nWy9Rn29I3Aaeb7b6M2gj5WGSZXtzvmnnpqD0OXJzrNd7sd45/O0FTEHEdcxNE/ReunZBG+Pwty9j\nCaC0fKfw2xPsHe8O86UUSUG+LxxMyX8TuJOmpSN17PvXgpz31KZ0wNXnR34fBx33kUw39tzWtFNH\nXfPF/k49YIyPAweapPWrVRLWgII0UY7b8+qAyspUTUBQgqW+eePczLN3wFlhW6hrm1a/41WLgK/3\njauUS1lE5embb5TI3kGz7XK/CJnHpf8EVdb+bGMwC3xZ9O9OtoHlbfKNlMwntlZD37RrCe8sk1B5\nc8zHcWeYP3qUTXr9XfFtU+2CDvbaHD/bvpUm2GJ4bv1b7GJuFiIho4VG92U+1deC1HJqpkzqi1Zc\nk0A5aUauYDCvUT8PMZ7oNQ2ANGdxUDveD6UeUWaNg/R9uoclkJk+T2o2ueZwPCioOanXv6sci/6M\nudr6cc549g44K2w7nGn+BH2OV8sI+LQNqVImoLSPKSChyAjakLhglBw3Pjuyp9/kUxrX+D4SZPB+\npRtY3qY0U9VAjdwg72XXL6MlSq/hp0GZICzPK6HnU0lBcKrZsjbuHHSOXwM0RjVbP7/nPqbJwxCD\nho6Dqecw+L0sI+zIt+Mlc16m/TrBALRKDrAEJml8ZZTTy6iZTPSDTfQ7aZkv5fe0AY6+J3BtL2mt\n9Irgcs7na5LmK4Gv8T4d1gGh7X0082bUGPeP5+mZ588gz94BZ4VbTsdjN5spMxrmQImHuD7EWEEZ\nMfXtKAvA0hjkauz2hEd2mxJk3EeAPy1uYGmbZUdf/Z4Dcb1mHlgWRErzDO/jsdrH+D4nGE7rKQhO\ntSSpeXEZ4Fz+VnfMOVsWarsYQAmfZzxpWrv/Tr2ftrq/tJ7T/vO1cYwp0OdRbrfVuVb3X1lOCOpa\nPGk6lHNgB2NRxAWWzYWan90Wu7ce1t/+LmRibdVAHol+cS1X/xh7Ztkmnr0DzgYvc9qptzsO/dsb\nkubgR85/2uKmk+HbGE6Hli3YsrXT5jLWzKP5TUgV/BuYhunWNBnbqKWVt6+Xpgfu9/Ic6k6pPd9J\ngohjDIKtrF5PQ3l3MYStvoTRBCS1JBqw1Ma3X5Ud29LNE7pQk/4Dr4jvKkHysiC9Td1vj0vJAZb7\nXpG2i0dcIebZcy1T8LRCsASi43q4JeYbBxlpKYN6rhatkvR480gKMlqddrXDw7gxbjmEOjtAOZM8\ndsNP79dyWRBYyUFLy6nePm3IU9cuBi3F7ZGLWwKhqSrYXsfcOW58Sv/2/l8XQkfa6ftOaTaIIJV/\nj29Mmp+mVUsS5+i4E2bL2GrZPfNcKSQUSVsiTaTLCYfWtnRw32LKtUCNrkHUhen0QrDuk8LnEc3z\nUhbeskYjByjkNNunRU3HcMwBx9JS9Y/xqg6h54hn74BzJ/curhKY0cNXSVUtT8Ztp84ckCwwRIxs\nDm3sKBtNya6d9z3VePTlrWgb29WeanQtltzQEXWzWL0QWz4++2z8bc1Gbn77E9Efng22JdkVCZC6\neWbcGMo5sMDcxKOB5AUGzcoruExNlBSElZybdzCtuMx9QvrnW49gW5UQTDWh6frL55H8Puk9+Xwh\nIHxZXEP3yoge20dM77vcy57vGHtZ0mE53x7nIs/eAedO7lFP18BMXPSkcpW+Idy+3b+ZpumvH2B0\nouUA5SpqiZzqfS/Xxhg/vtNtNqkAs01jcaxImFMkEG2AC4w5SxB5krL8WdSeHB+pVeBOriQ0pY/A\n22jV0+mbo/nJuG1u2uBF06LpkR/SVMDnZD6WraCpXaMo/ZMeYtAekjZngbwu0TTzbfWCMt07JECR\n4PE2RtChZWO1tBKW+ZBAAqK+T5XHIN3LtMOYdTDic+ceWtWznSfj2Tvg3Mk9QKFu1+UbBvlB0KIl\nFX5b2Xb9+TLXBvXjANNT7g7WQ/lSP4zT0nYs/52kRioHK/GeBcYoKK71kAnttOiHdONPx4fGGzFq\nrU7E3+he7lR6hMHWf23oS1s5AF1DVKpRomlWesyJ/NRd1qzlc/IEcxCeajrGr61SIT/yo2jThpbA\nbuuYTTu/a++vmd/0e/L5Yvt1pO8pgXz7GIRrc5OT1kYc+5fEN7w2+z5zznn2Djh3clgsPc5dthDX\nTy6kzaDMl5YTnLVJ8lM8zzXxACPo+TLbvOhEWYoI4Q6EcuNYT9WqHq3ENVXamL6EKWigKKibWErF\nXk67T5lgJRhBhY/Fb3tsnPtMarVvU5qbbcL/CgZnYhojLfJDAzabmBbXiyHeepi0DirL/ZfglMaN\nkhJS+y9jixbQBrvtYzb9/K7tLZo/GtdAaDW36r4zJafktnlDII9KDsgkkLKNbYyazV2Mmsx2jWL+\n/PXbr9aUZ++AcwePOSWVBMUYIWGdMvO/X8UoPO5gyArKQc8hpsCkHBGyrmF5ZbBGY8srzOaZf+O1\nMsEZF17bGBOV1RwIr2I4vfPkazTupCnTis3tsw17D1PBXTadjB+7WkZUeYolPwZ9PGtCIH+XEyQf\nhPQ7WIkHbTNd/JtMgf7iMPdlcrxyZlx9LSJqa2AOjWIbCOVmzPoaTr9z29zo+02CxjRhXtpGSaN4\neo65F5hn74BzB69CSPcIibwP/JQpk7Zhtpnm995HLdeG3c/5TTpcAJbVwfw0/wqmGqOSAzKNKTe5\n5dks8z7R72+gdsrjvg6xX1wrw2uOaEJ3XDG91rEszct0nPcwB3LcfNbjF/IQ07o9/JtxoCa1jKU+\n0/NJS2NVcj7GmPr+BENK/pa5n7dbW8vrwu1al3J0Tg585JqrVVvmHE18eftc84jDGhkbhbaeB6w1\n59k74NzBpy2kbWFFmwg/Zd7AKCQlQOGmAu2E2pYqeu4NOAck0lbO1cFSYHK/nhSI5ac2nhRNz2Zp\nj01uJ7dOb1EYl82FUaiTb8xUDp2t/gJyc5c+TDRebUIgfJdbqJkW8/Gkb9gCFMuajvQ781P8odlm\n2p/l6umsZj1wk27dhGEDiAUCfF2MXz06p3Ue5WNPzzg057OWe2X5+T7vAeuM8ewdcDa4bDoomWxa\nNojl7KD5KZNX1ZXZZGVCJnnv2Vms5RwINzEIb2S/S4FiA7H6d00dQvPfyYE1r7HTe3rLBc9ypz9t\nzo2LRqP5ssA0wyidnhfYlh2UCx7EqAWsfZsyUMyFoGZqWCDAq6ydE4waoXIIua3VPH3fhhwY1LVX\ndlvcV60tI3N8Z/5NjrGUwC3VjLT6/uih1OPHbH01XGvIs3fAWeGWU4F+emmNfOAq7QVyf4W+fsrN\nlkw5C0zDWssq/LnHu/+7RKCgCy9kv7efmsomDxK+mu+PVrMk2slbNtr47FzQLHP60+ccAap2kFrX\n5nHthm4eiO8onYb12jj6NyiHXaeaF26i4k6ZUqNWNp+VTBg9mqhp14IEmOO0O6H/srL0f8jmRT4G\n9M67mGrUWmo2tc/ns7hPnSOevQPOCrd5o8tNv8UBTV6zXd1w7T7a9vZ2b/r1XfS2BosDBbmB5lqO\n1g2ulr5f91M5wNS/BVE7hacmGp5/gsApVb49Riux2tiNupzjor0Ojq6F4aGs3KejtmYOMPjq9J2M\n+5w8+bywnHrJ/Gbn9KkBkLl8G3StVj+Izc1i91AWA8zHQPq7cVMdYgqa+jWWLfuA86nw7B1wVriG\n8O0cIeUNIr/my2JR1+P644b6kthY2vpS33Dn3xDSPqan8XL+jgUGX5ydrv6H5+1l45hewwGMTPx1\nF1ONQCmzJ9dy8aRT/Pe6mWT8XO6vXWJrYaSza0kLIQXhbQyak+WLTZb7eRltp14N3Mr10npYOX1z\nqa7N6QOxaf/voJb8zAa5MpcPYgp0ltMqzaWdcv6AZ++As8GlxW5tSi0bRKqC3mUL+hBrglUXCrq9\n3erLsgm6TmfspTC7g7m5hCJtSqaWsadI7lQszS5UpwcxFXrfxvopPH6jPGEZT99NZe2Xd4aVc2GM\nQNUBFv8b9+M4Rs2PIweBPAKtR6AuzLHRs9vKeZGGtWpjlP+9dvCw+7QuXDp41PatdAx41mPuy0am\nniMMBUiXzzJdTrXgWpVT4Nk74DySU6DRv1jyDf42lrUaOwjwq5ieBo+RfB36aoNIYUlamRvqhjDP\n2HJhhpgnLTvBNGnWDkYTA43NmMqm3LdFM7sQSy1KXjlany/cvMPNe6RWz31Q9P6O36B7T9r6nCGN\nEgkt7s9CayKujcBXMQovPXqn3AdeHsAa4xykBq5HS9XHi7/XDgYtJjfP8XdfH+HZc/Cw5lYcw13M\nMyZz8CvD52+OHhN7r5r/EHVBePYOOFe4fvIY6znPN3jd7yA+g2taHmQb8Lh34psK39T16IfTH/cF\navU+7FBSmU6+b2xyACFPb/StDjEHJ3pRvLZ3TJNOjfF/Or11YOVFWbDfOcAiALmPaVK0W8OYtc2z\n+Lw6sMn9SdoL0eXP5CBrgREY87pMR8o8WS/h2R7+XTP/5hmT+f4YNYMyqme8Sbm+Lj2fyQp59g44\nF7i+YMctlnyDp1OYZQPnmgFEgF/BsafB+PzL7L+aVmb+zTUHcQvxt7uYA7xjDJlDe7QDfIOl/5ca\njicwaJi+Kr5HvbrxuDlnaWLqc24aDUtJaJTMhBqAlHw8jGWrgy5vM/UhkX1Nx09PS9/+DTjI4gBY\n8nvKPDx94amPBTdRamZgfn0NHOd5SfQoLh4h9ZLZ5hiw3WJyc56MZ++Ac4FX5SCnhwjqZprwjDfZ\nZthfg0LvM1dJ13035rL75uG9tAlS+n6ZzEuarUoF5/hYyCRg0pmUCyjuELpbfMb4b2T5P3GA1uYo\nutz8aPfByn+j3BrIxou0dO0mkbRNmUiP+rqLQRiSNkeG3doZaMvrk1iLVCH+ijkPT2+dWOuaucor\nhQAAIABJREFUV9Auh0fbJhUO4GUFbs0P6QgBvoSx7pVV/HSZA56eyVb7t/Nonr0DzgVuASCtav18\nobed8tIKu+/hsiXG7YiSVzBoB3JH3VWYFVo3kbS/9zHV9uxjdJJdYJpKXjpGamPL2z4WGyxlpT3C\nAIZkgb+vDdfkPhHWu1namtYx0kwrLd932flh9+2p7F0iMKTaNySkDjD4oHANVLtJJLS7halTNDcn\nEFOoPdeAHQ5zoG3+5utTZpx9ByP4SjOhtu4Hq10nRwjwDdQKWNa+c/5dJeiJhVLzdcbLZhywb3KE\nIWJLVkxfXhui99F9VCbi2TvgXGFrI+5vQzutlJMrhWu4s+jyauN8U1hgdGpDbA2TnaYPrYKJb4JH\nbDwoEkTTfsjQUi03CU9WdlP5/2OMPgZSEB5jAHOaJix/t7K2ps2/qd28M37T772//F58bj3EtE4R\nYvBFaZtX9nPuYm4C/QbmGU7tqBJtXcd1L7Oe3sGosXkRVxm5079OOKiS83+7cL2mBbuMuRYxB5O5\nz8811JMm6uHtPYBO/06aNtp9VCbi2Tvg3Mitm0XbItJqg2gqValqjuG2y78LgS6ZdhyRR8Dkgnz5\nU0l/6ne5CZKQoH5L9fI2ArwvNugt8f70LfeRKhTHcZEbLKKu3n+RfT/K+6D7IZS1NbWkfscYT611\n8LDsKb5PaPB+yu/wPKaCUgKJl5vepz5+3xbtctB6hAFM5AUcW9Z1Ouan62MyrkQCF9DcrGZlyJWm\nEh4pxcdQvrusQC33MD5mC/W6vrFYoA6Q6ABD3zwvNbHKb3TOefYOOFfYPk2UTq/W6ZlrLbhKXFOp\n3sSYmpsLwNKJe4x2RwIUGZ7J+6MV2VtGo9QimDSAtEA7BwM/Xd9jfbcAI6IsipZrrmhc+L8fDJvh\nAvNoo9xHJH1n3t/S97RCZtcn9bet5tf8m/JKz63vk46f1HbtYPDTksUHt1Cv4RP9Udq1Uk9hKvxC\nxtW+PWS12qz8Hip3kb6brTH6IeaRUjSGC9ZuapbWvqENfvqd+0ua5Byg9CcidDZ59g44F1hXK5eE\nir3ZxQVr20j1dOo3Mdhvpd+I5tPSb3dNF/htJG1C2/v0qJ8tFXqL2roEkAiokPZCml3yiKR8wwsa\nivSaBQbtivQ/4FobEnQS7CzUd9P7a5/wcs1Ru6Pn6a4T2c9XP3iv+M6kAVqgDK2uzRVtzsR2KS/H\nLgYflxz46eBG+izUwKI8pNC37jGBrWad2OOUv5t9iJJ7j7Y/2WZp67vlWplcU1x/f+lrFMc936Oo\nqvs02t4LzrN3wLnAeorn1oyLeoSCnSb/MqbgRZ5iZLt8k1nu1GBtgqWIkXZnSl0129anF6rP0IV4\n+RvEfnEAoqnAZdsvop6EKlVn982p1irCpHVZP+e/tJ90uq6Phd0OAdJydFQe9npgPjvOcblW7Ag6\nvU/S+bNmdmldJ+MPGfUxrecRyUGcrunQtDo26ClpZTSfvNLfeEoBzUTH5157jSnnIs/eAecCt1RP\nze8pa0p0EMOv28SgMaFEVjy1NAczEji1C8m2d+ebg7Xht5w8ddVs+7PtxHG5eUFmDuXVa7X77SJx\n1jvqgMhWXctTYcu45fdvYa9gPP21Ik/XiC0ahrQNTYNoz+ccoNTNGbpAK/nzyLXGo7u4f0VJ69Oy\nTupgfJpvZPuTtWprctCjr6Ncu0hrND9Q1csp6NpQfe4R8HSAsiTP3gHnAi8TvdJm7tHABmkbbmI5\njFUKzj5NRVklK9XZlvAu25Rrvh52n+SzKZ1/SRsVzTT2ya0vj432jj1aDQvk9arte8dxvvUyDpDG\n+7lWC6vvGwHq8fAtUsFbPtm3RXvU15pmMmo307SC8fbxbzGzTKdhKB8SrmAKrE8w7GkLjL5Ih2g5\n0faA+V7g6dzEs3fAucC9p90x94bFSc5sJOwQ4ymgDnLCv0umI7lZ6jVNcnV26aRVV0enY1Dztyg9\nu1Ub1W5PT8diG6U5IX/HKHhatRpTAYuecZyba4nk6u/IQaU9tto6qJ/sn0d97uhVfNvWmoxcorXc\nVmqhVUvQPn6tZpbxGhq+r+RjQRFx5Nf2BgbfNg5gdjDVfPGDRdnZtt4vDzOekGfvgHOFe0+7Pffm\np483MBXMm82bfS6sc6Fe2qzC9V8Xi1v3ualrh7ggb/PcL/n71J9HZhYCEfTutj09P7mmfg/5xptq\nSlrAx7IaBX0u5Sf0deMxa0Y379xrmvtta4ucnLkmaxNjwrX2kNR0rXEwLetBbXe2Nf7Eb/uWtIH1\ntn7ytcWBu9SgSADyMqYg7ob4/cZk83mq8XQGRHSAci45F9KWffoyW7iIZKbIfVjaTs3pabJm0+Wb\nFQ+ffFBd3LbmQtOC9Jic9I2lpEHQgQZtnNppjDbZl8TY05icGBuvBHRtWo1UQ8bV3/0go1VzdRY5\nF/pb6je01pm+tmiuaxmIye+Df/9Xm8c0z1xMSd0eZs/pWbfTjJ+lZRxn2knnHZm2+FqQmioJQGSl\nb1pbxxiB4+ocg51H8+wdcJ6Y08Xc4qOg18GpOXC290PadPnz9ofNQm7UX6subl0dK7UO97v6n6vS\nOdDjdn/LnIPq86Imh+dH4RuorFCsbbz56bNlI0zV3btYc9zV79fU6edDfZ2D+baszTWwls7/XdQS\n96VO8A86v4llTtk352Ht/dO5yjWCY0FTPq7jvhGfd8eY5hzawTRfkwQgB5iCuH4/IOfZePYOOBe4\n96QbT2VcS4FC6GkbUswTEf9WryUTr9WL4ukgIgc+WrRS+XRacsYjocAL6rXa4+WmyoWAdJy9zjZx\n6RzHgR4BG823AYe/fxW1k28u5G5gnxngsuj3Q0yTiZUrIedjwN91PTUoPWvGFvQ6GE3vrYO1uLYI\nINL3fYgAV9mzXq22VX42T/xGfe8xy1rmknbtQtlxd7l5ou9H25iG3O9iuoe1fEM3x6w5z94BZ4Pb\nTmgSaEhTAxd6e5iabUomFKkV0FXFJQ2M1VdbFbzAGC1TcxCtjQs/GcXomr7x1rJ/ciBC73yAwUTF\nk3aRKWWBocAiFvgQU4CS+g6kQq622WpjRMLiRDxDi3pIBbvt+Lye6uva3CjPc/5+db+dVuGWmzWp\nXQ7E+0o5pM/OwQDXZLS//wkGACzNjvYYpP3hYyYdd1u1l9ah4zLmNYlkGYNjTLWWbdq+dZ7Pzg5Q\n1pZ7s6jm11NSL3KwXHQu2vImHbU19iZh97W8Kdihzz9UNqppCtblamRpt6Z+y40RUS9GtiXGsMQn\nGE+rWsI2TZCSaUwDdFpfeGp+qk7Nf8/9jdJxbPNDWtc1Y89z+Y0lOM+dj9P7W7MRH2Fq5kGMtZTo\nu9dz2cT/X6CdRr8NpKXhtojBSZ5rJXjZgFI7cswOsA9wWeZTDWhTm9xvDVFqeePhSV9T5e/VrrUe\ne49zE8/eAWeDS0LWPvlpjmDkeyDNES2bl64qTjeOsilljN9CLhj5/bfYppSWms/b6Mn1scA0s+su\nEwKPiut4H6hfMoOsVfDvGIOg0kJZS4mgeNuyIJlMr8+TeWk+K3Ie2CnUx2biXbc1U76HorCkhq8M\nyloFUxz32ner1dfi2hLSiMp3tuv+5G1fRt1Jnjif/23rlfrVeq9+GNIPDZoTfq4ljQClJ+R67D3n\n03F8DXj2DjgX2FrktpnkUWMBy+iQtsiEVKBxc5IEHddRy+URrl1gTzbc/ITIhSn5cuDA9z/YmNL7\nbKGhmzJoPPMS8el7L1D3J7mTbcrpNyKn2IcYwMkTmEYRkKqeC0nZx8UwzjsYIoCQ8XX2rFyI1eZW\nu5BoA5jruGbK1/dp+Kz72p63wNyUaX//XBDzObrHrueh7jx5HK8VpOXasZzky+Ar/B59z1rNSnk7\ntsaq3j8bjJb8dOy+yMzAumnY/j7rvz7OGM/eAeeRXNsQ0g20LUGSdoKwN3CprdE36/7aL/kJJrR/\nAwGew6iCRrZp8efbWRwtoaJH4lCUEfeD2RO/H6NW5TkHWdwshZgW9Ftg6mOi+RQ8iqnqvVSVt/0E\nnc8nS+tydsw85Xds87Npa8vSYuZjXRL2EVxwUMEj7zhAv4mp9k5qT2n+ECi5hSmQpkOKBCmak3zN\nz0s6rdadYsuHA31+hbWjR+OVgGQO/lr6Vwco+di0a6Wdu3n2DjiP4NbTW7r5SfWrtpHmC9ROwGRp\na7RNpNWsJJ9PaakpARVthq9g7jAnAUYubMrvwh1gjzGCE7r2VfGMW5hXeaZTrOa0eA+tvtk5M0gA\n8XFBjBkz86q8Yzbm9N5S0cazq8a2wWm/WUi/j4Nkvs70rMn2vLQi76i20xsoNQp2Ztm+rLi1dRLf\nW/qeSafYvA5Nac+y552tQWn/RhpoL/nelf1Wzprj+Bnn2TvgPIL7nQG5gLGFlg4Q6hEG1iafaxLk\npiRPU1IQ38I0nTtitJNrwoEAhqX2tc1NcZPRTEukJeHRO7uYn25ltAz1lYdWI0rHy3wjTp0Tg+aI\nj8FtZYy1DX+5KtNj59s6cl3o9gsYG6QjRkfRlnpMO5g6qxJz0+EPUZtb+frjzqSkTaG5a60Laa7R\ntRopyJBrgZ4pkxWON4XU/Ez6vlPrIak8F8YCWudRPHsHnDs5biZpSGv5HuuEpW3UsvgZgZpyBki5\nsOsnJus0ywGJtLnLsFj5PA4wNHDydfPd9XdaYBASvD+pulkHA7y/5AeQJqfLnyXzw1xj73kg2tyu\njnH6OwdydXOP/m3P9qY85TvYoFAWpqsl2SPwL0PApelQ5rKR5r/0EJACJ659sUouaMX2cq2ZHim4\nxZ7DNZmyPEOfKSQdnzHaLQu0l6Ok2tt3jckp8OwdcO7g/ATTClBKJyzNcW7503e+mfFCaaXTLPeF\n2MV4sryHAFdHbQqp5oRYd9jlm1V+KiaNTr5hhuv3xDMQU0F1H4N5qkcLpZ3M6+OYf09ugugX0Odh\nU+55B0tolcE1B6JvYgCjtM40Hw8NmNxE3XT4w6ytGkAt9Tddp3mqgLZIQe0QwM2xWnkGy5QTxzrt\nc196/JYxKV8/DsQ7r4Rn74BzB7ekVbfvXWCahrqc/GvZE2d6f+q4Wt/oLJCU27bb+iJT6evjpm9W\n1M8DjOpy3Vk0Lf5GNYV2MQVH3LFXO+XRabce9toTIXUezDT982+coClr//RxzM0R5MO0N8yLK+y7\nahqRmClYWx+acG8DqDXTFmljeeJBvQ9xzkXn/NgGpZvXQJct+LWxHhOBM3ael3MutYAbBzMr5Nk7\n4NzBudCXG5i1AWiOmz2n73ELMFf78g293nYJ5PT1gwtyuxhh2QFOi45JU/zr4ddadk4SXNopXFO3\nWydPq78lQXB2zTT966SmWdCFS6/TdyropYP1MabRNNJn4yYGXy8tcqtnfYzxD+NaiquYV8yumW0X\nYr5q2iDKp8KfVVozUlOzz8a1/i1753l+AGgDN72aGudRPHsHnDs5VdnLnBtS4JG5JHfUa13ILaeE\nuEFb9XiW1cQsX9Qr5p/YNDf+Ul/T38j5UAMS0pTGHQoR0/Dl9H0sdXt5bDRn4ZJW7Gybadq+dRl8\n180erRo+ufYOMeYc4fNDRtKQ83Q9Cq62Hq10A7nQrtXEuoE1/yzdbCt9xFJNTH4fz8lkA4rS3lX7\nlr3zPF4vE+m5RnJmnr0DzhNwW00Ry1GvxWO9dnqROREsv5beEMFxp6KetvXfSgBGVhlG5EDC1rj8\nCoZT6jbm1VfLGpT6u9iC7iKqoesAY5z2UBtL2+zKBb7ULmhp2VsOCyS0pQlSW9fWgeUFDIJYrtk3\nWP8py22L07XMS5SDibQ/1u8l81W+d9nfkhdO7Jv7/UDxYmgkZ+TZO+A8AetqZ7lxvodBOPaABMve\nzsGDPPWnJ6Tl3mf8qShvj/orN/mxTrc8LPQeAmwWvgmvclyOjAr3bam/9c8DW7V+3rkONHW/np45\nqX9nGnt+Gn8wrIl7aDm2tx0W+IGDNBiacM4d3FMz5z32+zEGU2TbGs61RzcxrZCtg4k4r9uicnJt\npJWp2tJa9ldU7gUdF0UjOSPP3gHniVgulnSx5dlO29vki5+n0qaN1rJDj1d7tqnodZOS/Q60ae2L\nTT4HXfX2ZKIqRK3ic7hWhl72VXldZh6UVOtzz9e5uReotuVRWRhjL7n/2+u5dAiAcrMjmZhkckbp\nKP6eWMO7Sj+pwrEFmjQtRznqpkeop+PaYrrkwGzcWnPQsVY8ewecV8i5gGxbqLl5hUf8UBghYsw2\nS9eQs99yas/SSSYv6hdt3XpbfBM9wZjHBDFPhFUzZXFnYyqSSG3VUmPzE177+CxjoonPLtvxzzvX\nTTP2mMR72/0T8u/O54r0WWoFxfwQEHPpRIG6I55xFVMA9gQGTQ4O/30L05IWHABJk5SVVZVAHs3t\nfq1f27d7QXwrPZpv2bXmvHY8ewecO3iMsBqntiyF/ckwwuti45/KFGP5AHA1N/EdU2DoguIh2omw\nSo54UtD/C9GPbeP5VzDNXdFzguyrrqo/uw84LgOK1o3z+bzAmNisNQKGR13pc8R+tqzFRA6ydVAc\n2+HrL9yfXyOzDX8Vc6HO25DlFPg6OcAUyJ8gwG8gN2Om/d9HzWdl2m9H5rNyNF9ugnJtyBnm2Tvg\n3Mg9G5p+b6tQlGCEb6ZclXxc3Symfr+y2nzP7EPd1CJT529iOLVZUQjUx+ewVFxsmW8W7m+rrqq/\nrwwtj+aHVc2zdeRynot8TFKQrN2bApocVOfATjsk5FE04x0yw++yJMQtTEEpB2S7w+9kkuHvso0h\nmSCv+UNtPkACKbr5MOZyWc23exV7QaLzmebZO+DcyKcV1park/NcHGNNR8u+X37Ke59tnj2bPFWM\n5QKD3o+r8o8wOh3yvBWU24GP0xuK4Fjum5UASl0YjjPrnLfwydQMsY8lUKBrW97EoE14EyWgaa1x\nFduWzqX1aK34nW2AaUcSbYn+kimWh0DvDn9fYAAmvEr2VQT4X0W7X1PGSoZR101gbd/Ocvp2s80F\n4dk74NzIvaaa5Z6Vn+6kQOzJYjrl+6UZcTcxmHdq9/BNnvvT5BEcuTOh7vxXSkGf9nX8GKUmnoPh\nfbl5QouWsLQ9PTkhzocQSMfvNmqVgNPrJTi7iqnfxqaYS9zhWppN7KzHrUXwUhBgR2HF9zzGYLos\nma0uY+pse4xBa6IVK6S8QekYpM+l9SSdxq8Za3CMmVKruZVrsPraPB8mzHPOs3fAuYPzU9hqFpl+\nckl9IVZx0q6ZovINmzZl2waen4pr/iaL4e8oOL02tCvDPmVby49Rekonk5r0h+B1jjgoOkQKLa/N\nl9xUcfZt97kGivuBbGfjkc/7fyrmwLfY2O9jqjn4YwzaiCOsRc21g3HNjGJpZ2h97qJ0Vk1BlUxt\nfxMBvqzM9wioA0j5GspQ+rT9bbTA+KrMhjUAp83582bCPOc8ewecR/CqF1m0kW+x/9cid073pG1X\nZS5t3hIkSH8TUm9zn5Mn2D2l1PjcfGAJjuXGyFbfk+aIg5ZN1DKC1ubLed2083nLi/fp5pgIzhaY\nJi97gAA/Zv+Wpg0CB21mx6h9sEPldTNKbDMKYBt0p23wTLfbGNfxjphf38YY3dYGauN6uIa5VnI1\nZsO2DLXpNz5vJsxzzrN3wLmTw8KTYXdjcnno16WnMR6CmPtCnPZJOxX4XMjwzTtVrWsgIZqJNofN\nmSewIidA2mzt1PgtY7DsGEVTAmlQeMKvO5iCl3viO5W1XS0C7ixzavqgfB9tlbrTMbuPaVQMYiwe\nyX197mOeq6QFfNTMk3mCszAv32Pvpkdp6QBX82fiOVRsAd/b/ziHbSC/3PfVAZzm7L/KvjivhGfv\ngHMHpwtSKxbYuuGVNh5LWyI3+nlsuLmZi2/eelRRfg8fQx5OicOmvx6bVhx3q6bLkSJ8iPmmrIE0\nzVx2/jZtDSC2aLZ0Myf9ew/TquDcZHKYXGP3q+8kn87hBcaq2XS/5hDL/ZVkpthyeoBaReG+PDI8\nVHuaCJ+0fQ3AaY7Ii5X2xXlynr0Dzh2cbwrXRmwYtdO0TPgktSW2g+Zq372k9VlgawhiOVQZMQCW\n3D9hfH/bwJxuL5cOjZL/tPD7IeZ+ANGkoFdetnwXzg9gSd+tpVqw7aAZr5NO5dfUdvl4LmP+yx25\n7yjfTWZ7vooR1DzAmpDOk7DtYqpVbQV5urZ3ue+Wz0kdiMrvMm3kofPKefYOOHdwaVNo3fC0yJL8\nNL3L/l+eyKYzB/SZpKyoFVurpLezgzHEmK6XppFD9Vn934k7tvZrtcK3uYW2BuU+pidpziVfBKkR\nyPvYo8I/ixzer1SBW3OuLAFkvqY2jfvT8bQBT833gz/vHsboInofecjYRj3BIaJmhkoBzgFa+X5K\nIK9nXY5bV3wMS+ZqD1M+wzx7B5w7ub4p1E6FuQZFV+dqdX2mMwe0CMAWUFTSKuVtcZUvhe1uDRv6\nK5hrI8YBMNuxtUWrc4ypWY36e2u47j3M1fXSTIWZ4LErHeunyvPiTGiDDSvXzw5Gn58282k5GZyt\n4dS0bHUwTtfFyJr8fW5jCihuiPl4JP5fVgB+Sdz/CmoApX0N2Oty/LqifrfsIXUtmPNa8uwdcD4F\nrqmWa9qXfGN4BZfNGNlWELAOiuz34Rv/AvMCfwQEtGdQ3ofUTNIyvnmf6qdHXWDK4nDHGIXaDSEw\nSCNEOTBy1b31jdO/x/uWMUGc9py2f5fZdDlY0OYCfQP6uwXgrbnKwUl6bfzG3I9LatluYgom5P1y\nrtJ7yblCjtQ0hzdF/57A1HxDbb2JOgC+Osyxdh+0sfOnTyPSrs1t1dY6rxXP3gHnFXOLajlu5nqx\nr3Rj4PVs+uvD6G22gKKo1dEBgeUEy//L+05pueUzpPDn6mzL9m2ZZyhSqCXFvLSXk/MlogRLurBL\nq+naY66ZFMjfQDPzrMdpUwfZtQgTPZtuGyBEDL4dm5hmEq6d1HMzQlxf5MdBZhP5PAqVJVB7E4NG\nh0w3XMsm54rUtkltDc1HWWSQtyuZMiTzxIYEduqOpr3zp12rKtd6ywHg/JorzzHP3gHnFXOfpkIK\nJwkCnkftVF9+fu1EVLNhWyf+FnW75GME+FfDe9wa3oW0JeSPU8r5coxBuOyw/liq+74NUdNkaL4E\n+dhRn+18GsvOkdp3XP0cluOpn5xjH/nvejbdcO0WxrIFOxhNI7yYJNdulKv1ppo7KUQ5WEKMfk/k\n8yTB1HXMU9ITSNJKNSwwpvLn13LfC20ceKZYyTK8+ghTkyBiKZS6d96MMStqe0i+d8l28yy/rmFZ\nS569A84r5n5NBW2seRVd/eTZouatC2ptg9A3nxrgIm0AN6+QkKGNWDqbau8enYRz0ENmlYU6vuM3\nWu7/sIepcyIiT6efnsplKKU2jjVzSGmOzHsCbUu2Z5kEy8Ain9P3MAhmLaQ7DbVNx1YHAfWoMUrD\nfx9Tc6Bm4iNARfMzaHjsMaL5XCpd8VKhb4gBPFGGXNKgcIdbe373zptWjUhbG5oPEd8LLo5D+Bnm\n2TvgfAocT4taKmipvl5g7iQnkzptYYgMoJBVy/zRJqj7gMwC21Jq02ZKWoZXC5swCTX+PtIEpkVB\n7BWub99o7VP2AQZND/1bamjk9ScoTTX5mFhhpSVtVj/gmnbu8sgry0xpC+hy+9IfhZg0L9zcIqtD\ncx+Xku+JNnfoGQeYrrUvDe0uUHfklYCHz0FL48jb2R3Gk/q9i2kdniNlPF4W84pASs20Utdc9MzD\nfB+I2Z9rczVqgLXf5pvfzkWevQPOE7OtibBOFVx9TRuPdJLbUp5hOeyV8jG0bmQlZzd70yu1kwKb\nB2zDvo3BCdCuRBvv58Kk3Fe+0dY1GLzfsn0KEbU0NPw7HaB8f0ug9c+p03eYzYVr0Fpp83xsH/Nn\nECAhHyUCudKsROvkofibBhCewzRyhn+zr2AKUOgbEgjiZijS1OgajLrG8RijGYj3+xWMkWBHGAAJ\nr2q8o8yrOpCoaS7Gz4uWQ0o+D9Lf5IEk1Zqexvx2rvLsHXCekC1NRHto8f/f3tfDWJJsaeUAizcG\n5jVwUAkECxoPvRKskLrNanNmwWCtnsF43ePMrMNiM2vsW2ORWCR8HAxcPLQIAyw0avXOe1tV3e9t\n9+xq3zpILJqun545GHnPixPnL05k5r2ZVXWOdDTTde/NjIyIjPPFd36C7/Rwx+UxI/RMHA4KPtz/\n/r16nfIdyuJEAu/0RU8uTrW7oy5ffwbFnXJpPkN97x3UdUm0E3Etw9kK/MN2v4RyZgzdqT9i16Rj\ndQtjzMIO+OIsv8sp/h5DftyAWT3bxo7xabXRZvp4PAp1o2hzi7IlNMZlBzqTRgEB/f8fYIzxwLpD\n35LrjgUD5Ry6hGH4LSiMkn3KsZxb9GgE3m4+b05gZB0/gkiQsN3XO9CYi975V1+Tu6W0k5O92DY+\nvshW+Rup1KPr6g1IXVB9epMHYHJjrkXzj35veR++E9HKTJ+CVZW2XINS5Bj4F41XsehaXJyQDard\nN3pf0UJoUaZH9o3OVLXZodIX6DZDQ0efge8GcSddgzp9F02/6wdNynb1GZFl57Me8zQ9xifqRvTe\nI56po8e4jN+lBzfiPHsJY2YMfS9+CgUsU3fLOyggm8dA4YF/1MXUqgrLXVacmdEy4TBYmH7fD8qW\nfc0BEJ9/9UZCn4P0N9QtRYtNRq7xBIbh99n4ZoXZjerqDUhdUH16ky5S0o9f//ZKvYa814+c6yCd\nbKXsvoA6GNFmYvqflbMGmL6pBcbRHe0Na+Opct0pAcfRAFQ0Brho+8GIVnpwe7yioClmRA4/p5Hd\nmO7O6XMjtq/f3qXzmiplfo3GnRbXo3OfF917qsxnvJaeUSNZPP7sT8n3ooG91zACInRz2mDefg8Q\n3PHy93QOl3lWz28e43MGeHKyBz7rzyj4o6eUSwbpmHM81dTVG5C6sFoLp+7S0Qxwu55XhmL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CJ4o+OO/y+LipXfegDIYy+54S3pvPKdxLkDYIOBcygxJxrQp8wSugMpi0nP2KHzFucULwynbUz6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\nOfn/w7HqK+VSVlwAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pentagon = ((0.5, -0.688), (0.809, 0.262), (0., 0.850), (-0.809, 0.262), (-0.5, -0.688))\n", + "\n", + "show_walk(pentagon)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To clarify, let's try again with different numbers of points:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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x6M02tZs/Q1/aukTsJsLvZlrnT9mi3/RF3fhcoiH3Wz7GhoffonMd3eUYGJ9E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mmk5Iq0DeUw7Jg1JfVQVFvnqN2zsnvWOeGYbyCGiW6gGEB3ZfxEUDJDznlnuq5pXGhV67Y/Vd2z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x+4uQc8BcDLUGeWvItSgrSJ+EhjAzl8zF0JIGuSqyR1lgMhA4rxAKSiBw+jiC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\nk9pkNClHxe9DBcKHJkvq2+WWfYfSrND8uOQwXE7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mqHP9+aObiMqLv4ba4s2eKxSX50Cm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\nltNxC1j3ES1rHxIlps6JTmZ+sO1SfmiKn0tt9pENnmtixROKOaivmv2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FdWK/YJNT3ZTHXy46AMahvtdO8zlPEdWiG//eZxGJSnfUJTHQVNr7GK6AiZ8ffdE51aW/cDCdPB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\n0/at6L7Q0iuwohOi2v3On6b5mQG1eMJSz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IbqxHdqO/vuTQJQmgOR51CkmSm9HDJ2KAI4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\nNv+aIPEQpQCldnu7wd8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ppZVWFq40AaWVVlpppZVWWlm40gSUVlpppZVWWmll4UoTUFpp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\nWlm48v8DHyzlqLKk1CIAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_walk(pentagon, 20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I definitely see a central hole, and five secondary holes surrounding that, and then, maybe 15 holes surrounding those? Or maybe not 15; hard to tell. Is a \"Sierpinski Pentagon\" a thing? I hadn't heard of it but a [quick search](https://www.google.com/search?q=sierpinski+pentagon) reveals that yes indeed, it is [a thing](http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/sierngon.htm), and it does have 15 holes surrounding the 5 holes. Let's try the hexagon:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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l7p8hJZk39GLkw6NbeL6+fyT/36/QbwMClkNIatahc18F5/4SOCIi98mi6GJD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VAAAg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\n343dUQ5fxLRY2VsYq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GBju9qWze784PMl+G9iSZtNm8sdjmYXzweNowjCiHbt8veSGGzJ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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hexagon = ((0.5, -0.866), (1, 0), (0.5, 0.866), (-0.5, 0.866), (-1, 0), (-0.5, -0.866))\n", + "\n", + "show_walk(hexagon)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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Qej9cpR8LSbWTZH1cHF+geWWiKLVOP0Fk7ipz7nyEnBkeTNdcD67db/R/rl+R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\n+Qz5JhGbYtptqdncNcMpidgONVPVs5mmU+xHKBn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W/QlKLVCKIxKHSXcN0C+KNVZ6XxCH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JAAAg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ETpyhUHPTv2+jNnFw3I/teULH+vwZstDGCIEHKNfGP6M+sDTSRqNW/P1fNdqvjHaGFNGj/h6n\nKA+mGygFZvf9oPmLyIP7jjwOnnFNkmtpB7U5BMj+J2yDmgjH5vVM7vX7T5DWv7aHvga1o3CZlLA2\nf9V7hc7SPLRW8mxLaP4MpQlI146a4pY2xxjmSk19Pg769yPkfcUImXfsni+lH7qXuX59bX7YmBOu\nJV8bKySF4OPGM7o+5vL9JXLm6ZPh+ZZ58BpSXqDW+/mNU3nfFzL+pe9J2/9GhQHPHqz+VirQtULk\nKdi6EhEjKKVSpEoD2xg55joS+tohJ6S1N+CVoRqGU4RE8xUQEdA8IWPOWX4Q78smiRYwU8S3TCil\nQJRD3jzBUmvTtJxONUrkUJiBf5/XzlDa6CPTTnT43EasubS+A/kG54LMiSjJnlyPNj/H3SOJFkim\nHmroZIZ3UYfVuvOmH64UNn4/fKfVJz2QGB3ijNbDcv0d0dwyJ0sPavd3KrrTmmstphgJpHo4terX\nADUKoGMQoVLfBffpnKhA5+gYf3ekRRFNFV4vIkY3SDTTRL8vkQQQL4ZIigqA/gyloM/nGNnGUGfm\nFbqMjCZpITs11anp1NflPWR07CtkvrIY2hYJKHeQDvdncq01t4/sWV9z/xo88xj99RLtOxWo5ygr\nC3tyRE2qVztZ1wrpr0Cn/HK9KK9U4XiGulZX6SRf8/ebqNuoQrPu6aRk4ns4336ktPYGvBJUbnDC\n7B7mRTpCjiyJHVrze7ftHbCFuY0azjsZ2axluFmtNag2Rc23Z5Omf4MLDHPUqbf1d2qCKgyp934L\nIVkhIQOuRU6hObJ2Vta7SN/11NSXENueVbjQPjh6EB3uZ8iIBOfDhcgl6mJ+Pgb8P/NOqBmwladE\nx17RMRduPCrASQ8FrouWMAwkLVfHVQUN7okl0iEYORP72Pi1xxPn/67NnSKJLqCosB2F4mo0CwX3\nK51v91DFR0jo0kfBPcvh+i7qMHJfX6z4/Y61TYXOGzYXmqdIC/LdQZlDRHnYCcp93VonRA5ba5jC\n6hOMIyHLzndaeyNqj64fFQIoQGtyxL6pJAsffK5eMZj93gAAIABJREFUK22/vZYZkaYkFWIUYVSH\n+7G6a6+dU6zT2hvwStB4tE2kIU/N9MqDWr3QVSMlLE7UwjUK3dRPkRhdawNFECE3hWcEVfRHoW4y\nTkWNIvoTSiEn2vw7qA+9edDHFvmzLiy4sKZ2ZjKv1rWbKBm4Uw85miP2x1ByiL9FK9SmuHuoc6Z8\niXRA537kcW5lU91vfHOOHFrN+e8lzFOT1x5Kh2WGCXPNjM2tmgMwvPf2yDOPkde97gf1xVITzymS\nM7MqB3mtlPcCFHTaCMjJ8H1H3iKhznN7uA/H2Frw9fgHe5/nKlIk6M7QTqbCfwu1Ey8w7gzfcgz2\nfl5ECv09nvDOPbR9Pti3LxALRPS32kMOWabJNnLyJqri6EVLQHGfuez4XgoMippHCTypXERniTqo\ntwTMy/Ku19Ip1mntDXglqCW1ZjSAcOuqWFjT3ssNANkAt1ELFVzAylBOkbSpXeTU6q1cK6pFqwa+\nQGJY7tDlFWkXSIfUZ6jNGEDMfA7gB2bZf9dq/9R4T0QrtKM7lCJfmzKRWqnVHCALhAco05rr4UIT\nksLbpAP0hbfWeLWI4bOqqenv/zHox5S8OrOhre6TQEFNM8ZOjbxRZ1WurQglVCLyRSb/C5QIwScj\n37wm/Tm19/ZMPPRFKfdtnTflBmooX+eRwhEFsWMkIS0Sxs4z71Pu/Vf4IVtq3I7SOqL5fvBN7m1f\nFzQ9KYLTaiOR0Af2fMt/zNd49N6vgrHnvGkBUq5fF3jYb/7m6EXPxEPBRN/lkTzkt47U3rTv1Kb/\nkj8pysM2qvL4WmaNjWjtDXhlqK+JEgXpJwSq3xlB9ZEW5DbPHSTNhAdpP0Q5dv7SEDj3mVBn3JZW\nQ8GJuUZ2UWuL15APTIdG30Id1hsxLydnFAjG0OkuEiOOzFTvok40p0yQ9u1j1OnoPw3eSbNZywn2\nvOQICjVFNZXcQ12YLUL6orXEtUtBq84Tku47PkebT5HX7kXEaNLZMPYM/aWvkIZ1r4a/1eTXEoSj\nKCxFUCIBBdja+iv4gRFnntW96ho1TXot86/P59RxXEy4X4WO2mEyRnr5biogGrl1DdmRm2jrHNl8\notlmV0j7e2VtafWV5QD2Ue9ZCnn8XivDbNT3A0TJ1WqUUE3aamKJ0YgSXaVJrI241GNOxNmV10vV\nN2veTZTHlYPzofSvOK29Aa88tRZWfK97jHu2w+ysdT7/FT+M2kJS7Jg7HzbfbcROYG4KWCHnGqEm\n4s6ljgQpNKqoTCvJm0fPKLlz5P+MXDMnup+bWouV0TdEfWX0/ugdLhh9iFoQuYeUsOrqMJY7SAes\nPvdtp60kmjqYCI6p5RkhoD4SK7mXBzkP1lhordcQwnvyvT6/vbHiPmDuEb3XNUFt2z/Z+87k9yVS\ntFdLWI4jInL7vTK1jtFbSAfkr0HhLF1nH7yaLAV6omy+D/VgO0YW3OfIZrje3K/QduQ+Gq59bWNV\nm1Hz/r089O9Y+nA8zCmTkLGvenhfQBLsdR+7g7v+tkBcAVnn6eLwTT/sT5DXcOTz1tuX5JsUbtTE\nOUNZXHBqYk0V7NT0q+8ay63imYJppue4jxcYrM8JF3RqZPQ1orU34JWnqU5LtSbrjqisVEkn1Vl3\n8fUXtMKN5Ttq2JLIT42e5GcuIDFEGGMguqDhrfq7+tLo9U9Rmphg9BjtlOL6bf59ggypt7Q5DN+8\nhTIHhdMZEkOakn6bYbrsu/scUGO8itIUtN95J5B9QOjs66nlKRy6o/ECtWOnrpMHUHQk/aaCXWv+\nyZhbbT5D8g9gqQJqpi0fF64Nzc45RfhZIvlcLIfx+QalJkxBojxA0m8qKC2QygnMZH1rRdwLtsd8\njJk7R0PV3e+BpkSib7eQhSEPzVUzDdcNUTM37d1GWnMfoHYIbeU1ohAeOaJSWImc47nHniJnK32M\ncr2wZATn/Sr6fkYUvD9DLKitkFCcU7n/K8T5glzJ0vTvauKmuSpyoma/xyJ4tO5ObLKuebQLzB4R\n52kjroA5lVDxeiLVNCMqb31t0ZS1N+C1oClOS/WCZ44KhcI1oVJcgbNEYWbIGnUpjNQCkdpd1alL\nNRkMi3/HvsFNP6b5OXFjtyJWVog1rmgz/87u+RK1TZj/8oByJ9cVcl2fXrtZOfZttJGDZ0i2eK12\n/Ci4LxLeeBgukfxuem1ptfUIZej3HBmNcuan6IGiBlGpAR6MNBm5oBEhSby+i9j3ISIKWucxeei3\n1CR1EVlYu4ucOI/9OLDn/TD32kt/1+gD16ubVnWP7CPu9yFKgcl9Zco06rltavZwB1ualPftmd+P\ntKU1pn6A6+8fSpspKFPoORrm/grKZIHPO7dRYjotq8F51qikKGeIo2pcd1zrJ4j2SzmO7Xdj0rlA\nIeIIcYBDlNYhRmdKk+zhudvzCtLaG/DakKYIj3/XBa8ha5cQw8+QxaeFvCIJmt7rPX8U1Syy3bXO\nx6HC0R2Uqb6p/UTtjIiafkuw4aHmjsL6O5A1ZjfDRJElc5R29F7Ctx79j4jDvPUeb7Mz1og0AmLK\n4REdFvy2QtW/lPctkVAqHloeBfMh4oiaOepcOZ787uEwvlG48EOU0LrnztA+jUWBnYc+RX0I0dnZ\n5/6PKBESrg99n+6TSDhTNIUwu+61qG9LuXeG0o+Dmjx5wU9QIjEUtiNB90P0fRnGosl8XqLItWeo\nk/D9o43rInjuPN+NKnm37j1DWQ8nCsGlOecDex/9o46DOffCnkTJomCDGOEuhXs+p6kL9JtHiP1M\ncltKhTTi6X3k/hWntTfgtaBIQ03XI1TDPbyjqAHVjg5Qaul6j+YwgL1TN9R+9c3cnl6tkSgPg2uU\nPeFjB3WUgN9zC4mR/KZzX4u+Q8wUqW3Roe8M/UqoEek7qDHfRT8/i8LiUV//AX2hxKH+1v/5tzqj\nUhjT+xjq6YJcC7WZI61PHdMlckpzHZOrqAUDIBeO6wmGZ0jo0xRHyCnz1BIMozHTcGIPG/43lPuE\nJteWXwUFLQoTFE6YMM1TB9xDnZaffglUNNRhVQXQVir6bJICXBHSfR8J15FSQMd2XQNzJEVCzWC/\neI65atGn9r3We309HaD25ZghodMqACqPWiAJdc631KE6dizPwpCub/UZdF8l/uZmdf67J8/WCEqM\ngruQ9FqHG6+9Aa88pUXkFV6vB4srSj3PyBZNznM6MAP1dm8xx4Pgd4evNVQ4S9uJvNop38PwS08+\nxSyVZMQ7QzsjSJabrJfcai6bUg9/ogsvqmE/D3IStTF73af+uvZIYkKy6D2st9LyywDS4UDGd4z6\nUKKwoN9+hFwt9TLqQ6eVnTUiFS4itMp9l+6gThy4QDognmfcl43x+y9Ie2IXyeFYBYbeGmm1gXPq\nwjnNItybUaboiCik+MFOAfzS0HZfD/Q1UuSrtXZ6ZslfBjxJD9KVUG/8yVMWKAV6d2jm/PeE/vPM\nvwv2J8HzXyHtj0P7BgVO+iC1siOrYOCm2MdQ5Hu8snArPb1/V0045L+agsCVxZx1ttWOKe4ErxGt\nvQGvPNV26lOMR09wMaqTEz3pZ8F7lcGoeWiGMhQwdt5qw5W06c6tD3Pk6qRz1L4eWvjuLdT1Wj5B\nCfVHvhlOZ0iHzw0krb8XDeBEpqOp91fD31Oeb72TqcQjzcrDBxdIh1DPVMdD4yT4/T5qyNo1/Aeo\nE4KxnVwPUeKtKX11je6GzTudob1POyht+XtBG6fSd43n+N6ePd/vJyLha48HmkfHKBrCrLF6kFBw\noWAxt2dbkSfMKv1ru/4MSXjU9ASfo9bsSeqkforIqTfvt2xqHs867P2P+vAeYodhf17X0nnnXkti\nfIR4Hz1B4osU6vgdzk/UtqgtPh7X0K9QXwYc9NPTO4LpCRNrZRHNs2VaAMZrTGtvwCtP5SK6jzoC\nQJGSlq14ifJQd+c45ohg1IDH0JdSde3kyEM1RXHUxa1+ZZvWmZR77mslT2eAmgRtDAVyIrwZZeyk\nsLSHlCxqYb/RT0ed4HrZT5WWwzejLJX0y3DEaY6kHWt2Uq/++yekQ8gdGf2w+jeUcPEMieldRWkr\nnw/XIxRmhbw+IoFwhVgz9b6qn4QnBVQmTLThAkpY+x5ie/sU8gKLPkeRSTOiQ2RhfIbShBL5FBwN\n46zrVjMrU/h7W/5V5+kVklAWISi7yPuvhTiskMwORFGXaAtgCyTz2DaSM+9F2fNXUIeZq/mgt/6Z\nXZZj8qx4T/oG16VXGaaQ3Hq3o3j/bu15Zv/v8QsKJ4fIUWNaqNMRjMgMeYKyJEYdDRP7tqipRROv\nqcnnGBFCgurMmIaCvGGIidPaG/BaULSIspCwg3gDzFD7MzAigZuBZpSpC5kHi8K6j1ALEOrTEmWE\njYQDQr+Ee2co7fNuBmBYIBrUYkBnqCOLeH92CMw5NlzLiezvpDlibZICjsPwpEcoiw3ym66FnyBO\nKMYDne282Og/DzR1QP0D6uiJlu8GhbTo3TTf3AzGgFD5w6EPFD6uoQyhPkDW9B8Pz/ihHJlpovac\n1yfoGH3/H4Yf5yiYcm+w2vIHKA9cJupTwVNNtsm5tX6fhjQrukMfFO4Jj7aIhLAVzueD9QxllB8F\nCxcS/nHoWysSjfQEOafRBSRh5XMoglge0gfD2uB8PEUs3K+G+1SApbnqZPjt06DdfPYMCcnleldT\nF9esRvfMkQQO+kzRV+qpvZco9H4w95FA4Wg495kKuxRQvEzIGylYfF+09ga8ltQO9VOb4zbiw/I7\n27D7o4u8/t4YpKuHTgRNOzM7HjayClueYG2BJFi0whSnkgpNUZTJFbS1HApobyNGb/zwUdIQy2i8\nVIC7Jd+MbOKtvpG5/b5xH81j0fXeeAGEk2sBhQcKM3WqtkdzRSt5mCbLU/ONhyYf2TNR5eHnWQuk\nb5GcMhVBYfuXKOv9tPK46CE1R/b3oRasZtLaZFu+a1+eoyOtas0acaPmIeYJieaQh6r/9hh1DiJf\nU+p4H9HJyByobwTDeHXP3ETNJ9x35tvgvYwmW8rf+vs15IzWvfnfR1JOXNDwPnyCLDQ+RFrXPTSG\nJkqdnyilgyJL6pvUipisM8Wi4tfbzd839GdaewNeS+qHg81QIx2YwIDOk2Olt+mJoGh7PBuq5yAh\n/B2hEvreKQ6FU4iMI2LMZyAakPvvApqGaOo4PBzGKuqHhu0uUPpVeGG/L5G1cA9DVrRDn6GpIHI2\n1LBudZj29qnfAYUtnXfmxFFfjV2UQuNnwzgsh/9/gjqEtDcvnmTsPsoDeizHzNjvETkaxfwbzHnS\n14LbkWR8L/2HaFY7sD6n/Zdo337z4ptR2Yhslq39F9zPx9cZHa8jR1l1EI3Wu455C3Vr8Qtdm4p+\naN/Pk8eGQphe6wle/qwL7o+RUzbw38g5NuoLr3GuauQtNuswrwrXGpHXGbw0Apq8Og6e2FBIa2/A\na0m1/8kVWcia2+CqMKDo4D9DWRWTwk2r3oYKHTsozS+fIcGwhPJ3kZEI9d2IGJNqU+osCHuG90xl\nXGSQeo19dfOJk4YFbqOt3Tk9QRx6S/8WH8MoX0j+foZ3KZyp8KFjsER2mNS1UfsVJSHl/wjWgs7D\ndZSana4TokcL5Iy0vXl4ilKgOkXN/Ofybo04o3+OHtK9nBbnNe1Ea8bXal2ALWupFxA7Jev7KPTw\n/3eRzVk6rr4m9+3aEnXq909Ro36av8jXIdvwBcroOPdTeQI1/9aO9/rOb4JrfOcN1D5f5E9uDuR6\nUjToPOjYbWQUpGVubc2Rmj4ZZci08b3U+C2ki4ivCizqW+dK39s2fyqAupJyC62CfmMRQhsqaO0N\neC2p7X/i2rMfOsqsnqKuanwfLcm77QfD0DVnrhm6jj30F6ijd1QbvIDsl3KI8nD34ntO7PseksOf\nXmfl2DHnvoUwjRlq7a6XoOo/Bu+todnx8u9ezZQCQyuaYLzOUu53yy4f+TJ9bOvEIf/zHCIrpCgK\nFZxcgJpBI87SNXdQfoxcNqAnaK5w/jYeoY7iuIk4Ss3XgWvY0ThTM/acRWoO2EdZn0URFApLHqob\nhf9H6NUStU/HCuVBzPaUySHznqd5Q300HGFZDfdetG+9i7S/b6L0V+uhQVPmkH1guQlFZvz/+gz9\nYHytq4DqplYVTFrROS5YXLJxjCNo6iADr7mj49VTJqPgiY35R2jtDXjtqO9/Qg1HDzDdTFeQNAV6\n1Oti9gP4fJJ3epczPa2YOZP2cfPopo+cBSN7/FtyfY64EJ8WRlSfCIdZo7wepLtoCxI9BAUow5HZ\nt5bQ1xM4WsXZNHOkI1D9eWs7uQJJgHWt2cPFowyopDPEfg7zSeMxvr7oN3SM0u/gd50+6XhGf69Q\nmxwZ0ca1qigHD86WgKyZfOl3tJQxWCE7FPthQmVj3353n41LqE1hy2Luy7ljyLqmrncB8x4Sf2Cf\ntTBkQrLq+XAB61eoM9i+hYTyaFsfo4wG2oUe9OU3OCZ3kRx9p0T3KNLoptXb9vd7yL5VGpXoY+6I\nce0sXe5P9cci/xpX+sq5czO584msRMVtcF+WjfnHaO0NeO1o3P+EC5lMdQ+tSJ/0Pmc0wBTH2bht\nnvHWq5eW2n0paNQmpn5FZTLyd1AeLr9FqX28jVLQafnpuMnkBGU6ac3keRWxFktaIUeraOjpBWxt\n/SWy2YLlBbTmR1l1Oh5nhnzyoNbIH2W2EYLiPgoPhmcXcMEhru/EMXEhkX0/RQrT5rUlsqbsiN7N\nZjvrds/knc9QzhWFUgpIY6jJHMmBkoIIw37zQZLnx1GFS0Nf+K6WSYmHIWvHcE3wOyqEuO8B162O\nv6KCl5FQCVUqMoJSzx2fpU+NZqalgzMFqSPEGZq/Rk7Yp+atJ/INrltNWeCh8UAtVNywta084AKS\nYPIFal8Xhi/7PHN8iRrTSVv9x5xnOoqjAirv87IcGjLPfxl9RR+muoK797PuM9eeozOumPR4RMQ7\nW/z0jUVU1t6A145i6ToqoEam5I6TtZZdvlMZ5/kXrsLz48nktqX9Klx5KuYMg9bvVPhzhUjL6dcN\nuoik4f0cKZQUKBmgClaqldxBP3QzV4xN/dXQ32coQ0X3bBzGPPQjDY9jXqe0Lp9XIfIUCcJX01+e\np7aG72Pi46B1ezgvUci7Hwr1estzfrMz1hEtsLX1F4ijtQAW16sF3pldu4OygrH7U3Cf0a9GHY0d\nZfEQaU2ep3mJorB2Cq5UPPgvk+u10AePENOkey1TChPKReYrzesROazrwReZUCN/ODWx+N6MTKlE\nvFZIa/cKci4lrid99glyOoQHyIU6ubbcD0ZNu3QMdxT1WPqvcxIha6Vja72+dF/N4EpdPa+eEbbm\n1THv1HDlO6PfegNo7Q14LakPDTpT4CHej50vkY3ngwJjTaC2h8aHgmv29L/ITKJ+JzWilhOpRiGo\nmUeFFTVJ6P/1moZu67Ot+iUATVb5APD6NO5/0zLnuJYVOffSmdRNViUEnN7hphlHjkr0LK8LdwCk\nhryPUlgicnaA9tjAvqnmSmWmPLSJRLkTo5v3lPblPVHm2SVqrZJz5vPMg6iV5I/P/iPiAwr2Lr12\niFLo9YPHUZze+lShXzV5Cjc69rflO1FFXvqBeSTMSt7la4f9uYKEwPhY0Nwc9eES6gimx40+e20d\nrn8e3DMkpLI3D17QsRTqax7Iw5yozBed90d0XfaUrzlFfOtaahE/KNdHDx33BJsqoJy/gvJrRmtv\nwBtH7cyrJfOrn9PDsI18tL/rWkFUbZMCgoZtAjmhkQooLGlfC0qlpkWN6BJyCKc661FAY1G/z4Y2\nzNFm+kDWgFW7V0ibJhHe75qhOjRGPia1gJIZjmfoVS1L/6/vPEB2OOQ7SwSl7ZTLgyMJi3k+tS0e\nKr6HWgj5I7L56l7wnRZpAr45srOoo0S7SH4Onw+/fYPkixGFx34CJk2L+z1HWjd+QO2hjiTytnmE\nmY5LT2haDX3wRG1ukvSD5xDZt0PXZ4S2qCbvyIm3RZOkqe9IXjdxNfJD1GuavjyKDPbGgv1lH1zw\nftR49ukwPx6ddEPWLfdcL6Lra5RrfUqdmovDc5EQyv4q2lVny838i+vrKXIAACMvyZ+U57UEJt8j\nbV4d51OJHXXfEFp7A944KhGGr9ETNEqNq6UtxOHH5QEWmZcUvXAv9GPUuSDUwZd5O/YRtT+uT/QH\nZMZ4hDLKIILax8Jj1W6vzosu/On9/g49fHpQN5muHpSK9KgwxLG6hBLB8b58jdixMXKKforaObbV\nlqhvOo872Nr6nzA93HeB5EdEhO8AZfp9Ck8UzKKD8aAx/pwjZk/2Z+fDuLtwfAPluqM/wx5SGYGe\nYBsJA/rbzvC9A3mnHkjRwQOkA9nRseuID9SppIJxz5Hc9+4M9fpjvx2J+RRxQUnOi6O2RJl8DfwS\nuTL5W6gFp51Ge/8r2hF3hyjXfA/9vYoYYdX52EFppi3rn6X3Et1xoZdKVGmezm3xMhgabcQxUsHy\nPGafTar7Db1EKhGGJ4gk5NrMoofhJVm4NYoRa50RYyXDiwQEapK+WRzi3EesTfTq4CwwXgywByF7\nng0VDlz7hd2rf58ia0dPkCMKFqijpt619y2l7608HGMoRWmuyWMXFaujaSOyy3MexxCUI/TTxUfE\n8eVB7QfzKRID7+WtORvGrzWf9PW4hDrS7DHqujfMWEzBaDa0QU1MPZTkuHFdhV06k3rkTkvQcKHS\nnWK557nWIoEyalNk0nrb3ksBlT5dVE4+H5lXKhon9ts3cOG5XJs+1/SJIZ+iqY1KiB7mUXXz1lzR\npBebSTKy0grLV16RC/fVfeK+UuSECFhL8F6gDgpQ/ybnIRSQIoWzbfZ5w2ntDXgjqWY416sFGdvZ\nI4jX73sXtRlJNTHmSFCGD3n3CulgVcZM/4nLwojm8lvkbxOl9CYxYZxeYzvIGFoObUAZtkpthsKB\nts8PojOkUgL8m8Leh8Z8HqNkwDyc3BZ+AdlJz32EbmI8a2ob8q01RHfUcwH0Axkv90Gh4PbTkfb0\nqIU2qdmD7XV/HiAJrK2DSNG3C6g14SNkgYTwfBlNlTRYfcaF2Plw/yNsbf190IavkYRy3UuaqEz7\nuW/vprBa+srUc6n7yZOE/dbaQ2fZyHkyMivwvVcQC5IRqaKi1xeo/WYivwrlAdGYUEheIPGcXyNF\nZ01dczSvuFLVSqjm61XXHAXbjDbXZpn37R1/h9rczXdxbnrIGPed7+EYed5QRWtvwBtJEZSXr/vm\nIRO4CmeW9bvmyBqMw7uaVCxyIFshF1wjU+G3CNFT66JpJtJotP1RhMYjpIPAHVh53xLJj8E3PX1O\n7qJEJuZIhxO1+BlykrwryDZ39vEL5APwFLHmr0LPAcrwzUvDu9Wfxh1Hx6r5cq7KRE3xYRCFuH6M\n7HR4DTl1vabMj/yBWjV3eu3UuXe/Go7hBWtvVAzR18G/IfsLeBKzX9i9S6TD5TfBeyk4XECpwXKe\nD5HW208m9P0IZR6gOGS0FPzoO+Zm15bjtJpL2Zdj1FlZH6A0IUQRdG5WcFOa+99MnfeoQKBHsOwh\n52vqCQmRIuKlI1aoE7RheKcWB4zmQvmflkCgz1v0HfbH5+UWylB5Ir2KBi/BZJL19z3zsipw/q0a\neY54wBtOa2/AG0sO5cXMgNqQ2vi5uGeymC8ag6DdlJoUczO8hRhiddIN5H4d0b3MPHmAmonSAXeB\nxIhPkMMJW0xToXZeWyGFpUbRB0A+nD3MM0onrtTSfo4R5acpzWe8dznc20rqxu9oAbkbyI7BR4hy\n0pRrhUxQHfs8zJN+Bi2ETQ+sHi2RHGoXmCbQqPmD3/X8N5FJj38/RVqXaobU+zS5mn+bh2kU6XJ/\nGKO9CX1ge+inUEdF9fZvvkZ/BZ3PE5QhtbvWR6JgKrQrYqNrngKOOty29ukptrb+Jrg+NveXgrWz\nRBmtpGuNZqaIN0R1pVp85Du7RoGYioXuH4+eiTIe93gdx5EIjfKLT4L54dp6Ak/zUH9fzV1RSHqZ\nfqLe5zUPeENp7Q1446glIce5QNwDfAelnZeHp1fofYCMJnhukF7oLZDRA0r+FDwUQXFtwe2tKyRm\npsmcPkGdx6RFNFHctusnyIfmVI0w0uKmEAUvh/y9PomOmQsCK2SB4hTlIfWOveORfStymPbspH/X\nabvmiph6SJC+RVtwa33PhdMZsjb6FOlQ/qgzb2coMwD3fEh8TVxGuy5Mz7QUEas+K3ryEJFPhlM5\n1hpd5Gs7Epjpo+DmU4/OisJPPceOjhXRzqivUUI9RyfUlLgfjCXNx1F49xLTikO2Mhzr2Gj+pANE\n/iT1fPSyMp8i8Vz/LpGUVntcQIxyoTgvV7S7l0Mpfu4NprU34I2inoRcStjquLqS+72SpmpVmtzr\n7oRnekSbumqBB0gMlH4X/Ld1kDFKqFWdt0ePkP1enIG2nnEHNQpQWieo1dZIOycqoPCxCmn+DBkn\nYX9q0tE3V9ja+k92TbNw1qnL0xrRA/AJEkPzeXezYc9G3hqLK2jX0HHGzbWhhygL0OkaZpZVd9yN\nvu//VwTFv893t4TW81RPXiFn/43MDRdH9rf7wfwx+EZrPahgx7E/sPYTqdMcKoqOEsFxtIpC0dK+\nP0eK4mGfo4q+it609t8usjBDBcL3jCtR5yENc6fQ5Wa0yEwyQx3+rWPiOWSIpPT8d/ZxvsSavbxW\nUbvf6LBip7U34I2iOM7dfQ48XbKmYtcFrP4EhPuvoy49r7H0aiY6RBmuGdH9xrvcJu3MSFEf1/oj\nDa/FQG6i1DZbTMOFrofDeJDR7yGhMa3kTUskX44H0GiIPCcewcND0Z1BdxEnXoravUTpyHlk38gh\nluUauoAU0snQXCJozG/CqAdtw37wfacVEsRO4W45tOkENUKm9CvUtn4y+kiI+3/sXg99bdFi4r0u\nsExFT3zt8j16zxyuuZdQvwuQXjU7eidQ+vGtxF/XAAAgAElEQVS0THLkBSoEsH6P+4K5kzz9ynz8\nqLDofn0Xtf9JVGhQiWYPFa7cQfVn6BfwZDuPUUaaEblxx1/15XGzMq/toay1pN/y/bZCylYdmclO\nUJvWpwgg5V4sf9tE8UygtTfgjaJyYdepydM9yqBatu9L6NedaMfSl/93jc9rabgzV+TsR4dUOr7q\nwUsmrUx7d6BDTD9wmKb8pPF7ZHL5BCWjb32L2hgh8uXwnZRELI+5Qt3Re1bVXKVno8J1ymT/ahg/\nt+Pn95UaYSvjroc8euI8Rzm8D2pi8vFp5aThwdSD0n3co6Rt+vfYIdYTavk8x2eqac+FKJpDNaqH\ndD3Yz+prMIPm1kh/q3mCyJ6HXF8P3qnteoA4okT3qpoSekJpC4nSoou+113gqMel9lnR9vdCv/nO\nXcRO61w3x6irpmubyI/0mvoRncn/aU6DXNNISReEIn+RKSUvIiFkY8qZSGtvwBtH7ciMKCqnJZ07\nbK/puGMHrLgtqvHRT8AzJeZ3lW1jXgzVuJ0B8eB0pq2HdoSowGgxPB+Fya6QBIrI/k0/gBZjfIQs\nHGhEBMkjVOh4HLW5Vz1VTXdsq8L6FEBcYFTofImyCvPK5slDHkvGV475EvUBeQ2xgyrf9ciufYry\nEKZA4D5KjIaJ1scKNcz+WOaOpssFynwW1xALMl9K++eNe3TOonVxgDpj6TN57vIwT7NgvEtENB57\noor63mfQej1pLl04mgfXtD+elXiG2MQElBWEdb+4Iy7X3RFKwdLD8E9RIws6776XtXCkXievaJmE\nKcRQEHHk7jZqoUXNrh5kQMSH11S44tqhA/d5a5719uLGlDOR1t6AN5Z6i3SadK6atJt1pkvkWXhQ\nf5Oo5ghh7AjBIVGzipPP5e+ppnJiDCWqLcJIgT27Tuppyw8QJ+biOzyrrd9zH+Vh5bbwz5FNQ9E8\nsiIymaqiY/QnoHBZpwdvoxMr5IiTKOQxMeF4vXmOmZW0JfKN+T3qZGk79l6amph91AVb5t/Rd98b\nxrRl4ntveI/nDIl8e4h86fPux/UnJAdgRpHRTKqOzJ7ddzsYK95LM1sbEc1rngchUYp9a58ieZdR\n76+HaDu458ibsu1RThkgHbqfoRQE/QCng260L1Q45pwrf+C8z5CQTJ27/4Ds83IPWYCIhOzIJKbK\nmAvNNPV4Ej9tDwURRbzoU6d7x9vgYebvoye4jAkhG1POJFp7A95oet5FWttZr8C1g/r+WrMrf/ec\nCo7oLFCGk7oGRSbHnBCtYokKqy6RNCL2RZnpM6SEbDsB4wKy0x/bywPA8ynMh3c8r5OejoUfNN5m\nHzdP7KbmNzJSNYGo1v8UffPJvJrnso15vsrfPAU3kA4rMv1j1Jo926Gpvo+Q1l2UVbS2u6fvv2/f\nvYW07iLhUsfMD+td5DXpz+jfui53gvc8QBJ+xvzCWuYS1jaagohSgNN7OE86/5Hpc44a8eFzNXpS\nzjeFczVbqE9RLqNQr52WOUmFYzU7tpLIKfrlodS3kcOyt1HvkR17RgXP1n69iaiuWbvWjSPPbIML\npuRt6iOzV32n5HcbIeQFaO0N2FBA4wKFm0goqBzCNbjYTu6ICH+PEn25YMCDybUtbuyp7WbbKWBF\nWrGbQfSgoPambdCoImrN7PMFjNf3UfoGKvCVQqFGFSillO153NxRUUsUeFgmGTxzo2iJ+wjyPkNk\nUqjnaz+YZz/I/8WeOUHyjaHjLft9jLqI4glqDfsMSTvWg4dzoFFHn6P0WWIyPnfajNCeKOw6GqNP\n0E8mdoyMBni2TzVhUTD1GkZcH5pdteVTpoI008HvyHNuPqT/j6/ph0gOnbvIyNeYMqBCie+B60Fb\nF8joht//hfSvVeU8Gm8XLubynCZQU0FhG2V26DuofbXolK0IVQu1UFTDhUoiltwvWqOMAsoH1qcl\n+gUA+7x8Q11aewM2ZNRzrsq/Rw6buvlVgxvTGqJwUIcz/QCiQJQySb5Yu8lgnPGQFtIXPeB4mKlT\n5FWUmUA1u6w6wD6Vb/v3SD9DCQe7bdvhZYXpNZpAn9FxdcZO5lhq4bGTLZAOCULZLpC6IPcu2s6H\nEXGdXEbK6tobp7FxZNi3CtA9LfghSkdIN+0BKZ/ObZR+HK12qBDMtRH5K+0jruLtWX23kcxEOlZc\nJ6VptFz3XOMzlLmJ9ED2NXbL2n0Pyc+G334ia8DRMhcQ7iOe/1OUgpiaXz9HbPZk8cztoM03UQvW\nXtdmjnr/6HhGDt9uqtEklEQ2vDQBy1Bo0VQPGFCzZ+QbpjmkoirNh3KvKws+9xsh5Zy09gZsyGjM\nw7v2lD9CdlrlwZvLh49rDZF/xgJZE7qMODRShZkZWiaiuN0LYTCqLbsTqh/qLS1Y28TDS23oHoEw\nBUVR6H+Bra3/Zu/4XeM5h/frei75N2V+kRZOwUq/+yck04SbhvS9zECsGuUBYqfFiHjvmGCi4/4i\nQoyPH6tB81BprcFWMrTo2zwkokR7+l0X7nRc1V+I5iM1hUTrPhJQeuZUvl9DihlR5IUUYeNygHxY\ner0cD3kmPUJ5GDuC0xrTb1CH8mrIcyuZHKP+Pm28l4hfzAdz3xxpdAWIbdH0B7U5Jj13w8ZxYd8j\nmuOmvsfIKGMUPRejSxuaTGtvwIaMaoGiNJvUG5EaRDt5UFtr2DcmpOgGmWmUx2Nl/9donhLijvul\nHv4akkxTCuvdtLRR/Vak4dFHoqVRz4Pr/I1Mj3boCKZmzY9oTDwVttrUIydaZuHUw+gSaibdIi8q\nxzbvIRVn0+cPUDqcRv0/QImqTSGiWHQ4jsYs+qb7C7mvjmrPrXT1NPP1wpNVkNM6ODzI8tyU5hxH\nw1QoXGBr6x+RMgLXpp08xx7BQ4GmV8U88mlp+VDpWl6h9M9Rn7BWhBZNF26SBJLw0tor/k31bVKk\nVvmY51Vx9OsAbcWKwo3X92L7PUqt3deaL7kwXlc+rvcikcBIGHtb5n4joLwArb0BGwqolNpbknmp\nldcbug0nlgfjnm0it/8rWqMF/SJEYgEtpFV+j4e1M1/AN3a/3eoPwcy2Y5oliYKLM685SidfHkq7\nSEXt9N7/K2i7joEegqo1R3kULst9LTSklehN+8lsojqubJPntdlBRtp0Tvn3pc53HSlZoQw5Zd/V\nb2SBVC36IbIgQQTtt6gPG5rlfDwj5IORNF6hm+86QUqvryajC0jOugxXbc2N13RxZEEP18+h5s56\nvXLcPHfNdflGaSKoFYmWoOrXH6DcsxQ+dF1EY34FaU+xrfPhmbvIPlenqB14WwoKBQqOcRTGr0LK\nYmgH+YTyizEB6zbK5Jas5RUpES6gRE7oLSSM89FKYFny3hol3Zh4zklrb8CGOtSHOVsbohU9EzE/\nQv8fyWZWXwrV/tV+vGfMrLbfpu/MkJzKjlA76artl0y4X18jzv+iNmkVmvaQbPbOTBk1xPayUN+U\nDLCroQ1PUI4V4XjOR51Aqp4PMtwIQVCbtvsIRQeVmjDIEFXgIcoQaXvqc0BfjcvDmNAMR5+RU7n3\nKyR/CD1kFD3SfDkUiChQqJDk/d9BiZY8Rfaz4FqZo1xvEeKzQi4wx+q2WnYhm0HLPcKDVcfBs8H+\nU/Ct0nerXq88gKMkimo6ivaz7kOOl/p1qJnW59Sjx4j+0QRCE43PgyJFGrHjma6PUa6n91Ajgo56\nao4c5Skq6Ci/aCGJzKTr++hA2qqRZ2oO2h7+jbIgt/JPRfOh8+g8RIWsjXDyHLT2BmyoQz1UJMfv\njx3qKozcQa1pA6XjKJAObXWcu4lcbXYHuTCcMjFFV6JwPKAWsuLKn/2+uAf/DWEQpWkovfux3X/J\n7i0jINJvUejrt0iH6xWUGuh95EOZSJZDuzfRPriUsS6kfTpn6vh7aWjHr5Dzt7gJ45q1fRuxiU8j\nSSgYRNr+CuOZQFvz+77dcx11QrqvUa5PHXtNKjYf+u2oj2Zq1bnWb+wE3/07lAKV+izwHW7ioJAV\nRVaVwmi0f2Nzq8/hx4jRGC9eeR21WWof6dCNENbo+ZYTttI9xKZJNR+pwKH9UXMLv5kP7fyuyEGe\nKO4MtYlvH2WpjpU993ajrZ53SE1nmZ9k3veTai7K9d0SZNoBAxuaTGtvwIZGKNoI5QaokYdSQ4jg\nXS/t7rDvYmCSWk2V0KkLCDxY9HC7g/pgAjQqIrc1Rona4xHB7S2fF3dqy/Vt4qRNakJStIAaWV/o\nKr/N90S1UvRAYQE9MngXICl0tLQzmpP0EPxLa+Mvg/Z5JElUv8UziHLOfV4134gLfDpmp8Oa0mis\nJ8PfO8Oa8TWn6JSuM22PCsrHyKiPtvFGY/6eoJ9C3okHPk2LkbnE0cpWTRbfm7VPVj1vPYWF61nX\nVJRywAWmMTNi3a+YR7mJ0QXsFjLhCAnXkya1+4W16RFK4YgITPydNmqpdPzneSqjkLhG4/73+zPO\n0zbUpLU3YEPPQfVhkg/+WnqP7LcrpDBa/VtNNppZ05/Tv0+Rc1K434DC+ICiMrmdPGSn+c7k56IE\nZ72oIYBJtdJvM5SaEw8dt0efoXTcc6ErgvW1X66x8qAqc23UAkPM1GtzwB7yoa4CzAWUuUUuBO2L\nhCAVDE4QZxD9ECVicTh8zwUebbPD7LyPRQ6jw4Bar6IO2uYzZOGAh+Fn2Nr635CEa8+3cWV4L9e5\n9usGShOIIigtE1xkdlBzlJsza226RrM+sfddb6z/yIwbCTst5aXMWZRoFyVapP+nkN5HBOp53EE5\nf1Oyru4jrpTuEUhLZBTG0ZgpwiCM1Fz1eyTUU3+/j7H+x/3ZICgvQGtvwIbOSbHGo5BmLb2nZzzp\nkAokjFq5FDDJb+zvR43vRtrZDIn57yBmzCpETbPTpntpYpoaNeRJoBxZ2Udtmin7mAUjXmceFvW5\naQmHLfi7N28RauKRJKRI22bVY60lpMJNLQSl9t5CjJzQl4N5ZUoTWdtfaht9k83bqE0vrYOZURxc\nt4zAuYN0oOk7dIyIYkWRPlpHhgc3w919rNWJOHJwpq8O++b5Z1pom+b3iH1k6mdKbb5tLnq7uj8S\nmmp/mV1koeQAvT7kNpwfOSgFel/vuk/nKHlW7XQ6XRi8izKfEp22te07MheneL5+bXxPXpDW3oAN\nnZNiTakP4+brd4LNmPwe8vudSb6DUrDZhYdh5menbcrnhUBjpnW9+b3UFw9/dM1Ms7/qGJXCT9lm\nP2QZKRElWuvB3+PzlvsSoTsQuh6MFTVkCmWRvwoPZQ3hdAGIwpiaq9R36A6S30MrD0/LZKOCUftg\nLg8eL3FAP4y/tzZPobSex/eYOxGrkKeZYFXoe4KWINhf4zNoYc14D/QOYTf5zar720pMy1+mRjn7\nQtJ50NAoSpHv1gyy7EtG1up17kJW5JyuwiBrkLX6qPdsEJE10NobsKFzUg0LRzUnWjBwm+GU92Um\nmZEDRquMQ7bn60PEZLfDd7fSuMff4KHswoYyvTEI3DW6KKJJoxT8MHIYPZ63UotsQdTuePu36Jtx\nyPgPETsgMuJmhowW+D1zbG39ZxtzXnfnwrbJLR+cbrLRg+4C/GDOToruI6JJ0igIXbQ20uGVgpUK\nDdSI49DPeq52kUNZIyGP4bTsT2Ta+3606SnCfTm+nh+EZpfpUYD1O8eEJJ/b1h7tCUo1ujqOBM1Q\nCsPnC+2d2v8XncMNTaa1N2BDz0HjG6nNFKa8o75Pc3pM26CZObYKx9XfLxlOdrgsD3C1Vfe0zAhp\nUW2y71wcv/cCsvMwD12tIaSHUR2dNK3PtR9Hum+GDLWzUKEflBSGoppH/n8+EwkvsPs9PJT9aj3j\nyerGfA/0gGEfLqLUhr+w+aRPANfJDAnt+4fhHQyHpWDNXB/tYpbx+uSa8dw/7fk6L5Jw/r3f34/l\nfnFzMItQ9gWJ6YpCT0jqR7LU40SB1BFPF4rouxUJOO4L9+5zjX+//9N47IZemNbegA19jxRv4r6g\nMP5OZwJ1gbq4HefXZGLzlR8CUw4XP6AZCtxmrGMMNXbk5P1uDooEpCl2ew/JHKuIC2kPnTMPUSct\n43geoTTDXEU7oZ3+vUAW8HaQ8uZEzqZ6v9d8itA8P4wo+Oyh7iPNOy4gcZ0QLaETqx9U050c2/PD\n750ve/P3v8fbAkrNAyJB8nrjfhX2xuauL4BNNePmcVKBPir857luDlEqLO6U7M/3c0O1x7Dly3L+\ntbShc9PaG7ChFyTdaHEiM3UqrBMVjb8zMm30N2ftGLloMqj6u67xLRAd2v32qnDkDrIt01ILbuZ7\n3ZHTfVs0K6jPwwO0whTj8XXo3dtGRh45ZwKlps9rS9RoT0/IUCIiouHBPTpEii5qjacegFFNm1Ze\njjPkKA93UNW+0y+Ea2Auv7cPy/aa9ND624j3Rg8t/H407vFaXZFgNkcUvlwLiRr9U3+j3mdTI3P6\nB3kt0C+Q8t1oGw5QI4GXwnaka25mO48y0lNkpgleG/peaO0N2NALUK0tUQuBMPooT4M7zUUCSWSa\n6EcklO2ajqCU33f04xA9J8O6vdpGRyRonmn55zjcrO/1LKRtx7la0KKZpKfNKdzeMgPNpS1k2MxP\no9FVNEF4bghmh12gXasoosWwblr1YPhNojSe+ZVrs6XZ30c5nhECpGuaESbL4X4XaG7b+/Vd+8HY\njkH57wRt0L0Rh1jH6/PFhJTewV/vO47NAZLJLPv4lO3i2lTz3z5KwatGVaYpOud1mud8qTN1hAQl\nAaX9XS+82VdGymffQRZqp9fW2tD3TmtvwIZegGKnUXUC3UOpPa4Q+0zowXEl+D1CU0qfgbptM0Qh\nxvV9zsBVEGBir57PTWSCihAJapBPhz6OOQJGiMoMNZPvObW2HE/Pr3W120azjmuXB8PYaT0UPbx6\n6AlRJ60Ee4T6kHBaIgkHkWnFtfKH9pxqw1HSOBX2ovws+v/dxj2HUL+j2LwROWD6+Jbz+KIa9zQh\naTxars5yrH33iBZv1wOUCsUMpeDFsgcR32BGYpYHON+hXY51K8rMfaWOOuOl7VLnZfKxGaJIxPSb\nZ6xlO9SsNgvHf0PfO629ARt6AaqhUYXSo6J8kd02uieKUHE0pW2nnqI1ZobhqEwbmi2fZb0Uhn1S\n05qhPMxnSKnUIXTWbFfdhzZ8XyNYHoGiNVHa2Vafb97ZtlYEzgJlci0/9BfIheVUEKFg8zaSj4oK\nBkRjWoLKMUqToufPUK38rr07yifDg3MsFbvSIeLaPEkIKtePmqFo3iCa4wc4D+iy+nHdXl8HfaG+\nt1fq3/KzNep5FbUyov9v1YNSIZLrguOkY6Dh1lzD/ls9l+db01FWZM7VT+0bdXh43Wblh5Ejus/V\nNuq9dB9jtbU29IPR2huwoQ6NQajpnlgbyM/XjLMUMq6g1GZVc+k5AboWz6RdUar2Xip4mgTctFIz\n9MysvAIzU/BH8HNUOZntosmnp72qFhkxNEewVENbIJleiD4cwDONvtja8Gy9Tq6NqvDASKDHyEz5\nDFtbv5Excca8iyRAMtOnM3MWDwQymsJIGtU8x6tZ57GPErNptlftK7Pa6jMUDHVd3LV3Lux9Xm+H\nJj0tmBel9OecR/vQhfpWWYMe+sL3a2G9KP0/kNZd6XtWr58rKCPDIsHLkwPqXufc+rpbIEoQN21N\ne8i2z78igDUSGvHDKY7o+fuKoBDB9RD/WkA5b183NInW3oANNeg8tuu+CaQFB89Q+jEoI58hIxQt\nO64jBMo81H7MdOx6sHvSsWMk05MLUJ4MrOUYqYnT6KPgz9GscBelyeeZ3LcbtMPLxFMIITNV6HmO\nxLwfWPvY3jZznL4mckRW7bgb2enpg6COpQ+DMVTSMaFApSnqo6gKfu8EZVI3lktoISS9bMB+sHyE\ndHi9gxg1OkEtVF1D6d/zgT2zROm/Q/oEtUljG2WV52wymmbKcURCo9RciNpGHVavz2r7fSx4sPYK\nYv4edaj6dcR7XJEjOt5TqInmQZHaacJ4jBZp9uuorxHyxjXONnDP3Buu36vGu2zDFaR1dgslH9Dy\nEq3x/H78jDb0Z1p7AzbUoBdLGz2FGahpCMO3GErqmT8vNTZkq/DWQphjlF3UBRQya9fetI16uK+C\n5+dyXaFuRYTI/D8O2qzv8zDiVfA+/qaOqHcQ5xVReLw2EUyZw8wkdV40e6um4+Y3T+X/am4Z8yXR\nMWd1aDWH8KCK5n6OOBttNh3k/tQJ8crfW2iZ+pf4dz6ya4cy779HfaB+E1xbIB1k6oRMxGJu9/Ig\nVKfMEmnr75toffpB7eiLfv8EJYr2EGV5gzokuRaUWqiP7j+aBKO51fk5wlhIf/7GDKwWHKNFLgAf\no67Js/jzu2ukg9FcOt6KhvUcjO8Ev7MEQjlem8ieH4zW3oANNai2XZ9XA9GDfts2m5sm8oZshQi3\nmQkZnCIofJdr+O9JmxS6VWYdOR4CtW8M83G4oAKjXME4f/sK+qYRINWxiQ7yU9SOxDdR58Xg2EV9\njNPz9/0RfF4o1H2Gra1/Hsb6oNOfJUrUyJ1I9e9n0ubPkJlyVESyh8QoUahq+fK4X4aaAFWAiDR2\npVsohUSaJBwJI32OJIDw7zkSQqPIjR+KPq4cn7vIfj09AbT2tYj3ZmSCuIHyEL5lbVUh0A/shA6W\nwlQrG7XvP0fd1CzE/UhnbCJNNJE9RUKu3EerFRXnaNES2b+JqFwtSNT9vYV4fUa1nmK+V469CmzK\nq87Hqzc0mdbegA11qGe6qe+tGVtfaOGGOoBG2sSaRC/ElgyOtnlN4a5VdYGklZKB8X6tZdJ3PMzM\nnSaOKwHzUUpaVDmeHI/eofMMyQfBc7JwbG8joyYaPuyQ/C7Kg7wPAY8fTpFQp6QoiZMXfdSDnuG6\nGJ6/3Xj/89AUpEwdjS+gLmypqMU+ahSDpOn71XzJJG4txIfr8C+GOVPTZgsp0j5pW/W9bU26bXqN\nD7vS7KOlFWbh/ekZ3x9L5PVa7vu4fbqW3WH6FtrlIDiXvhYVRa0LRJaomvMX99X5pGp/3iPMHqzm\nPtIp2uiW8r279m4X2PaDb28ie75nWnsDNvQ9UcTYxg+8lt/KDBoi3GcmPd8Y10o0CZQz317toLek\nXfp8xICA0r7fcpjtmTko4GnkCwWMJ8LEHlfjWwpREaOdGjkUQe7uMDiGJijtoxQWdawe27XvzvFe\npQVqk1hLKGghZYrO+DsWyGjFI6QIizNks1J2Bq2jlnrjwjUSmTZ9jfH3r+y6mz7KAyzP4VQTbOvg\nV7PP2P6JqnPXfZ/SjkTqXBxlsXV+Ewl312UvE8VM6ffjbxPxUaExzilUm7RmKPfM19jautjpryYi\nLNsUKUy9OdzQ90Jrb8CGvkcqNzW1rfOaiQj/ZgZQw7G7mBIqWzP9Y+RDo/RJmNY3h1hbtWQWQxvd\npq8OiXuoE4/RP0QRGxUwbqI+9KIoET9M4lwp/TmMmL8Le7fQ98fQQ3OJ+MB+1Liu4xwhBBH9Cltb\nf7RrfrhzHoiCXUAsLEbPqVY+R22mmqOu3dLq2wo56ofCq0P8nLe7qCNZFGVaYWvrU+RotPoA65nv\nxtfE8/k4lAc217aOWf2uzAOiKCWP9vNsyy5geymFjF5kgZuC5Qy1KToSGj2PUz/nTHpH7TsSCYuR\nIjZlb27oB6O1N2BD3zONaVvtZyiYuAMfNd0ZtrbeQ+k8OJ7vICMKO6gdHt0Dn0JVxCBd0z5GPuCi\n9OvUjPXgoT8CGZb21aN/PO+La9n8TulT0k4c19L4IqZca9m12YIa4i7SwcEDnG17hhTBQsj7HrKQ\nqeRREdq3B8M4+zMkP/wdiWHUlMLmNOkRDXEBk46o7nzMYn8UMP1bQBkxxHW0i9okNB+ua5TYXbvv\nrrTT/ZX2UGblZcRSlBiMB69nON4ZmW/fD+1syv39xwKXF1FGxtWCVC0QKALp/k0U4ksn3Lzfr6BE\nL1K5h3g/q9+JO59GQqMiGTlNQNs8Fu1JjfbhO9yUvUFJ1kxrb8CGvmcarylTakilpqnCwxRHTdUy\n+whBLWCwfXyeh4GaUFyA0RwF9DdwM4y/21PO7yE5XsLoCWrn11aSOM1UWjKymknGeS4ijbqlZZfX\nHwzfn6FEhnZQHiKcGzJipobXPtMZVp+hUHCIlByrh0D8l8ZvQE54dgUZOdtDcpZ0Z1/+f4ksaBHB\n4mGnYZ6tNP06zxQeDu173yEd1hdQoj1urvkI9Xol3ZKx1yRnut/4O80RTE7HdzxFGSnWmm/6z9TR\ndOO8QJHPFHqcrx8P/byLzAui/U1TpwuuM7u+QhbOnJ/UaGm5TzxLLfeIKx+sJaam3tLcE6Ec9Z50\ns53W67oAzRYdj+s0U92GXpjW3oANfc9Ub0Y9yKiVqgDgGSFLTbB+tzuS7SESKOJ2qYkGSBo2Nfzo\nwPGohNv2+w2kKBP+fYoUdqmMyA/Ylo/EGVLkjoZFtwr89YRAMm7VpKdodW+H19K9bn7YRy34aAZe\njoULXGrS0twxOu9Xh3Hu1cMZM/WwOGIk+Pqz/La2nePBg8iRrjHfm5XcEznpfo624EV6inSIz1Ei\nKCyVoGiI1jty3y/t0yd27e8b8x09nxy+z5f47Ka94+HQPneePUNGnSIExXPL3Eadp4QCSuS3FUcV\nZgG05iE1v9BMwK3xjcxV+i3u05bvWjYRtsf0+U11Gzo3rb0BG3oOqjdeZCaI6rb4plQtmzD3DfS1\nhxnKRFXt0Lz42QP0DywlZ1ie5dFtxhjeH9WemQ9tPZnwTSAf6C3TjMPMrjF7wjvPJaParRYkc0fn\nllnJaw5dRe1fcMnedxFlzRUNDb+PMvtoC6H4Am0BQX0FIuHQiUKR+/YQdn9g76YvRSTkuEbc60er\n7d4vVk++iK2tnyOFc1+0OVkhITo7iH2/tAbUtswRk+Fpojo+T/ORC1d1Do4+T/D9sULa3y7o8zcK\n1ZdQCtjaV5qzuM61SrJn8SXq4+OiiPOKky4AACAASURBVIfyp4y0xM7TXuhwbuM3njyt3k/sE9/V\nFzw2OU9eKq29ARs6J5UbT+tK9PIuuCYL5MNfM2MSTu4hIbpBmaeij6CUzNOL6K2CtkHuidAFPhOF\nCvN+L5ymDNafAer2+GFfalaJ2TJHR1RIj9B1PDZttIQHhMLu3m8VXtSME8HwM+T09BGi0RsLJzof\ne5TPf0c6DBWm13XRQ2J4IOt4f47aN+UU/SRh2saWaYbv8OfVlOKRTnOUfjhPUZsWgZynR4VTRxiO\nkMsL6NwzQaIKudGeUOHZI/IinuAZjbmvIn+kJKD097uibtG+8/4yClAzGCvvYF4WtvcITF/fR1DI\nRyj8tJzKx9CpJaiQTakBVo51LRRt6HuntTdgQ+ekWuOobbf1M3qQzZFzILiWSlJtKkJn3LN+By37\neK3JOLLB5+822kEERe3OatvWbKlk0Orsdl76DGWkAFDaqKmJOUx+hFKjo2mCv9Oer6agVr4LHy9F\nSsrU5W2EjGOrDqlTwm61z5wjLXR4x96zQkYV1KdADypNJe8CwneohRGPOPq60ceI5ojXNFBHLK2G\nedTDyYWbh0Gbbwz91XZrmykku4+G/n+KWciFu9pkUq8Bb0fkQL5CEjRvYcwptBQwtG7WE3l/5Nuh\nJp/IpKpr1AtHHiOt+8gHpUZhcju3Ue+j1v6adr3NTzfRPC+B1t6ADZ2Tyo1U1/EYf1YjUlqZR6n9\ntKJPVHss/UTqb+q9c/m+J3WbIRWqUw12idLxjloWmdbpwJRuDEyO6M/7nX5FJoIF0kHpIapq5snt\nT+31b9xCmbo9suc7c9V7FWGKxiuuIF221Q8j9zNxRCO6xusa+cQigep7AWxtfQvNK5Hb6QfVR8go\n02eoUQr/ttZLURPaHCnh3FfB3D5D3gc/DX73UgAkOuS2xvAYW1t/sGtEBtycUe7FfLhTQHR0Icp1\nooe/C5WH6NfWcZ5A098tlFmXKaCoaU3XGgVo/uv93Bney8SAHEOiikRLvNBeRC2fogeozYQLREhH\njSBpAMB4fqWx6xtaG629ARt6DqoFjbEw4hmYpj5f20atTZ4gRwz0qqw6itIz7YzVtyDET3TEU+bP\nkGzmZGLu5HqIuk7MDmoEZY4UdnsFW1t/Y7/9CbFGdgllvRvNhKlZcp9BQyjLcb890AWU6dbpI6IR\nTHfQczpuw9YzpFDSKMGZZ1El9E8zzEfIqeAjTfcpcorxI0S5MOJ+c8yeoTQfMpdFZGqhCYZhvO/K\neF9EecD+Qcbp0TA27yJr3nNkweSvkdLX8+COzHczpIMcqNeNmqvuouU7Ee3FUrjkPB8gcsAu741C\nguOon3K9MkEgnU817NqrOOt4OjpBf4xDmysmW/R0BAzd1zX0FGVV6Gj/PkHbIfuBtZm+TS4IumNu\nNoPWvGYjfLxCtPYGbOgHpsgZM1134eEEueJnP4V2er7W9OtvO/R8G6UAQGboB8YtJFSETncQOkZ9\nkJ7Bi/Bl8xX7d4x80B6jZob89s2BCZIRtvLCxMJC7nvPudDNJXy/apN66BFdcU1Zs9Xqux+hPHxu\noTycOebK+DVHjZKbW9TkkzTn3N9t1Ie3E+cr+pbD/LoW/97u/c7up3/DHpIjb/TOE+RIGAowdFb9\nPepKx0CurZPnpFy/Ohe9XCYuiPcdMsv9sS/v6CkNKrx4anoKENGcYBg/R8j4rJum3CfqLtqlI7ym\n1WoYU+Udl5CUh2jNEDXS/Dmeb0b3WbRXZ8hoFNfTRlh5BWjtDdjQD0y97Ihpc0dJy9y00GOgtQCT\nGfNF1JlO6VPSSkW+GBjeAilPhWvaH6JEGfTdt9DO6QCU/fPaNFGEiDLmVjRA7FQcf5/fvo46vFu/\nz3HSAy1yjF3I73z3L1EfTnQmbPlm9Jwf/4DSh4T3a1G8yHTlvioc4xbc7wehXo+ckFvv6pkTgCSk\nRALqHHVSNwpTTABXZjyt5+IQpZOnCuA+V/rdOrS1X1sr2nN+v87ZCrVfVURakNPNcAtkh1K2gajY\nvPG+lHslrpzuyJDfo+MTheBfQly+wn173FeIAlJbONzQj4bW3oAN/cDUStaUfnsLpdmhPojLd0WO\naO5D0UJGSIuBWbY0diAWEki0/19CWa10hWwT5yHp6Iv27x377VPEhzQRBg8TrgUUNaXFCIozTtXA\n9QBZDP1Upt1Db8jsNSnYnvyfAqGO5SnKseNh0xoDP4RU2HO/AI0sInJE34WW39Mhsh+Rrxv9FpET\nF1Bb6yUiF3o5ThQ0Fo1xUHNXy7mVwqVXto7mSueMB3WElrlgPFZk0E0tx8hCYy+HDOfOc+oAZZ2j\ntxr3OF1DRo40OSJNPxTYIsFN10VU10rRFDX50DzWykbr/e3nPdnQWmntDdjQS6Bs7tDDVAUJNTtM\njcZpRZ1EjJkU+US07tO/v0HWYCMhgXZ91zgdpXmInGSKTo7M5xKZk4CWE3AtJKjfi+Y1oTNwyThz\n+9WXSA8kH8f9YMxVA3Uh4SbUobKOKLmGpBH3nGh9HKLD7QnSYaOF336OMkz8hrRjhjIXDpAEkovI\ntVmi9cD11cuvou3/A2qUjPSVPfMJ6qR2nzTGwcPfPRwWyAKmC1o01VCoj5LrOVpWKgD9fc719gv7\nLutS9QQUD193k82tBj+I0BYgCUUadq3zxvWpjtgHyP4+x8iClgqEHDv3j7uEPtIbZY5ujffG9PMj\norU3YEMvgeKU1H7AXu9uzGl5BcgsNCKCsOs1JKbvaI1GLJwM19SHAAOD7TEgjXBpoRTqcxGFLkeH\nX743/q5+z6N6rst96odwnuqxKoR48Tlvu/afWrknjXMHXDXN6GF8hnS4uxOlPq9+M7fRFjgZkaO+\nFG+hFI6W2Nr6beMdK+TQbz7birgh0X+Hvgd+KP8HZLMm12ikibuP0BPkMFtdY0znr2PrAub9YA4j\n4cb3V6wYtNePJ/WL9ns0xjeKdyczod6z0/ieChrc0/soBT4KbJw3L1dQopR5H4yViahNXXEbvQr4\nHHV0Xrtm1obWRmtvwIZeAvVrZoxv8vSOHuTsgoEentTw1eyjaI1qlDwQmBuhRE0yEhDX/Yng78xE\nPRKhZddmXx4jIQFjNTkoUKgpzTPDurAwNVV5D873iCC2I4Lez5DRlFbItxdy5P/V9+AyssOiMv0T\ntAWUX1l79mW8WpqtE80u97C19WuUhe80GV6UlXU2tLeMxEqkqf9rTTy9nwcZawtFQuQCGRk8RC1I\n1QJmnkvuFTX76P6KFYNyLWzLv44uHVpbKSB8iOzbc1C1r0QYS+SyvEfNmHRojZxX6b9zCbGZr9W3\neAxbe6Nuo44fBaVIoYlQmQ2asmZaewM29BIow+rZJyFdLzf5GMTZPzA1xNEPTz80I20yEhY0o6oz\nvHa227ptrlUyG6gLVzOUhQAxMPFpVU3T89eRfQlafghvh+NdHjbxXMSmuch5l4em9vkq3DelfK+G\nc9Nx1wXMVmhnJKA8QfL1mcu1JbI23TLnRD4vSjmsu4zQ0NTq3l7OzSxYb4Ca0PJ4xD5A+fefIJ5f\nHm40vbVqOim6xkMzr/lyvmtFokZXPEHhCei0W+5fVQbqJITRfo/WY5zlOAsSceI2H/c5smB3EXU6\nBEcKx9ASb6P7evnYRojlAdzX6EX474aem9begA39QFQyPzKx+wMTGDv4zrcpY6TAtdk2sy/foc+4\nb0udmTXuc4uJ1t/PwhXDiqNDszy8po+Fmg3UgdW1732UToNxCYMYOSlNc2UK/m+tHwzHdl8krhMP\nO6eGvW/f9ORYLV+NLxD7i3zZuA7EKE5Evwrml8JwzzRAAVCRixx90143kQ+QIiea54VzF5naNDGh\nhr76mogdY2vEpKUIEBmp93OcPK2HzuheVAGE7XWfMpry3kctoLDfnN+obpKmQ+gjSGVb46i6vMdb\ne8rXRJxaYEMvndbegA39AFQffm1HvPxMxOymaSuxEMA6F8qQeSDETmnZcXBm76TWPZb0refE24LQ\nCeP3HHdVK2bbpmiVigRp0qxozPz/6kDo2XQZGRONQStKxmmB5BdEE8YBSkREHR8JsUdoTeQMOpXG\nhBDes0S9vnZl/rQAnwoJvtZccGS/a225b15w5OAMuX4OM6n21tEVJCFN+7iDscO4XuNqplCka45U\nHiDO9hwLKGWq+z4PoblrG3UqAX7v0J55NtxLgWZsbVxv8g3nP3WfVkV/433pQnbkmD4dqd3QD0Jr\nb8CGfgBq1+tRiiBrd7KMkZQ+o/RcHu4/Ql8IR0j8b/cvYPbNMkV+3OdSwCqh7R0kze4C0kHheVoW\nSAfWz5AiGQgNu1bcQzk0BDIyeZE5thJnMXqBfb9rzJOHYpRptsX8NettFK3TExTuog7f5AFxdeRZ\n9rnlADv27AmSc/XSrlHo2G+811PJu8DL953BI3PKdd4L6Y3QIz0k6ZBJvyuGUkd95vpuC/FlAcwk\ndNQmkEhgUKdoCtmMmCqRgvw9R6Hu2zuZG6aVoC3qoydta9Epah+uI5QReG7Cq81J5XwxY7OObaRM\n6HpawAWdDb1UWnsDNvQDUClsOLM6hWsj5XPjVT3b2gjrsESOmG4CcrPBJ/acQ61AmVGzlwciFrBK\nR1Ye8jo2j5EONoe0owybesgtkAvIKdTscL9rgcpU+U720aModlHD6dGB6v427Ku2Feekfw7GkeaJ\n+YTneZh9iTJF/ZhwwmcXyAJWzuXTj0zhYaZol/oiRMUp44J57T2mBTifoBb43kVexxyDHkrHPfFw\nmH9dh3sofYqiaKE5UsmDsfczT84StSk2Mk9SYXAhhe2YsgaWSMJTK1kg3/UlUvkFR1FJT5Ey/rpg\n4Q65kTmuTKNQm5Xfkn7GPHJDL5XW3oAN/UBUCxtAhmbb3u/Rpj3PPaUQ8BTpEI6cRal9KerC3+Zo\noz5ksoS0FebtC1h1Vl0nohKRR7+bibRuDhAfGJo7ZA76i2RUReuUEPV5f/jd067fQj4US3NRPTeX\nUBeHY54Jz0EyhVRw6iE/KyTTwp8676ImfA112YIp5OY2zotr8uoXoj4eFJijtPYLnNffoBTMXeBl\n+n0fI52XxUBeGJBzpmupNRa6Fy+gFGS4XjWs1lEjrssIUdAotQ/Qzur7EDUaqf/nnvUsxz5v6odC\nk5X3nSY19tmzySp6MsVsFkVllWa9Da2F1t6ADf2A1LOj1/fy0JwVm7b/7gjyj1K4q/ZHEwN/17oc\nQJ9xnRhzpFbKRGvbxqCf/rnPGQYe85dYIWWVjfJdeKSFH0r0F2mbu9LzbB/br99mu39u7dqRfhCe\nd03RhTW9jyaaGTKq8wXiJFskr5mzj3aJAmqdOjfeL/7/bPh+qyaPrp3ImfMYGVX4AAn12h2Z05sy\nNjPUuXaA8yMo0XhHa9b7f4wkoNFP4yi4j+uJJp8TlL42rbXJPXBjGJeLyMJJhPK4GVbNk+qnxW8/\nRZnzhe9TRJF7co6ESkZrXOeztQYoOLWKf36MOBqvFcUzFgXUF2Y29NJp7Q3Y0A9MtYawHWzgKyjz\nRMRhke1vqB08KoLX8oPBcP0Basa5ixpSJsOP3qNJ4VQAos+LHspEbk467XoytMFL23tfo+Rnl1Gn\nrmeRufftOy0ThTteck7c1u79u4Nc7DBGWlIbb6L2hzhDOth+iXSw7aCuXnwJMYLSyto6hdQEpdem\nmqOeYGvrp2gfdFxnNGMcd+6hs2o79D72weLcOIryKOjbHFtb/yTXW+1mll5d04+Q88C02qSFJN2n\nQgVS+rGwj/T78nwuvg+1jxqFo+UcKMj3SlqMzSm/r0IXFYfSjBspVZm33Qbzs2CUV04TZjb0Umjt\nDdjQS6LYsYzXnKneL+4r3xExa2WCZPJqn1ehRb9D+zUFixPkyIrZQN/aM39C3+atghFhctfED5GE\nDwplNH30x6E2b/DA1nT2kQ0/519IDNPHoNWXBXJhMzJkF8C80OPKiO30LJz+TOTsy76UfkulRj2l\nH1No7PkxYeUMfTSI43Az+Ba1+JWN81W4I3Qid3qmwHqAlExO379A3faxdmq73kW9b6Ksrqr9U+Db\nt28fSvtUoNZ51u8QMdN3LFEqCW6azWHvfaft3v79JdrOsFP95P7/9r7nx44jSa9orw8+6A94BwOG\n0fB6Zg3wZEONwcIAeWweKZ80J2p8ECXAQ81FsycfpAE8Mrza48KXPex/sN7TwljDMLyAAcMQekip\nf1CzEjXeGS0G2FmA4ntN9edDvpj88svIrHqvSdbr7gggILFfVVZWZlZGZMQXEWrRmmYdm2I9Dn5l\nPHsHgl8R11EMrfTXS/fjL8GfHBHQDs2rrTdaLXYlz30P2extG9JN2QR7IEM+yZnAWDn3eWBCczUx\nGFOBwBqeeYJSWfN8+Jp/YU/GwIRJSwB7wtTGSEM59Xr2/duG7yUXA+qkXvou9xpzbi6biyooPT5H\nsnxNfYYCcK2Pn6COOnqyHpNWjRpW8jgdOpdoYCF8goT/MTeUjvXfTXwHtoZpNekHzvftRRaZ8mT/\n3UP+hi33S692lr2zAq/NzdYHsaf/31RByd9Uu7zGFJzcvjOnjLUJBeQS8OwdCH5FXEZ4mBKhmSfP\nkeqefFJ9/HWeAROOnkunBUbrFSvTKAf2Md9EmddB+RxJKHAUkAlU28geIrt2TFHgKs+8Ef4U+fTM\nlgMdgweyIXtRAbrJ3ke92atAVWaBaOZzwxywRcfcQdxHrTVjJ2UVLqYombVHQ14Nu6J5Rqy4Gz9T\nLVzeu7WUGs/d4+GUemN1iIzpMIX1OdIa4OidZ+v54W/A67uNH7vtbC7VhcG4q//XaIstKM9Qj8M5\nhuGHNF8PpV9+duM6sojXiq5FU9qsxpKOL7uv3kVt9XmCnJtoiZwEspdXpMV8KMiJJMexJWNgf7Wg\n1BmRX8TeGvzSePYOBL9CrmuxvOdsFqv1xvMOyhO1Cmdth/36GZxaPls3YgP7cYSBbuK2sahyY3gU\nEx6sjKirgq0YGSxcpqbnEFTGc3BY4gIl2JddL74vvN5kFUPSUtj4PT+CF32VN2E12XMhPuMz+dsT\nZAwKK0g2txwObrgavuZN+KHgyr1cGZBnA9mlxf18E223HmfHtVT3GknVGu8z1Ja091Hm3zlEFsRq\nOeFwV7UkjQnm3yC5Krw8Mk9RV1fmMgRAL7txXvOKn2IrC4//E5RRT58irTlWOHT8DRB+B/mwwi6l\nlvWFn3uGumiftdHGlkzf7wxg+zbqsGXfNRS8Uzx7B4JfIZfC8hPUYEHbkFXocX4PO6Fy/gcVUqvq\n4/cVlDPkQnTc9kdy3YfwT35sSdiHV8skPXt8Y8obYS9Ness90m63bNsEvWUutaKI2tYzJCGhClC2\n1tTvZQJDk1KZQD1EiTFYrjdvw+jYczyXkglS/vuvnLGwTK5sFTJLXUtJeU79Wq3fiS19JjS9+yyM\n+wjt/BaK2TlF2TdObMbAzJwQsHaP/kL6Z98TWxSmhHM/gw/uNayMtXWEOgGbzcuURIqqpKgVj9v8\nIfwos6W896fIli3PpWSWOA84bPsM47b0oDL2PflumvHfehaZcP3sGM/egeBXzFlYapKwX6CueAuw\nslFjShisxidxDV005YGL2Ompn/Ett2VD26eNxctt4aUwb6UtN997KezzdXYi5E12Qc8wgc8hm/we\nY5sjW2YWSKdwbuenyEKSS9l7p8sFygrKe41nqOIF1ADIJdJJU3O7mOKikVa2NtS9YfwYOend/ppb\n4FBu42+QCgyOuXS0L+8X418qhZrZ1wM1pxxB7W+GlXbtB5d0sOfuIae9/7rzPmYBsu/C1pYpsGad\neCJttEpWeCBerUXE35tiSDTKTNf3AZI7tZetli2Wn6CO8HqOOnrI1nad0LD9HbVCin2FXvewKW0G\nz8qzdyB4Jq5N9pxnY6zmjecjthOkd5LlDeMAw/BHKAXvn6A8oeqG9gB16K6dIDVJUyttueE19GSu\nFiIWsGbpUNP1PSS3g/XPMDC1cpSfr1Yc28TVbfUOSkuL9YdrvCzXm6y22UtSx3PFoFnFzLCCqm6h\nFl4CDptFx+b/l43rPDaLjymkY5YIrMdx6Y5/DqvWgoDq8vQEuf23l5zOS6uuil5P4WJLohb8a+UI\n0rVk/VRFWiP2+Ftk0HrK0FsqvTqXC6S147klV78dh3pdvilz+BhlcUzv+2qlRWhbQ+vfuP1eDqhw\n/ewoz96B4Jm4dNl4Skhd8ybfw5E8t5FPQ+WGUn/4BygxHEv4NWIgrPVvlvI3A/n5dYByXzwhcY68\nwfPvLJxXyJlYbXNXgdWra+IB/u7Ku/JJWt1mK5TJsXjsFRDZjm4orQpqafCSdR2iLD64RFIWFfzp\njekhSoVSeayN99fzcjpynceqbLDiaSHs+vdD+NYyFaC2Vu3/P3XGrgcAZnwVr3lVlA1To+vMwvg9\nzJQv6P1vUfPZ8Jgt1vP8GGUEkKekncPHffE+YaHpHyPjxtRddYRxhYqVsJabhpVwtRhunz07eBae\nvQPBM/JUAFoWtArwtDBeFo4KcOMPX9OL/4X8ewwwulpvznzKtMgVBShqNVMVSNbmOSyJU/n7I5R4\nBfOZKyZB+Rw5s603HgYsPJV7PoZ/WraQUB53ttacgJNQtea0tApoQq+WEnqIhD0x5ewYNQ7nHPVY\nLJEEt2FEdIz+C5Ly0pvrr+DXQLI57+USeYIcQutlvlX3lo2xp4zY+1g4saavf4IMulaclaek/Ff5\nN1v8eG2YcNeimaxIeZipUtCX89oCawNJGbFcPawceAkQ7Vk/RAZvq9JbKiipD63vxix6reKOag2x\noqHe2rWCpHdQK9dty8jUvTD4lfLsHQiekesT/n71gZablQpKNo/77oUSt6JJyj6Xf6+kff7NNmgT\n/uz+4HvafuSsIBxgGD6je9kicYAMdvRDp30zOPfTBJm6ZMxErr7/n8v7GBbB3FB/Lc/wUtC3AX/l\nHLIAtr5mE7if8MtO8p7AbeVwGXPLTElW9jmysP5rDMOvO2PO/+bspgz6tt/NmtcKMzchr3WXzpBA\nzV5CM299v4/k3mAQrl7zKXK49ufST870auvWSxzHVgNfeNffoipTHI7+rjOn+u8z1HlJrF8toDl/\nN2ZBtT7zPmTgWgYJ8/NPO+PAli+zAIZl5JLy7B0InonLD9oHl6br9CRzQh8/uxc4r4iftTE90zZ6\nTXClzMrHz+XaU5TJq0wxMbdCP2Nk6oeat60/ZlVYSdtswlYh3noH+90UoKPGNUvUG/A7GzwjCbJ6\nXlu5WDwl6RjlRs+/tywh1jcV2Evnut+MvIPlKdGkZLYGvDb53lb/DD9hEUu2XlWI8vzbad6zUqyc\nZz1Hctmp8mG4rgVyOLtW832AdsSPun5a4FdzOXKOmrai7n8D/Mwz5OzBpqR9I9c9gv89mPJXW3La\nyf94H2JF3UK876CMONTDkeKxeB2aq7pW2IJ3nmfvQPBMXIdOtsCCHs6BI3m8JFBtc2qJg2jlSGBe\nIfvD7W96j7k5eGPOJufy2fuoI1p+RW2eIwkb22BzLpTaTbJEti4s4YNITXj1QpSBMqX/EjnMdCzP\niGIYeB5MOKt5f4Eag2AAXXtPtjB8g7puD9/Ha+dj+IX43kI/H8pX635pOHOPv0YNpD1HC4tUrlcF\neI9ViLZrn1Lbikv5vvRD3YwqRJ+t39cLw2XL3X9CBmzXUS79HEUK/PXqStl7sQUTyNXP33L6+LaM\nj6YgqMGptbXHvtGW8neG7EZW621pGSnb5tIMtev5Re+lwS+NZ+9A8Excb9CaNVUtLLe6H3e52X2C\njAHoneDMpfIm+sJ7hfoEx79ZUT/PZ22blBbUs/f1KgqbW+EE2fXhgfbsZLaHOlcL95HBr0v4xRH1\n1LpCOqU+cdrTfto7m/Cto7A8H3uNQ7D8MmZi57ZvISkwnjDlXCtqAQGS68KAkq15NneGly/H+qDP\n9fBI99fPeQdjBeLymPguiXp98xyvUKet/1NkRYLBuOy+4JwfN1Er6eYutfWprjCzPGg0EgtvU5hb\ngFMv7NbW86k8y9YU5+v5FsNwU8aGiwyunPttDGyfUOyarR/+zlVR44rKtSurbNtcR77VKfhS8Owd\nCJ6R6xNlD6TWA5jxxnCMMkNp70TKbggzfyuI1WP93U6+ns/ac2mYwNU8Lga4rU/BtcXJIinY522C\n+pfwXQ5s1jZlaSW/f4C2omNsacZ5c9cTdX2K9udfQ52BnDzN5uIhrRHP6rVEAkx6ysmvkQSxuSha\nbj12ham15vG6jcfUp1P4odKcU6N/Ys6CU92TGo7M69UUBm9uzIJgimPtbikVgpZVzawLfyR/P3Pf\nqbRgsIuq9S23EryZouFZnxRsbLib11C6Lu17a1kwamXQVxR5XayQgfB2n7mRxlyZPGfTCgYG7wzP\n3oHgHeV64+/lQmFXgWemvSX39bK13kJZadjAdGxa9/AIy/V9HyKn6FZlpcST1FYki6LwFBTDz1gf\njlFvpkv6G4eQchl6BgJqGK4JJk8JUEWmBiH7c1ea2f15bmUWNX6GbElaoFTisH4/Tzk5p98fos4y\n682hup4As2Rll1eZpCznOXkDNbbITtm9tO+6RswScAe14POY1zu7SdTd8hbKdcdKLa9pE9x/IM/5\nQ7SSAeYcKi3sF7uoWpYUVjTYPWhuTVVEDjAMP0GtuGQFyQ9v5m+OLSDaByCXOmDLikXY6Xjpuve+\nz7CgXCKevQPBO8x94WebnNYSOUWdpOohMipfXSytiJsFMrCQTdDvyYZobpHPaJN/KvdpMjndFFt5\nQBS/oGGL7L83sz2InyNZhW6ixj7oOGRFws/mextZKWpZpbLgqk3pY1E+hsFQwKvxvfW1+2hbQYzP\nUSfb4zXyFZIy6eEq7jjtm3BvgSDZpaXA37psQ34PFpyWZl1dbxbqq3P9VO6ze9Qlp247tSKcIdcf\nUuzEobTjF7vz3Y+lEpOu0Ui7cdS2bwAAIABJREFUt+CPB5AVDW6Xx+EQdSRb6mO9LsuDTj6IeFmf\nF/QMU0T1u/pj+TdXQGYLFStl7b0meGd59g4E7zD7wDrd2DkqwXABe0jAUxBrIrNb2DTvQI2vOF4/\n6wC18Lon9/GmZULex8hkTMle472B8qRo/92Dj5U5aggCfxxSe6oonKCMgPLAh2YNWDjPaYWEsuvm\nDOl0aoqQzVc2jae2PQsWr4GPkZSyp/Q3vuYMdtovx69lPTILigkcNtmrQmNWiydIyrMqejoOrDwc\no65PxRYWwzVwn7lGjlXj1QrTHzlz7ilV5gJUy8MZkmLesjy2XBu9XChekcsegFXdMV6h0RoYXH5/\nUzPCesoU409+Ic99v7Nf8FyFcnLJePYOBO8ot4B1fTOqAQPVTGtch+xu1ife1FbI7pcfyHOW8E3d\nfL8JMt3EF/DCpUvLyrHbfrrOK47mKQg965HnUtC08y2lx35buM/xhU5LadqDYWbafdOoGQME24n7\nw8b1ngD13jspvXluuD1P2HNf/MKXeR688gkHKHEYNeiz/EbU7WFuws+lHwpCZytZ/V34yoRveWx/\nk7VLwxf+vruw7+a9K/Nk71ErKP39xf8OSkvKEZLidw9+8r7D6v7gK8GzdyB4R3n8hKNmVO/UBRIa\n5mLxo4E8a019DW9aahY2pWKFXJyuB87lUyu/myo79+heszKUFoy6j2w5qENXvRNl+RuHdluUkZd2\nngWLCsrX3ee0Te6eMuNZ0PhaC+9eIEf5qPLDc3aMdPLurStr25QYjkJS3IZZwfj5Wq7AcqDcR6ls\nem42xbT0gMgL1PgLc32Yu4b/XlrK6qi30vWY+3kfJY7Ftzz632RLAR5Xkr21yuuhjrbyQ7T7e0xr\nfXLEneKNeO5a30J/Hwm+NDx7B4J3lKduYvWpiwX0M6STVt/E2rLWtK+pgZ8Zs8JFyFoRD3bq9k6G\nLQuKZ6UYs36cI4fu9t7dNn0VnAdI+J3nSC6LfbRTmfvK25Q58+exPd7t++/I2O1VbYyfnH2zfK0w\n34cfIcO4jW+kD6bQqKskC/22C4z7soesgHAYsM03hMu1Uo+tYktM0WeXlx8RN3V+t7mm/41a31bI\nZSCs35sqKbr+vdw/qoTwN8yKan8fCb5UPHsHgneYN93E0j1ty8u0e7Lrpt+uFfjrRSK0n9+3Ypiy\ns5C/fTHatn/C6/nmeyGYGl1jQMme9eXF+NprhewEbcyOJ1hW6/57Lrlt1tXeevxNsWnhMTTE2gsl\nb4O0x9Zv6rtmg+3xKWplWp+hLhcrk8DuJf+7eFHcszyk3+p8IrV1xVPs2gpLrZBr9mS2lo0dNhgr\n1P/2gy8Nz96B4EvM2RyrUTF8Ql5U15T3t06K5WmsbFcruLasHCfVRrmpCTi/I0e5mPDYc9tK97yD\nXlbRur+mdPHYaep0gMG/uZ3FWoCYheLiJu7UjmaabeXhUKuR8SO08mr4z7M5yu+T38+zyrXcUvx3\nznFiPOYq6Vl4dI2ZO0rnyfiB8z7eN2L/ZtdQK+namNDfxorRwpuxu6WnLLTWMluuxtaNVfQ2l6ZZ\nZXrWV30uK7GbW3SCd4pn70DwJWBv00t/883P+WSllVhZ8WBz7CdIlY755Fu7aXK7mtDpC2Th/Ig2\nvIfyHAs7nWYCLi0DQCk4LINqy+XEoFrLzjouDOtT6SN67jfOc1h4c74RD/eyqWLmFWS0E38Pl8Lg\nT43eGrM6cfjqU2ThzuP/HCkZ3m14uT/KMVSFIq/V1pj0rWu87oFkIWEhC+EjlMUCF+4z0r/fQh2R\ndADfStFac5u7ONrROmoVW0Kz2LbXstazOqv63P6+nmPq+i2fy9+jH5IdfKl49g4E7zi3T1f7aIVw\n5vvY3QKUZlg2x9oGZie0KZEI2rZtSnoCZTeD/c1vt353FW49PiIhYhajBdr5Hth6pIKKLUcL5Cya\nh/QMszao8Ob3bBcQHJ93dbtZ7ZNeoi8GabJg60dv1SG1/B6WebdVPbq06tTjp2tlhbI+0SbKqo25\nupEM+/PNep7+DhmLokrL2yPPYKW/xC6N4aC2ca+W64MVZbVutC0h9Rro4Uk8PM47qMeJFSW24njr\n7jbK79xzm4W75xLy7B0I3nHu59NoA/j8kyv71LmisZ7QOCFUbdpOfAdl9tIVhuFPZJOzE+iR/M0/\ngdbvzhu3mZ65/aX8v4a8amVkPZ16Sov68Xum85YLI797bw6nv7uZy/ubfql0KYhRCy62AL5sQcmJ\nv9J7foRh+FvnXcfGldv3xrWP78hrnasds7vxDlJ0kiZ5W6EWvIcorYieZdKijvbkOnuP8r3zfVrY\ns+VSHccvlfNvgO3xKsn1OjhAHdHkrRvNHnwEX9nVd25FY/kuwOBLxbN3IHjHue2GsIJyB/BCh2uz\nv4Vs6gnxgDYWNc3aJmUbM29EK5QKwrfrv3FUxaN1P1QAmqLUixhiZYgz2RoW5XMMw39Y/9cEl+ZA\nWSEJ1UO0hSNvuD1Tu2c6t5PiXZQn9lJpbM9h3+XTF1reSXYs+qV1jUa0vIGcXdVbEyr0zXrVVsT8\nvvRxT/leLcZnyhZbx06cfn1N7YP6ZWu5tkaV4/HUuY6Vd0vHr+7SVshy22LkK45sEVGr0Z8irbte\nKL/hqPz8PeV9/I3ad+9ZcdSKq8q7znEkaLvEPHsHgi8B16bbaaGP3gbhFbJLm9ExcgZQ3XT41KgJ\ny5SXGIafQivZ5r70K9dO28gPUOY6sTBgT3gCyfpiCpopdl6Ke18B8E3n7G7h06NFgJTv57fRMpn7\np/vWnKa/j1skvGv8LKjqFuB08oprseyt7XEt36u3Fk1x0LGvAc/p7xrZohlOmb3Eb7xmvSgkb23b\n98LYLq4L1XoPbtfyw/BBo20dSddxAVDu0yMZKx2TJyjfvZU/yPpyS9pjK055EOopzMFXgmfvQPAl\n4zHsyfj93mmeC/QBZU0SBcSeoDYHG4/niiifX7t5prhD2riPHlveDo5wsaq3HsC4Z9nx3C13kQV5\nv3rrtDT4PtakPaYW6dQWRrVy+xjJWmLA5S9RC2/ro1crx35jYf0QaiFru350LXjWK3PtcOI4tlhw\nZIvWpVJeIVfBXkKjYhLzGFqCw3I+/W/wRP7rvQcrWZplt43NSu/VeqfnKBPynVF/2ZppFcBL5bd0\nTdU4lzErSFhJrjTP3oHgS8b1JjpFIWiZjs2iwJVJsd6orCbJAopJyCfIM5QC7QzptDvWnzu0kXsn\n7ZY7xDZWBeN6zALkW9R1YdgKcI6kYGhorf6bT8aMPXnqjCHQzxfDmArvlM1ttCJvbExMWJ+gZc5P\n1/45huFducYEMVtEVBGx0O6vaNzPUVpceNzVQjfF9VNjFmrXzn3k9fOc2uO1+rnMOwtsUzD4meyS\n0Of9GDX40xQOTUhn0VteWn1+f/7G2B3pA5nT/U/kXubPkHPU9L6HE5ThyqaMPEKu/G398MPZg68d\nz96B4EvGpXBrm2zztX4uhPybmvPtdHfb2VxN4HJeEjsxs8ujhy2ZGlnguUNMeH6CYfg+0ol/SW0Z\nDuZ0LVw0RTlbDxg/c44yFJUL7VlGVgVHsgVlhVJImwWK8TpqOSgVlNq6MZYgy+4/RfmedTK7NIcg\n7gk8ILlKrB9folZo7P9X67bZguIJ6J7rjBXPMYXB8nJw3pND1OvkMVL+kz1sEk3STh9v7/MFMmiY\nlUmefw+LwfgOLhPABw3LOzKW94WVR1OsVTm27+QptX8KX0nifytWp6cYh/JyDXj2DgRfMt4kIqRX\nnM+P8jldb3gsVPlka5u1ovrfgXfSHO8PutfX93BfTUGz6s2aZp+FmKVcv72+/j2UQlcrP2s00gfS\nBwNHcpSMAo3beJvxgoHmivDS2e+jdsmxNe0mymRZryFZTvh9foNSyOn4Ppd+HMmz+Fpz/dhcKLB5\nX/7WA6N61gN2PbyGZAHi53+Mej2zpaMfWVOuNbZO8tq8C82lUuMzWplxPRAyK9+30KqPVd5vCtL3\nZe5+LOPxFbI1h5VwW5usJP1S7mWXUA2mbbnqgq8sz96B4EvGmwDTyg2FFQqzgnDxOwPutTZ6Fbim\nJLC5+FMk4fbQ7VfZ9xMkhaj9HlnAtDAvQO3G8DAUlqTK+qlYjR+g9Nvvo0y+9gayADpBxmxo+O54\nYcDW38fmtXQxee4kxleUrrPagsJgzftISo0J4GfreWSlgF1qJtzs2p7rpgd29ubKw1+YEDeLnmb3\nNaV7AT8UuZyn9ndiFhx1gT1DSmLIz+QClqxsjIGX+weK/nesIHl7L+3bx8642ndiFiqzCKr7y6Ld\namzYi3qX4EvFs3cg+BLyJsC0vMHraX+FXKGXBaXWXFEMCPvel7Jhsatlr9GfBXLEkG/Wzv02AXOI\n0i3hW19KIW+4Co3cYN//cyR3QJ3nIfXzPmplxAsz7imJC4xlW83/zlEUbEpPzFaMnltuRdfcouft\nYxj+bH2Npxy9iWRJMkAqu59UMB0g58tphT2P4U60YrStzTvwXZFs0TtEnSHX1rj1W8fCAKI6tqz4\nmbKteUM4aswHPre/Pd+Cs4mrJLdzm/r/OvXfrIXfYBj+AFnR4MSLHKmmkT4foMTmTLHmTA+XD760\nPHsHgq8w10LOcztwJdkFakCsCoj3aPMGcliygjs/aPSpxhX4fdZ+mqthiQTs4xP9PobhJ8jhroZV\nuIVknv8Rbdpat0UFfcb11EL2PkrXzlTMTY0Bal/nWQM0kuox6pDaz9d9awOoS0XTC1uHsK0PrZJ8\nB6Wg9SxHLJhVQLLiacrj8XpeNYeMZ9FbILkVbU6/QLJy8XXvo3RZaEj4av28rxvvrTVl7mAY3sbU\nekv13Hvhux42yautpbmLNMfKAglzw4qKuT6zcpzbMiV03Arrv9d4uHzwleDZOxB8RdnbPPIGaABX\nFWAavvsASfCrosCZU5+hLnHfs6C0km6Z4ORN3QNbqpK1EkHE78uuiW+QzN+9HC5AidPhEyMDDh8j\nKWqbYm6mFPtbos77waGxJ0guNB1zxuW08rBwtM8dGnev1pGNma0V7k9dq8VfdyfrseI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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_walk(hexagon, 20000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can see a little of the six-fold symmetry, but it is not as clear as the triangle and pentagon." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Snobol.ipynb b/pytudes/ipynb/Snobol.ipynb new file mode 100644 index 0000000..19e9147 --- /dev/null +++ b/pytudes/ipynb/Snobol.ipynb @@ -0,0 +1,276 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Peter Norvig, Nov. 2017
\n", + "\n", + "# Bad Grade, Good Experience\n", + "\n", + "Recently I was asked a question I hadn't thought about before: \n", + "\n", + "> *As a student, did you ever get a bad grade on a programming assignment?* \n", + "\n", + "I've forgotten most of my assignments, but there is one I do remember. It was something like this:\n", + "\n", + "# The Concordance Assignment\n", + "\n", + "> *Using the [`Snobol`](http://www.snobol4.org/) language, read lines of text from the standard input and print a *concordance*, which is an alphabetized list of words in the text, with the line number(s) where each word appears. Words with different capitalization (like \"A\" and \"a\") should be merged into one entry.*\n", + "\n", + "After studying Snobol a bit, I realized that the expected solution was along these lines:\n", + "\n", + "1. Create an empty `dict` (Snobol calls these \"tables\") whose keys will be words and values will be lists of line numbers.\n", + "2. Read the lines of text (tracking the line numbers), split them into words, and build up the list of line numbers for each word.\n", + "3. Convert the table into a two-dimensional `array` where each row has the two columns `[word, line_numbers]`.\n", + "4. Write a function to sort the array alphabetically (`sort` is not built-in to Snobol).\n", + "5. Write a function to print the array.\n", + "\n", + "That would be around 40 to 60 lines of code; an easy task. But I noticed three interesting things about Snobol:\n", + "\n", + "* There is an *indirection* operator, `$`, so if the variable `'X'` has the value `\"A\"`, then `'$X = i'` is the same as `'A = i'`.\n", + "* Uninitialized variables are treated as the empty string, so `'A += \"text\"'` works even if we haven't seen `'A'` before.\n", + "* When the program ends, the Snobol interpreter automatically\n", + "prints the values of every variable, sorted alphabetically, as a debugging aid.\n", + "\n", + "That means I could do away with the `dict` and `array` data structures, eliminating steps 1, 3, 4, and 5, and just do step 2! \n", + "\n", + "# The Concordance Solution\n", + "\n", + "I ended up with a program similar to the following (translated from Snobol to Python, but with `'$word'` indirection):" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "program = \"\"\"\n", + "for i, line in enumerate(input):\n", + " for word in re.findall(r\"\\w+\", line.upper()):\n", + " $word += str(i) + ', '\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's just 3 lines, not 40 to 60! \n", + "\n", + "To test the program, I'll write a mock Snobol/Python interpreter, which at heart is just a call to the Python interpreter, `exec(program)`, except that it handles the three things I noticed about the Snobol interpreter:\n", + "\n", + "* `$word` gets translated as `_context[word]`.\n", + "* It calls `exec(program, _context)`, where `_context` is a `defaultdict(str)`, so variables default to `''`.\n", + "* After the `exec` completes, the user-defined variables (but not the built-in ones) are printed." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "from collections import defaultdict\n", + "import re\n", + "\n", + "def snobol(program, data=''):\n", + " \"\"\"A Python interpreter with three Snobol-ish features:\n", + " (1) $word indirection; (2) variables default to ''; (3) post-mortem dump.\"\"\"\n", + " program = re.sub(r'\\$(\\w+)', r'_context[\\1]', program) # (1) \n", + " _context = defaultdict(str, vars(__builtins__)) # (2) \n", + " _context.update(re=re, input=data.splitlines(), _context=_context)\n", + " builtins = set(_context)\n", + " try:\n", + " exec(program, _context)\n", + " finally:\n", + " print('-' * 79) # (3)\n", + " for name in sorted(_context):\n", + " if not (name in builtins or name == '__builtins__'):\n", + " print('{:10} = {}'.format(name, _context[name]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can run the program on some data:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "data = \"\"\"\n", + "There she was just a-walkin' down the street, \n", + "Singin' \"Do wah diddy diddy dum diddy do\"\n", + "Snappin' her fingers and shufflin' her feet, \n", + "Singin' \"Do wah diddy diddy dum diddy do\"\n", + "She looked good (looked good), she looked fine (looked fine)\n", + "She looked good, she looked fine and I nearly lost my mind\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-------------------------------------------------------------------------------\n", + "A = 1, \n", + "AND = 3, 6, \n", + "DIDDY = 2, 2, 2, 4, 4, 4, \n", + "DO = 2, 2, 4, 4, \n", + "DOWN = 1, \n", + "DUM = 2, 4, \n", + "FEET = 3, \n", + "FINE = 5, 5, 6, \n", + "FINGERS = 3, \n", + "GOOD = 5, 5, 6, \n", + "HER = 3, 3, \n", + "I = 6, \n", + "JUST = 1, \n", + "LOOKED = 5, 5, 5, 5, 6, 6, \n", + "LOST = 6, \n", + "MIND = 6, \n", + "MY = 6, \n", + "NEARLY = 6, \n", + "SHE = 1, 5, 5, 6, 6, \n", + "SHUFFLIN = 3, \n", + "SINGIN = 2, 4, \n", + "SNAPPIN = 3, \n", + "STREET = 1, \n", + "THE = 1, \n", + "THERE = 1, \n", + "WAH = 2, 4, \n", + "WALKIN = 1, \n", + "WAS = 1, \n", + "i = 6\n", + "line = She looked good, she looked fine and I nearly lost my mind\n", + "word = MIND\n" + ] + } + ], + "source": [ + "snobol(program, data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oops! The post-mortem printout includes the variables `i`, `line`, and `word`. Reluctantly, I increased the program's line count by 33%:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-------------------------------------------------------------------------------\n", + "A = 1, \n", + "AND = 3, 6, \n", + "DIDDY = 2, 2, 2, 4, 4, 4, \n", + "DO = 2, 2, 4, 4, \n", + "DOWN = 1, \n", + "DUM = 2, 4, \n", + "FEET = 3, \n", + "FINE = 5, 5, 6, \n", + "FINGERS = 3, \n", + "GOOD = 5, 5, 6, \n", + "HER = 3, 3, \n", + "I = 6, \n", + "JUST = 1, \n", + "LOOKED = 5, 5, 5, 5, 6, 6, \n", + "LOST = 6, \n", + "MIND = 6, \n", + "MY = 6, \n", + "NEARLY = 6, \n", + "SHE = 1, 5, 5, 6, 6, \n", + "SHUFFLIN = 3, \n", + "SINGIN = 2, 4, \n", + "SNAPPIN = 3, \n", + "STREET = 1, \n", + "THE = 1, \n", + "THERE = 1, \n", + "WAH = 2, 4, \n", + "WALKIN = 1, \n", + "WAS = 1, \n" + ] + } + ], + "source": [ + "program = \"\"\"\n", + "for i, line in enumerate(input):\n", + " for word in re.findall(r\"\\w+\", line.upper()):\n", + " $word += str(i) + ', '\n", + "del i, line, word\n", + "\"\"\"\n", + "\n", + "snobol(program, data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looks good to me! \n", + "\n", + "But sadly, the grader for the course did not agree, complaining that my program was not extensible: what if I wanted to cover two or more files in one run? What if I wanted the output to have a slightly different format? I argued that [YAGNI](https://en.wikipedia.org/wiki/You_aren%27t_gonna_need_it), and if the requirements\n", + "changed, *then* I would write the necessary 40 or 60 lines, but there's no sense doing that until then. The grader was not impressed with my arguments and I got points taken off. \n", + "\n", + "Still, I was happy with my program. I felt like the\n", + "purpose of the assignment was to get familiar with a new programming language with some different idioms/paradigms. By using the indirection operator I learned more about \"thinking different\" than if I had written the expected program.\n", + "\n", + "# TFW you flunk AI\n", + "\n", + "Here's another example that I had completely forgotten about until 2016, when I was cleaning out a filing cabinet and came across my old college transcript. It turns out that *I flunked an AI course!* (Or at least, didn't complete it.) This course was offered by Prof. Richard Millward in the Cognitive Science program. I certainly remember a lot of influential material from this class: we read David Marr, we read Winston's just-published *Psychology of Computer Vision*, we read a chapter from Duda and Hart which was then only a few years old. The things I learned in that course have stuck with me for decades, but one thing that didn't stick is that, according to my transcript, I never completed the course! I'm not sure what happened. I did an independent study with Ulf Grenander that semester; my best guess\n", + "is that when I started doing the independent study that would have put me over some limit, and so I had to drop the AI course. \n", + "\n", + "So in both the concordance program and the Cognitive Science AI class, I had a great experience and I learned a lot, even if it wasn't well-reflected in official credit. The moral is: look for the good experiences, and don't worry about the official credit.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pytudes/ipynb/Sudoku IPython Notebook.ipynb b/pytudes/ipynb/Sudoku IPython Notebook.ipynb new file mode 100644 index 0000000..6ca53a9 --- /dev/null +++ b/pytudes/ipynb/Sudoku IPython Notebook.ipynb @@ -0,0 +1,1275 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
Peter Norvig, Nov. 2016
\n", + "\n", + "# Solving Any Sudoku Puzzle, Quickly\n", + "\n", + "Sudoku is a logic puzzle game. Given a grid like the one on below left, fill in the blank squares so that each column, row, and 3x3 box contains all the digits from 1 to 9. The solution is shown below right:\n", + "\n", + "
\n", + "\n", + "In this notebook I develop and implement an algorithm to solve any\n", + "Sudoku puzzle, quickly. It turns out to be straightforward using two computer science ideas: constraint\n", + "satisfaction and search. \n", + "This notebook is an expansion of my\n", + "previous Sudoku essay; that\n", + "one emphasized simplicity; this one emphasizes\n", + "efficiency and covers everything in more detail.\n", + "\n", + "\n", + "\n", + "We will use these definitions:\n", + "\n", + "- A **grid** is a 9×9 array of **squares**. We can partition the grid\n", + "in three ways: \n", + " - as 9 rows (of size 9×1) stacked on top of\n", + "each other; \n", + " - as 9 columns (of size 1×9) placed left-to-right; \n", + " - as 9 boxes (of size 3×3) arranged in a 3×3 array.\n", + "- A **unit** is a row,\n", + "column, or box: a collection of 9 squares.\n", + "- A **puzzle** is a grid in which some squares have been\n", + "filled with a **digit** and some are **empty**. \n", + "- A **solution** is a grid where every unit contains\n", + "all the digits from 1 to 9, and the filled squares of the original puzzle remain unchanged\n", + "in the solution. \n", + "- A **well-formed puzzle** has exactly one solution.\n", + "- A **peer** of a square is any other\n", + "square in the same row, column, and box.\n", + "\n", + "## Sudoku data structures\n", + "\n", + "Here are the choices I made to implement these concepts. I represent a grid as an 81-element list, with the upper left square being element 0, then going right-to-left and top-to-bottom with the lower-right square being element 80." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "Grid = list # an 81-element list, left-to-right, top-to-bottom\n", + "Unit = tuple # a 9-element sequence\n", + "Square = int # an int from 0 to 80; index into a Grid\n", + "Digit = str # a character from '1' to '9'\n", + "Digits = str # One or more digits\n", + "empty = '.' # a square that has not been filled by a digit\n", + "\n", + "puzzle0 = Grid('53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79')\n", + "answer0 = Grid('534678912672195348198342567859761423426853791713924856961537284287419635345286179')\n", + "\n", + "def is_solution(solution: Grid, puzzle: Grid) -> bool: \n", + " \"\"\"A solution to a puzzle is a grid where every unit contains all the digits 1 to 9\n", + " and the filled squares of the original puzzle remain unchanged in the solution.\"\"\"\n", + " def unit_contents(unit): return {solution[s] for s in unit}\n", + " return (all(unit_contents(unit) == digits for unit in all_units) and\n", + " all(puzzle[s] == solution[s] for s in filled_squares(puzzle)))\n", + "\n", + "def filled_squares(grid):\n", + " \"All the squares in a grid that are already filled with a digit.\"\n", + " return (s for s in squares if grid[s] in digits)\n", + "\n", + "def empty_squares(grid):\n", + " \"All the squares in a grid that are not already filled with a digit.\"\n", + " return (s for s in squares if grid[s] not in digits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Utility Functions and Displaying Grids\n", + "\n", + "Here is the code to set up all the units and peers and related data structures, alog with the imports and utility functions we will need later on, and code for displaying grids in a pretty fashion. Although we will mostly use 81-square grids, the function `use_grid_size(n)` can be used to work with `n`-square grids, where `n` can be 1, 16, 81, or 256." + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import itertools\n", + "import time\n", + "from IPython.display import HTML, display\n", + "\n", + "def use_grid_size(n=81):\n", + " global N, D, B, digitstr, digits, squares, all_units, units, peers\n", + " N = n # Number of squares in the grid\n", + " D = isqrt(N) # Number of different digits\n", + " B = isqrt(D) # A boxis of size B x B\n", + " rows = range(0, N, D) # Squares at left of each row: (0, 9, 18, ... 72)\n", + " cols = range(D) # Squares at top of each column: (0, 1, 2, ... 8)\n", + " digitstr = '123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ_'[:D] # E.g., '123456789' for D=9\n", + " digits = set(digitstr) # E.g., {1, 2, 3, 4, 5, 6, 7, 8, 9} for D=9\n", + " squares = range(N) # Al1 the squares\n", + " all_rows = [cross(rows, [c]) for c in cols]\n", + " all_cols = [cross([r], cols) for r in rows]\n", + " all_boxes = [cross(rs, cs) for rs in chunk(rows, B) for cs in chunk(cols, B)]\n", + " all_units = all_rows + all_cols + all_boxes\n", + " units = [tuple(unit for unit in all_units if s in unit)\n", + " for s in squares]\n", + " peers = [tuple(union(units[s]) - {s})\n", + " for s in squares]\n", + "\n", + "def cross(rows, cols) -> Unit:\n", + " \"A unit of all the ways we can add one of the row numbers to one of the column numbers.\"\n", + " return Unit(r + c for r in rows for c in cols)\n", + "\n", + "def union(collections) -> set: \"Set union\"; return set().union(*collections)\n", + "\n", + "def isqrt(n) -> int: \"Integer square root.\"; return int(n ** 0.5)\n", + "\n", + "def chunk(sequence, B) -> list:\n", + " \"Chunk sequence into subsequences of length B.\"\n", + " return [sequence[i:i+B] for i in range(0, len(sequence), B)]\n", + "\n", + "def first(iterable) -> object: \n", + " \"Return the first item from iterable, or None.\"\n", + " return next(iterable, None)\n", + "\n", + "def show(grid):\n", + " \"Display the Sudoku grid.\"\n", + " use_grid_size(len(grid))\n", + " CSS = ''''''.replace('3', str(B))\n", + " table = '' + D * ('' + D * '
{}') + '
'\n", + " display(HTML(CSS + table.format(B, *grid)))" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
53..7....
6..195...
.98....6.
8...6...3
4..8.3..1
7...2...6
.6....28.
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(puzzle0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can how the numbering scheme for squares works; I'll display a grid that is filled, not with digits, but with square numbers. Then I'll show the units and peers for square 20:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(range(81))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((2, 11, 20, 29, 38, 47, 56, 65, 74),\n", + " (18, 19, 20, 21, 22, 23, 24, 25, 26),\n", + " (0, 1, 2, 9, 10, 11, 18, 19, 20))" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "units[20]" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 65, 2, 1, 9, 74, 11, 10, 18, 19, 21, 22, 23, 24, 25, 26, 29, 38, 47, 56)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "peers[20]" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
BBC......
BBC......
RRXrrrrrr
..c......
..c......
..c......
..c......
..c......
..c......
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# A grid where 'X' marks square 20, 'r' marks squares in same row, 'c' marks squares in same column,\n", + "# and capital letters, 'C', 'R', and 'B', mark squares in the same box.\n", + "show(Grid('BBC......BBC......RRXrrrrrr..c........c........c........c........c........c......'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We need a test suite:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'pass'" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "puzzle0 = Grid('53..7....6..195....98....6.8...6...34..8.3..17...2...6.6....28....419..5....8..79')\n", + "answer0 = Grid('534678912672195348198342567859761423426853791713924856961537284287419635345286179')\n", + "wrong0 = Grid('532678912672195348198342567859761423426853791713924856961537284287419635345286179')\n", + "puzzle1 = Grid('4.7.6.8.5.3....9.....7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......')\n", + "answer1 = Grid('417369825632158947958724316825437169791586432346912758289643571573291684164875293')\n", + "wrong1 = Grid('427369825632158947958724316825437169791586432346912758289643571573291684164875293')\n", + "\n", + "def tests():\n", + " \"A suite of unit tests.\"\n", + " use_grid_size(81)\n", + " assert N == 81 and D == 9 and B == 3\n", + " assert len(squares) == 81\n", + " assert len(all_units) == 27\n", + " for s in squares:\n", + " assert len(units[s]) == 3 \n", + " assert len(peers[s]) == 20\n", + " assert union(['feed', 'beef', 'cafe', 'face']) == {'a', 'b', 'c', 'd', 'e', 'f'}\n", + " assert isqrt(16) == 4 and isqrt(81) == 9 and isqrt(256) == 16\n", + " assert cross((0, 9, 18), (0, 1, 2)) == (0, 1, 2, 9, 10, 11, 18, 19, 20)\n", + " assert chunk('abcdefghi', 3) == ['abc', 'def', 'ghi']\n", + " assert units[20] == ((2, 11, 20, 29, 38, 47, 56, 65, 74),\n", + " (18, 19, 20, 21, 22, 23, 24, 25, 26),\n", + " (0, 1, 2, 9, 10, 11, 18, 19, 20))\n", + " assert set(peers[20]) == {0, 1, 2, 9, 10, 11, 18, 19, 21, 22, \n", + " 23, 24, 25, 26, 29, 38, 47, 56, 65, 74}\n", + " assert is_solution(answer0, puzzle0)\n", + " assert not is_solution(wrong0, puzzle0)\n", + " assert is_solution(answer1, puzzle1)\n", + " assert not is_solution(wrong1, puzzle1)\n", + " return 'pass'\n", + "\n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solver 1: Generate and Test\n", + "\n", + "Here is a simple (but very inefficient) algorithm to solve Sudoku puzzles:\n", + "\n", + "> **Generate and test solver:**\n", + "First fill in all the\n", + "squares with digits. Then check to see if we have a\n", + "solution. If not, then fill the squares with a different\n", + "combination of digits. Repeat with different combinations until a solution is found.\n", + "\n", + "\n", + "

Sometimes generate and test is the best you can do. Herb\n", + "Simon, in his classic book [The Sciences of\n", + "the Artificial](http://books.google.com/books?id=k5Sr0nFw7psC) (page 194), describes the task of opening a\n", + "safe that has ten dials, each with 100 numbers on it. If the safe is\n", + "well-designed there is no better approach than to generate-and-test\n", + "with all\n", + "10010 combinations. The generate-and-test solver is simple:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def solve(puzzle): \n", + " \"Find a solution to the puzzle.\"\n", + " return first(grid for grid in generate_all_grids(puzzle) \n", + " if is_solution(grid, puzzle))\n", + "\n", + "def generate_all_grids(grid):\n", + " \"An iterable of all possible ways to fill in grid.\"\n", + " values = [(digitstr if d is empty else d) for d in grid]\n", + " return itertools.product(*values)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.210 seconds\n" + ] + } + ], + "source": [ + "def do1(puzzle):\n", + " \"Do one puzzle; showing puzzle and solution and printing elapsed time.\"\n", + " show(puzzle)\n", + " t0 = time.clock()\n", + " solution = solve(Grid(puzzle))\n", + " t1 = time.clock()\n", + " assert is_solution(solution, puzzle)\n", + " show(solution)\n", + " print('{:.3f} seconds'.format(t1 - t0))\n", + "\n", + "use_grid_size(16)\n", + "tiny = Grid('...44.3..4...241')\n", + "do1(tiny)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "That works fine for a 4x4 array. But on a 9x9, with say, 64 empty squares, there will be 964 combinations of digits.\n", + "Suppose we have access to a secret new custom 10 GHz\n", + "GPU capable of doing 1024 generate and\n", + "test operations in a single clock cycle, and let's say we can fit a million of these units\n", + "in a data center, and we could afford a hundred data centers,\n", + "and while we're shopping, let's say we also pick up a time\n", + "machine and go back 13 billion years to the early days of the universe,\n", + "and a fleet of starships with which we visit a trillion galaxies and\n", + "in each galaxy convince the inhabitants of a billion planets to each\n", + "buy a similar setup, and we all start our programs\n", + "running, managing to distribute the cases perfectly so that no\n", + "computation is duplicated or wasted. Then we can [estimate](http://www.google.com/search?aq=f&sourceid=chrome&ie=UTF-8&q=10+GHz+*+1024+*+1+million+*+100+*+1+trillion+*+1+billion+*+13+billion+years+%2F+9**64+in+percent)\n", + "that we'd be only 3% of the way through with the first puzzle.\n", + "\n", + "

Generate and test is not the algorithm you're looking for. Move along." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Solver 2: Combinatorial Search\n", + "\n", + "In Simon's safe example, he next supposes a defective safe, in which a\n", + "faint click is heard whenever a dial is set to the right position.\n", + "With this safe it only takes 100 × 10 trials to discover the\n", + "correct combination, not 10010. The moral is that if we have some selective\n", + "knowledge of components of the safe (or puzzle) that tell us if a\n", + "partial solution is on track, our search will be\n", + "much easier.\n", + "\n", + "

Fortunately for us, Sudoku is like the defective safe. To be\n", + "precise, it is like a safe with 81 dials, each with 9 numbers,\n", + "and sometimes if you put one of the dials in the wrong position you hear a sound,\n", + "but sometimes not (depending on the positions of the other dials and\n", + "on how carefully you listen). For\n", + "example, in the lower-left corner of the tiny puzzle above, if we try\n", + "1, 2, or 4 we would immediately get feedback that those digits won't\n", + "work, because they already appear elsewhere in the bottom row.\n", + "Therefore, the lower-left corner must be filled by a 3. There are\n", + "262,144 ways to fill in the 9 empty squares, but right away we can eliminate\n", + "196,608 of them; we need only consider the ones that have a 3 in that position.\n", + "\n", + "

Unfortunately for us, Sudoku does not give up all its secrets so\n", + "easily. Sometimes, when we consider a square, we can't immediately\n", + "tell what digit to put there. For example, in the upper-left of the tiny\n", + "puzzle, only 4 can be eliminated as a possibility. That's ok--we're\n", + "allowing ourselves the use of an eraser, so just guess one of the\n", + "remaining three possibilities; if it doesn't pan out, erase it and try one\n", + "of the others. This gives us:\n", + "\n", + "\n", + "

Combinatorial search algorithm: Start filling squares with digits, one at a time, always making sure\n", + "that the digit we put in a square is not the same as any peer. If there are several possible digits, pick one, but remember the others. If we\n", + "reach a square where every digit conflicts with a peer, back\n", + "up and consider a different digit for the previous square. Stop when\n", + "we successfully fill every square, or give up if we tried all\n", + "possibilities without finding a solution.
\n", + "\n", + "The progress of this algorithm can be described as a search\n", + "tree, where each node represents a partially-filled (incremental) state of the\n", + "puzzle, and a branch corresponds to filling in a square with a\n", + "digit. (We display the new digits in red.)\n", + "Here is a search tree for the tiny puzzle:\n", + "\n", + "
\n", + "\n", + "

A few things to note about this particular search tree:\n", + "

    \n", + "
  • Each successive level fills in one square, so with nine empty\n", + " squares, the solution must appear on the ninth level of the tree\n", + " (counting the root as the zeroth level).\n", + "
  • This is a well-formed puzzle, so there will be exactly one solution,\n", + " and thus exactly one node at the ninth level.\n", + "
  • A rectangle with a black X indicates an\n", + " inconsistency: there is no way to continue because the next\n", + " unfilled square\n", + " already has all four digits taken by its peers.\n", + "
  • When we hit a X we have to pull out our eraser, or in\n", + " other words we have to backtrack--go up a level in the tree and\n", + " try the next possible digit for the previous square. On the far-left\n", + " branch of the tree we have to back up three levels---erasing first the 2, then the 3, then the\n", + " 1--before we can pencil in another possible digit \n", + " (the 2 in the upper-left corner which we\n", + " see in the middle branch of the tree).\n", + " \n", + "
  • The rightmost branch of the tree remains unexplored--the search\n", + " proceeds left-to-right and has not got to that brnach yet. (But since the\n", + " puzzle is well-formed and we have found the solution, we know the\n", + " unexplored branches cannot contain another solution.)\n", + " \n", + "
\n", + "

The code to implement combinatorial search is straightforward:" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def search(grid) -> Grid:\n", + " \"\"\"Select an unfilled square, try each possible digit there, recursively searching.\n", + " When all squares filled: success; when no more digits to try: return None for failure.\"\"\"\n", + " square = select_empty_square(grid)\n", + " if square is None: # No empty square means the grid is a solution\n", + " return grid\n", + " for digit in possible_digits(grid, square):\n", + " result = search(assign(Grid(grid), square, digit))\n", + " if result: \n", + " return result\n", + "\n", + "solve = search\n", + "\n", + "def select_empty_square(grid) -> Square:\n", + " \"Return the first square that is not filled with a digit; or None if all squares are filled.\"\n", + " return (None if grid is None else first(empty_squares(grid)))\n", + "\n", + "def assign(grid, s, d) -> Grid:\n", + " \"For now, simply assign grid[s] = d.\"\n", + " grid[s] = d\n", + " return grid\n", + "\n", + "def possible_digits(grid, s):\n", + " \"A square can be filled with any digit that is not already taken by a peer.\"\n", + " peer_digits = {grid[s] for s in peers[s]}\n", + " return digits - peer_digits" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "The key function is search. It obeys the convention that if\n", + "it is passed Inconsistent (to indicate an invalid grid) it returns\n", + "Inconsistent, meaning that no solution can be found. Otherwise it\n", + "selects some unfilled square to work on. If select_square\n", + "returns None that is actually good news: it means that all\n", + "the squares are already filled, and we are done: we have a solution,\n", + "so we just return it. Otherwise, for each possible\n", + "digit that could fill square s we try to assign that digit to\n", + "s and search for a solution from there. If some call to\n", + "search succeeds, return it; but if a digit assignment causes\n", + "the search to fail, just keep going with the next digit assignment.\n", + "If all digit assignments fail, then the whole call to search\n", + "fails, and we back up to the previous recursive call. \n", + "\n", + "

We call this type of combinatorial search a constraint\n", + " satisfaction search: think of each square as being a\n", + " variable that can take on a value (a digit), and the\n", + " rules of Sudoku as being constraints on the possible values.\n", + " A state in the search tree is then an assignment of values to some\n", + " subset of variables in a way that does not violate any constraint.\n", + "The constraint satisfaction\n", + " approach has found many fun applications in puzzles and serious\n", + " applications in problem solving.\n", + "\n", + "

Here we see solve (and therefore search) in action:\n", + "\n", + "\n", + "\n", + "That's all there is to it! The only reason we don't stop this article\n", + "now is that the program is still too slow for some purposes. We're\n", + "not talking billions-of-years slow, but it did take 3 minutes and 45\n", + "seconds to solve this puzzle (a rather hard one). On a benchmark of\n", + "50 easy puzzles the program was fast enough, taking a total of 9.5\n", + "seconds (a rate of 5\n", + "puzzles per second, or 5 Hz). \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclock\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpuzzle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclock\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32massert\u001b[0m \u001b[0mis_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpuzzle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36msolve\u001b[0;34m(puzzle)\u001b[0m\n\u001b[1;32m 2\u001b[0m grid = Grid(digitstr if d is empty else d\n\u001b[1;32m 3\u001b[0m for d in puzzle)\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0msearch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mpossible_digits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m->\u001b[0m \u001b[0mDigits\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36msearch\u001b[0;34m(grid)\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mdigit\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpossible_digits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msquare\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msearch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msquare\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdigit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36msearch\u001b[0;34m(grid)\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mdigit\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpossible_digits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msquare\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msearch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0massign\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msquare\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdigit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36msearch\u001b[0;34m(grid)\u001b[0m\n\u001b[1;32m 2\u001b[0m \"\"\"Select an unfilled square, try each possible digit there, recursively searching.\n\u001b[1;32m 3\u001b[0m When all squares filled: success; when no more digits to try: return None for failure.\"\"\"\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0msquare\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mselect_empty_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msquare\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# No empty square means the grid is a solution\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mselect_empty_square\u001b[0;34m(grid)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mselect_empty_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\"Return an unfilled square with the fewest possible digits; or None if no unfilled squares.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0munfilled\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msquares\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munfilled\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0munfilled\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mselect_empty_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\"Return an unfilled square with the fewest possible digits; or None if no unfilled squares.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0munfilled\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msquares\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munfilled\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0munfilled\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: 'NoneType' object is not subscriptable" + ] + } + ], + "source": [ + "do1(puzzle1) # Should be 0.2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Benchmarking" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "puzzles = \"\"\"\n", + "4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......\n", + "52...6.........7.13...........4..8..6......5...........418.........3..2...87.....\n", + "6.....8.3.4.7.................5.4.7.3..2.....1.6.......2.....5.....8.6......1....\n", + "48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....\n", + "....14....3....2...7..........9...3.6.1.............8.2.....1.4....5.6.....7.8...\n", + "......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.\n", + "6.2.5.........3.4..........43...8....1....2........7..5..27...........81...6.....\n", + ".524.........7.1..............8.2...3.....6...9.5.....1.6.3...........897........\n", + "6.2.5.........4.3..........43...8....1....2........7..5..27...........81...6.....\n", + ".923.........8.1...........1.7.4...........658.........6.5.2...4.....7.....9.....\n", + "6..3.2....5.....1..........7.26............543.........8.15........4.2........7..\n", + ".6.5.1.9.1...9..539....7....4.8...7.......5.8.817.5.3.....5.2............76..8...\n", + "..5...987.4..5...1..7......2...48....9.1.....6..2.....3..6..2.......9.7.......5..\n", + "3.6.7...........518.........1.4.5...7.....6.....2......2.....4.....8.3.....5.....\n", + "1.....3.8.7.4..............2.3.1...........958.........5.6...7.....8.2...4.......\n", + "6..3.2....4.....1..........7.26............543.........8.15........4.2........7..\n", + "....3..9....2....1.5.9..............1.2.8.4.6.8.5...2..75......4.1..6..3.....4.6.\n", + "45.....3....8.1....9...........5..9.2..7.....8.........1..4..........7.2...6..8..\n", + ".237....68...6.59.9.....7......4.97.3.7.96..2.........5..47.........2....8.......\n", + "..84...3....3.....9....157479...8........7..514.....2...9.6...2.5....4......9..56\n", + "\"\"\".split()[5:6]\n", + "\n", + "benchmarks = {}\n", + "\n", + "def benchmark(label, puzzles=puzzles):\n", + " \"Run `solve` on these puzzles; record and verify results for this label; print all results.\"\n", + " n = len(puzzles)\n", + " t0 = time.clock()\n", + " results = [solve(Grid(p)) for p in puzzles]\n", + " avg = (time.clock() - t0) / len(puzzles)\n", + " for (r, p) in zip(results, puzzles):\n", + " assert is_solution(r, p) \n", + " benchmarks[label] = '{:.3f} sec/puzzle ({:.1f} Hz)'.format(avg, 1/avg)\n", + " for L in sorted(benchmarks):\n", + " print('{:10s} {}'.format(L, benchmarks[L]))" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(puzzles)" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3. AC 11.219 sec/puzzle (0.1 Hz)\n" + ] + } + ], + "source": [ + "benchmark('3. AC')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4. Dual Consistency" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def dual_consistent(grid, s, d):\n", + " \"\"\"After eliminating d from grid[s], check each unit of s and make sure there is some\n", + " position in the unit for d. If only one possible place left for d, assign it.\"\"\"\n", + " for u in units[s]:\n", + " places_for_d = [s2 for s2 in u if d in grid[s2]]\n", + " nplaces = len(places_for_d)\n", + " if nplaces==0 or (nplaces==1 and not assign(grid, places_for_d[0], d)):\n", + " return None\n", + " return True" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3. AC 11.219 sec/puzzle (0.1 Hz)\n", + "4. AC+Dual 26.392 sec/puzzle (0.0 Hz)\n" + ] + } + ], + "source": [ + "constraints = [arc_consistent, dual_consistent]\n", + "benchmark('4. AC+Dual')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# 5. Naked pairs" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def naked_pairs(grid, s, ignore):\n", + " \"\"\"Look for two squares in a unit with the same two possible digits. \n", + " For example, if s and s2 both have the value '35', then we know that 3 and 5\n", + " must go in those two squares. We don't know which is which, but we can eliminate \n", + " 3 and 5 from any other square s3 that is in the unit.\"\"\"\n", + " vals = grid[s]\n", + " if len(vals) != 2: return True\n", + " for u in units[s]:\n", + " for s2 in u:\n", + " if s2 != s and grid[s2] == vals:\n", + " # Found naked pair: s and s2; remove their two vals from others in unit\n", + " for s3 in u:\n", + " if s != s3 != s2:\n", + " if not all(eliminate(grid, s3, v) for v in vals):\n", + " return None\n", + " return True" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3. AC 11.219 sec/puzzle (0.1 Hz)\n", + "4. AC+Dual 26.392 sec/puzzle (0.0 Hz)\n", + "5. AC+D+NP 29.821 sec/puzzle (0.0 Hz)\n" + ] + } + ], + "source": [ + "constraints = [arc_consistent, dual_consistent, naked_pairs]\n", + "benchmark('5. AC+D+NP')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 6. Variable Ordering" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def select_empty_square(grid):\n", + " \"Return an unfilled square with the fewest possible digits; or None if no unfilled squares.\"\n", + " unfilled = [s for s in squares if len(grid[s]) > 1]\n", + " return min(unfilled, key=lambda s: len(grid[s])) if unfilled else None" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "TypeError", + "evalue": "'NoneType' object is not subscriptable", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mbenchmark\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'6. VarOrd'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36mbenchmark\u001b[0;34m(label, puzzles)\u001b[0m\n\u001b[1;32m 28\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpuzzles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0mt0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclock\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 30\u001b[0;31m \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGrid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpuzzles\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 31\u001b[0m \u001b[0mavg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclock\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mt0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpuzzles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 32\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpuzzles\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 28\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m 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squares filled: success; when no more digits to try: return None for failure.\"\"\"\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0msquare\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mselect_empty_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msquare\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# No empty square means the grid is a solution\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m\u001b[0m in \u001b[0;36mselect_empty_square\u001b[0;34m(grid)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mselect_empty_square\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\"Return an unfilled square with the fewest possible digits; or None if no unfilled squares.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0munfilled\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msquares\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munfilled\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m 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\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munfilled\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0ms\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0munfilled\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: 'NoneType' object is not subscriptable" + ] + } + ], + "source": [ + "benchmark('6. VarOrd')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "

However, if you want to solve a million hard puzzles, you probably\n", + "don't want to wait a few years, and you would prefer a\n", + "faster algorithm.\n", + "Look again at the search tree above, and consider how we can find the\n", + "solution faster. Here are four general strategies:\n", + "

    \n", + "
  1. We could try to move the solution to the left. Since we go top-down,\n", + " left-to-right, this means we would find it sooner. This can\n", + " potentially be done with better value ordering, the order in\n", + " which the function possible_values considers which digit to\n", + " try next. If we were able to choose right every time,\n", + " there would in effect be no search--the solution would be in the\n", + " lower-left corner of the tree and we would arrive at it directly\n", + " with no backtracking.\n", + "
  2. We could try to move the solution closer to the top. If we only\n", + " fill in one square at a time then the solution will always be at the\n", + " same level (the number of empty squares in the original puzzle).\n", + " But if we could fill in several squares at a time, the solution gets\n", + " closer to the top and we can find it faster. Filling in multiple\n", + " squares at a time can be accomplished with constraint\n", + " propagation--using the constraints imposed by the rules of Sudoku to\n", + " conclude that an unfilled square must take on a certain digit,\n", + " thus sanctioning us to fill in several squares at once.\n", + "
  3. We could prune branches (mark them with an X and backtrack)\n", + " earlier. This can also be done with\n", + " constraint propagation, but in this case rather than filling in\n", + " squares, we would notice that some\n", + " square has no possible digit, and thus that we can backtrack immediately.\n", + "
  4. We could consider the squares in a better order, a process called\n", + " variable ordering, which in our program is implemented by the\n", + " function select_square. At each node in\n", + " the tree we pick one square to branch on. The current\n", + " implementation of select_square just considers the squares\n", + " in order from 0 to 80 and chooses the first unfilled one, but it\n", + " could be more clever. A\n", + " different ordering could be better (or worse) for any of the three reasons above.\n", + "
" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/TSP.ipynb b/pytudes/ipynb/TSP.ipynb new file mode 100644 index 0000000..7e75acb --- /dev/null +++ b/pytudes/ipynb/TSP.ipynb @@ -0,0 +1,4651 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Traveling Salesperson Problem" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the [*Traveling Salesperson Problem*](http://en.wikipedia.org/wiki/Traveling_salesman_problem): \n", + "\n", + "> *Given a set of cities and the distances between each pair of cities, what is the shortest possible tour that visits each city exactly once, and returns to the starting city?*\n", + "\n", + "In this notebook we will develop some solutions to the problem, and more generally show *how to think about* solving a problem like this. [Elsewhere](https://research.googleblog.com/2016/09/the-280-year-old-algorithm-inside.html) you can read about how the algorithms developed here are used in serious applications that millions of people rely on every day.\n", + "\n", + "\n", + "
An example tour.
\n", + " \n", + "# Understanding What We're Talking About (Vocabulary)\n", + "\n", + "Do we understand precisely what the problem is asking? Do we understand all the concepts that the problem talks about? Do we understand them well enough to implement them in a programming language? Let's take a first pass:\n", + "\n", + "- **A set of cities**: We will need to represent a set of cities; Python's `set` datatype might be appropriate.\n", + "- **Distance between each pair of cities**: If `A` and `B` are cities, this could be a function, `distance(A, B),` or a table lookup, `distance[A][B]`. The resulting distance will be a real number.\n", + "- **City**: All we have to know about an individual city is how far it is from other cities. We don't have to know its name, population, best restaurants, or anything else. So a city could be just an integer (0, 1, 2, ...) used as an index into a distance table, or a city could be a pair of (x, y) coordinates, if we are using straight-line distance on a plane.\n", + "- **Tour**: A tour is a specified order in which to visit the cities; Python's `list` or `tuple` datatypes would work. For example, given the set of cities `{A, B, C, D}`, a tour might be the list `[B, D, A, C]`, which means to travel from `B` to `D` to `A` to `C` and finally back to `B`.\n", + "- **Shortest possible tour**: The shortest tour is the one whose tour length is the minimum of all tours.\n", + "- **Tour length**: The sum of the distances between adjacent cities in the tour (including the last city back to the first city). Probably a function, `tour_length(tour)`.\n", + "- **What is ...**: We can define a function to answer the question *what is the shortest possible tour?* The function takes a set of cities as input and returns a tour as output. I will use the convention that any such function will have a name ending in the letters \"`tsp`\", the traditional abbreviation for Traveling Salesperson Problem.\n", + "\n", + "At this stage I have a rough sketch of how to attack the problem. I don't have all the answers, and I haven't committed to specific representations for all the concepts, but I know what all the pieces are, and I don't see anything that stops me from proceeding." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here are the imports used throughout this notebook. I'm assuming Python 3." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "import random\n", + "import time\n", + "import itertools\n", + "import urllib\n", + "import csv\n", + "import functools\n", + "from statistics import mean, stdev" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# All Tours Algorithm: `alltours_tsp`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start with an algorithm that is guaranteed to solve the problem, although it is inefficient for large sets of cities:\n", + "\n", + "> **All Tours Algorithm**: *Generate all possible tours of the cities, and choose the shortest tour (the one with minimum tour length).*\n", + "\n", + "My design philosophy is to first write an English description of the algorithm, then write Python code that closely mirrors the English description. This will probably require some auxiliary functions and data structures; just assume they exist; put them on a TO DO list, and eventually define them with the same design philosophy.\n", + "\n", + "Here is the start of the implementation:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def alltours_tsp(cities):\n", + " \"Generate all possible tours of the cities and choose the shortest tour.\"\n", + " return shortest_tour(alltours(cities))\n", + "\n", + "def shortest_tour(tours): \n", + " \"Choose the tour with the minimum tour length.\"\n", + " return min(tours, key=tour_length)\n", + "\n", + "# TO DO: Data types: cities, tours, Functions: alltours, tour_length" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: In Python `min(`*collection*`,key=`*function*`)` means to find the element *x* that is a member of *collection* such that *function(x)* is minimized. So `shortest` finds the tour whose `tour_length` in the minimal among the tours. \n", + "\n", + "This gives us a good start; the Python code closely matches the English description. And we know what we need to do next: represent cities and tours, and implement the functions `alltours` and `tour_length`. Let's start with tours.\n", + "\n", + "\n", + "Representing Tours\n", + "------------------\n", + "\n", + "A tour starts in one city, and then visits each of the other cities in order, before returning to the start city. A natural representation of a tour is a sequence of cities. For example `(1, 2, 3)` could represent a tour that starts in city 1, moves to 2, then 3, and finally returns to 1. \n", + "\n", + "**Note**: I considered using `(1, 2, 3, 1)` as the representation of this tour. I also considered an ordered list of **edges** between cities: \n", + "`((1, 2), (2, 3), (3, 1))`. In the end, I decided `(1, 2, 3)` was simplest.\n", + " \n", + "\n", + "Now for the `alltours` function. If a tour is a sequence of cities, then all the tours are *permutations* of the set of all cities. A function to generate all permutations of a set is already provided in Python's standard `itertools` library module; we can use it as our implementation of `alltours`:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "alltours = itertools.permutations " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For *n* cities there are *n*! (that is, the factorial of *n*) permutations.\n", + "Here's are all 3! = 6 tours of 3 cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cities = {1, 2, 3}\n", + "\n", + "list(alltours(cities))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The length of a tour is the sum of the lengths of each edge in the tour; in other words, the sum of the distances between consecutive cities in the tour, including the distance form the last city back to the first:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def tour_length(tour):\n", + " \"The total of distances between each pair of consecutive cities in the tour.\"\n", + " return sum(distance(tour[i], tour[i-1]) \n", + " for i in range(len(tour)))\n", + "\n", + "# TO DO: Functions: distance, Data types: cities" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: I use one Python-specific trick: when `i` is 0, then `distance(tour[0], tour[-1])` gives us the wrap-around distance between the first and last cities, because `tour[-1]` is the last element of `tour`. \n", + "\n", + "Representing Cities\n", + "--------------------------------\n", + "\n", + "We determined that the only thing that matters about cities is the distance between them. But before we can decide about how to represent cities, and before we can define `distance(A, B)`, we have to make a choice. In the fully general version of the TSP, the \"distance\" between two cities could be anything: it could factor in the amount of time it takes to travel between cities, the twistiness of the road, or anything else. The `distance(A, B)` might be different from `distance(B, A)`. So the distances could be represented by a matrix `distance[A][B]`, where any entry in the matrix could be any (non-negative) numeric value.\n", + " \n", + "But we will ignore the fully general TSP and concentrate on an important special case, the **Euclidean TSP**, where the distance between any two cities is the [Euclidean distance](http://en.wikipedia.org/wiki/Euclidean_distance), the straight-line distance between points in a two-dimensional plane. So a city can be represented by a two-dimensional point: a pair of *x* and *y* coordinates. We will use the constructor function `City`, so that `City(300, 0)` creates a city with x-coordinate of 300 and y coordinate of 0. Then `distance(A, B)` will be a function that uses the *x* and *y* coordinates to compute the distance between `A` and `B`.\n", + "\n", + "Representing Points and Computing `distance`\n", + "---\n", + " \n", + "OK, so a city can be represented as just a two-dimensional point. But how will we represent points? Here are some choices, with their pros and cons:\n", + "\n", + "* **tuple:** A point is a two-tuple of (*x*, *y*) coordinates, for example, `(300, 0)`. **Pro:** Very simple. \n", + "**Con:** doesn't distinguish Points from other two-tuples. \n", + " \n", + "* **class:** Define a custom `Point` class with *x* and *y* slots. **Pro:** explicit, gives us `p.x` and `p.y` accessors. **Con:** less efficient.\n", + " \n", + "* **complex:** Python already has the two-dimensional point as a built-in numeric data type, but in a non-obvious way: as `complex` numbers, which inhabit the two-dimensional (real × imaginary) plane. **Pro:** efficient. **Con:** a little confusing; doesn't distinguish Points from other complex numbers.\n", + "* **subclass of complex:** All the pros of `complex`, and eliminating the major con.\n", + "\n", + "\n", + "Any of these choices would work perfectly well; I decided to use a subclass of `complex`:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Cities are represented as Points, which are a subclass of complex numbers\n", + "\n", + "class Point(complex):\n", + " x = property(lambda p: p.real)\n", + " y = property(lambda p: p.imag)\n", + " \n", + "City = Point\n", + "\n", + "def distance(A, B): \n", + " \"The distance between two points.\"\n", + " return abs(A - B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here's an example of computing the distance between two cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "5.0" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = City(3, 0)\n", + "B = City(0, 4)\n", + "distance(A, B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Random Sets of Cities\n", + "---\n", + "\n", + "The input to a TSP algorithm should be a set of cities. I can make a random set of *n* cities by calling `City` *n* times, each with different random *x* and *y* coordinates:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{(193+375j), (427+384j), (497+585j), (179+546j), (224+543j), (245+643j)}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "{City(random.randrange(1000), random.randrange(1000)) for c in range(6)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function `Cities` does that (and a bit more):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Cities(n, width=900, height=600, seed=42):\n", + " \"Make a set of n cities, each with random coordinates within a (width x height) rectangle.\"\n", + " random.seed(seed * n)\n", + " return frozenset(City(random.randrange(width), random.randrange(height))\n", + " for c in range(n))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are three complications that I decided to tackle in `Cities`:\n", + "\n", + "1. IPython's matplotlib plots (by default) in a rectangle that is 1.5 times wider than it is high; that's why I specified a width of 900 and a height of 600. If you want the coordinates of your cities to be bounded by a different size rectangle, you can change width or height.\n", + "\n", + "2. Sometimes I want `Cities(n)` to be a true function, returning the same result each time. This is very helpful for getting repeatable results: if I run a test twice, I get the same results twice. \n", + "But other times I would like to be able to do an experiment, where, for example, I call `Cities(n)` 30 times and get 30 different sets, and I then compute the average tour length produced by my algorithm across these 30 sets. Can I get both behaviors out of one function? *Yes!* The trick is the additional optional parameter, `seed`. Two calls to `Cities` with the same `n` and `seed` parameters will always return the same set of cities, and two calls with different values for `seed` will return different sets. This is implemented by calling the function `random.seed`, which resets the random number generator.\n", + "\n", + "3. Once I create a set of Cities, I don't want anyone messing with my set. For example, I don't want an algorithm that claims to \"solve\" a problem by deleting half the cities from the input set, then finding a tour of the remaining cities. Therefore, I make `Cities` return a `frozenset` rather than a `set`. A `frozenset` is *immutable*; nobody can change it once it is created. (Likewise, each city is immutable.)\n", + "\n", + "For example:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)})" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A set of 5 cities\n", + "Cities(5)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)}),\n", + " frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)}),\n", + " frozenset({(172+20j), (234+40j), (696+415j), (393+7j), (671+296j)})]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The exact same set of 5 cities each time\n", + "[Cities(5) for i in range(3)]" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[frozenset({(414+310j), (776+430j), (41+265j), (864+394j), (523+497j)}),\n", + " frozenset({(814+542j), (29+476j), (637+261j), (759+367j), (794+255j)}),\n", + " frozenset({(439+494j), (211+473j), (585+33j), (832+503j), (591+15j)})]" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A different set of 5 cities each time\n", + "[Cities(5, seed=i) for i in range(3)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we are ready to apply the `alltours_tsp` function to find the shortest tour:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((6+546j),\n", + " (199+147j),\n", + " (350+65j),\n", + " (737+26j),\n", + " (847+187j),\n", + " (891+465j),\n", + " (554+374j),\n", + " (505+548j))" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alltours_tsp(Cities(8))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "2509.307587720301" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tour_length(alltours_tsp(Cities(8)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Quick, is that the right answer? I have no idea, and you probably can't tell either. But if we could *plot* the tour we'd understand it better and might be able to see at a glance if the tour is optimal.\n", + "\n", + "Plotting Tours\n", + "---\n", + "\n", + "I define `plot_tour(tour)` to plot the cities (as circles) and the tour (as lines):" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_tour(tour): \n", + " \"Plot the cities as circles and the tour as lines between them.\"\n", + " plot_lines(list(tour) + [tour[0]])\n", + " \n", + "def plot_lines(points, style='bo-'):\n", + " \"Plot lines to connect a series of points.\"\n", + " plt.plot([p.x for p in points], [p.y for p in points], style)\n", + " plt.axis('scaled'); plt.axis('off')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tour(alltours_tsp(Cities(8)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks much better! To me, it looks like the shortest possible tour, although I don't have an easy way to prove it. Let's go one step further and define a function, `plot_tsp(algorithm, cities)` that will take a TSP algorithm (such as `alltours_tsp`) and a set of cities, apply the algorithm to the cities to get a tour, check that the tour is reasonable, plot the tour, and print information about the length of the tour and the time it took to find it:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_tsp(algorithm, cities):\n", + " \"Apply a TSP algorithm to cities, plot the resulting tour, and print information.\"\n", + " # Find the solution and time how long it takes\n", + " t0 = time.clock()\n", + " tour = algorithm(cities)\n", + " t1 = time.clock()\n", + " assert valid_tour(tour, cities)\n", + " plot_tour(tour); plt.show()\n", + " print(\"{} city tour with length {:.1f} in {:.3f} secs for {}\"\n", + " .format(len(tour), tour_length(tour), t1 - t0, algorithm.__name__))\n", + " \n", + "def valid_tour(tour, cities):\n", + " \"Is tour a valid tour for these cities?\"\n", + " return set(tour) == set(cities) and len(tour) == len(cities)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 city tour with length 2509.3 in 0.110 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(alltours_tsp, Cities(8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## All Non-Redundant Tours Algorithm (improved `alltours_tsp`)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We said there are *n*! tours of *n* cities, and thus 6 tours of 3 cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)]" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(alltours({1, 2, 3}))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But this is redundant: `(1, 2, 3)`, `(2, 3, 1)`, and `(3, 1, 2)` are three ways of describing the same tour. So let's arbitrarily say that all tours must start with the first city in the set of cities. We'll just pull the first city out, and then tack it back on to all the permutations of the rest of the cities. \n", + "\n", + "While we're re-assembling a tour from the start city and the rest, we'll take the opportunity to construct the tour as a *list* rather than a *tuple*. It doesn't matter much now, but later on we will want to represent *partial* tours, to which we will want to append cities one by one; appending can only be done to lists, not tuples." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def alltours(cities):\n", + " \"Return a list of tours, each a permutation of cities, but each one starting with the same city.\"\n", + " start = first(cities)\n", + " return [[start] + Tour(rest)\n", + " for rest in itertools.permutations(cities - {start})]\n", + "\n", + "def first(collection):\n", + " \"Start iterating over collection, and return the first element.\"\n", + " return next(iter(collection))\n", + "\n", + "Tour = list # Tours are implemented as lists of cities" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can verify that for 3 cities there are now only 2 tours (not 6) and for 4 cities there are 6 tours (not 24):" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[[1, 2, 3], [1, 3, 2]]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alltours({1, 2, 3})" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[[1, 2, 3, 4],\n", + " [1, 2, 4, 3],\n", + " [1, 3, 2, 4],\n", + " [1, 3, 4, 2],\n", + " [1, 4, 2, 3],\n", + " [1, 4, 3, 2]]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alltours({1, 2, 3, 4})" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note:** We could say that there is only one tour of three cities, because `[1, 2, 3]` and `[1, 3, 2]` are in some sense the same tour, one going clockwise and the other counterclockwise. However, I choose not to do that, for two reasons. First, it would mean we can never handle TSP problems where the distance from A to B is different from B to A. Second, it would complicate the code (if only by a line or two).\n", + "\n", + "We can verify that calling `alltours_tsp(Cities(8))` still works and gives the same tour with the same total distance. But it now runs faster:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 city tour with length 2509.3 in 0.018 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(alltours_tsp, Cities(8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's try a much harder 10-city tour:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2291.8 in 1.636 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(alltours_tsp, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Complexity of `alltours_tsp`\n", + "---\n", + "\n", + "It takes about 2 seconds on my machine to solve this 10-city problem. In general, the function `TSP` looks at (*n*-1)! tours for an *n*-city problem, and each tour has *n* cities, so the total time required for *n* cities should be roughly proportional to *n*!. This means that the time grows rapidly with the number of cities. *Really* rapidly. This table shows the actual time for solving a 10 city problem, and the exepcted time for solving larger problems:\n", + "\n", + "\n", + "
n expected time for `alltours_tsp(Cities(n))`\n", + "
10Covering 10! tours = 2 secs\n", + "
112 secs × 11! / 10! ≈ 22 secs\n", + "
122 secs × 12! / 10! ≈ 4 mins\n", + "
142 secs × 14! / 10! ≈ 13 hours\n", + "
162 secs × 16! / 10! ≈ 200 days\n", + "
182 secs × 18! / 10! ≈ 112 years\n", + "
252 secs × 25! / 10! ≈ 270 billion years\n", + "
\n", + "\n", + "There must be a better way ..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Approximate Algorithms" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What if we are willing to settle for a tour that is short, but not guaranteed to be shortest? Then we can save billions of years of compute time: we will show several *approximate* algorithms, which find tours that are typically within 10% of the shortest possible tour, and can handle thousands of cities in a few seconds. (**Note:** There are more sophisticated approximate algorithms that can handle hundreds of thousands of cities and come within 0.01% or better of the shortest possible tour.)\n", + "\n", + "So how do we come up with an approximate algorithm? Here are two general plans of how to create a tour:\n", + "\n", + "* **Nearest Neighbor Algorithm**: Make the tour go from a city to its nearest neighbor. Repeat.\n", + "* **Greedy Algorithm**: Find the shortest distance between any two cities and include that edge in the tour. Repeat.\n", + "\n", + "We will expand these ideas into full algorithms.\n", + "\n", + "In addition, here are four very general strategies that apply not just to TSP, but to any optimization problem. An **optimization problem** is one in which the goal is to find a solution that is best (or near-best) according to some metric,\n", + "out of a pool of many candidate solutions. The strategies are:\n", + "\n", + "* **Repetition Strategy**: Take some algorithm and re-run it multiple times, varying some aspect each time, and take the solution with the best score.\n", + "* **Alteration Strategy**: Use some algorithm to create a solution, then make small changes to the solution to improve it.\n", + "* **Ensemble Strategy**: Take two or more algorithms, apply all of them to the problem, and pick the best solution.\n", + "\n", + "And here are two more strategies that work for a wide variety of problems:\n", + "\n", + "* **Divide and Conquer**: Split the input in half, solve the problem for each half, and then combine the two partial solutions.\n", + "\n", + "* **Stand on the Shoulders of Giants** *or* **Just Google It**: Find out what others have done in the past, and either copy it or build on it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Nearest Neighbor Algorithm: `nn_tsp`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is a description of the nearest neighbor algorithm:\n", + "\n", + "> **Nearest Neighbor Algorithm:** *Start at any city; at each step extend the tour by moving from the previous city to its nearest neighbor that has not yet been visited.*\n", + "\n", + "So now, instead of considering all *n*! tours, we are generating a single tour. It takes O(*n*2 ) time to find the tour, because it has *n*-1 steps, and at each step we consider each of the remaining cities.\n", + "I implement the algorithm as follows:\n", + "\n", + "* \"*Start at any city*\": arbitrarily pick the first city. \n", + "* \"*extend the tour*\": append to the end of a list of cities.\n", + "* \"*by moving from the previous city*\": previous city is `tour[-1]`.\n", + "* \"*to its nearest neighbor*\": I will define the function `nearest_neighbor`.\n", + "* \"*that has not yet been visited*\": I will keep a set of `unvisited` cities.\n", + "\n", + "That gives us:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def nn_tsp(cities):\n", + " \"\"\"Start the tour at the first city; at each step extend the tour \n", + " by moving from the previous city to the nearest neighboring city, C,\n", + " that has not yet been visited.\"\"\"\n", + " start = first(cities)\n", + " tour = [start]\n", + " unvisited = set(cities - {start})\n", + " while unvisited:\n", + " C = nearest_neighbor(tour[-1], unvisited)\n", + " tour.append(C)\n", + " unvisited.remove(C)\n", + " return tour\n", + "\n", + "def nearest_neighbor(A, cities):\n", + " \"Find the city in cities that is nearest to city A.\"\n", + " return min(cities, key=lambda c: distance(c, A))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note:** In Python, as in the formal mathematical theory of computability, `lambda` (or λ) is the symbol for *function*, so \"`lambda c: distance(c, A)`\" means the function of `c` that computes the distance from `c` to the city `A`. \n", + "\n", + "We can compare the the slow (but optimal) `alltours_tsp` algorithm to the new fast (but approximate) `nn_tsp` algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2291.8 in 1.681 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(alltours_tsp, Cities(10))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So the nearest neighbor algorithm is a lot faster, but it didn't find the shortest tour. To understand where it went wrong, it would be helpful to know what city it started from. I can modify `plot_tour` by adding one line of code to highlight the start city with a red square:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_tour(tour):\n", + " \"Plot the cities as circles and the tour as lines between them. Start city is red square.\"\n", + " start = tour[0]\n", + " plot_lines(list(tour) + [start])\n", + " plot_lines([start], 'rs') # Mark the start city with a red square" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the tour moves clockwise from the start city, and mostly makes good decisions, but not optimal ones.\n", + "\n", + "We can compare the performance of these two algorithms on, say, eleven different sets of cities instead of just one:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[1.0,\n", + " 1.0,\n", + " 1.0,\n", + " 1.0,\n", + " 1.0118279018107388,\n", + " 1.0121039193389436,\n", + " 1.107851821362778,\n", + " 1.139713084817861,\n", + " 1.1531140497779002,\n", + " 1.1972133336642432,\n", + " 1.2160497559961319]" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def length_ratio(cities): \n", + " \"The ratio of the tour lengths for nn_tsp and alltours_tsp algorithms.\"\n", + " return tour_length(nn_tsp(cities)) / tour_length(alltours_tsp(cities))\n", + "\n", + "sorted(length_ratio(Cities(8, seed=i*i)) for i in range(11))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The ratio of `1.0` means the two algorithms got the same (optimal) result; that happened 4 times out of 10. The other times, we see that the `nn_tsp` produces a longer tour, by anything up to 21% worse, with a median of 1% worse.\n", + "\n", + "But more important than that 1% (or even 21%) difference is that the nearest neighbor algorithm can quickly tackle problems that the all tours algorithm can't touch in the lifetime of the universe. Finding a tour of 1000 cities takes well under a second:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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UM526k9aAvAmyBZZsUK5uE1fD0HeUIedCw5U7Uu5xDRFO2gP/GFX43fbEdvu1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\nMy+Ht25G753cPPfl1tEb2+N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B3NcwkwpEV/krihdDmyrltdOxxpQ8qvj51lV+lU4+Olc/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LAxWJcH1KVp4dItjF3Sy2tpDZjJi2z0qrKecDTIzdWdO9kf/rc7jGwM9uHCnbDodSzZluw8EH5M\n6QzTeXWg+tLh8bwXfgaLDxbC6bAvQtUTrKNIj5dwWsz4evLxRIC/l7rwt6p6wvE0g3PcdL1bmH9v\nSX/jzzb2Sa+H1TchfvwhyLSYNXUtivJZdkaRjRhuu6n7Vo3Jzk4oj1HTM3ly3X6msAWrhAN0uu8I\n/sY7LGaEPufX4xZhcwgusjPuhCWrUfvHQSgueMTAHX031pZSQoPAOqH69GvRNHzLQZrUsJbvsE6z\nkbvSrDK2y7YoXdLAIHcMqI1cVDj2usYtQm0RPy0v+KtArgCZDjIVtVONARkOdfMqdRTl2z5wYx7B\nIt/adjsIs7pnJr0Xr0UY2FCsPSN5rPqbEc8rOKJ1vb0fVXldWP68BuSA3P2r9mSnJ9bIxmpkmwoy\nhelQMS2ssP7P+0343/z9rIafd3mD+Xn5//di8VoxM+mwZfCXMSD1qP3kKZANaDq9OWik4UQ0u9Cn\nQfaGYc8Vc3C5bA7SCsYvSaKZe32m3416p9gDfNQraGrCC0EuRTNZfQfkB+gt6BoUfO23aqPw3ssm\nXOiYTrpZ+f3Ct4tQS+Zf3yffAvXvQfsbzRtdVjjqpBgRv6rWU58OEDhDoHOhkfn2tdz7fpAD09wE\nUW+1d+CGvlC/Gfo9mveQrvpEpyfY83+CHs9mMWaaGcHvstazwb5Zm3yXJ0vQtz8s4dv8nfs+lG1B\nFLsgUQl/FapTHwZyRzomnbwMRSgdyq5sS+EbwdDj0CCwJephk//g0jZmNMGA+cGgNa/dM+6EV19R\nXolA14YkqjQ3B78U3/3vsLiRmCjc9Is+z43H26iCgGkOPPD7ch3XRsfYPHAGhj4tADm+SNrpuE64\nU9VxHRtNxul4kL+kW1MazynbwXXJWpC1MGNTmjHCn84Ley/lon9zT3gCM+yFws0enpc5LdfbBp34\nzvOiqhwTpvhCgW4bKozil/wbBHobDo+NooiPcjXIF9L3ucNNUL8DTr61iAUJchnq8fRRVMWzvzuT\nmtQkYZpe+B48dzvIN4o6uMqH1Rp26TKNUviK4GFgy2OcXW2G+vxflZ7mtsC7vIb+8Rvh7tEp6DgE\n5GX1fLnk3ebFrbFvlHqTkbHu407yVHK9zdl44QrRpDoyAqQdAeOp1Zkjpj+xThUlRQdw50lTfbnm\nptqTn45R5FiKwoxO1PFFNgvb1bdD5XfHzg4ygA086uJ2qL72HRQPpyfIPq4SA+qH3i3/Yms7W3Ph\nXrYFetxTDkwanJZWaX5XzGHd5wG4eE1Fys8uOed7Vw6FJWvg9Nnpk7v46TDgUbh/kao00kA7hGn5\nwp9BBjmupS+ArFQ89/jbUAYe66CG2V6ry84LHaL9joXjGAVyg/u4Tao4/zo61hJ46cq/9aLeY3ID\nyD9Rg+mbIPfCkEXmd+JgkJPGn9YBIXpYZZ07kd1v058GcnUxdVUnO5T5sDC/gxpi6kDmw+I31ZvG\nSY83HeRndia3HRYmZpsilWvsyEZ4yeAFc+5XYEoi0mK1A9zsiyU+f3G2Ol033exY6sF6JjQVcAP6\nDchIh999EOQFkJFF24qIuD5vFP1c2fj1cIsTuOQYkJeL45Eh26OuoFH+MEvtUyScnxbVOLQBORvO\nscBr2BOeJO0laXnyP13SnwtydjF1fePPaU/o6o6t61/ddcvSFuTFtAyS7Ka3UaDXe5psxH9gTXwD\nzltaCdNP65VSjPdHTP3O/vHmelu3UVyTiW+mk9aL0M23bpO3/z6+uIYQTK/ld9eB3AxSKvqg1uBB\nk178pDdRw/6d9jSenvvkYUfC5dvgnEdc56OyiXZrrEQS+2lZ77i2WrfRG3DXRpvuP/h7W4yEObVh\nSr5wuhGb9oBcbed5ucgHDT/eQIxbYUpiboBuUnFR8071lgJYS+N/LvugUcefKMaF0e+tNMNXx6Bt\nQfrYDhOPpgNe0IjO5HeKpVH3efn93mUoMSqFvHNm58VBi4vJzNW6jWbeGrM4QTXYDw3q2V8/F3dQ\nlyXlUESvF3BV9x6KVtofTvujXaddlM4+HOjVJ7fjh7nt3QOoMXxI5KqrOTsePyjpBvJgdJBpdaAR\n10PRKDxPKhn0BIGEF81j3Eqvx5M7QQYUE6w00/B/2+ewHtRE0/7r1RheLN3s/W87G068CwbvdJHO\nLPTsg8V7yc5L7V7TDduPw5PmhuGNJ59rr7uhUj6Dhu9/Nf7dCRvhmM8VNz/1gg/GINhmGE7lhDvT\n0sKNrz1AuY6Nehtwi2R3o30470NQHfTv9rR4B3wM+wuQS9IweTbmmL4BFi+DsWvT1p+feVJBBkxU\nyck2prGvEorOi7axUPS2c4kEk5T46wrHLIT1oNVV6YT63wEGbQ7SaGBDxdU221wpXfo+CBe96+Zy\nZ5Ms3RO2az3+/LPZg/jcDOjyfpCnQcabx+NJie1vhAV/B7kLjvlcMa6IfQWOmxPNC3Hs7Kjr9YCd\naW898TfYXbQ0OGL0bCgDuuUS7KDH0XDF9pZ0cy10nbV0B3xMu4gywFB2X10n5mgDnR9sro0s2D//\n4rt4Jcw2QgKU6fFlkKUWw9VSeO4WkAaQ06IeO55bal0onH2CRHWhSZJ+86CTVsbphcjPEHWj/eI9\nzSElB9+Jsy2kOWz89eSB60ieA9RFeFfIfsJa21c3/gkbi6HLKcb0h+bfpw+8jNJxsqj79NnvQdtl\nuuGfEbpBNEhQLeNlB+sxP+3GjQL1Lazm3tCcT4t3oEzUI9B8rqV4Ju/zUHw9yaH0ZalvU3NsZPF9\nvXeKgknZYGClxK6Yhd5Hq+Grz1z/b0HOgMXLYey66KKzubHV+3+XqNO30/SSd1FQqH2LUJXFz132\nucoiQBR10Cldhi/Pe6OETn+KGwNIbxUQ5CPudcZ72NjHY1L1maEdzHRskLSBl0GBYKREdexjNsHU\nbcF2/Cq1vDctORvknubaG6r9tHgHykQdQ9nIBvIRGPsvy4a1GcXOjsFDj4COvRt0l2o3qxowD8lj\nDEvjvV530NHehAaMnI3P3hH8zcm3msfSw+JB0bURBi/TwLJeL6jUadfP2yXlO4aBzFVX1AtWJo8l\n/mCwb7RdM+UXSK43C1jZOXPTHnDwxDUw8sX0WZe8dvo8BGPfhbo1ZmlaDkcx5dum48c8cAd+rxO7\nO62djsfOdvVcCbW71L52T3wt+L1fbZnXpiJjaMa0o9V+WrwDZaLeWZYa60DegmdmRbHWBy2GH56G\ngnytRlObRRg9yJSn/VH19/dfVFmoHRs1iUP45K/bVC1dXbz/vJ0J0TydN6PYLN8y121bvD1X2Rec\nibZJkpbN59ia9jAV/k28ETeNLSS8KZuQUrNItOe/CXPeTmsLQmGkT8vPL3UNYZdaNJvSE5QBudK1\nUYytRuEqzPVktc3Z2+o9xw7G2Dnk4eU/HPIBOKJQJDOqsTe0xNNyDe9amB1uKm9+z6P5IU+oML41\n6OkjKCrha+VF1Q9LHlg9KMKBR1NEN34PXrVeoMO96cfgGjSVZGA2M6HmuK3fDJesU7CmNL7zts3S\nljYya7COi77Z1scTEw6GKdvh7F7Q4S8wKNFzx2zI7rUtqg5IRlU08R90vC0N7UBao9GdqTDQXTdk\nkB+D3E2GbEoWeu+AufVJ9flceOfD+M0w7B3bxp7GH92NLvZberAtf/R8bkn/RgyR7P+uT8s1HGCS\nqQKPXEnKrDAge4P0QpOEvIFGsn4syihJuu0LVsKSFWkksjgpBs3mc3r5YPo9XLrevDFeYWVCdze9\nuH6YNq6ig3XiNyido/NfMLdZvwPkUdQIOQyuPlN1zV5/f3WN5qB1lfLDffEWuz9dX71k9bFOSztU\nLZcFGnt1NF1jsB2Qrmiq0I9lGUuovTK9r+qIgqH9DkumNTO/eV4y1fVuqbhPuh3ilfGZsLaSEVQr\n71+yFnrd9+/utbNrXC3WcEELsVKfHKsbrKxBg0SO0u/jdMWBq3JH1Jg8uTLZPearHvH0iM7bvtld\nvhXVsT6Ipn4bqbg3SQdPUeiQSdF9hYfltzGnqet9NLtuYxevNLfZ8TaQU8u/uxHNDboJhXH+NQx5\n0k115N22uoWMvv5D1c9vHRuLNTZPbQQ5gwBAXLtZCuI1/Dl3nXVcAJKXuav3HOh8R1lIaV/8upT9\nQG5FMWg+Hb3NFntTzMZvnj9+V2d//OAa6fY3eGgVdLzVngb1dMNB0Xww1FWlYYs1XCWdOppT83IU\n9/0BNb65SXsgbeDVl2Dc+ujiWyiawec3PUEuVZ9vMRwm5z5qZjgb4mfx6JDJzF+MnrWyQEa9CV3W\nqER1xp3wzA3lw/dGkLZp2gRphSIdjtU0iiYaDH0G5KPResNXf7+knz/ZjXkcgxfDPZNRrJsX1Ctr\ncMExJiZgP82KVp21KSWQi/RgCXsf9dtRDb5szkfncZzB483v61989r7d5WlBwleXoKiRqw7+9RwM\nd9bratIJ2+LbKIoZLz+Hfg+n0++m020WLZHn6Yu9jkikZxMsWYnBwypLm3YaXLQCZIMG2vn/bvLN\nHrStSG8t2zjKG2UXTVaSvi37IT9oJ3Tf2hIbkNqRwu02v+db8eOy8dXpvnwQxWfv212eFiR88xBU\nF+MZzht0Mn6NBxpVrGdCtB/VrT9//2wLp8NNxbURazfZGwY+Hp2nBtGrvx8FNaz2qSa/ZXWFtNGz\n/Y0w5KmW2ICK8rPf3R77HPXfXPn/f66kvw8tVpqAVqHPjW8V3YoIUip96L1gW5Tb/uQh0Tfefsvc\nt70CfRRZ31Aq7d8Jllyl9TS+BQvqRdY3FNPv6tafvxx8iJmmB32yqBaSaFAqvbYYmr4R7MeBwNYH\nRO4Y5H1TK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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1000 city tour with length 21275.9 in 0.145 secs for nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, Cities(1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can we do better? Can we combine the speed of the nearest neighbor algorithm with the optimality of the all tours algorithm? \n", + "\n", + "Let's consider where `nn_tsp` can go wrong. At the end of `plot_tsp(nn_tsp, Cities(10))`, we see a very long edge, because there are no remaining cities near by. In a way, this just seems like bad luck—we started in a place that left us with no good choices at the end. Just as with buying lottery tickets, we could improve our chance of winning by trying more often; in other words, by using the **repetition strategy**." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Repeated Nearest Neighbor Algorithm: `repeated_nn_tsp`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is an easy way to apply the **repetition** strategy to improve **nearest neighbors**:\n", + "\n", + "> **Repeated Nearest Neighbor Algorithm:** *For each of the cities, run the nearest neighbor algorithm with that city as the starting point, and choose the resulting tour with the shortest total distance.*\n", + "\n", + "So, with *n* cities we could run the `nn_tsp` algorithm *n* times, regrettably making the total run time *n* times longer, but hopefully making at least one of the *n* tours shorter. \n", + "\n", + "To implement `repeated_nn_tsp` we just take the shortest tour over all starting cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def repeated_nn_tsp(cities):\n", + " \"Repeat the nn_tsp algorithm starting from each city; return the shortest tour.\"\n", + " return shortest_tour(nn_tsp(cities, start) \n", + " for start in cities)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To do that requires a modification of `nn_tsp` so that the `start` city can be specified as an optional argument:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def nn_tsp(cities, start=None):\n", + " \"\"\"Start the tour at the first city; at each step extend the tour \n", + " by moving from the previous city to its nearest neighbor \n", + " that has not yet been visited.\"\"\"\n", + " if start is None: start = first(cities)\n", + " tour = [start]\n", + " unvisited = set(cities - {start})\n", + " while unvisited:\n", + " C = nearest_neighbor(tour[-1], unvisited)\n", + " tour.append(C)\n", + " unvisited.remove(C)\n", + " return tour" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qfBetXJHSA5P9HC2uHRkhO0nWB/0S9AjXsoR/rO4dzEaGQ14yK970DTZAW1rn4qmgt4G+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\n6Xs8Hk8R4ZW+x+PxFBFe6Xs8Hk8R4ZW+x+PxFBF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 city tour with length 6734.1 in 0.002 secs for nn_tsp\n" + ] + }, + { + "data": { + "image/png": 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ktJzESmACrLMU9hsTFzfRQGlhxp9xsSnHFHbceLk/x53IajAVOFLKTaqSXONd\n6Uez6oXABhU2ezOGAn8CuisqURYnoif6ZiQeALvB0LZwYaNMyzsGiptCzYLNuAt4P1UMS75IHZ8R\n7utUmHEALpXMNhKLfctTnTi4GO2FC8iqUPj7AoOAneKo8AGiwKNPo/Z/AGafTYAmu1b9ZGySvAXy\nQIpZcGezZvmYBe8E3J/jPtMglftzt/3NuAhXRvK9yntx5Y7Ec2b0gqn3mJ38a9zMYnFQ+itcNc3Y\nCPgX0F9igVepMmbubFiapJB78GMvXQoTBGjGqriaxFNz1Wf6pKoHO3sqsB7u99rSjLE4p4sxyWJt\nyo+eN0OHqTBm5QJMCDLCq59+ZCY5EHg2ilwdBfytuttmcRD82MuPVLPg3K3u3Gqi1xNw4e/Q9R73\n/0KS6r5+8TiJM6KN5W2B53Apt980Y4YZd5jRP3LIKEOWXgzDVq45IegwzKdU4H+mvy2wjISZ5GPg\nn14lypL65UkPFBtmtIMN2+czhXcS89GAQs8Wq97XbdrC5jtD9/OkB2cnPsOXuBn/v6KJXAegJy6N\n+P1mfIQzA40B3pT4pRCy+yX/E4Ks8ZyedEiUKvakqJpUE99pR0MLrbYGWhl0rksV/d/r4ajqlbkW\nw9ob5Was+KWGBh0HmpBuqcyoUlz3qKzpJNBi0POgs0Ad8lFyMw4tjteuovlOw3Ag8DUud0U/qUbu\nhEAgNkRFcCbjPMs6S13Og6d6QM+HoN842P/fMPhT+CZHaTdiOVt8AFe0vW86H5ZYLjFO4mKJTkA7\n3Kp+C+BpYL4ZD5pxdJRUsUSYfSlcsjyO5l5v5h2zHo/DrrvA79vAzqdLvYsiQ12g/DCjGTAMOAQ4\nFxgpudTR1bN4mrEWLuviQokb6jdyqk1Uf84BEr+bcS5wuxnPKkNTjVxk++NRw4yNcaagXsA/zJhP\nwhT0uipFHxdXkNj8P8HHU6HnZ7Ez9/pb/tS/MlJooeW7gfpEhbDvA62d5nfWB80BHVW/sZNVETv5\n+zj8VkAvgE7LcZ8NQJ1AF4PGRVX0XnNm4Hv75KqiWgHOTQvQIlBH37Ika96Cs8wqF9kIwR6BeBHl\ng7oFZ4Y4SRlGV5qxFTAOOEbixezlqJxD6odv4O5dYNOLJR7Kts9cYEZHnIvm5kozEWIWYzTBeQT1\nhAuPg6FrFEOQmBnDgW8lzvEtSzJ8e+9EeLdTBgIAmNEAGAwMxSn9wySWZ9qPxIdm9AVGm7G/xORs\n5EliPurvOCGUAAAgAElEQVQIjDXjY4l3sukzF0i8b8YzuARjF+RpjKXAC8ALZp9tB026V/1E/PSG\nGd2AHri4iljieyM3IgQxBfwTJTV7C7dJ2U3iimwUfgUS/wVOAJ42o30uZJTLNnsS8KQZLXPRZz24\nFDjRjA3zP1SqGhnrb1SY8esmytF1O3C2xE++5UmFR6Ufv13tQHlg1qydWdcRZv3HuteeW5lxI/Ai\n7kfbXa4iUr2ReBoYCjNfMevxeGLM7IOsJJ7ApWQYFVWV84LEfNxq6K/5Hy1ZkNjJs+DI0cC7Zgwz\nY/X8y1ErpwFfQcyr5Pnb7OgyAvqOda/x24wJrTRb8s3Rs36FqaNA6+ZvzEHf5HITErQS6CnQnX7P\np1YHzQftVJhrV1NvgNqCHgB9GcURrOThPLRxsRtq7/N6pNO8Z9kMBAqJj6yR+RozciV9E7hF4s76\nylkPOf6MKwvaXcKbQjGjE3ATsBpwlgqY2tiMfwMzJGJvsYiJTT8QyA9mrGHGHlE95Pth996FD3jK\nT5CVXNre3sAVZuxen77qyf3AOsBBHmVAYhIu3fk1wHAzRpmxSb7HNWNvXNGlv+V7rFwQlH6gJDDD\nzFjfjF5mXGrGE2bMAuYBVwPtgf/Ch+OTbwjm05Eg1SZk/ceUmAEcBTxixgb17S9LGX4DzgOui8o6\neiOyYDyK8555G5hoxvVmNM/HeGY0wuXOP0Pi53yMkWvKwrxTXJF85Uu61ylSLJsD2wHbR6/bAb/g\nitFXtPeAmapSd7nwlaAKMaYZ58Cnx8Gf34d1Whb6Po8SrY0BRkncUYgx08GM9XDR1AcClwP3Rg+p\nXPV/MdBZoleu+sw3Ja/0Q7m34iD1dfqmN7ywBgnFvj2wFa5mcWUFP0ViYfpjdShoNtTEmFt0gLVa\nwt1dcjmm6/+YaXBNU1/3uRnb4Tyg2itmFaMi2W4C1sXZ+8fkoM92uNXEziqmGgK+d5Lzv6tev2x3\nCY+BfsHTyMt1uvTXKDvjXaCTQV1Aq/uWN/vj1FpRpskGhTl/hc3qCBoOGub7PKeQzaK0Gp+BngVt\nUc/+ngIN8X1cmbaYROTmk9Ztkm+i7dHXjPHAN8C31Vr0t+sbQd974PaN4lb9pvRItdk5fYJE92Tf\nKEYkvouSinUgp5WwUp2/bTuZsZZcorNCmDqHAFPNuFNiXg77rTcSAp4y4wVc1PV4M0YCV1Scn3Qx\n40DcivOw3EuaX0pW6UfZDk9wRR+SZSqcNha4AVg7ausALXAbQNHfvusAtzfLdzm8AKTOKLngS08C\n5ZM3gS7kVOmnOn8NVwZmmvEsPPg09L46nzV9JeaZcSfOjn5sLvrMNXJR1jea8QBwBfCxGcOAO5RG\nXe6oyt8/cTmZso7Y9obvpUYelnBbg+4EfQ96EO7ulW12PmfSkWq2vmN9H2epNXj5HDjz12LIolj/\nY331Ihg8M5cmw+RBZ+78gdYGnQkX/lAIExCoGWghaDvf5zpNebcGvQT6GHRgXYVdQFeCHvUtd9bH\n61uAHF20lUAHgcZEN9vloPUS7yeP5Ku731R20kEfgRr6Pu5SaaDdQV/BdXuXeqS2uxePm5uPh1td\n93khJzHR/ssrdSnQuLTI3r8/6CPQy6AOKT63WRR528a3zFkfq28B6nmhmrsZjGaA3gYdBWqUu/6T\nzZ6OngUfjMWVjCvaCx+XFv2IFoJ6+JalMMfrb8O1kGODGkYKdD/f5zwLuQfj8uHfAVq3qjPH2fNh\nfCw3qtM+Rt8CpHchqnvQ/LU76BbQd6B/g7rma0aRbPYUrSwuweUc6e77/BRrizxZPgH9xbcshTtm\nfybD5JOY05fB+y+AmuXh+vYCfQBa2fd5z0L2tUA3wcxva+ZNOqqozY7eBaj75CdNkPUbTLwF1Nbz\njdEDtAB0IR6SPBVzA62Cq450o29ZCnvcfl0ra05itm2Pc4f9CK7dO5fuyZHJ5D+gP/s+79kfw76j\n4+AKm9Nj8i1A3Sc9Hv7HqeVTW9B/QU+D1vQtTzG0SBncBxpNjv3V496c0j3+i7htWMMrF7jJVG7l\nAu0UrYiLMraiFJ05iiD3Tn6SVeUKOV/kPYHPgbejQhyB2jkP2AEYoEopEsoB5xp5yPVw8RzoNw56\nPhSP6PChHeGqBjXdkzsMq0+vEm8DY3EF5YuQ/OVN8kUR+Omn8j+Oz0mX+AU4w4z/Ai+bvXo9DN0m\n5PqpiRn9gNNx+UqW+JbHD/s2h30flrjItyQJ8jq5ugRX6ORuucIrRcT0ITCoc830IMVb9KkIlH7x\nnHSJR8yu/wbmvwBjGoYo3qqYsRNwF7CvYhatWWA2ASb4FqIq+ZtcScwx417gSuDE+vZXSKTFs82a\n9XABmYXL1ZRPiiLhWiJ0fP0NYfNOMHkH6YUPfMuVDB9FOooBM9bHRaIOlnjKtzw+idJ/XCoxzrcs\nFSRPeDf0d2h3oHT6i/XvnzWAT4AecnV+A54ogpl+hR3UpT0w4ymgExBLpR/3PQgfRLVLnwFuLneF\nH7EJMNO3EJVJPqMd+hbsd5cZnSUW1K9/fohSHVwH7JcbqQPZUBRKvxrDgbNw1XpiSPz3IAqJGQ2A\nh4HJuFxHZY0ZjYG1gNjlFKo8uarAjDWBp812Owp+H1LPfaq7gNPN2Efi5dxIHciUojDvVMaMVXDV\nkLpI8ZotQcjfXx0zbgK2wdnx60xmVeqYsTWu0MgWvmVJB1ccZdoouGcfuKZJfe/paCP/MmCHcvPc\nigtF4LJZlchT5mHgaN+yJMP9CEb3cK54p86Ecz8qY4U/CLeUPzgo/BXEzrRTGxKCU/+XUPhQT3fO\nJ4GfcCUeAx4oOqUfMRw4xiye8kuLZ7tN29tOgju+LVOFvw+uPN0BEt97FidOFJXSd7RYL1f7VO4h\nwjnAsMjUFSgwsVSaaTAF+BHYw7cgdfAOsL1ZUe6dZE1kwhgBHBJHE5xnilDp5zZASWIi8AZwdn0l\nC2ROUSr9aLYwnJgWaahA4gdgPhSH/TYXmNEC56lzjsR43/LEBbNm7Zw773lHwKF93N5PsTB9CJw+\nL6H4cxIrcxFwlhkt6y9fIBOKbiO3AqdcPv8MjnsB1m4R18hXMx4CXpHi4W2Uz3J5ZqyKC7l/VWJo\nLvosBUphc9/s1fNh9CCYNztXAUpm3Ag0ljg5J0IG0sN38p/sEyE1bQenLYlb4qqacupM0O2+5Uic\ns+yqiKVxnAYaCXokZBytfm7inTQwzet7E+i8HPe5VpS3fivfx1dOrSjNO44Ow+DqXHkU5JF/fQEX\nHGrWf6xZ1xF+l/UdhiVmm5Djc3YZsDFwrMQfOeivhCiJgL0OwPRcdihXjPwa4Npc9huonSLeYIz/\nD8kp+D7XwR1rQ5Pu/vPw5OecmTEAOAaXRG1ZffoqTUoiYK8j5CV9wm3AYDO6K0ZpKUqZIp7pF0PK\n0w7D4I6Nfa9GEpuI322V63Nmxq7ATcBBEl/VR87SZfoQZ8PP3UZoxTUtxArSjHWBVclDFLHEcnj+\nRrjgcbP+4/yvhssA3/albFtk0/85zjb9OBRgqGrHny04S7k6Z6CNo8ph+/o+13FviYpVZ30FR0yo\nz32az72ZFNe5O2h8/s5L4Y4lNBWzeWfxcvj8V9hvNKzTMp4pTwu3rE/tlVPZjt8EOANnRp31Gywb\nB6/8JZtzFmVNfA4YJlHvLIylTkVeGzP+BvwsMTv73lLtzcwcRrXcOTki5/b8Sl0X+ljKniJW+hwK\nGz0pvX6sb0FSc+UUGHIIDFsln7UAkrsEnrW32VsPQ+eeVR86GwJXAafMhoe+yEb5mNEQeAx4WeK2\n+h9BWTEL6Fq/LlLtzbRuW79+U9IRFxCZB+K/N1dqFLFNnwHASN9CpMKMTaHHBdCul8vDk8/SeNtd\nXXO2dNN6cP8+sGhGcjv+Z9OAfpmGwrsEXNwC/EKIqMyGWTgvp3qQaj9rq65mPGfGYHf/5YwO5GcT\nl+LYmysxfNuXsmmgzUALQSv7liWFfA1Bb4HOyPM47UDXwCW/pNo7qM1mCnoRdGSGY54NmgZq6vs8\nF2OLrtnc+vWR6poesS3oUND90V7LZ6BbQPuDGmcpr4EWg9bMz/kINv1Ct2I17xwBPCLxm29BUjAU\n+AE3I84pUZK5HsCpwK7AA/DOC7C0V7K9g9rKvZnxL1wqi7RWTGb0wiXL6iLxU04PrGxo1wCOaW32\nwX9g/rxs9qES1/S7W2DbveA/T1bqZyrwaLQi2xaX5fQC4JGohvMLwIvAJxLphONvACxWnpLmuWPZ\nbn+4djp89CZ8+UX89uZKDN9PnUxbNPP4BLSLb1lSyNctWoW0ynG/zUGnR8c+FfRnUBP3XnazJVBj\n0PegNmmMvz3oa1An3+e4WFsuZ7Wur10fgiG/w+7/TuNaNwf1A90Dmgf6HHQ7qBdo9Vq+dyDoxfye\nF+0GmuT7+pRL8y5AxgKjHUEzQOZbliSyNY9+TL1y2GcH0B2Rcv539FCpcewJl8C+Y91reooEdC/o\n/Do+0wb0Behg3+e4mFvqdAxdM0rHkHh4fCi4XHCJoMdiaNotzWtu0X11LuhV0E/R67nR3y0xzvHv\nwWlzMrmnMj8vGgq6zvf1KZfmXYCMBUY3gq70LUcK2R4E3ZGDfhqCDgb9BzQfdFmuVw6VxtoN9EGq\nhyioCegd0EW+z2+xt9RxG5cK9BtoWWQ//yayyc8FzQR9HO2jvOP2is79yin8c6rFXBy+OLtVg1aP\nZvx3gGa7cd8bCScuKIStPXrg7O/7+pRL8y5ARsKiBpES3NK3LElkOzL6cWa1YRb1sV4065kHeh23\nKdcwz3KvBJoF2jHFe0+ChsdxZVVsrbbEa9GDvnG0WlwH1Aq0IWhT0JagbaJVbmc45h03w899Erdo\nFbAFHPt2IZLEgRpFK41mvq9PubRi28jdA1go8ZFvQSpjRjvgH7g6sD9n+F0DuuA2ZvcHHgX2l5iW\nazmTIfGHGQ/gcue8U+3ta4A1gcOktDb9ArUyfQgM6lwzxfL0IXLlJNMqKWn26UfQdod8+LdH1/lj\ns8WLC+Q/3wn4SGJxjvsNpKDYlP6RwEO+hYAqEbBtYOOtoM+90q7vpv99GuO8kE4FmuIST50qV3il\n0DwIvGnGuXI1iDHjRKAPzlPnFw8ylRy1eVJl1tP0IdCkFyxtmr9o74JFk+8J/CfHfQZqw/dSI90G\nWhX0Haitf1my98LA5au5HucJ8wxoX2KQfx4+mgSH/sfZnfuNgZlfg9r7liu0VNeraTdnw8+Pzb1Q\n/vPBnl/4VjSVs8zoC5wu0d2/LF1HwJgBNWdBPR9yBdGrf56VgD/hZvW7APcDd0rMKojAdeBWLUdM\ngr+vmzA7nP4lPNYt+EvHl8Rqsz6rBp/90wj4BmijYN4pGMWk9B8HXpS4178s/cfCqEoPnzm4kr1T\nv4eFz1cKfloTF/x0CvATcCvwb2Vo9883mT7EAoH64h4oe98Fm3eB15+u/kDJZ1nPcqcobPpmNAd6\nAn/2LYujsr1zDi7w9gqgyZqwdACctrvZlAmw3X64TJRHA29Jcd0MDUmvAoUjSYLAAZWLC6WoKeyx\n+FBpUSwJ1/oC45SnUPDMqVwUYziRwo/eawLcsj7cuhWwhcRAiTfjq/AhJL0KFJZU6ZRP/8CMeXD6\nB3ks61n2FIvSH0BMvHbAeWHA6B4ua+bU75PPkr/7TkVTSSr3lZ0CgdSkWlnOeA/oDDOnJH9/x25m\nbFIQEUuY2Ct9M1oBOwHP+palMtLi2c7evfD5Yp8lV32I5TMFdCAAqVeWc2dLzIM5nyd//7efgbfM\neMWMw6KN4ECm+HYfqquBzgAN9y1HavlCatjQQsuk1fWbqSMdeCPQ4ZGr5yLQ3+MYoR/nFnvvHTMm\nAUMkXvYtSyry7doWCJQadf1m0vlNRaaeE4DjgJnAPcBjipl3XNyItdI3YzNgPNBW8c2dHwgEPBKV\n7zwA593XGfg3cI+UrxKPxU3cbfpxL5YSKHHMmrUz6zrCrP9Y99qsnW+ZAlWR+FXiKYkDgO2ARcDT\nZkw24y9mNPUsYqyI7Uw/SkT2MXC0xETf8gTKjxT+4jPDJnf8MaMBsA9u9t8dGIUz/0yS4uw+nX/i\nPNPfAWgATPItSKBcSeVPvs1ffUoVqBuJ3yVekOgHbAnMwLl9TzXjtChavixXcnGOyD0SGFnuT+WA\nT1L5k+91hBk9gIXAV0leK//7G4k/CidzoDoSC4FrzLgOl9Xzz8BVZtPGwSE7wz/blFPkbyzNO9HS\n7Atgb8Usd36gfEidk+hPI2HCOcB6QMskr5X/vQYuqViqB0Tl1+8zfUCEHDXZYcY6cNyLcOuO5ZZz\nKq4z/VgWSwmUG6mKnky7JJo9Lqyrh8izZF1qPhg2xBUQqfz31c1YRN0Ph6+AH6DZhiFHTXZIfFPA\nQjGxIq5KPzbFUgLlS9WiJ1t0gBYbZLqJK1cRa37UaiWKMG1BzdXDJsCu1f6+Gpz2K1zcpOaew8xh\nQMnOVHNHwQrFxIrYmXfMWBX3A9lGYp5veQIBWFET4UPgJInXYiDPqnDEq/Bw15rvnjITbt9NYkHh\nJSseEt5ZF2/iqpT+Ckz8CSbuLy2e4Fm8vBFH7539gKlB4QfiRGRr/ydwhm9ZACT+lzpHzUoAH5rx\njBn9zFil8BLGnyjn1LFw5U9wLjAMeKop9B5eyl48cVT6scqoGQhU4gFgdzPa+RbEkSo76gM9gPWB\nx4HTgXlm3GTGNr4kjS8dBsG9TcspjXOslH6lYimjfMsSCFRHYgmugMJgz6IAtWdHlVgi8S+JPYEu\nwBLgWTPeNuNUM9byKnxsKL8CQrGy6ZtxLNBHoo9vWQKBZESz/LeBdtFDoGiIXKH3xiUo2w94EVev\n+RWJ333K5otyLBUaq5k+wbQTiDkSs4HXcSUwi4ooSvVliSOAjXDHMQyYbcYwMzb1K6EPyq+AUGxm\n+lGxlA+B1hLLfMsTCKTCjD2Au4CtSiHa1oyOuNn/AOAT4P+Ax4ttJZMtbtP2L2/BN/Ph0w9LPcAt\nTkr/DGB7iWN9yxII1EaUDPA94EKJF33LkysiL58DcA+A3YAncQ+AN0o9HYoZHwP9JD70LUu+iZN5\nZwAw0rcQgUBdRArwZmLivpkrJH6ReFKiFy5J2UfA3cAnZlxsRlu/EuaVVqQRQFcKxGKmH4qlBIqN\nKIhwDrCHxMe+5ckX0aqmE3A8cAgwEbf5O1piuU/ZcoUZTXD5kRqX+ooG4jPTD8VSAkWFC47ibpwf\nfMkSlVWdKHES0BYYAZwEfGnGLWZs71fCnNAKmF8OCh88K/2KXNZw8QXQu30pR8EFSpI7gCMqcrOX\nOhI/SzwksTewM/At8KQZU8w4w2WuLEpaUyamHfCo9BN5L8YMgL81hpH7Qu9XguIPFAsS84HnccW5\nywqJzyUuBzYGzsY9BGaY8bgZB5jFNpljMlpD+eQp8jjTT1WVqHTDnwMlyc3A4CJTcjlD4g+JsRID\ncemiXwaGAnPNuMaMzf1KmBZls4kLXpV++YU/B0oPiUk4hdHLtyy+kfhR4m6JzkAPnH55zYw3zDjR\njGaeRUxFmOkXhopc1pUp/VzWgZKk5Nw364vEhxLn4xK/XQPsj5v9/8uMPaNU1XEhzPQLQ/mFPwdK\nlieAjc3YzrcgcUPiV4lnogLl7YEpwC04+/9QMzbwKyFQZhu5Xv30E/U9W7eFLXeBJgdIF471JlAg\nkCVmXAS0lzjOtyxxJ/L93xEX+Xs48C4u8vcpiWWFrvtbTtG4EJPgLAAzhgFrSpzqW5ZAIFPMWBuY\nAWwusci3PMVCFOTWB/cA2Aneex5u3RP+2bZqXeLMylRmKMOPwIYSP+Sj/7gRJ6XfGvgA2KhcTn6g\ntDDjHmCuxFW+ZSlGnKnnxKfh5m0Lleq43KJxIT4RuWXt8xwoGf4JnBzKE2aHxFz4/rsCe/WVVTQu\nxEjpR1T4PDfwLUggkCkS7+OSlB3iW5bipeBefWW1iQsxU/qRz/NCgs9zwBMVqUHM+o91rxlHiN8M\nnBltVgYypuBefWXlow/EMorwZuBMXC7vQKBgJFKDVESKLwUGdTZrlskm4nPATbi6tP/Nj6Sli7R4\ntlmzHjBzmDPptN8eDrpcenB2noYsKx99iNFGbgVmNAQ+Bw6UmOJbnkD5kKt6qWacCXSROCznQpYZ\nZpyIq5t9YJ76vx74RuLafPQfR2Jl3gEXzAHcRohwDBSc1m1ytIn4f0BPM9bPjVxlzUNAp6jmRj4o\nu5l+7JR+xN1AHzNa+BYkUB6YsRtsul3yTcQlGbkQSywGHgROyZV85UpUL/te8le3IGzkxgGJb4HH\ngUG+ZQmUNma0NONfwEjY7ZKam4jnfgt37m7G4Rl2fQtwohmNcypweXI7MMCM5nnouxVltpEbO5t+\nBWZ0xKVp3VDiF9/yBEqLyC34ZOAyYDhwpcRPiRQA67V2boLTh8DitXFmhneAU9MNHjTjGeBpiXvy\ncxTlgxkPA5Mkbspxv2UVjQsxVvoAZrw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 city tour with length 5912.6 in 0.157 secs for repeated_nn_tsp\n" + ] + } + ], + "source": [ + "# Compare nn_tsp to repeated_nn_tsp\n", + "plot_tsp(nn_tsp, Cities(100))\n", + "plot_tsp(repeated_nn_tsp, Cities(100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that `repeated_nn_tsp` does indeed take longer to run, and yields a tour that is shorter. \n", + "\n", + "Let's try again with a smaller map that makes it easier to visualize the tours:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2381.4 in 0.000 secs for nn_tsp\n" + ] + }, + { + "data": { + "image/png": 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UsCIiKVHAioikRAErIpISBayISEoUsCIiKVHAioikRAErIpISBayISEoUsCIi\nKVHAioikRAErIpISBayISEoUsCIiKVHAioikRAErIpISBayISEoUsCIiKVHAioikRAErIpISBayI\nSEoUsCIiKfl/otWLcOBvkAEAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2297.7 in 0.000 secs for repeated_nn_tsp\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2291.8 in 1.619 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "for f in [nn_tsp, repeated_nn_tsp, alltours_tsp]:\n", + " plot_tsp(f, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This time the `repeated_nn_tsp` gives us a tour that is better than `nn_tsp`, but not quite optimal. So, it looks like repetition is helping. But if I want to tackle 1000 cities, I don't really want the run time to be 1000 times slower. I'd like a way to moderate the repetition—to repeat the `nn_tsp` starting from *a sample* of the cities but not *all* the cities.\n", + "\n", + "# Sampled Repeated Nearest Neighbor Algorithm: revised `repeated_nn_tsp`\n", + "\n", + "\n", + "We can give `repeated_nn_tsp` an optional argument specifying the number of different cities to try starting from. We will implement the function `sample` to draw a random sample of the specified size from all the cities. Most of the work is done by the standard library function `random.sample`. What our `sample` adds is the same thing we did with the function `Cities`: we ensure that the function returns the same result each time for the same arguments, but can return different results if a `seed` parameter is passed in. (In addition, if the sample size, `k` is `None` or is larger than the population, then return the whole population.)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def repeated_nn_tsp(cities, repetitions=100):\n", + " \"Repeat the nn_tsp algorithm starting from specified number of cities; return the shortest tour.\"\n", + " return shortest_tour(nn_tsp(cities, start) \n", + " for start in sample(cities, repetitions))\n", + "\n", + "def sample(population, k, seed=42):\n", + " \"Return a list of k elements sampled from population. Set random.seed with seed.\"\n", + " if k is None or k > len(population): \n", + " return population\n", + " random.seed(len(population) * k * seed)\n", + " return random.sample(population, k)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's compare with 1, 10, and 100 starting cities on a 300 city map:" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def repeat_10_nn_tsp(cities): return repeated_nn_tsp(cities, 10)\n", + "def repeat_100_nn_tsp(cities): return repeated_nn_tsp(cities, 100)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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KiMRlM/aVP/Pq52Svaz8jWVOIrvJMSKt8ZcuOOBWNzDsM9SI4M8Nzjhp+yn1z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\nWRwUvj9dF8PozfD+k8HTJP8GeYKYHMZelgrpHgCXD9Ss7b8Fw6oJMKi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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "299 city tour with length 12752.7 in 0.014 secs for nn_tsp\n" + ] + }, + { + "data": { + "image/png": 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WBZn7RykqoHPufOVHe8VBhNeVYj4wTinOAW4Tl9laleJw4C449swolkjdp8D0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\nXyBTQaokz2/3tIscSC+QTSB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l+5xIu6rAIVeUvNO9pp7c5tHHwnWvibxU4APKHs07Tu9s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\nMaMMXmqTZGOgckatqJKV4M5AgpwMstSlYsuhx53XQLsp6bl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "299 city tour with length 12070.6 in 0.127 secs for repeat_10_nn_tsp\n" + ] + }, + { + "data": { + "image/png": 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G7wArgPradmpnU/1mCnAnsAf8/k8f/CMz0DV6fQMRPlLq40egdCpMqVahwtCD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\nZHXq++wUdIc9Xida+rROqYBOgbcM5AzvfeDcjGTV+QzIfLi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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "299 city tour with length 11598.6 in 1.285 secs for repeat_100_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, Cities(300))\n", + "plot_tsp(repeat_10_nn_tsp, Cities(300))\n", + "plot_tsp(repeat_100_nn_tsp, Cities(300))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we add more starting cities, the run times get longer and the tours get shorter.\n", + "\n", + "I'd like to understand the tradefoff better. I'd like to have a way to compare different algorithms (or different choices of parameters for one algorithm) over *multiple* trials, and summarize the results. That means we now have a new vocabulary item:\n", + "\n", + "# New Vocabulary: \"Maps\"\n", + "\n", + "\n", + "We use the term *cities* and the function `Cities` to denote a set of cities. But now I want to talk about multiple trials over a collection of sets of cities: a plural of a plural. English doesn't give us a good way to do that, so it would be nice to have a *singular* noun that is a synonym for \"set of cities.\" We'll use the term \"map\" for this, and the function `Maps` to create a collection of maps. Just like `Cities`, the function `Maps` will give the same result every time it is called with the same arguments." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def Maps(num_maps, num_cities):\n", + " \"Return a tuple of maps, each consisting of the given number of cities.\"\n", + " return tuple(Cities(num_cities, seed=(m, num_cities))\n", + " for m in range(num_maps))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Benchmarking\n", + "\n", + "The term *benchmarking* means running a function on a standard collection of inputs, in order to compare its performance. We'll define a general-purpose function, `benchmark`, which takes a function and a collection of inputs for that function, and runs the function on each of the inputs. It then returns two values: the average time taken per input, and the list of results of the function." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@functools.lru_cache(None)\n", + "def benchmark(function, inputs):\n", + " \"Run function on all the inputs; return pair of (average_time_taken, results).\"\n", + " t0 = time.clock()\n", + " results = [function(x) for x in inputs]\n", + " t1 = time.clock()\n", + " average_time = (t1 - t0) / len(inputs)\n", + " return (average_time, results)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note: Each time we develop a new algorithm, we would like to compare its performance to some standard old algorithms.\n", + "The use of `@functools.lru_cache` here means that we don't need to to re-run the old algorithms on a standard data set each time; we can just cache the old results. \n", + "\n", + "We can use `benchmark` to see the average call to the absolute value function takes less than a microsecond:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(5.00000000069889e-07,\n", + " [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "benchmark(abs, range(-10, 10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can see that `alltours_tsp` can handle 6-city maps in under a millisecond each:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0.00032370000000003785,\n", + " [[(574+214j), (236+141j), (556+348j), (677+277j), (833+33j), (578+224j)],\n", + " [(433+6j), (396+143j), (527+431j), (167+227j), (113+100j), (127+105j)],\n", + " [(571+206j), (724+42j), (703+269j), (797+331j), (543+474j), (310+248j)],\n", + " [(12+30j), (344+45j), (693+77j), (548+186j), (279+508j), (171+229j)],\n", + " [(243+271j), (379+72j), (859+331j), (840+411j), (651+478j), (8+369j)],\n", + " [(672+502j), (820+460j), (887+489j), (853+65j), (422+69j), (433+135j)],\n", + " [(38+119j), (644+90j), (622+288j), (602+511j), (509+424j), (275+536j)],\n", + " [(18+208j), (832+456j), (483+477j), (314+533j), (314+539j), (23+596j)],\n", + " [(274+560j), (213+594j), (248+84j), (550+317j), (508+577j), (377+575j)],\n", + " [(813+467j), (438+216j), (270+118j), (71+18j), (125+320j), (199+578j)]])" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "benchmark(alltours_tsp, Maps(10, 6))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Benchmarking Specifically for TSP Algorithms\n", + "\n", + "Now let's add another function, `benchmarks`, which builds on `benchmark` in two ways:\n", + "\n", + "1. It compares multiple algorithms, rather than just running one algorithm. (Hence the plural `benchmarks`.)\n", + "2. It is specific to `TSP` algorithms, and rather than returning results, it prints summary statistics: the mean, standard deviation, min, and max of tour lengths, as well as the time taken and the number and size of the sets of cities." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def benchmarks(tsp_algorithms, maps=Maps(30, 60)):\n", + " \"Print benchmark statistics for each of the algorithms.\" \n", + " for tsp in tsp_algorithms:\n", + " time, results = benchmark(tsp, maps)\n", + " lengths = [tour_length(r) for r in results]\n", + " print(\"{:>25} |{:7.0f} ±{:4.0f} ({:5.0f} to {:5.0f}) |{:7.3f} secs/map | {} ⨉ {}-city maps\"\n", + " .format(tsp.__name__, mean(lengths), stdev(lengths), min(lengths), max(lengths),\n", + " time, len(maps), len(maps[0])))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How Many Starting Cities is best for `nn_tsp`?\n", + "---\n", + "\n", + "Now we are in a position to gain some insight into how many repetitions, or starting cities, we need to get a good result from `nn_tsp`." + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def repeat_25_nn_tsp(cities): return repeated_nn_tsp(cities, 25)\n", + "def repeat_50_nn_tsp(cities): return repeated_nn_tsp(cities, 50)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 5668 ± 488 ( 4674 to 6832) | 0.001 secs/map | 30 ⨉ 60-city maps\n", + " repeat_10_nn_tsp | 5232 ± 374 ( 4577 to 6172) | 0.006 secs/map | 30 ⨉ 60-city maps\n", + " repeat_25_nn_tsp | 5159 ± 394 ( 4620 to 6069) | 0.014 secs/map | 30 ⨉ 60-city maps\n", + " repeat_50_nn_tsp | 5118 ± 386 ( 4512 to 6069) | 0.029 secs/map | 30 ⨉ 60-city maps\n", + " repeat_100_nn_tsp | 5113 ± 384 ( 4512 to 6069) | 0.034 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "algorithms = [nn_tsp, repeat_10_nn_tsp, repeat_25_nn_tsp, repeat_50_nn_tsp, repeat_100_nn_tsp]\n", + "\n", + "benchmarks(algorithms, Maps(30, 60))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that adding more starting cities results in shorter tours, but you start getting diminishing returns after 50 repetitions.\n", + "\n", + "Let's try again with bigger maps:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 7789 ± 458 ( 6877 to 8632) | 0.002 secs/map | 30 ⨉ 120-city maps\n", + " repeat_10_nn_tsp | 7316 ± 334 ( 6646 to 7870) | 0.021 secs/map | 30 ⨉ 120-city maps\n", + " repeat_25_nn_tsp | 7242 ± 287 ( 6725 to 7870) | 0.053 secs/map | 30 ⨉ 120-city maps\n", + " repeat_50_nn_tsp | 7189 ± 295 ( 6646 to 7742) | 0.106 secs/map | 30 ⨉ 120-city maps\n", + " repeat_100_nn_tsp | 7173 ± 289 ( 6646 to 7736) | 0.213 secs/map | 30 ⨉ 120-city maps\n" + ] + } + ], + "source": [ + "benchmarks(algorithms, Maps(30, 120))" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 8668 ± 485 ( 7183 to 9636) | 0.003 secs/map | 30 ⨉ 150-city maps\n", + " repeat_10_nn_tsp | 8220 ± 364 ( 7290 to 9197) | 0.033 secs/map | 30 ⨉ 150-city maps\n", + " repeat_25_nn_tsp | 8117 ± 326 ( 7222 to 8918) | 0.083 secs/map | 30 ⨉ 150-city maps\n", + " repeat_50_nn_tsp | 8086 ± 300 ( 7237 to 8676) | 0.166 secs/map | 30 ⨉ 150-city maps\n", + " repeat_100_nn_tsp | 8062 ± 284 ( 7174 to 8603) | 0.331 secs/map | 30 ⨉ 150-city maps\n" + ] + } + ], + "source": [ + "benchmarks(algorithms, Maps(30, 150))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results are similar. So depending on what your priorities are (run time versus tour length), somewhere around 25 or 50 repetitions might be a good tradeoff.\n", + "\n", + "Next let's try to analyze where nearest neighbors goes wrong, and see if we can do something about it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Problem with Nearest Neighbors: Outliers" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the 20-city map that we build below:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAEACAYAAAAk4WSCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "outliers_list = [City(2, 2), City(2, 3), City(2, 4), City(2, 5), City(2, 6), \n", + " City(3, 6), City(4, 6), City(5, 6), City(6, 6), \n", + " City(6, 5), City(6, 4), City(6, 3), City(6, 2), \n", + " City(5, 2), City(4, 2), City(3, 2), \n", + " City(1, 6.8), City(7.8, 6.4), City(7, 1.2), City(0.2, 2.8)]\n", + "\n", + "outliers = set(outliers_list)\n", + "\n", + "plot_lines(outliers, 'bo')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what a nearest neighbor search does on this map:" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "20 city tour with length 38.8 in 0.000 secs for nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, outliers)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The tour starts out going around the inner square. But then we are left with long lines to pick up the outliers. \n", + "Let's try to understand what went wrong. First we'll create a new tool to draw better diagrams:" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_labeled_lines(points, *args):\n", + " \"\"\"Plot individual points, labeled with an index number.\n", + " Then, args describe lines to draw between those points.\n", + " An arg can be a matplotlib style, like 'ro--', which sets the style until changed,\n", + " or it can be a list of indexes of points, like [0, 1, 2], saying what line to draw.\"\"\"\n", + " # Draw points and label them with their index number\n", + " plot_lines(points, 'bo')\n", + " for (label, p) in enumerate(points):\n", + " plt.text(p.x, p.y, ' '+str(label))\n", + " # Draw lines indicated by args\n", + " style = 'bo-'\n", + " for arg in args:\n", + " if isinstance(arg, str):\n", + " style = arg\n", + " else: # arg is a list of indexes into points, forming a line\n", + " Xs = [points[i].x for i in arg]\n", + " Ys = [points[i].y for i in arg]\n", + " plt.plot(Xs, Ys, style)\n", + " plt.axis('scaled'); plt.axis('off'); plt.show() " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the diagram below, imagine we are running a nearest neighbor algorithm, and it has created a partial tour from city 0 to city 4. Now there is a choice. City 5 is the nearest neighbor. But if we don't take city 16 at this point, we will have to pay a higher price sometime later to pick up city 16. " + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(outliers_list, 'bo-', [0, 1, 2, 3, 4], 'ro--', [4, 16], 'bo--', [4, 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It seems that picking up an outlier is *sometimes* a good idea, but sometimes going directly to the nearest neighbor is a better idea. So what can we do? It is difficult to make the choice between an outlier and a nearest neighbor while we are constructing a tour, because we don't have the context of the whole tour yet. So here's an alternative idea: don't try to make the right choice while constructing the tour; just go ahead and make any choice, then when the tour is complete, *alter* it to correct problems caused by outliers (or other causes)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# New Vocabulary: \"Segment\"\n", + "\n", + "\n", + "We'll define a *segment* as a subsequence of a tour: a sequence of consecutive cities within a tour. A tour forms a loop, but a segment does not have a loop; it is open-ended on both ends. So, if `[A, B, C, D]` is a 4-city tour, then segments include `[A, B]`, `[B, C, D]`, and many others. Note that the segment `[A, B, C, D]` is different than the tour `[A, B, C, D]`; the tour returns from `D` to `A` but the segment does not. \n", + "\n", + "# Altering Tours by Reversing Segments\n", + "\n", + "\n", + "One way we could try to improve a tour is by *reversing* a segment. Consider this tour:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cross = [City(9, 3), City(3, 10), City(2, 16), City(3, 21), City(9, 28), \n", + " City(26, 3), City(32, 10), City(33, 16), City(32, 21), City(26, 28)]\n", + "\n", + "plot_labeled_lines(cross, range(-1,10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is clearly not an optimal tour. We should \"uncross\" the lines, which can be achieved by reversing a segment. The tour as it stands is `[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]`. If we reverse the segment `[5, 6, 7, 8, 9]`, we get the tour `[0, 1, 2, 3, 4, 9, 8, 7, 6, 5]`, which is the optimal tour. In the diagram below, reversing `[5, 6, 7, 8, 9]` is equivalent to deleting the red dashed lines and adding the green dotted lines. If the sum of the lengths of the green dotted lines is less than the sum of the lengths of the red dashed lines, then we know the reversal is an improvement." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(cross, 'bo-', range(5), range(5, 10), \n", + " 'g:', (4, 9), (0, 5), \n", + " 'r--', (4, 5), (0, 9))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see that reversing `[5, 6, 7, 8, 9]` works:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "tour = Tour(cross)\n", + "tour[5:10] = reversed(tour[5:10])\n", + "plot_tour(tour)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is how we can check if reversing a segment is an improvement, and if so to do it:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def reverse_segment_if_better(tour, i, j):\n", + " \"If reversing tour[i:j] would make the tour shorter, then do it.\" \n", + " # Given tour [...A-B...C-D...], consider reversing B...C to get [...A-C...B-D...]\n", + " A, B, C, D = tour[i-1], tour[i], tour[j-1], tour[j % len(tour)]\n", + " # Are old edges (AB + CD) longer than new ones (AC + BD)? If so, reverse segment.\n", + " if distance(A, B) + distance(C, D) > distance(A, C) + distance(B, D):\n", + " tour[i:j] = reversed(tour[i:j])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's write a function, `alter_tour`, which finds segments to swap. What segments should we consider? I don't know how to be clever about the choice, but I do know how to be fairly thorough: try all segments of all lengths at all starting positions. I have an intuition that trying longer ones first is better (although I'm not sure). \n", + "\n", + "I worry that even trying all segements won't be enough: after I reverse one segment, it might open up opportunities to reverse other segments. So, after trying all possible segments, I'll check the tour length. If it has been reduced, I'll go through the `alter_tour` process again." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def alter_tour(tour):\n", + " \"Try to alter tour for the better by reversing segments.\"\n", + " original_length = tour_length(tour)\n", + " for (start, end) in all_segments(len(tour)):\n", + " reverse_segment_if_better(tour, start, end)\n", + " # If we made an improvement, then try again; else stop and return tour.\n", + " if tour_length(tour) < original_length:\n", + " return alter_tour(tour)\n", + " return tour\n", + "\n", + "def all_segments(N):\n", + " \"Return (start, end) pairs of indexes that form segments of tour of length N.\"\n", + " return [(start, start + length)\n", + " for length in range(N, 2-1, -1)\n", + " for start in range(N - length + 1)]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here is what the list of all segments look like, for N=4:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0, 4), (0, 3), (1, 4), (0, 2), (1, 3), (2, 4)]" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all_segments(4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that altering the cross tour does straighten it out:" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tour(alter_tour(Tour(cross)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Altered Nearest Neighbor Algorithm (`altered_nn_tsp`)\n", + "----\n", + "\n", + "Let's see what happens when we alter the output of `nn_tsp`:" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def altered_nn_tsp(cities):\n", + " \"Run nearest neighbor TSP algorithm, and alter the results by reversing segments.\"\n", + " return alter_tour(nn_tsp(cities))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try this new algorithm on some test cases:" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 93.2 in 0.000 secs for altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_nn_tsp, set(cross))" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2333.4 in 0.000 secs for altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_nn_tsp, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It fails to get the optimal result here. Let's try benchmarking:" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 5668 ± 488 ( 4674 to 6832) | 0.001 secs/map | 30 ⨉ 60-city maps\n", + " repeat_50_nn_tsp | 5118 ± 386 ( 4512 to 6069) | 0.029 secs/map | 30 ⨉ 60-city maps\n", + " altered_nn_tsp | 4820 ± 233 ( 4450 to 5346) | 0.008 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "algorithms = [nn_tsp, repeat_50_nn_tsp, altered_nn_tsp]\n", + "\n", + "benchmarks(algorithms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is quite encouraging; `altered_nn_tsp` gives shorter tours and is faster than repeating nearest neighbors from 50 starting cities. Could we do better?\n", + "\n", + "Altered Repeated Nearest Neighbor Algorithm (`altered_repeated_nn_tsp`)\n", + "---\n", + "\n", + "We have seen that the *nearest neighbor* algorithm is improved by both the *alteration* and *repetition* strategies. So why not apply both strategies? " + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def repeated_altered_nn_tsp(cities, repetitions=20): \n", + " \"Use alteration to improve each repetition of nearest neighbors.\"\n", + " return shortest_tour(alter_tour(nn_tsp(cities, start)) \n", + " for start in sample(cities, repetitions))\n", + "\n", + "def repeat_5_altered_nn_tsp(cities): return repeated_altered_nn_tsp(cities, 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see it in action:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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pChI60o9cOQOAK4H/Al0lvvQqqlFOPhJevBT6rVSpeV4qCRfi2GnNzKPgd8cD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\nbwEDouRWORNFWFwD/Aac3FT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 city tour with length 5701.6 in 0.541 secs for repeated_altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(repeated_altered_nn_tsp, Cities(100))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks like a good tour. Let's gather more data:" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 5668 ± 488 ( 4674 to 6832) | 0.001 secs/map | 30 ⨉ 60-city maps\n", + " repeat_50_nn_tsp | 5118 ± 386 ( 4512 to 6069) | 0.029 secs/map | 30 ⨉ 60-city maps\n", + " altered_nn_tsp | 4820 ± 233 ( 4450 to 5346) | 0.008 secs/map | 30 ⨉ 60-city maps\n", + " repeated_altered_nn_tsp | 4640 ± 194 ( 4298 to 4991) | 0.148 secs/map | 30 ⨉ 60-city maps\n", + "----------------------------------------------------------------------------------------------------\n", + " nn_tsp | 7789 ± 458 ( 6877 to 8632) | 0.002 secs/map | 30 ⨉ 120-city maps\n", + " repeat_50_nn_tsp | 7189 ± 295 ( 6646 to 7742) | 0.106 secs/map | 30 ⨉ 120-city maps\n", + " altered_nn_tsp | 6589 ± 202 ( 6188 to 7016) | 0.036 secs/map | 30 ⨉ 120-city maps\n", + " repeated_altered_nn_tsp | 6402 ± 185 ( 6015 to 6779) | 0.701 secs/map | 30 ⨉ 120-city maps\n" + ] + } + ], + "source": [ + "algorithms = [nn_tsp, repeat_50_nn_tsp, altered_nn_tsp, repeated_altered_nn_tsp]\n", + "\n", + "benchmarks(algorithms)\n", + "print('-' * 100)\n", + "benchmarks(algorithms, Maps(30, 120))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So, alteration gives the most gain, but alteration plus repetition gives a modest improvement in tour length, at the cost of 20 times more run time. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Non-Random Maps\n", + "====" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I thought it would be fun to work on some *real* maps, instead of random maps. First I found [a page](http://www.realestate3d.com/gps/latlong.htm) that lists geographical coordinates of US cities. Here is an excerpt from that page:\n", + "\n", + "
\n",
+    "[TCL]  33.23   87.62  Tuscaloosa,AL\n",
+    "[FLG]  35.13  111.67  Flagstaff,AZ\n",
+    "[PHX]  33.43  112.02  Phoenix,AZ\n",
+    "
\n", + "\n", + "I also found a [blog post](http://www.randalolson.com/2015/03/08/computing-the-optimal-road-trip-across-the-u-s/) by Randal S. Olson who chose 50 landmarks across the states and found a tour based on actual road-travel distances, not straight-line distance. His data looks like this:\n", + "\n", + "
\n",
+    "Mount Rushmore National Memorial, South Dakota 244, Keystone, SD\t43.879102\t-103.459067\n",
+    "Toltec Mounds, Scott, AR\t34.647037\t-92.065143\n",
+    "Ashfall Fossil Bed, Royal, NE\t42.425000\t-98.158611\n",
+    "
\n", + "You can't see, but fields are separated by tabs in this data.\n", + "\n", + "Now we have a problem: we have two similar but different data formats, and we want to convert both of them to `Maps` (sets of cities). Python provides a module, [`csv`](https://docs.python.org/3/library/csv.html) (for \"comma-separated values\"), to parse data like this. The function `csv.reader` takes an input that should be an iterable over lines of text, and optionally you can tell it what character to use as a delimiter (as well as several other options). For each line, it generates a\n", + "list of fields. For example, for the line `\"[TCL] 33.23 87.62 Tuscaloosa,AL\"` it would generate the list `['[TCL]', '33.23', '87.62', 'Tuscaloosa,AL']`.\n", + "\n", + "I define the function `Coordinate_map` to take an iterable of lines (a file object or a list of strings), parse it with `csv_reader`, pick out the latitude and longitude columns, and build a `City` out of each one:" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def lines(text): return text.strip().splitlines()\n", + "\n", + "def Coordinate_map(lines, delimiter=' ', lat_col=1, long_col=2, lat_scale=69, long_scale=-48):\n", + " \"\"\"Make a set of Cities from an iterable of lines of text.\n", + " Specify the column delimiter, and the zero-based column number of lat and long.\n", + " Treat long/lat as a square x/y grid, scaled by long_scale and lat_scale.\n", + " Source can be a file object, or list of lines.\"\"\"\n", + " return frozenset(City(long_scale * float(row[long_col]), \n", + " lat_scale * float(row[lat_col]))\n", + " for row in csv.reader(lines, delimiter=delimiter, skipinitialspace=True))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You might be wondering about the `lat_scale=69, long_scale=-48` part. The issue is that we have latitude and longitude for cities, and we want to compute the distance between cities. To do that accurately requires [complicated trigonometry](http://en.wikipedia.org/wiki/Haversine_formula). But we can get an approximation by assuming the earth is flat, and that latitude and longitude are on a rectangular grid. (This is a bad approximation if you're talking about distances of 10,000 miles, but close enough for 100 miles, as long as you're not too close to the poles.) I took the latitude of the center of the country (Wichita, KS: latitude 37.65) and plugged it into a [Length Of A Degree Of Latitude\n", + "And Longitude Calculator](http://www.csgnetwork.com/degreelenllavcalc.html) to find that, in Wichita, one degree of latitude is 69 miles, and one degree of longitude is 48 miles. (It is -48 rather than +48 because the US is west of the prime meridian.) \n", + "\n", + "Now let's create the map of USA cities, and find a tour for it:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "USA_map = Coordinate_map(lines(\"\"\"\n", + "[TCL] 33.23 87.62 Tuscaloosa,AL\n", + "[FLG] 35.13 111.67 Flagstaff,AZ\n", + "[PHX] 33.43 112.02 Phoenix,AZ\n", + "[PGA] 36.93 111.45 Page,AZ\n", + "[TUS] 32.12 110.93 Tucson,AZ\n", + "[LIT] 35.22 92.38 Little Rock,AR\n", + "[SFO] 37.62 122.38 San Francisco,CA\n", + "[LAX] 33.93 118.40 Los Angeles,CA\n", + "[SAC] 38.52 121.50 Sacramento,CA\n", + "[SAN] 32.73 117.17 San Diego,CA\n", + "[SBP] 35.23 120.65 San Luis Obi,CA\n", + "[EKA] 41.33 124.28 Eureka,CA\n", + "[DEN] 39.75 104.87 Denver,CO\n", + "[DCA] 38.85 77.04 Washington/Natl,DC\n", + "[MIA] 25.82 80.28 Miami Intl,FL\n", + "[TPA] 27.97 82.53 Tampa Intl,FL\n", + "[JAX] 30.50 81.70 Jacksonville,FL\n", + "[TLH] 30.38 84.37 Tallahassee,FL\n", + "[ATL] 33.65 84.42 Atlanta,GA\n", + "[BOI] 43.57 116.22 Boise,ID\n", + "[CHI] 41.90 87.65 Chicago,IL\n", + "[IND] 39.73 86.27 Indianapolis,IN\n", + "[DSM] 41.53 93.65 Des Moines,IA\n", + "[SUX] 42.40 96.38 Sioux City,IA\n", + "[ICT] 37.65 97.43 Wichita,KS\n", + "[LEX] 38.05 85.00 Lexington,KY\n", + "[NEW] 30.03 90.03 New Orleans,LA\n", + "[BOS] 42.37 71.03 Boston,MA\n", + "[PWM] 43.65 70.32 Portland,ME\n", + "[BGR] 44.80 68.82 Bangor,ME\n", + "[CAR] 46.87 68.02 Caribou Mun,ME\n", + "[DET] 42.42 83.02 Detroit,MI\n", + "[STC] 45.55 94.07 St Cloud,MN\n", + "[DLH] 46.83 92.18 Duluth,MN\n", + "[STL] 38.75 90.37 St Louis,MO\n", + "[JAN] 32.32 90.08 Jackson,MS\n", + "[BIL] 45.80 108.53 Billings,MT\n", + "[BTM] 45.95 112.50 Butte,MT\n", + "[RDU] 35.87 78.78 Raleigh-Durh,NC\n", + "[INT] 36.13 80.23 Winston-Salem,NC\n", + "[OMA] 41.30 95.90 Omaha/Eppley,NE\n", + "[LAS] 36.08 115.17 Las Vegas,NV\n", + "[RNO] 39.50 119.78 Reno,NV\n", + "[AWH] 41.33 116.25 Wildhorse,NV\n", + "[EWR] 40.70 74.17 Newark Intl,NJ\n", + "[SAF] 35.62 106.08 Santa Fe,NM\n", + "[NYC] 40.77 73.98 New York,NY\n", + "[BUF] 42.93 78.73 Buffalo,NY\n", + "[ALB] 42.75 73.80 Albany,NY\n", + "[FAR] 46.90 96.80 Fargo,ND\n", + "[BIS] 46.77 100.75 Bismarck,ND\n", + "[CVG] 39.05 84.67 Cincinnati,OH\n", + "[CLE] 41.42 81.87 Cleveland,OH\n", + "[OKC] 35.40 97.60 Oklahoma Cty,OK\n", + "[PDX] 45.60 122.60 Portland,OR\n", + "[MFR] 42.37 122.87 Medford,OR\n", + "[AGC] 40.35 79.93 Pittsburgh,PA\n", + "[PVD] 41.73 71.43 Providence,RI\n", + "[CHS] 32.90 80.03 Charleston,SC\n", + "[RAP] 44.05 103.07 Rapid City,SD\n", + "[FSD] 43.58 96.73 Sioux Falls,SD\n", + "[MEM] 35.05 90.00 Memphis Intl,TN\n", + "[TYS] 35.82 83.98 Knoxville,TN\n", + "[CRP] 27.77 97.50 Corpus Chrst,TX\n", + "[DRT] 29.37 100.92 Del Rio,TX\n", + "[IAH] 29.97 95.35 Houston,TX\n", + "[SAT] 29.53 98.47 San Antonio,TX\n", + "[LGU] 41.78 111.85 Logan,UT\n", + "[SLC] 40.78 111.97 Salt Lake Ct,UT\n", + "[SGU] 37.08 113.60 Saint George,UT\n", + "[CNY] 38.77 109.75 Moab,UT\n", + "[MPV] 44.20 72.57 Montpelier,VT\n", + "[RIC] 37.50 77.33 Richmond,VA\n", + "[BLI] 48.80 122.53 Bellingham,WA\n", + "[SEA] 47.45 122.30 Seattle,WA\n", + "[ALW] 46.10 118.28 Walla Walla,WA\n", + "[GRB] 44.48 88.13 Green Bay,WI\n", + "[MKE] 42.95 87.90 Milwaukee,WI\n", + "[CYS] 41.15 104.82 Cheyenne,WY\n", + "[SHR] 44.77 106.97 Sheridan,WY\n", + "\"\"\"))" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_lines(USA_map, 'bo')" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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HwJDfEVt4+t1whU/ND+Dwf6juGXfBnh64egqJJWd6WToCarrDy09mfUVcKaiy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\nhmEYRlFMWRiGYRhF+X/yRvdjURKB8QAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 13562.6 in 0.297 secs for repeated_altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(repeated_altered_nn_tsp, USA_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not bad! There are no obvious errors in the tour (although I'm not at all confident it is the optimal tour). \n", + "\n", + "Now let's do the same for Randal Olson's landmarks. Note that the data is delimited by tabs, not spaces, and the longitude already has a minus sign, so we don't need another one in `long_scale`." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "USA_landmarks_map = Coordinate_map(lines(\"\"\"\n", + "Mount Rushmore National Memorial, South Dakota 244, Keystone, SD\t43.879102\t-103.459067\n", + "Toltec Mounds, Scott, AR\t34.647037\t-92.065143\n", + "Ashfall Fossil Bed, Royal, NE\t42.425000\t-98.158611\n", + "Maryland State House, 100 State Cir, Annapolis, MD 21401\t38.978828\t-76.490974\n", + "The Mark Twain House & Museum, Farmington Avenue, Hartford, CT\t41.766759\t-72.701173\n", + "Columbia River Gorge National Scenic Area, Oregon\t45.711564\t-121.519633\n", + "Mammoth Cave National Park, Mammoth Cave Pkwy, Mammoth Cave, KY\t37.186998\t-86.100528\n", + "Bryce Canyon National Park, Hwy 63, Bryce, UT\t37.593038\t-112.187089\n", + "USS Alabama, Battleship Parkway, Mobile, AL\t30.681803\t-88.014426\n", + "Graceland, Elvis Presley Boulevard, Memphis, TN\t35.047691\t-90.026049\n", + "Wright Brothers National Memorial Visitor Center, Manteo, NC\t35.908226\t-75.675730\n", + "Vicksburg National Military Park, Clay Street, Vicksburg, MS\t32.346550\t-90.849850\n", + "Statue of Liberty, Liberty Island, NYC, NY\t40.689249\t-74.044500\n", + "Mount Vernon, Fairfax County, Virginia\t38.729314\t-77.107386\n", + "Fort Union Trading Post National Historic Site, Williston, North Dakota 1804, ND\t48.000160\t-104.041483\n", + "San Andreas Fault, San Benito County, CA\t36.576088\t-120.987632\n", + "Chickasaw National Recreation Area, 1008 W 2nd St, Sulfur, OK 73086\t34.457043\t-97.012213\n", + "Hanford Site, Benton County, WA\t46.550684\t-119.488974\n", + "Spring Grove Cemetery, Spring Grove Avenue, Cincinnati, OH\t39.174331\t-84.524997\n", + "Craters of the Moon National Monument & Preserve, Arco, ID\t43.416650\t-113.516650\n", + "The Alamo, Alamo Plaza, San Antonio, TX\t29.425967\t-98.486142\n", + "New Castle Historic District, Delaware\t38.910832\t-75.527670\n", + "Gateway Arch, Washington Avenue, St Louis, MO\t38.624647\t-90.184992\n", + "West Baden Springs Hotel, West Baden Avenue, West Baden Springs, IN\t38.566697\t-86.617524\n", + "Carlsbad Caverns National Park, Carlsbad, NM\t32.123169\t-104.587450\n", + "Pikes Peak, Colorado\t38.840871\t-105.042260\n", + "Okefenokee Swamp Park, Okefenokee Swamp Park Road, Waycross, GA\t31.056794\t-82.272327\n", + "Cape Canaveral, FL\t28.388333\t-80.603611\n", + "Glacier National Park, West Glacier, MT\t48.759613\t-113.787023\n", + "Congress Hall, Congress Place, Cape May, NJ 08204\t38.931843\t-74.924184\n", + "Olympia Entertainment, Woodward Avenue, Detroit, MI\t42.387579\t-83.084943\n", + "Fort Snelling, Tower Avenue, Saint Paul, MN\t44.892850\t-93.180627\n", + "Hoover Dam, Boulder City, CO\t36.012638\t-114.742225\n", + "White House, Pennsylvania Avenue Northwest, Washington, DC\t38.897676\t-77.036530\n", + "USS Constitution, Boston, MA\t42.372470\t-71.056575\n", + "Omni Mount Washington Resort, Mount Washington Hotel Road, Bretton Woods, NH\t44.258120\t-71.441189\n", + "Grand Canyon National Park, Arizona\t36.106965\t-112.112997\n", + "The Breakers, Ochre Point Avenue, Newport, RI\t41.469858\t-71.298265\n", + "Fort Sumter National Monument, Sullivan's Island, SC\t32.752348\t-79.874692\n", + "Cable Car Museum, 94108, 1201 Mason St, San Francisco, CA 94108\t37.794781\t-122.411715\n", + "Yellowstone National Park, WY 82190\t44.462085\t-110.642441\n", + "French Quarter, New Orleans, LA\t29.958443\t-90.064411\n", + "C. W. Parker Carousel Museum, South Esplanade Street, Leavenworth, KS\t39.317245\t-94.909536\n", + "Shelburne Farms, Harbor Road, Shelburne, VT\t44.408948\t-73.247227\n", + "Taliesin, County Road C, Spring Green, Wisconsin\t43.141031\t-90.070467\n", + "Acadia National Park, Maine\t44.338556\t-68.273335\n", + "Liberty Bell, 6th Street, Philadelphia, PA\t39.949610\t-75.150282\n", + "Terrace Hill, Grand Avenue, Des Moines, IA\t41.583218\t-93.648542\n", + "Lincoln Home National Historic Site Visitor Center, 426 South 7th Street, Springfield, IL\t39.797501\t-89.646211\n", + "Lost World Caverns, Lewisburg, WV\t37.801788\t-80.445630\n", + "\"\"\"), delimiter='\\t', long_scale=48)" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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kThKhI/Asbs9tSxQlwJKFKVSsk4XTbQ/odoUqz/iOJNAdeKOuzkoWoTXwPHC9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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50 city tour with length 10236.7 in 0.125 secs for repeated_altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(repeated_altered_nn_tsp, USA_landmarks_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can compare that to the tour that Randal Olson computed as the shortest based on road distances:\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "The two tours are similar but not the same. I think the difference is that roads through the rockies and along the coast of the Carolinas tend to be very windy, so Randal's tour avoids them, whereas my program assumes straight-line roads and thus includes them. William Cook provides an\n", + "analysis, and a [tour that is shorter](http://www.math.uwaterloo.ca/tsp/usa50/index.html) than either Randal's or mine.\n", + "\n", + "Now let's go back to the [original web page](http://www.realestate3d.com/gps/latlong.htm) to get a bigger map with over 1000 cities. A shell command fetches the file:" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "! [ -e latlong.htm ] || curl -O http://www.realestate3d.com/gps/latlong.htm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I note that the page has some lines that I don't want, so I will filter out lines that are not in the continental US (that is, cities in Alaska or Hawaii), as well as header lines that do not start with `'['`." + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def continental_USA(line): \n", + " \"Does line denote a city in the continental United States?\"\n", + " return line.startswith('[') and ',AK' not in line and ',HI' not in line\n", + "\n", + "USA_big_map = Coordinate_map(filter(continental_USA, open('latlong.htm')))" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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O8iCp6b6KbhSUz2Ut4/Du0Q4ScdFf8e/JJXhDBBUVtCGEG8iQSl47KICNHwBr\nz/Ib4pAAOs9qoaldmQ9J+TYeqm+U3ZPA6rcoTCnJ+3V/TeRFOIAcQ/yMWT1x/+bvw/xSZq51F/J5\nGT1ngNvfs5Fl7xFA+5isp27+7asi7wCP//7mWqucAf7DXP+0/zTKRUysOc/bt3UogJ7cibTZG0mx\nPrtHaJwbBf/RuMYQ5qQNG1/s6TDfv8tn4Qul3S/ygoUqcpNl/GMqxHQtWSiHfhchgtflb6NCR024\ni5qQp3pzU6NgMfbXN8fPnpbrg6tMGJOlz8G/bK05MKyG83OaKz7U5fYzKgHn9k/Ra1DfI1w+jlEB\nrH4vH5r8gJBIs/0TwC0TmU9I/X2PkALUzOVQPo6LL6O7cgb4j5Mzw2SnQ16z6Dkf/hGX5dxuDkgf\nnazl33zlvY2YdoKiyKzM5djTIT0voaixB43/6wcJHgsrRJjYvIUK3tgcld0i71B9QkhNQYe1+YKg\nw6bX1selMuv9Glzs2siPndIOakLWWndmuLfRWj1VT5zLyKfmVbc++BzYd4jsoLhL2BrS/cIu1KUn\n1K4VwNeEzMm4ODO6K2eAZcwRd659mF3Alg/sBWi/zGZW/4o/pQWD9HXZMBC7BdDFIGUWL7bkPtFx\n/fR4kFxNjK+i4INcQqKK1rHfudscpHxiZtQLn08QZ16iys1yRXdMn9uWD2jB0CNsAaIA8pTWQvn5\n6ENLjKmOByqk/CyUz7B90NbqFcCf/nw+AdGvsfoiunaIzH9DCRZOa3qImtOJsiwSs6lVzgC/YaiM\n1n0iX5QkQ9uU193xjJ31KoR9ei6uWfg0gWKnNJMPKq9i8yi9cXS9FfK8WI3H/S6o51EQCqEn7ZhE\nvs1n6HnoE9lGb4ar8gl4PJLrg+Q7c7+3MHBF+n5ffoNqNSGrw+nP+Kqw8y30fBbTR0Gd1MO0q4x3\n09QTyr/LBJV7N2zoO78GlTmWe8aAkELiyxqvlGBhfSrMGJNmMWNadvrjI6LcH3Fjm1bMfXkelN0z\nX84xu5Zb9Nxi3ydsYbj6XOgCLiP6x28G0ltjQpo/QX72fD4pTcdoah+kQSZ1k4hydK5/GmwNgz4H\nX8UgULL5v/O4FP45LYLZoEwhzPsKGvGz+E11apNuH8w0XOVE3iKA9Qz/ZoEyDo1Z5TQo/+EdDGii\nG9pFjmXhJmDzhOGTFFKDeUJIKJMHhYx02irsIAlujsP9QHO9Vc6Ae6GHRESF2NvVorcB3Px8hDp/\nw8wAfH9pG0L7AAAgAElEQVTcB2WGTO4RwM1vNiMT3f0uQk/7jZn/7Ospx+XmM3JzmDoxMydSlcTZ\naxQ/2stsAH3n/JtviHlJCBpmZbfIb877mA3KNO9tGg+ZQ1sDdicDuk/rZKLhKzJBUGn5HP99IhM8\nXBj4kJCbe9iacgWoyNZ/HtgsgI0iH+a6WQDr6nPP+SRGBbBJAL9N/J0bY9IsZlQLiYiqfyRM7Hfj\nZhi/+puzUzszyN08ufIqzN91nMo2hnV1s8OdhSp5hUc56RtlxyCw/KiNcBoTHWSevLkNjnNc9gRs\n/hzIItenC1iRniPX+Oy/maYOShBuP58Jwv6gTZ9fV24h4+CdWcfmgYaLQBoS0mx2/VE+6IEF/GMD\nN2gn+fYXgBWv8DkqSgPmNIfu81JrfUJkWtPGcVlNr33QPmg092A2k1vlDLg3sphTvf0yG/FTuHng\nopGChRtxQiXj1M/RIZOylkGks7yN3gSp2Hi9bjgHWzIk5Klru5DgbP/8TSaJy8MjdYLVTUo+yOma\nkKaGmBM0uUkzjuDCkWKE1sHlQWwQ+WioXM0TZp6saDRig+fLtbp559YxZSpVeRxUboie+2Kuee4Z\n696RY1nzTHYIUgCEnKm26wP698pM6oI08SdqlmHKnQutcgbcG3Wsv0BfKC6nWEwZzJhTUVjtAfez\n9EXps4fHOMtjTv10UmN2D2Vuu09wNZy5jy3vOFV+mQEhtZap65k51cHwfNn+nMBXOFvKPBmjOegh\n3KEhv74sbV6I0RFm+jumhGpN+LQ/+uASu664jX+zkFrw+qflvytPS+3kpsflz9x71Wu/6HPGbfjr\nJ+nfH9D6DA8rTo3Zn6pmwMugV+pzdQD8TrHiPHAfR1ztAf45atPS0UYfqn80m8az4vSxzvJQf4Lp\noDRDUl0x7ebJ1RdFRm2Q28ZBQjaov+u2bcWruQb0GtWtXSALT3GZx7rmEFc4yn6fZt/3C6mRHRBS\no9Bt9O4NzZjP4bB7bzwl18MaC9o8jm9nWDRntjLeq+4j2CFsH4ISnA+JzLezRruGGyOnWQ5ofVKC\n+uI0JxXei6tmIGzhujYcXx2A8pPl3NpMMZXV5pU7Xenj4DQPzlkeGqlkRjnl/DPDMoqF6v/A1HPC\ntULKVGKa+VQkkx4Oqvr2nxgzbcjMqwhxAru0L79QzP5G1eUwx2lqB0oA9r9NR3x5tRIW0p5fgyqr\n/bbTUtD0sr4wd2CH0jS5tTUqpFA4KKQpUx3yaiKDCa+JfMQYNcYdQhYw2k38vkPkx993Tmo06wr5\n9y72VjkDTuaCNhx3pnfo5h0jWMpwnNt9upywvEM2zlkeEk5MYfybJ/t1H8jrKCgEJTRD/U2UEzZE\nAOh5BT4oEVddc58TuLWNL1XqF4oZn+uflgLP3LwXbkIWnKGF9BbJadBNa3yxLEq4ycbnXdD3cCHj\nCoiPmtcDxP+5tU45pmtCYjbdIaSQ2Vcft66xqTX5+VHkc04Kf5+piZkuLEI2HMp5qU5jMSf7cJOV\n/FBU5bJw9d79fHMc1EdlNto5Fy/49CgnE67B9M9QWs4OIWPanxCZuSIUaoQSbH6UWn4MlPbpivpx\nO4Hl/a58BJ+WSYUc9xIakqhvev3n5bPuFnlNhFsD+7V7p/JIjvBZ76pAmBmCev1Rehx7BH8o4cyx\nap5cwk3//5DIclDMdW8KzSHBI/DaSX5V72FzqVXOgJO56JKV4VEuRZ4lrytfq7DHIUS4ZuEzf0Sb\nw4ww5DVGohTHy0D9g/dBVodoN/78mri55d7ZnccdPpM2//2+PAtf2DDlADfNKUqLYbWtYVq7YnMW\nhmmz0dYLdOTdViFRWblnU7/vE1Kz2GE8Q/dZ7BYaKuwocNd78r4eYt3r/qg+Zh6U4FM/3ydMtIfU\nGmuVM+D+yGPjy+MiHtwOQ/pet/07zOfB8xLjs4grWRkwfuKkS23cYVXVims3HB+NBAqQjlnNjGJG\nY7UT+EihEU/ZuvHXCNf/XhPSfEOFoKqfaQctzwOVs3DncX9tB/N3tzKmOjKgYyJf47tnVB44VDTU\nmhF3DsN9QmpV3LrfzKy//QJYJYDfqfO8W6RIp5L346oZcH/wfTV6k2RDMxnIcgqjidzM6sk5+QzR\n/H0crtCtP2s8AZCMNDmSQVroxe7dYbVhzwo50Zs+C5/tfPVpx3isueAELD8XIcmDjfieTIyp4nAw\n4ZoFl9ymm6BGhTRR3fS4nYhpan+qKVu9KSA5M99GApSzJoDVmmah+yZkAqz2jKADVzZ3nHnvASEF\nZ98E0HEe+JLIBPnnmPW3VuS1Fh5BOLWCe3LVDPAfYfipz75HWIs1vyl1DNJx3hQEgRXBw+VSsEiw\nsRpHyPWN5pDQc8VtIne9g6nEq4cEH/I4KoBbx8PfcdjGHicA4sKl80JJRRzF1TzhtY7QhD6XAB4V\nEl5DabBUrkMvk5TG+ds4M1/HKRoOf+UpGQiwR0hHMjeesKTUjA8ucEAJxxsZfu4xeNgipMlL7RFr\nz/reWWrxrXIGWMacESwuO73lULwA/NMf25EeFIhbSBQO+0G8w/MbG77bSEIdr1nkhVD3iG2j3seM\nf5/IC5KakPHvOiCb+thXnQ4VjuF+jZjgg/h1k3+OsufnBMb5opuP3/ne2saHOu8XeQ1DCD6LWoWb\nTq37M/QYW9ukM9tEsVUZ4ZwpVF1Hly12CyHqPblCkvcI4LNjwLpJ6aN4SGTv5SkBdAr5+7uFxH0K\n12ZSa2BPrpoBlrEoO2xOYHRJO6mOULqDWFDUaS6kVrQrsibq9xGoq9QGSvk49GiYkNO5+eHvFnTO\nioqH1/lSc2v6bq4/Gq4FhAYVlAEB3z2arwcxFRKqOfS7x7NQTDfa8fSsdWVayf2OESwPGu/Cdu7W\nvw0jyXPjuB7NZwg3T/Z89h7ygjZEaJn+GsX7qkmgZ9xeg/cLaSI2neZbibmg10ZqDa7TqhlgGWPD\nDt2nCP7D0xd4TchN4V+K/Mm4IZRbxinLhTCGoq7y12cfdkiugeskp/6/aZzOhlchjLr5aUhIpE59\nA173UmiOh5unUM1i5Wm5oWUCklk3o3Y95T1CapzmyXm94B3NoVpbrKlRhwDX+esnkuq4+bXCRonD\nBVWpjq/6FpPhn11bE1IQ9Qt58v/sabe5kAqNVVXpdD/GQP29mGP3hz6nVtKeXDUDTuYsFd6/8fLw\nHzrwHJUFeuOp0Cgct42ai7gR3sVcv344fqPikqOyegf8h79mxI9uqsfDd5yS96w8DfzGmHHKq8Xb\nrYv6LHYK23cyBUlhhP/e8CY9rlsm8r+vCfvkqpuB1jzDO+NjnOodg1Iw6weVrrNMLsdwfj1Rz7pX\n5IXKNguKxH2Iii34ZGOHuZ31rneqb/YuR/8BIZPwzHVFvbME49GU/bhqBqKYDdh4efiPm0VmNqH6\niMv4Due5kQ1Rnfx8MA36qY4DoguZO5epKs93ZnawQogjzW4xGfadRzLYjH3se7THwOUQ9BsAdK5E\nslEhoaxj5jYPeZ43A6n5uk9IOzxnAl1HmZOMuXhKew9c6K+r2mFMwSe96BQlMMNP+ra/xhXSO2DM\nv/73G0/lIwWToGhGq5yBKGZzi7dWX0CbDJsrdzreI+RJeD3jiNa1k+L5EjzfvhBSly/EZ9JQ9/IO\net6sl9XBkG35URlX3/c+sPJVaarpHpEftT7PzQshdo9VbXpcvscaR3lN83crR/PXurKk9wobE8s0\nwZgtAxukzUD319dln+AdtT2sr6ScKDG+/9C1m782DJeM5oub/y0CWH9BQqO4v//UmtcqZyCaYSio\nDRp62Q1BoDZf/uQT8wGWO674UNjsQ1a4QxzAn45z1HlERgaZOEVba0DvS3mtbEjIJCvyNO1w6Jer\nneXH7BOM3cxmtfFcfhybR4GbfgFs08JOuVOxQoc1Hbtybt3mGle2tqkBbxP5PB9VEjTEV1IE+2wz\nGxZMHZhCDlGxUXqyTxWpyL3T1UJpS1I7u/EUsPWD6f5GL/ZWOQOFmCY/vAEBrH4D6GRUVfWhu2HE\nYxd788bkfi7z8U+EhBHyzzKhFFyaCieU1zzT3HlS4+ZK2HLJigoaxRSUTwhp3uh7B/i1V4CthnBU\npkBfyU8ebFDyHVIIaVQAdwm7nzjYCttno1eOLCpYzKJUMeZUFQDChby3D8q19xVhhwBvFcDnz9W1\nh65YU1dqJX57VTNQiGkr7M6MpriX+OCmHIZHXB9NGB5VuWaqrM+YfIxiocXuMZrF6V0Ahm6zRtGT\nafhcqSiwPKoo2NKbYYeBbKNdV09EvONn9b6dwQ8OsEFN0wo1eVm8DYeuO9C1OyakeTE0Uouao1hf\nRO776nKZj/J1TZQGt1cAvSKv/SqBza/LqvemudwqZ6AQ07nFrJ/QVCTQV4TEidkr8sXjbagQd99C\nEJtJ08xUcfZhNrrpGepUGTbGGM3CFYpJZRmHY1kVFSp5rYPOwG4k8919yPAGKBjCJgRyXLV1x8MD\nJVzgfmHrlZ6j8A3afn/Kj8gFYLRrf1eOehdgoD95NrXyW+UMFGI6Z+dUOQD7BJ1R3COAvknprPVn\n4fo+yqrMVDafjWgWXJRLuM9C9qNA6fTTtBB8pT7KyRyCQhsmjMMivpr3/jJfDh36nPcZ3XgK2HIu\nP9c9k3LNUveG5qT0v0tv6ncHjzdMs1AawtqRTHvQ/We6RqBqhvCRiPY75+qM7BeNoEun1sD6rpqB\nQkyjtU2eUncLoFPwdY1HhXQSiqgF1aiZqviYYpO64pMWXWPMggdydTq6+LngNjAuIoY6nYZW7+sc\n9sOHUFnBXxMyuutOpoaEsseHgwe630l4NFDenMZpaVIb5jOeu0fyEVdceOmG4PXq91lQznmzKp+e\nn6IETUxdFi6qUeFgTZmzJiW4YhIUzW6VM1CIaagY/73GohXaolLq/BdE/pTW4QAiVAv2zrot3IbO\n4DczvraE3X/xpC66v/CkxXLfA8c396GHaBaufAD33GTvhkvu0k1Cat6ocqXxp9RsLuKdr26zoIIl\n8Se9yWueELbP7m4hczFc826tTeuQkF3DaY5mFrn6uSZkAECs34M6DKlosXx5gKr3pIuhVc5AIaax\n4Vim0n5VW5D6InpQ26D0RbzRym6VffqibFwbu98e7xIIRU0j9gfeGGx5+HPcRZaKzpHsj5sLN5xF\nfo59KK7lm6VCNnP3ehbCblPh3kdChFHWz1NCahJ31//tfi9+barkO+qdh8CACCFrS6j+2gfdIe9c\nQETHoNRyu+uoAWRyZXJsT0OrnIFCTKPzSHbSXCVopNC7BPD5+odzQFuctwtg9TkzkSf72P3OM3uD\n9G/Srk2peI5F+IbcuNO4Ua1H58FX34JyFJubhJk7op+IfWYwEx6GnvuYOQsxE7nXs0tA6mPlzVx+\nrTe27KwN6yGvD8WnWiuysGPdDBhyuODw1mjU26r3pIuhVc5AIabR2pY5cjdoi9I80d0rpF/joPaz\nmYhmYifFh+WFhdsWL79JPzN8Y3B/jD7TWYjTuKkZ78Pu/IYYM1iMZrH8KBOCa82Zz7HtHyuFFZUP\n9w55H8UFewxgoPIXWj6LSdtnMSSAzxq/j9EmzQx79XtaiKXW3FY5A4UZn4qn7xNZBAm1sO4QsrpW\nn3A5f2M0C5uXRqJwOpzqOf/MMmC7G8nJ0E+7RaOXODu5uRHHmu/aB3mHcR4ym3fm9hAblVk1UF1r\n+jxCMb2oZ28TwG0C+LKgQ3990XoxiXdTc82E25phvPrBRteeBgRw65t0ZByZNxLop9pI/E6IPPhl\nEhTT1SpnoCHm0domT4C9kzwQ21Yh0SrdGkOoz4Lnw71h+s1GKrpjI4t1E/aBxxQECvmQ3YKwMX+L\nNWcEJDdvvvKYkLrkRrtXSO3zK9bGa8+rHolDrSfqIMH5ELq9mEX83K11rj9iPrwaonvuY4occXPu\ncnqb/sR8Rjo/D93M3CazUxWtcgZKGQQWbgLuYEpL7hFA51n6o1YoqebJ1s4M9vMQao+P83Xk7/V9\n4LEgcqpcp74pmKGsvpMsBwnvdjo24sj296EnUHJhvy6nvR5AofdNCRDuEKKc09xGv+GYu0Kef02E\nvJ/weVPfQv8xKeQ431eMNnefkNFL7oJIzEFKAEeEHdm1TQALf6vqPedibJUzUNpApFlq3F5wK8ek\nMDHtrO6Es4I8RNnuGzcl6R+4z+TAOQqV2cS2j9vjojZdDhKer5XuHru5+cY6+V2bs9+0lc01pWH2\nEDkMvkxsU3gVzeKe0oDrcCQqQ/+mx2NP33GQNuF1xTNtTvlunhCh9cFtP5Ved9wMle05n8xP098q\nZ6DUwaC1C/jseD0+XWS1e7fW5N/0hLOVp8pUcfMf0VP152/4QD6HQ/YMN+E0mgyYfYyqBoJpYhiw\nNtqwfjlnMp/P4h57uGaRH1coBIfLAW5u6iZsiA6Rre7hfBa2tmaPmUpuu084HPpdtja5aTJ2XYSu\nO+7wE6axqRyW1W/F89faJsvgcqZlvgZHas1rlTNQ6mDQPkhXOrMTd8rOxM4+wKeErTpvP8/bysNM\nCEV9A3Y/rop5oeGw+ik9xAHObThhPou48Zl+HWrj9WdZu0/WXEgwJ4iVEKLmqiZk6dGN41khIyvS\nSJmACD9VkSTAoj628PeR3V8MIVYKRs60fLDwd5pa8VY5A6UOxulkM23xOkroQ0JiS+VLkcY9W20E\nZp3gKfj0c5SpKC56pXEAw5Id0i+4/C4FIncc0CJ+E5+8xjzlf1XYORrcOgkTvJEC0DBvueZKP5Hb\nld+k6UkY99dEkdoOvnXX6OEku784jpPU5H5D2O8zZW1X0SpnoNTBsCfG7UK3oec3FRLnpoFNWAds\nKxfwLFSw+PsoEovvCv0tNzO9KM+8eWmf8bNCxeXRae0514Mg4kJXs99RIHsxp3VKsxgSwI2jBp5X\nofWVf1Yjxbg2HJP8KCEdl6So9dclo8q2C+nD2C1k7XUJgdLs/SQ1431UzUCpg3FiEm15mT7hlQN3\nnG1oOrTyQ4KpcVDpqchvYomBeKBA4LyhrW/HCLtwG7vrsKDukSZBeOpeZPNhaiqbR0PBGvPrItfH\nGVl+VuGPKU3CB5Ro+iyG6mMz+/ajK5c15/Y4dQG8VvgwqdxrlMuVcfvDUmtOq5yBUgdDftx6pE9H\nvTSjvomVV0hFPn/50Syb1az6la+eFt5neIRVY3PnRGMNzuvI+nQ5sWPMEWGnXN681CtM4LmQzTAM\n1sK9XvLPUSfs/UKiww6JWM3WiIY6S/PXQ4SmxuZhxCWK8hFkO+pjHKrzlYFzug8nXPTfBhF72Eit\npD2iagZKH5CMpBi3M0mFANaMyGvK1ywMHrr4D3kguO+y/BRhz/JF6oTndbj51yOFwuY5XLPgwngf\nsjb2sPDRMvIg1HM4JNyHCq8/d7Klt1gXmciXv95OFOX9NVxuyqiQAICmluAGlrTHlmpYVN0qZ6Ap\ng5o6Yeq20t0C6DwnF6GedBR2sos/nbEQBiTqLd1HOTb/sGeF1IgeEjIUuJeFcLf7nTJRvW0LbyFC\ntKxwn4XCLVKmvwEhbdxUJjI7t8PZhsVpKj3B+TnZc7iNtJ9YI0KEnJ7dmhsXrqveI22C8zvhXf4p\nLtQ1vhiWzUf5h7rUIveIqhloyqDQPig3CSUEKIGgIJj56JOsv7KyZDNTWNg4ygvv9Qk7m1/OPPcv\nzhWp/9B4dE1M1NhUPs0bMl6fgxChtJ4h7RpOU1l+NDTQIHsOt5HezWyCflOd267vCtflN96igJeS\nFx1rTP97fDEs+/1w85dCaKerVc5AUwYFldQTZ2riVWzKRJMrKdlG89CYCWk6o4nsa7j4eK42ctHQ\n26IRXZytm/Jbbb0gTSHtg/a1zjKoXXId6dE48ZE42XOoeVsj6NygMFMdrKzpPIAhvYb4jdcd9ebN\nqWGCBmKKYXUM2u9ZZXUnzaLKVjkDTRsY1j/tPyWbSVicim3WKtBtp7bjLt9no3kD05dbkee3fRDY\nes7exL4WOJdhmb/FnK+u0FW1MZmoqLvJueM3wN7jdBRTUHht4Lvc9kHm5B4QwMYPZJhvnKnOv87M\n53IagHonprDdI7JgB+q+7hH7fSqMqfZBWcvCFCJbXgbWT9jPWfdS+PxtngAWbqp6r7lYWuUMNG1g\nQU5s/RTD2XZvPJXFeu8TeYdkMadbjBDIPr51dT/BncHghlkfXOZw94i7+t3K03borzsjN35sZZn3\n1PPXjtDvRcFoBKPqBp1ki73L/mNAxykpwMywan/p2bB3rgswtWnryY8ugasnrOq8tRM5NTrGmJlv\nYgJf9k4C/+I9iWfVPijHbz7HAvfU1uXCTRJrKqdFkegIqZXfKmegaQOT9txR3meRB7ujoy/uJ+67\nR2Qnv2JOt1jzUmxEi/95vFPfjobZKfIO496XXD6LmLEVMbPlo4ts2GspAF0AfaGourpmqjfzfi40\nlkcCkM80w1KV6WljVF2T8PWybVw3w7m1EepbOCik013593zQJqbAeaq+frYLueHf8qyt8bsPXw4B\nPlz1fnMxtEswp+m9DwHfATAPwAUAawAsAvAhAMsAfOKK7NrXXgXGACyo//x9AIsB/K72uwUA/gSy\nz28B+CWAPwAwWX/GDgBLAFx5tZuvq67O+lS0wHHfikPA4WV5Pr6+DLjwGPBoq/x5DMCulS0ti3qE\nOFPL3//cALBrZdbHo3X+9f4OLwNOHJI/q+veBPARbQ7GADzwAfBftwO9uyS/I68Czw1kz4wZW+w8\nAPI9PQ/gTwF8U+Pr765raVnUBiz7CXCij+53ApJfSfL6FYeAs6eB3nnAwteA0RflfK04BIx15vsZ\ny92fH8NJAH+k87QU2PUk/T5WHAK+e2l+/r8Jua5eehzoHaPnNpSo9fLdS4Hv9AG16zSettP3q2/h\nTQDfBjAM4EoAyy4Dfq8P+PYJ4PQJ4FuL8/fJdyfndd1d2bp5HsC/AfDHam7mAV+8Vn4/6jnfB/A/\nAPwe8t/U19W63A5c+TFmvXwsbn4SFaKqpVWzWthpOsPVz05jKgNVOTVN+7EQEumTS7qjcWsMuzYD\ncOeL1ddbnFaTP0m66jjrz4rXnJqvWbS2AV1nucx4O7hB77eHeN+cdhWWlOYPjY1BEHaHVYf6d9zw\n7yGarwpB1iMK1XimsJlYM1142Gv3aP4ZDwo6F0VpjUmzqLJVzkDTBhaUN5D/cOhoDqpi2FoBrL5A\nq+H57Nl6v9TG5ERYtYWLyXvxUEJ3CKT+tyL1yJvts2htsx3v9wvpT+qfkHO18Lfs97jZKE/qivrh\nk9JofjafiXkfRcKq6bnKZdg7ovfU9RtEKD6T7NdlzltHBABQASGudbTuuPTdqD5MEM6pdTmcfZ9W\nYmjyWUxTq5yBpg0sOG8gS37iPzK9QPw2YRem1wXGuuN+XtS9dOEi2jlofiR8RIt/bnynavW3oj6Z\ncMDD2IixQP/LeekM5XlwQ7X7x5znbeVpYF3wXJXj2A/1O6m/3StchxObv+4RmQNCJVLKDHHu3YVr\nFmZeBxdpl31TsIo/JUExXa1yBpo2sOC8AT35iXVqCvnhrBG0+ahfyCipPYLKvYhNruMjs3LChYho\noU+a/Pz4NuleIuQxtqZBeFis+/1x74jdiIZdfPACvDuw1oXJ204hTTSWNkOOOT//FpCgFbgQqynL\nezoGgY3nZG5MmNmTHpuZ92Frz+4+KMDDqQANLc9ln3NMqVXbKmegqYOz8wZq7o+Aw3NaJeSpZ7ug\nN5IHhQsyJD76KQTh1QyJpMbXOHZOjJZg3xeSCMgl14WGtPIao4cPJnzUXxed5213fcPbLoBVE8D1\nR/3mnlATpZnjEJo71Ffj122MiUwJp82jvtN8JqjWjkjh2z4Iu1YJMf/31+ew3DWcWjmtcgamdbCZ\nCjsh7aM6fHJNAHcJ22ndL4DVdWHBndBYW2t07oG8nvtgqTh3P6ZP5ByRG3isluDjxzcn4clybN7H\nsI8PShCGCTmOt9WnY5Ba3fyZ5WXNd++vQFeu873v/ZBaGaFrnR/354Q8ePF+otSqaZUzMG0DdarX\nuv1X/X+DkMLjHpG/Z1P97yrv4H4Rl9UcgydkfnB87egycKTiT+GuMfigIXzCJHSTv/4osNUE9ptQ\np9/GivhEV5GLhqRwRy7l+fVrygrvTAn0O49nByEVZVQT8vS+akJiZ5losmFVBLOIse4RYPUbEmDy\nzuOhc1BWrZPUpq/N8TwLnajY829CxnRfQJZ3sACAgMyXAIDPA7in/vtfArhcu3YMwNcBnEc+RwMw\nY/Ldce15EuJMraVlUY+ML8/i7YHeP+PzEsw8EZsHP1FzdHgZcOIHwOGlTF6GJ1af48eXY2HmhowB\n2HVCyzvYDqhcicX/D7D9U0ArgLMAxkYAvBzGh03+d8Xx1vo6sGApPyaKOP7mWfyafMmx99bXyCvv\nAlffADzVl/G086zMcVgOYDeAAQD/UO+78xJg/uXAF/qAb/1z4NwF4MgSmfPwMPJrXM57/rl3/BhY\nuiR/3Tc+nY3ZnoMsr+Wqq4HX2jLecuN8TIing76TRNNMVUur6Wruk8zqc8bvhDQ33SmyKJKHhDRD\n9QngyyLv69gnaFTb4gVo8vdNneDOcVmzRSJs4uaI/H3hENoQs1mINlbM3GWG0ca/G9qEVTRvxOez\n8Fe/45+tR83tFjRo4ZDIw4yokOE1JFCm/B1nBqNMsgraftN4tn4530zSKGZqq5yBaRuo06xhmndU\nyODt9YVOwX58Vdu0NwqgR+TNUxk6aUFnb5fk6/Pn7A/chccT74wOmKNCiJ/uiKuFm4AtH9ibZFwo\nZFgRIx6ZtRwhq8YZXmM7/75NiPyFm1xIsswcM/VC1jyTvYPb3uP9IzxcOD3nnIPdTKyjwr716pV0\n+HhqM69VzsC0DdSbW6Dbf/cI+aFuq39IvrDbNczf/fZ3B28T8kPbx/R92+myP7AyfRb+52w+Y9dr\nfu5HH9EAABkpSURBVMIrgOy+QjSU0CRE7n5X1BanufROAT7SBwGf1qXmJl8O1v+++DBXW4NWbb9w\nFyIy+W/3JOzlwryZg4Zy4Kd6FLOlVc7AtA6WjX5Rp8LOYfmR3/AK8HkhTU77BX+K2i+AB4Q8TVF/\nV87cos7efQLYyvTdd658QaGcop3DdZRbIhrKTMAqYsJxRQDFbR6NRS/5y6s2ak7jhQmf9yDfAQV7\ncevP7E3bdYgxCyF99jRjqrrAlTil+d9ak4CSpradLx7lnvsw6JHUZk6rnIFKB+88Sfe8KkNm7xT8\nKep2AayfzMeG63+fsmU7zTj8B3W349lrhY6a26R5aGvOff7a0fH8F4pe8moW/qis7hG63rvvIHBQ\n2OOfuodYL0NC1m/Q53rbOI1dZmZeq34VLLjex71CVv4LzcZW96kcn+4RGTI8VW43MF9mIGitpDZz\nWuUMVDp474ew8jRw7XtyY6Z8Fg/W/3/TK0x8fd3cMCQ80MsMHwrIkAMs7B5p7jyUC7Xuv8+dGVx8\nfCo5zYRa72AK8xTJ97Bs8Z6DgIklpd9DIQlwuRKU+YjK0VDac/doVkcj71uj566xkGz6QJGHS09t\ndrSLKHSWIi5889N3Af/+0iwk8LYJoG0+cDeAhZDQ5bsA/EX9+sXzgf9yLTBshLrqoagqdLEGYOI9\n4I1ns2dSoZhfBvApyFDdRcjDNu+GDO1d2OR5+HhPS0vf08DpK4HW14CzLxaHI9eJGu/Os8BPPx8P\nxx1C4ibgw5/MQ63vuhL4wz4Zuvk8gL6zwEeeBd4wxsiFto5eBQwa4cQKZrymhZpy9//0LDDWSoen\nnh624dEnQM/10AfA2Ie0fiaAr8/PnrP9JHDtDcD3luTn+u+eRR2O3T3ncaHHRnjsqwAGgB9ZYeDN\nec+JmkpVS6sqm1tF1n/3hJAlMLlTZPekEYqpZYqrPnyFXXQzQMegPPnurmsVnCmKRimN9SP454Gz\nRxfPGm80css/7vZBWZFt9VtAt5BzaYYcmyfwGNA/DkdszUjeDOMydXKRYtQ9HHDknvrfpnxMRr98\nImf4nDYPRTi12dMqZ6DSwbMqMmUHvvVnQMeoDJPVY8X3CAkid8sF+WEu3JSFCuqmg4cEV4OB563z\niDR33HgK2Ppens98Hod7TCFhuhQw3j6Rj8Y5mOPZ7/wtDiTY2Ls0EVmHhDQlfkHka1zbWdLud1Es\np6KIYCTuId6Rbfay++Brl9SvUQcbFsU1lP9GDg+pzfxWOQNVN/tD4IHk6h8Ws+mr8NkeLaZcaRNc\noaQau0H5+Sz2wYaddFeethFU94os6ssPYzLdp8z8uHUhTWl06p34NQttnF2y9sLa92VN9l/9sQ23\nEY76G/6+deRZv0M9f//2F1wYUiihPkSeT7dgSm12t8oZmGnNnY/ReUTWLRBE21T/eE3HZU3wQIMD\npZ+6GsVkql/DRG9tsK7Nz5u+uYWbP3waiPy7irxZO0IBzOXHrWsMnGO4V9hZ0ncaphzFz8JNNv7U\nHiEj5lQyXRzqryd3o4tzuvPv76bH6bDamrAF/9aJTKMg31FQ5Tn7W/GDG6Y2e1vlDMzExp+WNxwD\nbnNs/AeZzYmrouYuo1mMd59m4Sr6o06va96gr9lLboC0gN00HnLKpCOVzOz3vpofTkUXTvo74HJk\n7nq3LvyP57OuyUJT5/l3HpZ46Z8vPa+BL2wl/24KpZ0CuP0D+X6UyVCZU2tCIhDo87tT1KHtORiX\nt4utNb4gU9XfdGol7C1VMzCbmvw47he8SelA/UM1YSx6P6A/fr6Mpp8X2tZcPIlsoL4Bq42bPnHS\nfhKqz7BTpty0zA1mj1A5JLJvd1+2QNE3LU6z6BikeY8R9gdEaOKlf76UMOg84ivRmmVQHxDSF0aZ\nDBXeE1v/eqSoZqEdpghhU6v3nSA85lqrnIHZ1LJT325B+y1UotHCTfmNfOGmkuEynLZml3+DFiZ7\njTG4I7dsfqiNsia42g55E8yt43Q2s8whceMQmaa1msggMnYLmf+y6jSw+QKnlYTVi3blOBTRLHwZ\n5b4qePr93LUHhdRcOcGzZqSIzyJbP0PCV8cltbnVKmdgtjX5ga09a5+Gt5xzJRqVGSpajq2Zc5Sq\nzfKp+mZwt5AbuitKZu0IjYarksF8xYXMOuZCAGvqwiJEswiB7OCEZ4hmMSSA3zC0xT0CWPdSEYe+\nX7Ogkjg3axhP+v2cIN0uZFb1Da+4NavwmtaYQiPYKzIsr/BDRWqzu1XOwGxseYfrGtLh2tznN2Zr\nln24zFF+zYLeHC00XMNR7HLQmpFJU5sZ47PY8rJW6Gc4tMY0/S71cVA+C6Utqmio28apkqnhEWuu\niLSOQenv2SOkiWm/qGe2d9H3uzQLpUWte8nl7wl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_lines(USA_big_map, 'bo')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's get a baseline tour with `nn_tsp`:" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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DEqlepx7rDrfkgb61yDcA8ZtFrga5179xgosa8t3vB/KwmzOXDEgvkL+hOP87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\n5kI7Bbh+n98F2XjR+L2WTu4d3DcH+DIXeBJqzjIeTMlcdLstMq6hXpf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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1089 city tour with length 52879.1 in 0.177 secs for nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(nn_tsp, USA_big_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now try to improve on that with `repeat_100_nn_tsp` and with `repeat_5_altered_nn_tsp` (which will take a while with over 1000 cities):" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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qxb/3vf4t+yEcVwwFwPrXgfe8fnUuhFufglO7BtfkKoHrgAec97rrZ9mJcOYT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\nYN+c9lBC34KvN2ddVuxNvol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vLy8bh7DbvTZsGvaDMKbR7uaIEvrmi9rT/mdH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\nfAB1sck/jZPqINjgemqvH6ZrnlQJtndqfSSbhKMngWhXVcfDKlFYRMW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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1089 city tour with length 50802.6 in 17.126 secs for repeat_100_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(repeat_100_nn_tsp, USA_big_map)" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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HZ18xEXjX3u+KOij7kSMs9XvQepL32ztALbDwaLXvzNDhHaj99lD2/27AWGDt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\nz6t5umop3LETZvdONw5ZBL+7Xs3zmLZ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Kr2tkoh5C84dWrpWuoopQuTC+3zXzFCdi8YuZ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\nAVUbYUZuZDzIw8fg8kbI3gQLwtc2G/d9SPHYFk/9EiEZEGGRBERPnGb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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1089 city tour with length 44234.6 in 23.149 secs for repeat_5_altered_nn_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(repeat_5_altered_nn_tsp, USA_big_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again we see that we do better by spending our run time budget on alteration rather than on repetition. This time we saved over 8,000 miles of travel in half a minute of computation!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Greedy Algorithm: `greedy_tsp`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At the start of the *Approximate Algorithms* section, we mentioned two ideas:\n", + "\n", + "1. **Nearest Neighbor Algorithm:** Make the tour go from a city to its nearest neighbor. Repeat.\n", + "2. **Greedy Algorithm:** Find the shortest distance between any two cities and include that in the tour. Repeat.\n", + "\n", + "It is time to develop the *greedy algorithm*, so-called because at every step it greedily adds to the tour the edge that is shortest (even if that is not best in terms of long-range planning). The nearest neighbor algorithm always extended the tour by adding on to the end. The greedy algorithm is different in that it doesn't have a notion of *end* of the tour; instead it keeps a *set* of partial segments. Here's a brief statement of the algorithm:\n", + "\n", + "> **Greedy Algorithm:** *Maintain a set of segments; initially each city defines its own 1-city segment. Find the shortest possible edge that connects two endpoints of two different segments, and join those segments with that edge. Repeat until we form a segment that tours all the cities.*\n", + "\n", + "On each step of the algorithm, we want to \"find the shortest possible edge that connects two endpoints.\" That seems like an expensive operation to do on each step. So we will add in some data structures to enable us to speed up the computation. Here's a more detailed sketch of the algorithm:\n", + "\n", + "1. Pre-compute a list of **edges**, sorted by shortest edge first. An edge is a pair of cities; if the list contains `(A, B)` then it does not contain `(B, A)`, and it never contains `(A, A)`.\n", + "2. Maintain a dict that maps **endpoints** to **segments**, e.g. `{A: [A, B, C, D], D: [A, B, C, D]}`. Initially, each city is the endpoint of its own 1-city-long segment, but as we join segments together, some cities are no longer endpoints and are removed from the dict.\n", + "3. Go through the edges in shortest-first order. When you find an edge `(A, B)` such that both `A` and `B` are endpoints of different segments, then join the two segments together. Maintain the endpoints dict to reflect this new segment. Stop when you create\n", + "a segment that contains all the cities.\n", + "\n", + "\n", + "Let's consider an example: assume we have seven cities, labeled A through G. Suppose CG happens to be the shortest edge. We would add the edge to the partial tour, by joining the segment that contains C with the segment that contains G. In this case, the joining is easy, because each segment is one city long; we join them to form a segment two cities long. We then look at the next shortest edge and continue the process, joining segments as we go, as shown in the table below. Some edges cannot be used. For example, FD cannot be used, because by the time it becomes the shortest edge, D is already in the interior of a segment. Next, AE cannot be used, even though both A and E are endpoints, because it would make a loop out of ACGDE. Finally, note that sometimes we may have to reverse a segment. For example, EF can merge AGCDE and BF, but first we have to reverse BF to FB. \n", + "\n", + "\n", + "\n", + "
Shortest EdgeUsage of edgeResulting Segments\n", + "
—— A; B; C; D; E; F; G\n", + "
CGJoin C to GA; B; CG; D; E; F\n", + "
DEJoin D to EA; B; CG; DE; F\n", + "
ACJoin A to CGB; ACG; DE; F\n", + "
GDJoin ACG to DB; ACGDE; F\n", + "
FDDiscardB; ACGDE; F\n", + "
AEDiscardB; ACGDE; F\n", + "
BFJoin B to FBF; ACGDE\n", + "
CFDiscardBF; ACGDE\n", + "
EFJoin ACGDE to FBACGDEFB\n", + "
\n", + "\n", + "Here is the code:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def greedy_tsp(cities):\n", + " \"\"\"Go through edges, shortest first. Use edge to join segments if possible.\"\"\"\n", + " endpoints = {c: [c] for c in cities} # A dict of {endpoint: segment}\n", + " for (A, B) in shortest_edges_first(cities):\n", + " if A in endpoints and B in endpoints and endpoints[A] != endpoints[B]:\n", + " new_segment = join_endpoints(endpoints, A, B)\n", + " if len(new_segment) == len(cities):\n", + " return new_segment\n", + " \n", + "# TO DO: functions: shortest_edges_first, join_endpoints" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "**Note:** The `endpoints` dict is serving two purposes. First, the keys of the dict are all the cities that are endpoints of some segments,\n", + "making it possible to ask \"`A in endpoints`\" to see if city `A` is an endpoint. Second, the values of the dict are all the segments, making it possible to ask \"`endpoints[A] != endpoints[B]`\" to make sure that the two cities are endpoints of different segments, not of the same segment.\n", + "\n", + "The `shortest_edges_first` function is easy: generate all `(A, B)` pairs of cities, and sort by the distance between the cities. (Note: I use the conditional `if id(A) < id(B)` so that I won't have both `(A, B)` and `(B, A)` in my list of edges, and I won't ever have `(A, A)`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def shortest_edges_first(cities):\n", + " \"Return all edges between distinct cities, sorted shortest first.\"\n", + " edges = [(A, B) for A in cities for B in cities \n", + " if id(A) < id(B)]\n", + " return sorted(edges, key=lambda edge: distance(*edge))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the `join_endpoints` function, I first make sure that A is the last element of one segment and B is the first element of the other, by reversing segments if necessary. Then I add the B segment on to the end of the A segment. Finally, I update the `endpoints` dict. This is a bit tricky! My first thought was that A and B are no longer endpoints, because they have been joined together in the interior of the segment. However, that isn't always true. If A was the endpoint of a 1-city segment, then when you join it to B, A is still an endpoint. I could have had complicated logic to handle the case when A, B, or both, or neither were 1-city segments, but I decided on a different tactic: first unconditionally delete A and B from the endpoints dict, no matter what. Then add the two endpoints of the new segment (which is `Asegment`) to the endpoints dict. " + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def join_endpoints(endpoints, A, B):\n", + " \"Join B's segment onto the end of A's and return the segment. Maintain endpoints dict.\"\n", + " Asegment, Bsegment = endpoints[A], endpoints[B]\n", + " if Asegment[-1] is not A: Asegment.reverse()\n", + " if Bsegment[0] is not B: Bsegment.reverse()\n", + " Asegment.extend(Bsegment)\n", + " del endpoints[A], endpoints[B] # A and B are no longer endpoints\n", + " endpoints[Asegment[0]] = endpoints[Asegment[-1]] = Asegment\n", + " return Asegment" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try out the `greedy_tsp` algorithm on the two USA maps:" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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yDoB5g7kXzOYTrVvP6FFh9ddhnkGdkKT+gV914TeG1uyG2YZ8TzbVzJjnoLzb\ntFl70v5hv9/OqYL8BaQoxlreC7I4xn0lIKvjvj/emuo+Jr5qO/TOPSMtEb0a8ejgrHhZYu0wmQiX\nPQI4DlMAV//cfE+9kWg4e8GEeHsWGQYJ0wJxSgrYkHrpr83Pu/NyBbM4qHFVNCvJ0J/LTcedTHoB\npnTAFVvSDEebsgf552GS69zGqxtyorecA2DeYIc37oGgO1vPB76AfApkJ9xWlCk3pTbq8DazUdTt\nCXTl78PeYUbq5s2ahPuzG/aSZS1VTed7GnRftHrpB6PgjjaoejzcS0w+CNIGclI2xvtM5lHdb1PN\nLHaNvSfKy5r6CEs1Ygumm7oJ5TL9OtQfMt+jnQoOG4NdDiOFDTBoVxQhyv5s+VVDbsIYnZHBO19a\nAjKpmWo6ORyw6lZTlQv8SsxxEvoMTBG4WZwYi3sERojykOr5OTleW84BMG+wW3fD9Y97DXqFDTDK\nl0XSnEAw2bvkfSCvgEzMrp+CfjCiM8jRiO9QRLmnRgVPJee21XN+I6xWsSRJNRJtnA2+N8n90gTy\niaRG8qTzmPB+l3G0+GfZItdwycLELduM+te+i0p3fqFdhaqZlCViDkKc3K3e6Y9dGvR8tlJdcLxa\nInCfBbu6yDxfzaKQv1USazJLS9da7vdHbruD/eoFSsQhGCdW6o6M1jLXAJg3mNwJ8u/e76LzDGX4\nrq+CNJBhRLcDW1iUqXtTFjWFZW21c6/VrweDvEy664Cx8O9VEKBNTZEkieHoriTIMjnCll+DVEe7\n35qCyfy5pTKpZRHmgTTmCbhpG8zssN8TNzuuSYc/aos5m/LQyJoX8fafDTHX+ZBroyhX5J5RTSnY\najc6qTGiUpj419af5mOFwBjDuoootZJpnLa040t8//uJxmJRUkcyVeOJ2nIOgHmDyUCQl7zfZc9t\nGt4zCGQbyBnZwRvmC+4WdyeJT29uyNpqS1o2ot38vTsoy48w5nVCUwcsetd8WMZ0RhtA3e+q2JkM\nASdF2FIP8jX7+z1Ed1m4uszWx2ceivbMMdVN189XNvtSgsSK/fESNVM+KKvzQ1McO4nTh60csA1h\njvIFD7orUIarK+Ofj8cWwYgOR3ryE6dg2vVwo/2Vj9vnyjROG6G8x/B/rWvMI13wvXdtFYfXMdcA\nWJDGKSB7QE53vovPbcZ8Rx9Uzd3R2cNrg+2GAzD+9fBUA34D/sDN5nTIFU+HIV47crzq52HeQObx\nFPTz+rYTc+VfAAAgAElEQVRrGHrOm8uyJiNA/qDev8DnCOBPGTJvi8ohZe7fjGwmtsLs2Dmx7PAv\n2gXynGqLIvX+cdRx9lQ2ZYYo4ijVX2EDjNnrJRqllojyoneU2+h4gVKBQQJzJUhsMlfDqHn69WRn\nHM2iYBvTac/aa5v7Qc3wh1ctQYXFwdTzzenxjD/ovd/k9abPY3t6Puamfxv6fK5x4rHQTuYYvETo\nSqUaX4Av/iaVOnAQtm2FvXugA+jturMD6JX+7t7zYOPSVKpvPVy0FM46Wz23rl6ktVk/kUr17ad+\nLyyBQ/vhf16G1iwh3rbVDNtZLfCtT4jQnUqNWQkX9Pc+1xvo9n0e+lF4YxMUPwD/eAa0nwVnvg2H\nPgXrgQt872jZqv4/62zv+3V/p50Bj90EMweqOeqdfm7mRlhfZx5P6z/Dhq1w7VNwxlnqHevq1W8z\nLw72o3/zX+vqze+13c9fgEuh9Vx4fROUPQunlcKAD8Nc4BzXuFu3Q8EZ5jGfebbImuZUqm8pbFwK\nZ56txnCoN6yscJ5x9g0wIQiObU63vQHMUp+3fRd6n2aCwfl80VJnDmzvbdoD3wa+iDNXdwE7d8DT\nNfDaN+GMImgH3l3rfpuzp886Gy7aCuv+Dc6+FDrOgTuBc4F7ToI7gK/4+j/zA3ATal/p79qALwGL\ngS8AX8XZZ/bLC8e29J75+kWw5QL42yR4cy0Ur4X+H9B7yn02vX2cORy+AUzGWffeQMk58MAeuG8k\nvDzTWVvVVyrVdzhMewR+VAC7UHP6FWDXSbAQ2AYcSo/1VuBfUHvrdOAWFD4ZB/wj8CFgEVD2D1Fj\nf09cuaZWdu5oxi4vJ2AqQOLnNqdtDpZS9OtAezZdiL3f+fug+F+iOSWTa7Di+g2wWosNRXHxyTyn\n5CGQmfaxxvcYc+4ft0F5i41eY3tO3Vu/FxbtgYnPRLkIJ3UGgCkvhUlnQXjiuK3GuSdO2V231OaO\nfRi4WSVKNFdYNM+P5q796hebiskU+Frv+t6srow+A+OblTSXRCoKy8XkHlOceCJ3apVmgRtc468Q\ns3qvKv3XPf6RL+QaJx4LLecAJDukurShzSf+unfDEWbyQLb4MOsNOv2vqjj8jMujD4If+bsPRlj0\nqKnehKn/aduSeUwVLYPxTyuEPfAT2c+F25A/eVO4GibKXdcUbFfQDya9YVZH+Pua2wGzYlWeiwNT\n+D1zDsIVv1PjL/4Z1GyIeq89+niFQHX686o0khsryivoguXmPa319mEBrWHfL3E1u7oy3pk1Rbzb\nUr+EMVT+85E0s8IC8ToQ2Gw4i9P3TReXvaYp6l3vhXZMqqEc8X8T8BOUqqYX8IEzRP4wSImqH3wM\nTj9P3d8B3NwNXe+3qSW8/dp+z/xSIjA/BH4JXCFCY/B3v1pk3b2w8f/BkP5wCo6qpQOlbtCwuufh\nfX8Pj93kF9+D/R/aD9/8DPxQomBX8zn6Ma+6qPl3qVTfUv97MutrRhUsOjVcDWNX1YismYBLTZRK\n9e2XSl25DMrOhjc3waIPwLaXHHWZqa+v/D2UPgQzPxlXLWZZM4/qJHjPW3vg49fAH4c777gTmN0O\n/7eP/72O2uV9F6rvf4JS/fQGVqNUMb8GlgM/AD6D2is3AF8eBgc2eM/KO8BaHBWtWz3q/4zrPvdn\nt2o0TF3pvj56jvls9TJ8d9WHYVENzBzo3WO287kBNQ/u86HUYibVl9OfWz28CaVa+0Z6fOsxz8Wf\n0jB/Cvg34EVAPpJKXdMJfTpgxypYX5f0XJwQV66plZ1LsYf1Oxzd5Y/C2G5HygivhXtkJQv5BCrd\n+dBkz9mMydorKty9MAKm21QitkH3ZZZ2PZMStHHUbbrZgq/M9zjzpaOPtapmhCflRnSdjOzTWCQf\n/xUP+N/rlUqa0xyt5nh1TIEOQhsvXuPw+PT9gw85Z8X2V8PTKIbcWt3BwNdpotJ2B9OFEEi3clEZ\nyN1Qvy++ZOH1aoueu1KjKiva3Xn0GvWsVi/552KS71zNFSVR6HmuFrhezC7N7z3vqJwDYD5wBf2C\nXg3GzeULWGo2LKzHZlEM1+0z6X6zg1f+EWQjyJQMnr0KXt8AV1oQSebF4OG0/sE8OCa3zp4rQRse\nCR26ljFtLiUt0YyE7isY5Jb9vgyPp4hHqPTzfjfpZlFqJo1Q9T51B+35xz36EJS2B20UeuxzBIra\nXK6paUQ6arU6YytEeUONE1VV7opdFiLRDy77E4xKw7jAhXB//Xu4e3AQcc/uirYzOvXEo5F/3Jxf\npV3BvfFpAzFrFCjqhJE71BwvcM3fAokIAHzPxV3kHAD7wRy9Jqoqnrm+QbNAyf54JUarW7EkgYsP\np5wKsgae+c+4gVm+538Dcov5t4J+9roIOm1F9hKD/b5pr5COQYmDKMP7MnOH3rGG2Sz0b+78QOZx\ncTiA084RqnvsVfLMaxEnniLM3uZ/vvZAsMRnsyiuvkKUz3+dwOj0b7Zxj0jHv0Snz0i6N5yxm4oG\nTdcIt8m5TxcfGtEJY9Y6iD4q95Z7rcsfgdtb7XEweg+WvxCfMRm01/vuVaKkjcouGHEwOH/XibMG\n/owM5jk90VvOAbAfTlvdW4c7DEoW+r7BB+If4myCjaQXyP3wygOZJekbt0aJ7yUXhM+D34PFlLoh\nc4nBjAgnb4K/3AfyDry4zGKgNkSgm/qavs3GHZrnJYyD1Bx3+LjsMSEqn1UUMQnCFpfwFvSDmbuC\nc2ULtvSraRoFqtu9z09Kf28jBtrrJzp9hmtvPJ49YdEeQxX7nWBDa/bc4uCe9Xs66T006vfKIy6K\n2ZvcHR27pNtiUaq7KwUGClwhzrPl4p2/ZoEJvr0xRWC+ZJI88kRpOQfAjiRth73QRSwKioOpCSaJ\nEq39h7jnVC1On/JVkFVJcgbF8/pxexGN2uJNcTJNoCQ0mjv6kMcp6HS4BO0ZSsKILy14+6r8A6x8\nS81RPKkrOA/uZHpalx8+Lvt639WtCPRcSRKpbO/v+j954a19Ro239NdetaLt+bHd3jksO2Qe21BR\nnK4pUaXO2RUviyzIp+wFjoKeT+EBsYvTcInYVTaXuuC7RxQiNnHrpjKmUW7S/j2o03P479OEQGdV\nGCtK9bZKVDBinTjzZxvHYSmoK1uNxPHYcg6AHWG4XQndqignJ466r/h5b/lJc+KvbCQLs8++TAd5\nDeT0JIQomZqiul0RB790NfztOO9TcIa7rCZbC38Lt0M4MMxtjwtDeNyAfs8qcdJc63smtqk5jKod\nMug++OyzCqmYuNykMRdz9wWjiScHJBS7HWWab38vNMyzCIw5FITXH29RtCytnmwK2iiqVqpo/ud+\nALID/vh5qDGoloL51rxjd8eAVAhc5TpzNsmnwkcArRKQRVOg4Tf1rcep1VyrxJxu3A2jJhoV4sRV\n6BiM+QKVlnEs8cCUaxx51HFyrgGwI6hoj6jwQ2xCWvP2JkWcZuQ19S3YuAPk/AgYmoIHz7bpxx8w\n91HnQyaNAoM644xZve/JL8Ds17Px/snUwynJ+oTfv0JUhTT3GlQ0Q8lyuHMfXP4QzDH87laJ6Bw/\no9cog6+J+zQnVnT2wS27g/tnyB/Cxucg8dFrlEToJ/7zxMth2xCpyasovGKbee/OboVpn1a/29PW\nexkknfHZdB5nuOC3we7PKWYy1Fe3KsbPdDb03g2b5z5jnT3i9hi7VRyJxr1nl4hiMGvTn90Bi1WW\ncdzjgSnXOPKo4+RcAxC+0eN4RIUbHp1NX70a6vbDpx9Igjjtm7TiUeeeT38c6ny5Z7ycX3R/pRZp\nQbtMuvu9cldwzLPeNdsB5Lcg12e/FibnABPCzU79p6rrue/TiMVfSrPPWKXiWvQu1rxbutxpmaEi\nm98rR0TlUwpDvn99Am54Ip56SXs/+efNVJPFjYRM9qiaziCswTmM9rbyrlFITrO/mKOxL30rHIna\nvBFNUl6jKNui2zPRvqfMLtOqpKpqE7rgWwJDxFwmYLF4c0BpyWKkOARmoet//ziC9pVc48ijjpNz\nDUA4krIVfgkckmIo3QnV+3GV2ozrwRIOg+1Aub2Rxq+C3z7N4ayXfp1yHOIW1wDaLioFhEYM81ph\nyHaY2Q7TXvYSJnkfSCvIP9jHF9fLyW2HKGxQ0cO1fp/9BN5Bfs67aiWU/AJu2RmtsjAhVLcB0hvl\nG08yapfwxIpFy2BxFwz9VVzJ1v5bpQ/Oxa7fJhxQhNBtPwpH+vZ9FU5k7PCNtki5FZYiS274p4tC\ntFUHVRyUzenBRhjsXnNmI/mEDQ4RGyJeJO+BXRxCoW0W1QKF+4MSyZhOuGR5WqJa7cRqZIZDTpSW\ncwBCgYuhwgg3GGfvAWXuo1Fgkk+SqOuCur0xiVvAmGwex/i95sM+arXTj9/zZsZOp7/KP5hcEMPn\nTtdHtpVT9QeS1QuM6YYr37b750/bZl4f0/tr93h16UlTTruluigOenEApnhzFC/fWHSmZA1nlfjS\njzcR6WEW8EazSFdG9VVIWvsJG1RtbBPcoy1G8SJLhUgntXdwz9veUdUGFV3pAkxNimEsbFB7q9zi\nfntNmoiNlWBaj3ZRqr6rRRGMIQJFAlNF26hszh1h5zXXuDEn+DjXAIQj6ji5ecI4u54og7n6q7DA\nx0GXWdRjV72ZDXFS4715HczaGE+NYBt71XOZxQSEBzWGv7NcbEGO8PS3YPra+EFVlyx3HU6D0TOq\nmI0fUWn7l9/2o/Ns6foSphoXdocE77olCRpzRzCXS5AhCBIxwzuKw5Pu6TY21E5nZlySOGGEEZfF\nAoWbFcIfuBmG7lBuvpcsh8s220sQawnLVFLZNM4R3Y5koSPeK8WxP7htFpmdzXyTY5tYOJt5cSfc\nuMpM9cN0xtlJFiB1IBtg7e9g4TYY87hjrDS9M1ntAfNYJz4L899S73FnG71VlLvn2MM1AOxjr411\nMILPRx+ocC79Hs/9DuJZuBOq/xR/7cZ0OlzzMIO9wWbLcquVRrkryRUb0lwcSOu7IySHUBhD19Xc\ntx/R+b2f/OMwzWeYJOF/dvB25TxR0mKS/OLDHUa0bF5M94hyT3Uj+UZxUor4v/fbBcrE8XBsT//f\nLN5xtotyfZ0ksCz9jJvoNPv6z+xs5pscL8TiznYVwGYiFvZ4jLTbZmS6C++79GGc9Cxs2AzydZBG\nkA8694VJM5mJrJYDGsJd2QyH7QKfbbURUO87/eOwuT56osVDEMOSw+/JTiqsFyhzZYgNVFOL4Kr9\nBM72nikvQsVLYfEW4TAakbhPMtHS4vVtZhWKX0dvkg4qd6u1jkqdIeKVSiZJEl27glVHtY/cqaQC\nvfZhKrpGMbsi+1N9u5G4//sqw1iWuMaxSrxGav1bnSgnkOtFqZmKBG4UL3HQ6tLP7lUSzijrmPIt\nBEflGoBQ4GIhHHukN8jn4G8vKt/6cORtfteMnbBxO0i/pHAlH2tcI6z7gA2wqAWiDaLOOKZtde41\nBSM1CtS6qtY1ClR3mxGDI1nEtzfVdAb7apboXFIaQUcbIO3SwaQ3YVKX+f3aCBwG4+wmeGiGiquw\nSSYF/WDWazClyQxnn7EcTsw3qDM8oCzKk6pdHNWaTfLwu8W67SL2qHbzM+41XiVwrXi9m9yIXcOw\nxPXX/b1pvd17vUK8hKZClKpplagYiWZR0netqFQdIwVK2/DGnGR8PvPtmE1Rrq84FcbO/QDMx0k9\n3Av1ectQuOs6SJWJrFqV2bv+7XQYv1zkwebg/a+thZvPgZ1tsPNJ2Jhl2mJbeuZuy+feqIpjD5b6\nU2ir3+NUtGvdBK/thGkbYP9BeGMPNF0KPzjHeW5+OzT0cWD7e4CUqiZ2CSpd9lTgv9J/9XvKfhyV\nDl6l9770UfhqhVq3XjhVy06JfJb0HlBpqqcutaURt1cyfO0ArDjZu+beynDhMB7ogMfvgu98JLhH\n2+5NpT67EEY/CF93rcO0Nnh7LbS/oVLUV/wE7u2vfl8PfOUQfO8kb3rzz6X7/SJqn9/teldX+v/1\nwLw2OKNFwV7wPnNlxj79VQr5O8+D+1EV8nqPgnefgovOgfF4z1L9OdD4TbjIv58Gwo7tzrgHpftK\npZ+93zVPOk25O216NxxGPx3AMx3Q0dvp/+708xruk1BV8/Q8fQuVkn05cCD9nv/jW9+ynSJrziV/\n9cyVa2oV1uJVGAvjyONz/NnlUeqJzLWZSBa6GJRN/VG0DGa8Cnfs0YFY3ndKOcjLIL1czxXjSUE9\n0pesza0LvkfgNheXV9rOYbflJMGSmcVwxJ9b25rZbE9ee0RmHk+3t8KSrrA5sHvaVYgT4a2L8Ojf\nl/j7ajLHkVjnsMmsv7++W7ke+79fKDDUFu/kU0maHCT8hmmTzaK6Ha7Zp8ZdIWZ13SjX/1e59uB4\nscPtzfaQb1ni41wDEH7I7RGm4Qc5XgBNPIOhKd+S0bPGKN7HH2tSm4WpzKzN/VO+APIiSF/Xdyl4\ndS3c+KQ3F1VYqo1mUQZLMTRvVTU1ntqN8eCL4+lTuzGZ/cekZonv9RMDxn7OfjATBOUQYZorreIK\nc1BoFkfXrjOfahuAdz7tMJhiFkavMTsyaNWOqZ/RB81wmnI5jU3v0yXpv8VtiuEYuBmGuLyhBlhi\nGMYJTBRvn5PEMXJPFuX2qonSrWnYzWcy1zjsRGo5ByD8wJvSIpty1xw+yLvjphOOh5yDKcyVd46J\nixn0fPYBgEZPE1cg3ICGJIFaTr+SAvm/II+DvF9998B0mL/fC+84QxoMd2TtdLEn8dMSz8gdznt/\newt8bmu8TLNVPiTsnosFW+C/fxiHECeR/Mz3TmoPizNJ8r4o6SrceD5dVHyAp98uFQyp8z/peubF\nzwdT+Ys4uno/gTS5HjcLVFqC7q52xVdoiXKxkA6Adb0jFsPlzJ2NGZwqyuBd0QWDuhSBqBWn5oTe\nizqXU75A0dFoOQfAfgjjc33Rz/i5/gENitMx3Xv1obDiSHZvIHu+pqQShx2Byt+BXAFSB5/bEca1\nBvuUXiA/B2kAOQVu3x2O9N3t2nehqM3h4EzEUh/0qztd77wfZFr4OOPEg9xWFEynMnkTfL8cpBTk\nelRix0XK8ygeEfXOdeVKuPxBVbAnmFIi3nrFqaESFdCn59KW+fQKQzr8mkPBWu5mzlq90+Z6XGg4\nE43p78d2OjUsbOOJl3HBgcPmOLDEAI9Wv7ldYfUaXSVQI0oVOkFUDq73XlbYI91yDoAVsFhpNkx6\neu3Kt0CUWD3qIFz8pCOlaL1qWMF292e/2st2IG7sMn9/w2swsSkKIQbH4L7/lt2w/hmQdpCXQL6r\nUozER4qq7wvPV5z+4i4Y3WWODjeN/9b09+4De5UolYHWL2vJb+AONYarfg71B+Ga++1jtRH3metB\n/gfkQZA/we3vmO9b9DbIH0F+DfIjkG+ogMZk+8YLj7sk6WGCcSBT5BPlSq1+L2kJSgU2N2Z3nQX3\nXLhTiGgVlE2aumB5MOeYjgh37z1TGVaTR5ZmiKJzuUWvfb2oeKLPtKvMAPo3t+rMLd0MkZ60b+Vb\nyF7ONQBWwKzGP7+rYyAitRjK27xiqZtL05suLGWE+Focg7pN4hgRq/ZEdP9jHsNjc/ATlUaBYe2O\naiIsTYfu03Tw3Womfc8C8Zb3lPR30yRYa+OS5fHVQDaGYOZrIJNBKkBKYMKz5vv8zgdyCtzyqnnf\nlLd5YVXqTK9Bf1CnUoFEZzs+MntdI8ElohgdExIssVROdKcQaRZ3UKL3bGhDuJZexhwO8nT2SVj0\nvOmMaEIYf968a+8e95XdMLIzWNK02dD3QlFqqOi9kW89sE9zDYAVMCNys6XZ8Adg+UV4v5+39ske\nL17OONoLJ0S1YDDKhnnc2NRFSWpj6INdthomRKR1COPk9P81ncqQ6Nd/6znTSeI0svETi1FbktlS\n4npM2e67eodCaMNWQ8n90Phn+OvKoCRX3Gb20hm8Fmr9zIfAp9N7Y4jATRLHYJqdqrGwAcq2GFKt\ndAXjMmzz6/aSC6ZaT8r5h+/FgEfWMnv9mSE77FKc3kduIlCXhn+x4bdGUbEcbonWxvTlJYuebjkH\nIBS4gAgfjXjVpvWL8O4NZUo0NllUrhobwo+XWCyZx421Wp2FmwtDVO53BAyQ/Zx5Mc3dmHejjeYa\nETWm56mkRRW5H9jheL7UC1y/DW5+Nz6x+8EolYAxznzbpCLNYTYKzHoHzjo36P57xS7zuK7pNn9f\n4fp/kqh6GtqJwWaMT2JUH9AQ1NcPP2hZ9ybvfoqTQiSYisRu2DavTXBfuWFK4pFVH7GmbsZulcAY\n8dZZdxMfbeB2ExGTu24+jccRwce5BiARsDEQr+LS/JKFe0PdKuY+3C6fRcvgjk647sFsN118I67b\n3pIsh42XqzM/a5+7xZ0gFXZY/SlGopLzDd0ZtUYO3PJbeOKuMJ2+d36KljkV0UyRzO1iiWoXs32m\nvDv4nYhTEEc/r5PR+Qsw+efWj9gGNPjGkFYDmdJoa0Tu58yDsQLRc2ErjZqMC1fvmfqWd8zjm71e\neXGM9WHMUXmLM+5yceIsjCotl6TlZoou26zO/Xs7K+yRbjkHIBGwng2pda5jfTrXAQ1KPeLnNkYL\nDO6AykjOV71n0S6ofa4nNp9zuOu7bAbfONKBvX/9rB0ZmA9zdStUvAz1e+G+asf4OagTKvZD4Vtp\n54AuKN3lTkRndyEeGsuFGOQzIFtA3pdsLqNUIyUt4dyw+7tCiz2pyvedjnMw3Vv3JtzeZibUNZ1e\nZKpjCsYb4L9HlARTLsGCQEmcIW7eHm289++BMEbkme+YMgbb4TEZ673ny7x3b02Pe7446k6Pk8FB\nlRrFnZ5Gz3G8BIn5ll3LOQCJAbaK8ZrLG71GbdIFojxEatMbcU4aYYSreZKoFJLDLs+DXGH+LXk6\ndYcIjV6jENEcw/NOH879pmCoaQeharuXyDaK0psbuWnbPDZFeQCl5+J3ILOSz2FUxH65xQA8Zq93\nXKXtMGItlPncTieJU69Zf1cldhXOTS9D+SN2V1d3TIUmAqZ7V4jSxbsRZHn6+zi2ksqVMK8ZHplr\nv2/GzrhuwU6/t7equijm/FDB50b9Prn0UtGsxq7nRnsz6vN7ONdbLTyxCwa1qJrkbntjXvV0pFvO\nAcgI6ADC0FLG0B1QZKnypUX78DTiSWwMyeGWX4CMjzem8PdaJIWuOG6E5nfVG5BYmKSi7Ud+tcnQ\n52PMQ2EmUoV93O4StmFZiLUzQCA1RpeKJRm4Fa71uYpOSiNsu3FYwTS2M5xQazWQNtz6s7TqeiB+\nzn+KxE1bAfIwSHnQZqNTsLzyMNSsySyppr+meRBBg3xIZWo2Frsqtru8a9WxDrbzawXG7YWqV2Bl\ni4qvCSfM+XZkWs4ByAjogNudO1/9HMNBdKdLdhueg4cmXj6qzNJ6gHwZ5C7zb8kkGjtxsZelDB+j\nPwuoGD47cxGl1jDNkfPdwl2qbkdmnKBXQtK5kQ6/o9ipARIMrIwiyg6irUgHImqj9sybgoGB7n7d\nRCqoRnTmS7sm6xKwmsgukhDi3BRn34GshDvmBWMjKg+oEqd37oNrH4iv1nTDESU5SQoV7/IfhvNl\ncBxx1EdqPO5zfDhGSmCGuFLctKvf7fsy17jpRG45ByAjoD2b2R83oXW/I8WLMMypQsL71q1n1FQg\nN4H8j/33gn7w+Xdh/NPR+mEbUSt/Ea5+C8YfdHOV0WNMKlmEuWJeZogyjuZMvfOQCTG22WWcOchM\n3ScFIK/DI3PsTEakg0IaYa4QxcyY5tqm6hq1Os6+A3larb1f6k7mLWRnJuzzBjILlX/sfcH1C6sv\n75YG/Q4Ccw3P3BO6L3ONm07klnMAMgL6sJ5TJ1kT12Z2cyi3ivKEGdINn3rLpp8N9j29xXa4slFT\ngVwNsirini0g/xzdlw2O8u4oxGD2cqloVnES8WwWqh+bK3PFoaScqRe2TIlxFKGXlCpqlWz9QH4C\n8l/x9o7dJuYg0bLVyoNnvMuOskJgcLe51GjRsniegPIKjGnz3pMcscaTLLTqt7wFRv4OnnhHeQ9q\n+5nHDnTI7I2mAwlNHmw1nfYMA3avv1zjphO55RyAjIBGJxlsFCVBuCULEa8aoESSGsHghR+rKmom\nDnLCM0k5U+dZ+QhIi31M2mOqxJoiw3t/5qm9VfDahKeCPvy6UtqNnXBzC3ykxM5N2xDY6J1JOdPw\nPnW97Kgkgqao4PmS9u56Cma/Dis2BIsVVe+w1+CW8SCvgvSOty/jewN5iYffjjJFFGetI81tEc8l\nLQ7xfn0TDPalRU+usom2WZikldqDwfxUboJn8ka75zAsQdXV0CfMe6vskANDvcDYbqViyxOKI91y\nDkBGQHv05XMFbhF7grtRonSgZt93b796w85rg5Ktyj20aBmc1h9kOMhjsLjDvImv/n20p8hp/VWN\ng7FPRvuoRxM29VzlH+C2d1R/w1bHQ8jycZDtpDPQmvuWk1G5mX6Gq95F8P0muE1G5riShV8FEp+L\n9MY7LBRH5eN+dqIvU2rJSph7yNQ/yLkgO0Eujd6TyeMMgnD756ZenEp1tojndoGbtsDKxY4KdpLr\n9yQSnWf/FvuZBOcem3vyPSGfx1iSBrYLDH/Yt/fOURUqp/rcZKtb1fj8sT159dPRaDkHICOgPQFG\n80SVUawQZdyuElWQR28krYsXccTbuOmqDxvcDsCr60BqVTI+/33T31Gup2H6ZDtByFS1lXYVXg6L\n3g3XDfsRg3wHZGn0PMupIE/CCz+xe7KYotYz86ZR/fnnIr4axXmv9qyxpVOPU5970H0gT4PUxduT\nySKYg/tZJNiWHIYXvjNcGdhtyH/2644UsSp9DnSJ0ep9yfemDr4zrbkNXn3uNCKf7+qvsEG1MZ1e\nl9ebt8PGt1V52qJlipG6fTf8eamCq7BBBR+WtEDZrqRSUr71XMs5ABkBfdhnXUTl79ERuiYvqGZx\nchLGVSwAACAASURBVBtpL4sRe92BfE6fNm7Jj2D8CDIaSYcRhMxjLEwH3FwQyYH5+j/BXfthXmG8\nuR59cbDuRVypx8aZRtW3mOJKTW0z+k58wfseN0dc3hJuMPanhzHdM6dZqequjGVot/czsiV6rsL2\nnghUrwZ5E347yx5HUrkS7rakLxnQEDbv4YQuuOb2OhTa/VfP/bUCy0TZMA4nuDRILN8vt6R98XlR\n5V1mc9lyDkBGQHs8capE2SXa08TAtIlni9l/2ymQEh0ZHIa447jb2u/JRLKwP1MYQAwhUo3V9z36\nPSbimbxCoHlsjy2CuTonksVgfEcbrH8qaKjXyfa0oThTIj5pryoGFT1njmHbbJyO3suFDXD9Pi/H\n7VbTfP5d0hKOHd7in8EbXZmpM+MmDFRut1CzyfuOOoFRh5wcWvq3RvGmVI8rTep7B/oi7PN5oHLZ\ncg5AxoAfzrNTIYp7qRWL26IoUTxOhG08ySIISxyEakXuDyvkNjEyoZ73nUmy0/Z0TIYILD4A8ig8\n+70w77GINbToyee9CZOfDyd055wHNavtBFN75ISntzD3P11ghIFLb5QgATGp19xBglHpMQLpa0RJ\ny7NFEZ8RXfCzn4fDO2EDVF0MsieO9Bac+9JdZseIe3zf3blXSaVGYvV2kDjHUyHa99gEw3fNolRS\n+TxQR7vlHICsgEfnMpogiqupEpUi4EpRKqkKUYRigkT7iUdFBsc99PrZOHrh2j0w+4AXWXjrCwTf\now/4VW/G93yyIvwYB9lKaH4NMgKmvpSJaiA4H6ZCO34Vmj95XZi0ppmJ6PQW3v4XbIFJG80qLBPy\ns7mUBlWdwfeajNbR3LNhPorVety5Pw4CtexFXzp0W5GjGa+a53xkS3DO3O7s9uSI9j1WZZjvvNop\nVy3nAPTIIOgzFooPKaJQJYpw1IlKKDhXOFwS1MQpelwy05xtMDI4GgZ9gO/Ya4uSDR5yW2qKMOOt\n54D73BWjvIT873FXV9Pf+z2nwgmhE33rRgbNgX6iYeqpeAC3tBgWqW+KMJc5IM/BmCfM8JgIiJsJ\nifbc8r5X2x/c70o2D5l40oXMW5NT791k+7p7sEo6GSbN+dc0U+luoShDvf/Z8QJ9bsk1znkvtpwD\n0GMDoaAYSjoUwagURSSmCZR3KGJS0RwMOJsYGcCWEIZ+qgTohGficXg9oUry1juwwxVVD8Lu4hmO\ndAc0mAsL2V2U1XNjnrAj3fC5cPp4bJHyVIuLnMNsOFM2K68cOV/dZ0JypYa8Y6YqjIE1skT/62f9\nxbns80Ag79PljyYnsklS2ug1v/B8kGfhT1+0e/W5K/HpM1ZmCNA0SbCe9zWZU5FXiDKaDz6QVz8d\n/ZZzAHp0MBQUw+BOtakqRBm8GyVtyC52As5GtsBAQ3H6zEVci3fSIV1UyfxMfMN2Jh5TQfiKltlr\nIES7eJr7tSfusz8j18Dn92QjWYAMBtkBXxsaLj0EpLGNUPhb87tqVnuf86uw+owNdwm2Ifrb3gFZ\nBjevC6qsdGW4aIKT9g7yEcexlneGEdl4+85LaGc0wl8fA0nFk9gqV6rzdvXbSVKWO31Ut3vHqTUF\nC0QxhHlV1NFuOQegRwdjLHwkloOQHfINvjvUz/6AXVceT4WQiceUGU7buGsOwrIbw581cekTX4jg\nhF3PXPNLePlXIJvhgelxbRZBOKQfyDaQayNgbDLbdSoOJees/dUQb29VMS5xgtWqVoBMhFkbg+9s\nFhi4w0m5b7dZmD3DkruTZm5jm9gUl5mwq5aigxTTzxdDySGvpmB6ep9UZXxO8y3zlnMAenQwlLfE\nTyvh9hVfIE7xlehiQ+Z3RwVWDeo0qYqSea/csjtbtZmd6NSsAXnM/pzp8M/fB7MiUnf7n5n1Dlz3\nScvYAz74wXka+6RS9T35BTOMOmeYjtifLsEcQyMtSD0e4VXvmbMRbv5bkJBklv4+yJEHK78p1ZN/\nfzWLkmCT7Qv1vprVULfNvC+zY04imKeY3nJ9xkJZtzch6CSJqvGRb0em5RyAHh0MJS12TstRi6iD\nEpbnpieRsHY/rM24b9W/nA4b34Gy32TjNmhHaOd/DOQNkEHJxneFqYxpVpHp8WH2Izib/eQ68aaH\nKDTAXB3hKeV2gggjCGHBiFXPqkSP0U4JljWwxJxc1u6oV8M9sHx7qgrEqC7MrhhX1UoFjykRYHSQ\noqu/YvhUB1wlXucVJz4q345eyzkAPToYa0nViaIyqpo4vJ5Jdxwtdldl3LfqX74M8v2emSebiuWP\nn4fPvZUsxYMpCVyka+vuJMQuvo7dpgaqcCPnAwoJ/eNVMPKQre6FM09+SWVUe1yXZfu+qG5N18lo\nUpHNWpKISpRosllot3F339HZldN7qswmTSYl9OZ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33VcvvHN4DuosVDWKrDHMv23O3eel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\nUBRFUWJRZaEoiqLEospCURRFieX/AY5SUy5TwxCZAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1089 city tour with length 46981.5 in 1.052 secs for greedy_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(greedy_tsp, USA_big_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The greedy algorithm is worse than nearest neighbors, but it is fast (especially on the big map). Let's see if the *alteration* strategy can help:" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def altered_greedy_tsp(cities):\n", + " \"Run greedy TSP algorithm, and alter the results by reversing segments.\"\n", + " return alter_tour(greedy_tsp(cities))" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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32GhzGHOO6sxZUctlREOa7Py4RcQtBTYhcGVRPGZZERoB2wJ278aQondwVz0Y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\nQqS8wtW1GjAFBq2E8p+ilsk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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 14133.3 in 0.022 secs for altered_greedy_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_greedy_tsp, USA_map)" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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PNDXAwxW2+vW+zGR4F/A0MBr4g6XuyTBruT8vvPDsqycDr7tDsFf+3N5X69+E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\naM2HSv2xEErfcC9od+8IF3jWQu8s2VqAWehqgLvXw333A68H9xEWiR1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1089 city tour with length 43769.9 in 4.177 secs for altered_greedy_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_greedy_tsp, USA_big_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's the best result yet on the big map. Let's look at some benchmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " altered_nn_tsp | 4820 ± 233 ( 4450 to 5346) | 0.008 secs/map | 30 ⨉ 60-city maps\n", + " altered_greedy_tsp | 4766 ± 207 ( 4320 to 5185) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " repeated_altered_nn_tsp | 4640 ± 194 ( 4298 to 4991) | 0.148 secs/map | 30 ⨉ 60-city maps\n", + "----------------------------------------------------------------------------------------------------\n", + " altered_nn_tsp | 6589 ± 202 ( 6188 to 7016) | 0.036 secs/map | 30 ⨉ 120-city maps\n", + " altered_greedy_tsp | 6539 ± 240 ( 5994 to 7203) | 0.037 secs/map | 30 ⨉ 120-city maps\n", + " repeated_altered_nn_tsp | 6402 ± 185 ( 6015 to 6779) | 0.701 secs/map | 30 ⨉ 120-city maps\n" + ] + } + ], + "source": [ + "algorithms = [altered_nn_tsp, altered_greedy_tsp, repeated_altered_nn_tsp]\n", + "\n", + "benchmarks(algorithms)\n", + "print('-' * 100)\n", + "benchmarks(algorithms, Maps(30, 120))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So overall, the altered greedy algorithm looks slightly better than the altered nearest neighbor algorithm and runs in about the same time. However, the repeated altered nearest neighbor algorithm does best of all (although it takes much longer).\n", + "\n", + "What about a repeated altered greedy algorithm? That might be a good idea, but there is no obvious way to do it. We can't just start from a sample of cities, because the greedy algorithm doesn't have a notion of starting city.\n", + "\n", + "Visualizing the Greedy Algorithm\n", + "---\n", + "\n", + "I would like to see how the process of joining segments unfolds. Although I dislike copy-and-paste (because it violates the *[Don't Repeat Yourself](http://en.wikipedia.org/wiki/Don%27t_repeat_yourself)* principle), I'll copy `greedy_tsp` and make a new version called `visualize_greedy_tsp` which adds one line to plot the segments several times as the algorithm is running:" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def visualize_greedy_tsp(cities, plot_sizes):\n", + " \"\"\"Go through edges, shortest first. Use edge to join segments if possible.\n", + " Plot segments at specified sizes.\"\"\"\n", + " edges = shortest_edges_first(cities) # A list of (A, B) pairs\n", + " endpoints = {c: [c] for c in cities} # A dict of {endpoint: segment}\n", + " for (A, B) in edges:\n", + " if A in endpoints and B in endpoints and endpoints[A] != endpoints[B]:\n", + " new_segment = join_endpoints(endpoints, A, B)\n", + " plot_segments(endpoints, plot_sizes, distance(A, B)) # <<<< NEW\n", + " if len(new_segment) == len(cities):\n", + " return new_segment\n", + " \n", + "def plot_segments(endpoints, plot_sizes, dist):\n", + " \"If the number of distinct segments is one of plot_sizes, then plot segments.\"\n", + " segments = set(map(tuple, endpoints.values()))\n", + " if len(segments) in plot_sizes:\n", + " for s in segments:\n", + " plot_lines(s)\n", + " plt.show()\n", + " print('{} segments, longest edge = {:.0f}'.format(\n", + " len(segments), dist))" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5 segments, longest edge = 335\n" + ] + }, + { + "data": { + "image/png": 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+yiJ2ZRHwOHCwp76XIkJX3MTgPN+yGMXJXG4oWFqPejLQX5U3fMtTkyAS5QVg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\n4lsWwx+mLIxMIcK/gOmqXFX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4ALgDaK/Kkao82EihgOTPLGIXi4CHgMM8jb0GEXriHgzO9W2LUZzM1YaCNf2o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\nI13ICUc/XIntCmAErnf09Hz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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 segments, longest edge = 1021\n" + ] + } + ], + "source": [ + "visualize_greedy_tsp(USA_map, (50, 25, 10, 5, 2, 1));" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Divide and Conquer Strategy\n", + "\n", + "The next general strategy to consider is *divide and conquer*. Suppose we have an algorithm, like `alltours_tsp`, that is inefficient for large *n* (the `alltours_tsp` algorithm is O(*n!*) for *n* cities). So we can't apply `alltours_tsp` directly to a large set of cities. But we can divide the problem into smaller pieces, and then combine those pieces:\n", + "\n", + "1. Split the set of cities in half.\n", + "2. Find a tour for each half.\n", + "3. Join those two tours into one.\n", + "\n", + "The trick is that when *n* is small, then step 2 can be done directly. But when *n* is large, step 2 is done with a recursive call, breaking the half into two smaller halves.\n", + "\n", + "Let's work out by hand an example with a small map of just six cities. Here are the cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ4AAAEACAYAAABCu5jVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cities = Cities(6)\n", + "\n", + "plot_labeled_lines(cities)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Step 1 is to divide this set in half. I'll divide it into a left half (blue circles) and a right half (black squares):" + ] + }, + { + "cell_type": "code", + "execution_count": 91, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(list(cities), 'bo', [3, 4, 0], 'ks', [1, 2, 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Step 2 is to find a tour for each half:" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(list(cities), 'bo-', [0, 3, 4, 0], 'ks-', [1, 2, 5, 1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Step 3 is to combine the two halves. We do that by choosing an edge from each half to delete (the edges marked by red dashes) and replacing those two edges by two edges that connect the halves (the blue dash-dot edges). Note that there are two choices of ways to connect the new dash-dot lines. Pick the one that yields the shortest tour." + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# One way to connect the two segments, giving the tour [1, 3, 4, 0, 2, 5]\n", + "plot_labeled_lines(list(cities), 'bo-', [0, 3, 4], 'ks-', [1, 2, 5],\n", + " 'b-.', [0, 1], [4, 5],\n", + " 'r--', [0, 4], [1, 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we have a feel for what we have to do. Let's define the divide and conquer algorithm, which we will call `dq_tsp`. Like all `tsp` algorithms it gets a set of cities as input and returns a tour. If the size of the set of cities is 3 or less, then just listing the cities in any order produces an optimal tour. If there are more than 3 cities, then split the cities in half (using `split_cities`), find a tour for each half (using `dq_tsp` recursively), and join the two tours together (using `join_tours`): " + ] + }, + { + "cell_type": "code", + "execution_count": 94, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def dq_tsp(cities):\n", + " \"\"\"Find a tour by divide and conquer: if number of cities is 3 or less,\n", + " any tour is optimal. Otherwise, split the cities in half, solve each\n", + " half recursively, then join those two tours together.\"\"\"\n", + " if len(cities) <= 3:\n", + " return Tour(cities)\n", + " else:\n", + " Cs1, Cs2 = split_cities(cities)\n", + " return join_tours(dq_tsp(Cs1), dq_tsp(Cs2))\n", + " \n", + "# TO DO: functions: split_cities, join_tours" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's verify that `dq_tsp` works for three cities:" + ] + }, + { + "cell_type": "code", + "execution_count": 95, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3 city tour with length 1203.4 in 0.000 secs for dq_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(dq_tsp, Cities(3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we have more than 3 cities, how do we split them? My approach is to imagine drawing an axis-aligned rectangle that is just big enough to contain all the cities. If the rectangle is wider than it is tall, then order all the cities by *x* coordinate and split that ordered list in half. If the rectangle is taller than it is wide, order and split the cities by *y* coordinate. " + ] + }, + { + "cell_type": "code", + "execution_count": 96, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def split_cities(cities):\n", + " \"Split cities vertically if map is wider; horizontally if map is taller.\"\n", + " width, height = extent([c.x for c in cities]), extent([c.y for c in cities])\n", + " key = 'x' if (width > height) else 'y'\n", + " cities = sorted(cities, key=lambda c: getattr(c, key))\n", + " mid = len(cities) // 2\n", + " return frozenset(cities[:mid]), frozenset(cities[mid:])\n", + "\n", + "def extent(numbers): return max(numbers) - min(numbers)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's show that split_cities is working:" + ] + }, + { + "cell_type": "code", + "execution_count": 97, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Cs1, Cs2 = split_cities(cities)\n", + "plot_tour(dq_tsp(Cs1))\n", + "plot_tour(dq_tsp(Cs2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now for the tricky part: joining two tours together. First we consider all ways of deleting one edge from each of the two tours. If we delete a edge from a tour we get a segment. We are representing segments as lists of cities, the same surface representation as tours. But there is a difference in their interpretation. The tour `[0, 2, 5]` is a triangle of three edges, but the segment `[0, 2, 5]` consists of only two edges, from `0` to `2` and from `2` to `5`. The segments that result from deleting an edge from the tour `[0, 2, 5]` are:\n", + "\n", + "
\n",
+    "[0, 2, 5],    [2, 5, 0],    [5, 0, 2]\n",
+    "
\n", + "\n", + "You may recognize these as the *rotations* of the segment `[0, 2, 5]`. So any candidate combined tour consists of taking a rotation of the first tour, and appending to it a rotation of the second tour, with one caveat: when we go to append the two segments, there are two ways of doing it: either keep the second segment as is, or reverse the second segment.\n", + "\n", + "**Note:** In Python, `sequence[::-1]` means to reverse the sequence." + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def join_tours(tour1, tour2):\n", + " \"Consider all ways of joining the two tours together, and pick the shortest.\"\n", + " segments1, segments2 = rotations(tour1), rotations(tour2)\n", + " tours = [s1 + s2\n", + " for s1 in segments1\n", + " for s in segments2\n", + " for s2 in (s, s[::-1])]\n", + " return shortest_tour(tours)\n", + "\n", + "def rotations(sequence):\n", + " \"All possible rotations of a sequence.\"\n", + " # A rotation is some suffix of the sequence followed by the rest of the sequence.\n", + " return [sequence[i:] + sequence[:i] for i in range(len(sequence))]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see if it works, first on the 6 city example:" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "6 city tour with length 1431.7 in 0.000 secs for dq_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(dq_tsp, Cities(6))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That is indeed the optimal tour, achieved by deleting the two dashed red lines and adding the dotted blue lines.\n", + "\n", + "Now for the USA map:" + ] + }, + { + "cell_type": "code", + "execution_count": 100, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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fCZbpRYSdgI5ALz/mD35v6vw98Bl1JwJ5FvlPRFMXr38WsBXwsFfIrU6IFJeK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\nBDopa1IAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 14883.2 in 0.142 secs for dq_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(dq_tsp, USA_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not quite as good as `altered_greedy_tsp`. Let's alter it!" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def altered_dq_tsp(cities): return alter_tour(dq_tsp(cities))" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 14209.6 in 0.109 secs for altered_dq_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_dq_tsp, USA_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's just remind ourselves how the algorithms behave on the standard test cases:" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " nn_tsp | 5668 ± 488 ( 4674 to 6832) | 0.001 secs/map | 30 ⨉ 60-city maps\n", + " greedy_tsp | 5392 ± 306 ( 4554 to 5967) | 0.002 secs/map | 30 ⨉ 60-city maps\n", + " dq_tsp | 5268 ± 236 ( 4743 to 5752) | 0.042 secs/map | 30 ⨉ 60-city maps\n", + " altered_dq_tsp | 4953 ± 221 ( 4575 to 5399) | 0.049 secs/map | 30 ⨉ 60-city maps\n", + " altered_nn_tsp | 4820 ± 233 ( 4450 to 5346) | 0.008 secs/map | 30 ⨉ 60-city maps\n", + " altered_greedy_tsp | 4766 ± 207 ( 4320 to 5185) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " repeated_altered_nn_tsp | 4640 ± 194 ( 4298 to 4991) | 0.148 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "algorithms = [nn_tsp, greedy_tsp, dq_tsp, altered_dq_tsp, altered_nn_tsp, altered_greedy_tsp, \n", + " repeated_altered_nn_tsp]\n", + "\n", + "benchmarks(algorithms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of the non-altered algorithms (the first three lines), divide and conquer (`dq_tsp`) does best. But interestingly, divide and conquer is helped less by `alter_tour` than is the greedy algorithm or nearest neighbor algorithm. Perhaps it is because divide and conquer constructs its tour by putting together pieces that are already good, so `alter_tour` is less able to improve it. ALso, `dq_tsp` has a standard deviation that is much smaller than the other two—this suggests that `dq_tsp` is not producing really bad tours that can be easily improved by `alter_tour`. In any event, `altered_dq_tsp` is the worst of the `altered` algorithms, both in average tour length and in run time. \n", + "\n", + "`repeated_altered_nn_tsp` remains the best in tour length, although the worst in run time." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Shoulders of Giants: Minimum Spanning Tree Algorithm: `mst_tsp`\n", + "\n", + "\n", + "\n", + "\n", + "
Joseph Kruskal (Wikipedia)
\n", + "\n", + "\n", + "I hope you now believe that you could have come up with some ideas for solving the TSP. But even if you can't come up with something all on your own, you can always [Google it](http://bit.ly/XNGt2y), in which case you'll no doubt find a giant of a mathematician, [Joseph Kruskal](http://en.wikipedia.org/wiki/Joseph_Kruskal), who, in 1956, \n", + "published [a paper](http://www.cmat.edu.uy/~marclan/TAG/Sellanes/Kruskal.pdf) that led to an algorithm that\n", + "most people would not have thought of on their own\n", + " (I know I wouldn't have):\n", + "> **Minimum Spanning Tree Traversal Algorithm:** *Construct a Minimum Spanning Tree, then do a pre-order traversal. That will give you a tour that is guaranteed to be no more than twice as long as the minimal tour.* \n", + "\n", + "What does all this jargon mean? It is part of *graph theory*, the study of vertexes and edges. Here is a glossary of terms:\n", + "\n", + "* A **graph** is a collection of vertexes and edges.\n", + "* A **vertex** is a point (such as a city).\n", + "* An **edge** is a link between two vertexes. Edges have lengths.\n", + "\n", + "* A **directed graph** is a graph where the edges have a direction. We say that the edge goes from the **parent** vertex to the **child** vertex.\n", + "\n", + "* A **tree** is a directed graph in which there is one distinguished vertex called the **root** that has no parent; every other vertex has exactly one parent. \n", + "\n", + "* A **spanning tree** (of a set of vertexes) is a tree that contains all the vertexes. \n", + "\n", + "* A **minimum spanning tree** is a spanning tree with the smallest possible sum of edge lengths.\n", + "\n", + "* A **traversal** of a tree is a way of visiting all the vertexes in some order.\n", + "\n", + "* A **pre-order traversal** means that you visit the root first, then do a pre-order traversal of each of the children.\n", + "\n", + "* A **guarantee** means that, no matter what set of cities is selected, the tour found by the minimum spanning tree traversal algorithm will never be more than twice as long as the shortest possible tour. None of the other algorithms has any guarantee at all (except for `alltours_tsp`, which is guaranteed to find the optimal algorithm, if it has enough time to complete).\n", + "\n", + "We will implement a vertex as a Point, and a directed graph as a dict of `{parent: [child, ...]}` pairs. \n", + "\n", + "Visualizing Graphs and Trees\n", + "---\n", + "\n", + "I think we will need visualization right away, so before doing anything else I will define `plot_graph`. I will make it plot in red so that we can easily tell a tour (blue) from a graph (red)." + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def plot_graph(graph):\n", + " \"Given a graph of the form {parent: [child...]}, plot the vertexes and edges.\"\n", + " vertexes = {v for parent in graph for v in graph[parent]} | set(graph)\n", + " edges = {(parent, child) for parent in graph for child in graph[parent]}\n", + " for edge in edges:\n", + " plot_lines(edge, 'ro-')\n", + " total_length = sum(distance(p, c) for (p, c) in edges)\n", + " print('{} node Graph of total length: {:.1f}'.format(len(vertexes), total_length))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's try it out:" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 node Graph of total length: 10.9\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Ps = [Point(0, 0.1), \n", + " Point(-2, -1), Point(0, -1), Point(2, -1), \n", + " Point(-2.9, -1.9), Point(-1, -1.9), Point(1, -1.9), Point(2.9, -1.9)]\n", + "\n", + "Ptree = {Ps[0]: Ps[1:4], Ps[1]: Ps[4:6], Ps[3]: Ps[6:8]}\n", + "\n", + "plot_graph(Ptree)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now our plan is:\n", + "\n", + "1. Implement an algorithm to create a minimum spanning tree.\n", + "2. Implement a tree traversal; that will give us our `mst_tsp` algorithm.\n", + "3. Understand the guarantee, \n", + "\n", + "Creating a Minimum Spanning Tree (`mst`)\n", + "---\n", + "\n", + "Now let's see how to create a minimum spanning tree (or MST). Kruskal has a very nice algorithm to find MSTs, but with what we have done so far, it will be a bit easier to implement another Giant's algorithm:\n", + "\n", + "> **[Prim's algorithm for creating a MST](http://en.wikipedia.org/wiki/Prim%27s_algorithm):** *List all the edges and sort them, shortest first. Initialize a tree to be a single root city (we'll arbitrarily shoose the first city). Now repeat the following until the tree contains all the cities: find the shortest edge that links a city (A) that is in the tree to a city (B) that is not yet in the tree, and add B to the list of A's children in the tree.*\n", + "\n", + "Here's the code. One tricky bit: In the first line inside the `while` loop, we define `(A, B)` to be an edge in which one of `A` or `B` is in the tree, using the exclusive-or operator, `^`. Then in the next line, we make sure that `A` is the one that is in the tree and B is not, by swapping if necessary." + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def mst(vertexes):\n", + " \"\"\"Given a set of vertexes, build a minimum spanning tree: a dict of the form {parent: [child...]}, \n", + " where parent and children are vertexes, and the root of the tree is first(vertexes).\"\"\"\n", + " tree = {first(vertexes): []} # the first city is the root of the tree.\n", + " edges = shortest_edges_first(vertexes)\n", + " while len(tree) < len(vertexes):\n", + " (A, B) = shortest_usable_edge(edges, tree)\n", + " tree[A].append(B)\n", + " tree[B] = []\n", + " return tree\n", + "\n", + "def shortest_usable_edge(edges, tree):\n", + " \"Find the ehortest edge (A, B) where A is in tree and B is not.\"\n", + " (A, B) = first((A, B) for (A, B) in edges if (A in tree) ^ (B in tree)) # ^ is \"xor\" \n", + " return (A, B) if (A in tree) else (B, A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's see what a minimum spanning tree looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 node Graph of total length: 11518.4\n" + ] + }, + { + "data": { + "image/png": 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NVaX9Dtx6COwW9vMjUL4fbbw+aha7wesKO/l+fzy/B9sn62GFrjBfaM+bkMRc9FpUMFpd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\ngcXA4m2ydCFtBKB6QT7HTW1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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_graph(mst(USA_map))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This algorithm clearly produced a spanning tree. It looks pretty good, but how can we be sure the algorithm will *always* produce a minimum spanning tree? \n", + "\n", + "1. The output is a **tree** because (1) every city is connected by a path from the root, and (2) every city only gets one parent (we only add a B that is not in tree), so there can be no loops. \n", + "2. The output is a **spanning tree** because it contains all the cities.\n", + "3. The output is a **minimum spanning tree** because each city was added with the shortest possible edge. Suppose this algorithm produces the tree T. For another putative spanning tree to be shorter, it would have to contain at least one city C whose edge from its parent was shorter than the edge in T. But that is not possible, because the algorithm always chooses the shortest possible edge from C's parent to C.\n", + "\n", + "\n", + "\n", + "**Note:** There are refinements to Prim's algorithm to make it more efficient. I won't bother with them because they complicate the code, and because `mst` is already fast enough for our purposes.\n", + "\n", + "Turning a Minimum Spanning Tree into a Tour (`mst_tsp`)\n", + "---\n", + "\n", + "Given a minimum spanning tree, we can generate a tour by doing a pre-order traversal, which means the tour starts at the root, then visits all the cities in the pre-order traversal of the first child of the root, followed by the pre-order traversals of any other children." + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def mst_tsp(cities):\n", + " \"Create a minimum spanning tree and walk it in pre-order, omitting duplicates.\"\n", + " return preorder_traversal(mst(cities), first(cities))\n", + "\n", + "def preorder_traversal(tree, root):\n", + " \"Traverse tree in pre-order, starting at root of tree.\"\n", + " result = [root]\n", + " for child in tree.get(root, ()):\n", + " result.extend(preorder_traversal(tree, child))\n", + " return result" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To better understand pre-order traversal, let's go back to the `Ptree` example, and this time label the vertexes:" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "8 node Graph of total length: 10.9\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "P = [Point(0, 0.1), \n", + " Point(-2, -1), Point(0, -1), Point(2, -1), \n", + " Point(-2.9, -1.9), Point(-1, -1.9), Point(1, -1.9), Point(2.9, -1.9)]\n", + "\n", + "Ptree = {P[0]: P[1:4], P[1]: P[4:6], P[3]: P[6:8]}\n", + "\n", + "plot_graph(Ptree)\n", + "plot_labeled_lines(P)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A pre-order traversal starting at 0 would go to the first child, 1, then to its children, 4 and 5, then since there are no children of 4 and 5, it would continue with the other children of 0, hitting 2, then 3, and finally the children of 3, namely 6 and 7. So the following should be true:" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 110, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "preorder_traversal(Ptree, P[0]) == [P[0], P[1], P[4], P[5], P[2], P[3], P[6], P[7]]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And this is what the pre-order traversal looks like as a tour:" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_tour([P[0], P[1], P[4], P[5], P[2], P[3], P[6], P[7]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can think of this as starting at the root (at the top) and going around the outside of the tree counterclockwise, as if you were walking with your left hand always touching an edge, but skipping cities you have already been to.\n", + "\n", + "We see that the result is a tour, but not an optimal one. \n", + "\n", + "Let's see what `mst_tsp` can do on the USA map:" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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DOsaMYuBroMwbz3h/56myXmT6cGdCq/49yqv3ss6SxMrVc3a/BDyoujFwoAqV33+/v7uf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\nMAzDSMr/BwzNZAmFc5HQAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 17924.5 in 0.004 secs for mst_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(mst_tsp, USA_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not so great. Can the alteration strategy help?" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def altered_mst_tsp(cities): return alter_tour(mst_tsp(cities))" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 city tour with length 14105.0 in 0.022 secs for altered_mst_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(altered_mst_tsp, USA_map)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Better. Let's go to the benchmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 115, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " mst_tsp | 5953 ± 361 ( 5334 to 7030) | 0.002 secs/map | 30 ⨉ 60-city maps\n", + " nn_tsp | 5668 ± 488 ( 4674 to 6832) | 0.001 secs/map | 30 ⨉ 60-city maps\n", + " greedy_tsp | 5392 ± 306 ( 4554 to 5967) | 0.002 secs/map | 30 ⨉ 60-city maps\n", + " dq_tsp | 5268 ± 236 ( 4743 to 5752) | 0.042 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "benchmarks([mst_tsp, nn_tsp, greedy_tsp, dq_tsp])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not very encouraging: `mst_tsp` is the second slowest and has the longest tours. I'm sure I could make it faster (at the cost of making the code a bit more complicated), but there is no point if the tours are going to be longer. \n", + "\n", + "What happens when we add the alteration strategy?" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " altered_dq_tsp | 4953 ± 221 ( 4575 to 5399) | 0.049 secs/map | 30 ⨉ 60-city maps\n", + " altered_nn_tsp | 4820 ± 233 ( 4450 to 5346) | 0.008 secs/map | 30 ⨉ 60-city maps\n", + " altered_mst_tsp | 4823 ± 227 ( 4354 to 5250) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " altered_greedy_tsp | 4766 ± 207 ( 4320 to 5185) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " repeated_altered_nn_tsp | 4640 ± 194 ( 4298 to 4991) | 0.148 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "benchmarks([altered_dq_tsp, altered_nn_tsp, altered_mst_tsp, altered_greedy_tsp, repeated_altered_nn_tsp])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now `altered_mst_tsp` is in the middle of the pack, both in tour length and in run time.\n", + "\n", + "So why would we want to use the rather complicated minimum spanning tree algorithm, when the greedy algorithm is simpler to implement, runs faster, and produces shorter tours?\n", + "\n", + "Guaranteed Tour Length!\n", + "---\n", + "\n", + "The great thing about the minimum spanning tree algorithm is that it comes with a *guarantee*, which none of the other algorithms offer. You are guaranteed that the tour length it comes up with will be no worse than twice as long as the optimal tour. (And, with a bit more complication, you can modify it to give a guarantee of 1.5 times longer.) The guarantee works like this:\n", + "\n", + "1. The minimum spanning tree, by definition, connects all the cities with the shortest possible total edge length.\n", + "2. So if you could follow each edge in the spanning tree just once, and that formed a legal tour, then that would be guaranteed to be\n", + "a minimal tour. \n", + "3. But you can't do that in general; in general there will be places where you skip to the next city without following the spanning tree. Any such skip, however, is a straight line, and thus will be less than you would take if you went to the next city by following along the spanning tree.\n", + "4. If you did follow along the spanning tree, you would follow some edges twice, and some edges once. Hence the total length of the tour would be at most twice the spanning tree, and thus at most twice the minimal tour.\n", + "\n", + "A guarantee is great from a theoretical point of view, but in practice the greedy or nearest neighbor algorithms do just better than the minimum spanning tree, on the maps that we actually see. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Shoulders of Giants: Held-Karp Algorithm: `hk_tsp`\n", + "\n", + "\n", + "\n", + "
Held, Shareshian, Karp (Computer History Museum)
\n", + "\n", + "\n", + "\n", + "
xkcd 399
\n", + "\n", + "Another algorithm that shows up with a literature search is the [Held-Karp Dynamic Programming Algorithm](http://en.wikipedia.org/wiki/Held%E2%80%93Karp_algorithm), named after giants [Michael Held](http://www.computerhistory.org/collections/catalog/102650390) and [Richard Karp](http://en.wikipedia.org/wiki/Richard_M._Karp). It is an algorithm for finding optimal tours, not approximate ones, so it is not appropriate for large *n*. But even in its simplest form, without any programming tricks, it can go quite a bit further than `alltours_tsp`. That is because `alltours_tsp` is O(*n*!), while the Held-Karp algorithm is only O(*n*2 2*n*). How did Held and Karp achieve this speedup? They noticed that `alltours_tsp` wastes a lot of time with permutations that can't possibly be optimal tours. Consider the following 10-city problem, with a 6-city segment shown:" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(cross, 'r-', [0, 4, 1, 3, 2, 9])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `alltours_tsp` would consider 4! = 24 different tours that start with those 6 cities. But that seems wasteful: there is no way that this segment could be part of an optimal tour, so why waste time on *any* continuation of it? The proof that this segment can never be part of an optimal tour comes down to two things. First, we demonstrate another tour that also starts in city 0 and ends in city 9, and along the way goes through cities 1 through 4, and is shorter:" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_labeled_lines(cross, [0, 1, 2, 3, 4, 9])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Second, we need this key property:\n", + "\n", + ">*Given a start city A, an end city C, and a set of middle cities Bs, then out of all the possible segments that start in A, end in C, and go through all and only the cities in Bs, only the shortest of those segments could ever be part of an optimal tour. \n", + "\n", + "Of course, we don't know that the optimal tour goes through exactly those Bs cities before hitting C. But if it does, then we need only consider the permutation of Bs that leads to the shortest segment. So we can throw out the red zig-zag segment above, and keep the nice smooth blue segment.\n", + "\n", + "So far we have only been talking about segments. We know that the TSP is defined for tours, not segments. So even if we find the shortest possible segment, it might not be the shortest possible tour. But here's something we do know: a tour has to end somewhere. So just find the shortest segment from the start city, `A`, to every possible end city, `C`. That will give you *n*-2 segments. Out of those, don't choose the shortest *segment*, but rather choose the shortest *tour*.\n", + "\n", + "That gives us our algorithm:" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def hk_tsp(cities):\n", + " \"\"\"The H eld-Karpshortest tour of this set of cities.\n", + " For each end city C, find the shortest segment from A (the start) to C.\n", + " Out of all these shortest segments, pick the one that is the shortest tour.\"\"\"\n", + " A = first(cities)\n", + " return shortest_tour(shortest_segment(A, cities - {A, C}, C)\n", + " for C in cities if C is not A)\n", + "\n", + "# TO DO: function: shortest_segment(A, Bs, C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now for `shortest_segment(A, Bs, C)`. It is defined to produce the shortest segment that starts in city `A`, ends in `C`, and visits some permutation of `Bs` cities in the middle. If there are no `Bs` cities, then of course the shortest segment is to go directly from `A` to `C`. If there are `Bs` cities, then one of them has to be the last `B` city visited (just before visiting `C`). So for each `B`, find the shortest segment that first goes from `A`, through all the other `Bs` cities, then to `B`, and finally to `C`. Out of all these candidate segments, return the one with the minimum segment length.\n", + "\n", + "**Note:** the decorator `@functools.lru_cache` makes this a **dynamic programming** algorithm, which is a fancy name meaning that we cache the results of sub-computations because we will re-use them multiple times." + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@functools.lru_cache(None)\n", + "def shortest_segment(A, Bs, C):\n", + " \"The shortest segment starting at A, going through all Bs, and ending at C.\"\n", + " if not Bs:\n", + " return [A, C]\n", + " else:\n", + " segments = [shortest_segment(A, Bs - {B}, B) + [C] \n", + " for B in Bs]\n", + " return min(segments, key=segment_length)\n", + " \n", + "def segment_length(segment):\n", + " \"The total of distances between each pair of consecutive cities in the segment.\"\n", + " # Same as tour_length, but without distance(tour[0], tour[-1])\n", + " return sum(distance(segment[i], segment[i-1]) \n", + " for i in range(1, len(segment)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's all there is to it. Let's compare `alltours_tsp` with `hk_tsp` on 10 city tours:" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2291.8 in 1.650 secs for alltours_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(alltours_tsp, Cities(10))" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 city tour with length 2291.8 in 0.037 secs for hk_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(hk_tsp, Cities(10))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that `hk_tsp` returns the optimal tour, and it is a lot faster. We can take `hk_tsp` into uncharted territory well beyond the reach of `alltours_tsp`:" + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "14 city tour with length 2886.6 in 1.464 secs for hk_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(hk_tsp, Cities(14))" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "16 city tour with length 2868.6 in 9.018 secs for hk_tsp\n" + ] + } + ], + "source": [ + "plot_tsp(hk_tsp, Cities(16))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not bad! In 11 seconds, we did what `alltours_tsp` would have taken an estimated 200 days to complete! Let's repeat the table of expected times, comparing the All Tours algorithm with the Held-Karp algorithm:\n", + "\n", + "\n", + "
n `alltours_tsp(Cities(n))``hk_tsp(Cities(n))`\n", + "
expected time ≈ O(n!)expected time ≈ O(n2 2n)\n", + "
10 10! tours = 2 secs 0.1 secs \n", + "
112 secs × 11! / 10! ≈ 22 secs 0.2 secs\n", + "
122 secs × 12! / 10! ≈ 4 mins 0.4 secs\n", + "
142 secs × 14! / 10! ≈ 13 hours 3 secs\n", + "
162 secs × 16! / 10! ≈ 200 days 162 216 tours = 11 secs\n", + "
182 secs × 18! / 10! ≈ 112 years\n", + "11 secs × (18/16)2 2(18-16) ≈ 1 min\n", + "
252 secs × 25! / 10! ≈ 270 billion years\n", + " 11 secs × (25/16)2 2(25-16) ≈ 4 hours\n", + "
502 secs × 50! / 10! ≈ 5 × 1050 years11 secs × (50/16)2 2(50-16) ≈ 58,000 years\n", + "
\n", + "\n", + "So if we had some patience, we could find the optimal tour for a 25 city map, but we still can't handle the 50-city landmarks map.\n", + "(There are refinements to Held-Karp that can handle 50-city maps, and could do it even with 1960s-era computing power.)\n", + "\n", + "We're starting to run out of tricks, but we have one more general strategy to consider." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ensembles of Other Algorithms: `ensemble_tsp`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When we have several optimization algorithms and we're not sure which is best, we can always try them all and take the best result. We will define `ensemble_tsp`, to combine the algorithms we have previously developed. First, if the set of input cities is small enough, it solves the problem optimally with `hk_tsp`. If the set is too large, it tries a selection of algorithms, and chooses the best resulting tour. The result is guaranteed to be as good or better than any of the component algorithms; but the run time is guaranteed to be longer than any of the component algorithms." + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ensemble = [altered_dq_tsp, altered_greedy_tsp, altered_mst_tsp, repeated_altered_nn_tsp]\n", + "\n", + "def ensemble_tsp(cities, threshold=16, algorithms=ensemble): \n", + " \"Apply all algorithms to cities and take the shortest resulting tour.\"\n", + " if len(cities) <= threshold:\n", + " return hk_tsp(cities)\n", + " else:\n", + " return shortest_tour(tsp(cities) for tsp in algorithms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's go to the benchmarks:" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " altered_dq_tsp | 4953 ± 221 ( 4575 to 5399) | 0.049 secs/map | 30 ⨉ 60-city maps\n", + " altered_greedy_tsp | 4766 ± 207 ( 4320 to 5185) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " altered_mst_tsp | 4823 ± 227 ( 4354 to 5250) | 0.009 secs/map | 30 ⨉ 60-city maps\n", + " repeated_altered_nn_tsp | 4640 ± 194 ( 4298 to 4991) | 0.148 secs/map | 30 ⨉ 60-city maps\n", + " ensemble_tsp | 4630 ± 187 ( 4298 to 4991) | 0.213 secs/map | 30 ⨉ 60-city maps\n" + ] + } + ], + "source": [ + "benchmarks(ensemble + [ensemble_tsp])" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " altered_dq_tsp | 6771 ± 220 ( 6273 to 7248) | 0.347 secs/map | 30 ⨉ 120-city maps\n", + " altered_greedy_tsp | 6539 ± 240 ( 5994 to 7203) | 0.037 secs/map | 30 ⨉ 120-city maps\n", + " altered_mst_tsp | 6616 ± 213 ( 6268 to 7010) | 0.050 secs/map | 30 ⨉ 120-city maps\n", + " repeated_altered_nn_tsp | 6402 ± 185 ( 6015 to 6779) | 0.701 secs/map | 30 ⨉ 120-city maps\n", + " ensemble_tsp | 6390 ± 184 ( 6015 to 6779) | 1.100 secs/map | 30 ⨉ 120-city maps\n" + ] + } + ], + "source": [ + "benchmarks(ensemble + [ensemble_tsp], Maps(30, 120))" + ] + }, + { + "cell_type": "code", + "execution_count": 128, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " altered_dq_tsp | 9750 ± 288 ( 9187 to 10167) | 3.052 secs/map | 10 ⨉ 250-city maps\n", + " altered_greedy_tsp | 9229 ± 261 ( 8723 to 9606) | 0.215 secs/map | 10 ⨉ 250-city maps\n", + " altered_mst_tsp | 9484 ± 142 ( 9190 to 9668) | 0.221 secs/map | 10 ⨉ 250-city maps\n", + " repeated_altered_nn_tsp | 9187 ± 194 ( 8785 to 9390) | 3.524 secs/map | 10 ⨉ 250-city maps\n", + " ensemble_tsp | 9153 ± 216 ( 8723 to 9390) | 6.959 secs/map | 10 ⨉ 250-city maps\n" + ] + } + ], + "source": [ + "benchmarks(ensemble + [ensemble_tsp], Maps(10, 250))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So the `ensemble_tsp` returns tours that are shortest, but the run time is slowest, as expected. It improves on `repeated_altered_nn_tsp` by less than 1%." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Further Explorations\n", + "\n", + "\n", + "That's all I'm going to write for now. But there are still plenty of open questions for you to explore:\n", + "\n", + "* **Branch and Cut**: this is a technique to cut off a search early, when a partial solution is obviously not optimal. We saw how Held-Karp cuts off some permutations of cities when another permutation is better. A refinement on that is to keep track of, say, the best total length of the segment going through all the Bs cities. Then, any time you have a partial segment through some of the Bs cities that exceeds the best total, we can stop right there, before even finishing all the Bs. With this technique, you can find optimal tours for around 50 cities.\n", + "* **Linear programming**: Lookup the topic \"linear programming\" and see how it applies to TSP.\n", + "* **Heuristic Algorithms**: There are many approaches for using heurisitic estimates to find good (but not optimal) tours. For example, *ant colony optimization algorithms* make random choices of which edge to follow, and then the edges that occur in the best tours get reinforced with some virtual pheromones, and other ants tend to follow those pheromones. *Simulated annealing* takes its inspiration from metallurgy.\n", + "* The **[Lin-Kernighan heuristic](http://akira.ruc.dk/~keld/research/LKH/LKH-1.3/DOC/LKH_REPORT.pdf)** is one of the best.\n", + "* The **[Christofides algorithm](https://en.wikipedia.org/wiki/Christofides_algorithm)** gives a guarantee of 3/2 the optimal tour length (improving on the minimum-spanning-tree guarantee).\n", + "* `altered` as a function: we defined a lot of one-line functions that just called another algorithm, and then calls `alter_tour` on the result. Can you write a function, `altered(func)`, which takes a TSP algorithm as argument, and returns a TSP algorithm that does the original algorithm and then calls `alter_tour`?\n", + "* Why does `mst` produce an optimal result, while `greedy_tsp` does not, even though the two algorithms have similar structure in the way they iterate over `shortest_edges_first`?\n", + "* The code in this notebook was designed for clarity, not efficiency. Can you make the code faster?\n", + "* [William Cook](http://www.math.uwaterloo.ca/tsp/) maintains a great page on the TSP.\n", + "* William Cook also has a [draft chapter](http://www.math.uwaterloo.ca/~bico/papers/comp_chapter1.pdf) on Discrete Optimization featuring TSP. Like my notebook here, Cook goes through a variety of algorithms for TSP, describing each one in prose and in concise, elegant code. The difference is that his code is in C and has an imperative style, while mine is in Python and is largely functional. His code is much more efficient, but if it is 100 times faster, that might only mean two more cities, so the algorithms are more important than the efficiency of the implemenation details. (Also, Cook chooses a different set of algorithms to explore.) I find his explanation very beautiful and concise, and I think it is very interesting that\n", + "there can be two quite different approaches, which (in my opinion) both turn out very well. \n", + "* If you are heavily into math, there's a [taxonomy](http://cstheory.stackexchange.com/questions/9241/approximation-algorithms-for-metric-tsp) of solutions.\n", + "* What else are you interested in?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/WWW.ipynb b/pytudes/ipynb/WWW.ipynb new file mode 100644 index 0000000..b222814 --- /dev/null +++ b/pytudes/ipynb/WWW.ipynb @@ -0,0 +1,871 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# WWW: Will the Warriors Win?\n", + "\n", + "## 18 April 2016\n", + "\n", + "The Golden State Warriors have had a historic basketball season, winning more games than any other team ever has. But will they top that off by winning the championship? There are 15 other teams in contention, including one, the Spurs, that has had a historic season as the best second-best team ever. The web site fivethirtyeight, using a complicated scoring system, [gives](http://projects.fivethirtyeight.com/2016-nba-picks/) the Warriors a 44% chance of winning, with the Spurs at 28%. Basketball-reference [has](http://www.basketball-reference.com/friv/playoff_prob.cgi) the Warriors at 41% and Spurs at 32.5%, while a [betting site](http://www.oddsshark.com/nba/nba-futures) had the Warriors at 54% and Spurs at 18%. But what's a good way to make a prediction? There are several choices:\n", + "\n", + "- Subjective impression of a team's strength? Or a statistical model?\n", + "- Predictions based on:\n", + " - Holistic impression of entire postseason (e.g. \"I think the Warriors have a 50% chance of winning it all\")\n", + " - Series by series (e.g. \"I think the Warriors have a 95% chance of beating the Rockets in the first round, then ...\")\n", + " - Game by game (e.g. \"I think the Warriors have a 83% chance of beating the Rockets in Game 1, then ...\")\n", + " - Possession by possession (e.g. simulate games basket by basket, based on past stats)\n", + " \n", + "Here are the top four teams with their Won-Loss percentage and [SRS](http://www.basketball-reference.com/blog/?p=39) (Simple rating system: average margin of victory, adjusted for strength of opponents):\n", + "\n", + " TEAM PCT SRS\n", + " Warriors .890 10.38\n", + " Spurs .817 10.28\n", + " Thunder .671 7.09\n", + " Cavaliers .695 5.45\n", + "\n", + "I decided to go with a subjective impression of one team beating another in a single game. For example, I might think that the Warriors have a 58% chance of beating the Cavaliers in any one game, and from that compute the odds of winning a series:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def win_series(p, W=0, L=0):\n", + " \"Probability of winning best-of-7 series, given a probability p of winning a game.\"\n", + " return (1 if W == 4 else\n", + " 0 if L == 4 else\n", + " p * win_series(p, W + 1, L) +\n", + " (1 - p) * win_series(p, W, L + 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6705883933696" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "win_series(0.58)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In other words, if you have a 58% chance of winning a game, you have a 67% chance of winning the series.\n", + "\n", + "Note that I ignore the fact that games aren't strictly independent; I ignore home court advantage; and I ignore the chance of catastrophic injuries. Why? Because all these factors would change the final winning estimate by only a few percentage points, and I already have more uncertainty than that.\n", + "\n", + "Note that `win_series` takes optional arguments to say how many games in the sries have been won and lost so far. Here's a table showing your chance of winning a series, given the current tally of games won and lost on the left, and your expected percentage of winning a game at the top:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def percents(items, fmt='{:4.0%}'): return ' '.join(fmt.format(item) for item in items)\n", + "\n", + "def series_table(pcts=[p/100 for p in range(20, 81, 5)]):\n", + " print('W-L | Singe Game Win Percentage')\n", + " print(' | ' + percents(pcts))\n", + " for W in range(4):\n", + " print('----+' + '-' * 5 * len(pcts))\n", + " for L in reversed(range(4)):\n", + " results = [win_series(p, W, L) for p in pcts]\n", + " print('{}-{} | {}'.format(W, L, percents(results)))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "W-L | Singe Game Win Percentage\n", + " | 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80%\n", + "----+-----------------------------------------------------------------\n", + "0-3 | 0% 0% 1% 2% 3% 4% 6% 9% 13% 18% 24% 32% 41%\n", + "0-2 | 1% 2% 3% 5% 9% 13% 19% 26% 34% 43% 53% 63% 74%\n", + "0-1 | 2% 4% 7% 12% 18% 26% 34% 44% 54% 65% 74% 83% 90%\n", + "0-0 | 3% 7% 13% 20% 29% 39% 50% 61% 71% 80% 87% 93% 97%\n", + "----+-----------------------------------------------------------------\n", + "1-3 | 1% 2% 3% 4% 6% 9% 12% 17% 22% 27% 34% 42% 51%\n", + "1-2 | 3% 5% 8% 13% 18% 24% 31% 39% 48% 56% 65% 74% 82%\n", + "1-1 | 6% 10% 16% 24% 32% 41% 50% 59% 68% 76% 84% 90% 94%\n", + "1-0 | 10% 17% 26% 35% 46% 56% 66% 74% 82% 88% 93% 96% 98%\n", + "----+-----------------------------------------------------------------\n", + "2-3 | 4% 6% 9% 12% 16% 20% 25% 30% 36% 42% 49% 56% 64%\n", + "2-2 | 10% 16% 22% 28% 35% 43% 50% 57% 65% 72% 78% 84% 90%\n", + "2-1 | 18% 26% 35% 44% 52% 61% 69% 76% 82% 87% 92% 95% 97%\n", + "2-0 | 26% 37% 47% 57% 66% 74% 81% 87% 91% 95% 97% 98% 99%\n", + "----+-----------------------------------------------------------------\n", + "3-3 | 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80%\n", + "3-2 | 36% 44% 51% 58% 64% 70% 75% 80% 84% 88% 91% 94% 96%\n", + "3-1 | 49% 58% 66% 73% 78% 83% 88% 91% 94% 96% 97% 98% 99%\n", + "3-0 | 59% 68% 76% 82% 87% 91% 94% 96% 97% 98% 99% 100% 100%\n" + ] + } + ], + "source": [ + "series_table()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And here's a function to tabulate the chances of winning each series on the way to a title:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def playoffs(name, rounds):\n", + " \"Print probability for team winning each series.\"\n", + " overall = (1, 1, 1) # (lo, med, hi) probabilities of winning it all\n", + " for (opponent, probs) in rounds:\n", + " this_round = [win_series(p) for p in probs]\n", + " overall = [overall[i] * this_round[i] for i in range(len(probs))]\n", + " print('{} vs {:8} win this round: {}; win through here: {}'.format(\n", + " name, opponent, percents(this_round), percents(overall)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I enter my subjective probability estimates (low, medium, and high), and likely opponents for each round, for the three top contenders:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: 93% 98% 99%; win through here: 93% 98% 99%\n", + "Warriors vs Clippers win this round: 83% 91% 97%; win through here: 77% 89% 95%\n", + "Warriors vs Spurs win this round: 39% 67% 87%; win through here: 30% 60% 83%\n", + "Warriors vs Cavs win this round: 71% 83% 93%; win through here: 22% 50% 78%\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.75, 0.83, 0.85)),\n", + " ('Clippers', (0.67, 0.73, 0.80)),\n", + " ('Spurs', (0.45, 0.58, 0.70)),\n", + " ('Cavs', (0.60, 0.67, 0.75))])" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spurs vs Memphis win this round: 93% 98% 99%; win through here: 93% 98% 99%\n", + "Spurs vs Thunder win this round: 39% 75% 87%; win through here: 36% 73% 86%\n", + "Spurs vs Warriors win this round: 13% 33% 61%; win through here: 5% 24% 53%\n", + "Spurs vs Cavs win this round: 71% 83% 93%; win through here: 3% 20% 49%\n" + ] + } + ], + "source": [ + "playoffs('Spurs',\n", + " [('Memphis', (0.75, 0.83, 0.85)),\n", + " ('Thunder', (0.45, 0.62, 0.70)),\n", + " ('Warriors', (0.30, 0.42, 0.55)),\n", + " ('Cavs', (0.60, 0.67, 0.75))])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: 93% 98% 99%; win through here: 93% 98% 99%\n", + "Cavs vs Hawks win this round: 39% 71% 93%; win through here: 36% 70% 92%\n", + "Cavs vs Raptors win this round: 29% 61% 80%; win through here: 11% 42% 73%\n", + "Cavs vs GSW/SAS win this round: 7% 17% 29%; win through here: 1% 7% 21%\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85)),\n", + " ('Hawks', (0.45, 0.60, 0.75)),\n", + " ('Raptors', (0.40, 0.55, 0.65)),\n", + " ('GSW/SAS', (0.25, 0.33, 0.40))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I have the Warriors at 50% (for the medium estimate of winning it all) and the Spurs at 20%, so I'm more of a Warriors fan than fivethirtyeight and basketball-reference, but I have very wide margins between my low and high estimate: 22% to 78% for the Warriors; 3% to 49% for the Spurs; 1% to 21% for the Cavs. Interestingly, while fivethirtyeight does not think this year's Warriors are better than the 1995 Bulls, they [do think](http://fivethirtyeight.com/features/the-warriors-still-arent-the-best-team-ever/) the Spurs, Thunder, and Cavs are the best ever second-, third-, and fourth-best teams in a season.\n", + "\n", + "\n", + "\n", + "What's better--a holistic guess at the outcome, or a reductionist model like this one? I can't say that one is better than the other in every case, but it can be instructive to examine the cases where the reductionist model differs from your holistic impressions. For example, look at the low end of my prediction for the Spurs. I feel like it is crazy to say the Spurs only have a 3% chance of winning the title, but I don't feel that any of the individual game win probabilities (75%, 45%, 30%, and 60%, respectively) are crazy. So now I know that at least one of my intutions is wrong. But I'm not sure how to reconcile the mismatch..." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# WWWWC: Will Warriors Win Without Curry?\n", + "\n", + "## 27 April 2016\n", + "\n", + "The Playoff picture has changed! \n", + "\n", + "We have some results for first-round series, and there have been key injuries to players including Steph Curry, Avery Bradley, Chris Paul, and Blake Griffin. To update, first I make a small alteration to allow the current state of a series in terms of wins/loses to be specified as part of the input to `playoffs`:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def playoffs(name, rounds):\n", + " \"Print probability for team winning each series.\"\n", + " overall = (1, 1, 1) # (lo, med, hi) probabilities of winning it all\n", + " for (opponent, probs, *args) in rounds:\n", + " this_round = [win_series(p, *args) for p in probs]\n", + " overall = [overall[i] * this_round[i] for i in range(len(probs))]\n", + " print('{} vs {:8} win this round: ({}) win through here: ({})'.format(\n", + " name, opponent, percents(this_round), percents(overall)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We don't know for sure how long Curry will be out, but here are my updated odds for the Warriors, with the middle probability value representing the assumption that Curry misses the second round, and comes back in time for the Western Conference Finals at a mildly reduced capacity; the low and high probability values represent more and less severe injuries:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: ( 88% 97% 99%) win through here: ( 88% 97% 99%)\n", + "Warriors vs Blazers win this round: ( 39% 61% 83%) win through here: ( 34% 59% 83%)\n", + "Warriors vs Spurs win this round: ( 13% 61% 83%) win through here: ( 4% 36% 69%)\n", + "Warriors vs Cavs win this round: ( 29% 71% 87%) win through here: ( 1% 26% 60%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 3, 1),\n", + " ('Blazers', (0.45, 0.55, 0.67)),\n", + " ('Spurs', (0.30, 0.55, 0.67)),\n", + " ('Cavs', (0.40, 0.60, 0.70))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Spurs and Cavs are rolling; let's update their odds:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spurs vs Memphis win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Spurs vs Thunder win this round: ( 39% 75% 87%) win through here: ( 39% 75% 87%)\n", + "Spurs vs Warriors win this round: ( 17% 39% 87%) win through here: ( 7% 29% 76%)\n", + "Spurs vs Cavs win this round: ( 71% 83% 93%) win through here: ( 5% 24% 71%)\n" + ] + } + ], + "source": [ + "playoffs('Spurs',\n", + " [('Memphis', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Thunder', (0.45, 0.62, 0.70)),\n", + " ('Warriors', (0.33, 0.45, 0.70)),\n", + " ('Cavs', (0.60, 0.67, 0.75))])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Hawks win this round: ( 39% 71% 93%) win through here: ( 39% 71% 93%)\n", + "Cavs vs Raptors win this round: ( 29% 61% 80%) win through here: ( 11% 43% 74%)\n", + "Cavs vs GSW/SAS win this round: ( 13% 29% 71%) win through here: ( 1% 13% 53%)\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Hawks', (0.45, 0.60, 0.75)),\n", + " ('Raptors', (0.40, 0.55, 0.65)),\n", + " ('GSW/SAS', (0.30, 0.40, 0.60))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So my updated odds are that the Warriors and Spurs are roughly equally likely to win (26% and 24%); the Cavs are still less likely (13%), and there is more uncertainty.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# WWWWCB: Will Warriors Win With Curry Back?\n", + "\n", + "## 10 May 2016\n", + "\n", + "Curry has returned from his injury, and after a slow shooting start, had the highest-scoring overtime period in the history of the NBA. Meanwhile, the Thunder lead the Spurs, 3-2, and the Cavaliers have been dominant in the East, hitting a historic number of 3-point shots. Here is my revised outlook: " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Blazers win this round: ( 91% 96% 98%) win through here: ( 91% 96% 98%)\n", + "Warriors vs Spurs win this round: ( 39% 71% 83%) win through here: ( 36% 68% 82%)\n", + "Warriors vs Cavs win this round: ( 29% 61% 83%) win through here: ( 10% 42% 68%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 4, 1),\n", + " ('Blazers', (0.55, 0.67, 0.75), 3, 1),\n", + " ('Spurs', (0.45, 0.60, 0.67)),\n", + " ('Cavs', (0.40, 0.55, 0.67))])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spurs vs Memphis win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Spurs vs Thunder win this round: ( 16% 36% 49%) win through here: ( 16% 36% 49%)\n", + "Spurs vs Warriors win this round: ( 17% 29% 61%) win through here: ( 3% 10% 30%)\n", + "Spurs vs Cavs win this round: ( 29% 50% 87%) win through here: ( 1% 5% 26%)\n" + ] + } + ], + "source": [ + "playoffs('Spurs',\n", + " [('Memphis', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Thunder', (0.40, 0.60, 0.70), 2, 3),\n", + " ('Warriors', (0.33, 0.40, 0.55)),\n", + " ('Cavs', (0.40, 0.50, 0.70))])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Thunder vs Dallas win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Thunder vs Spurs win this round: ( 51% 64% 84%) win through here: ( 51% 64% 84%)\n", + "Thunder vs Warriors win this round: ( 17% 29% 61%) win through here: ( 9% 19% 51%)\n", + "Thunder vs Cavs win this round: ( 20% 39% 71%) win through here: ( 2% 7% 36%)\n" + ] + } + ], + "source": [ + "playoffs('Thunder',\n", + " [('Dallas', (0.75, 0.83, 0.85), 4, 1),\n", + " ('Spurs', (0.30, 0.40, 0.60), 3, 2),\n", + " ('Warriors', (0.33, 0.40, 0.55)),\n", + " ('Cavs', (0.35, 0.45, 0.60))])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Hawks win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Raptors win this round: ( 50% 80% 93%) win through here: ( 50% 80% 93%)\n", + "Cavs vs GS/SA/OK win this round: ( 17% 39% 61%) win through here: ( 8% 31% 57%)\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Hawks', (0.45, 0.60, 0.75), 4, 0),\n", + " ('Raptors', (0.50, 0.65, 0.75)),\n", + " ('GS/SA/OK', (0.33, 0.45, 0.55))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So overall, from the start of the playoffs up to May 10th, I have:\n", + "\n", + "- **Warriors:** Dropped from 50% to 26% with Curry's injury, and rebounded to 42%. \n", + "- **Spurs:** Dropped from 20% to 5% after falling behind Thunder.\n", + "- **Thunder:** Increased to 7%.\n", + "- **Cavs:** Increased to 31%.\n", + "\n", + "# Time to Panic?\n", + "\n", + "## 17 May 2016\n", + "\n", + "The Thunder finished off the Spurs and beat the Warriors in game 1. Are the Thunder, like the Cavs, peaking at just the right time, after an inconsistent regular season? Is it time for Warriors fans to panic?\n", + "\n", + "Sure, the Warriors were down a game twice in last year's playoffs and came back to win both times. Sure, the Warriors are still 3-1 against the Thunder this year, and only lost two games all season to elite teams (Spurs, Thunder, Cavs, Clippers, Raptors). But the Thunder are playing at a top level. Here's my update, showing that the loss cost the Warriors 5%:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Blazers win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Thunder win this round: ( 26% 61% 74%) win through here: ( 26% 61% 74%)\n", + "Warriors vs Cavs win this round: ( 29% 61% 80%) win through here: ( 7% 37% 60%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 4, 1),\n", + " ('Blazers', (0.55, 0.67, 0.75), 4, 1),\n", + " ('Thunder', (0.45, 0.63, 0.70), 0, 1),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# Not Yet?\n", + "\n", + "## 18 May 2016\n", + "\n", + "The Warriors won game two of the series, so now they're back up to 45%, with the Cavs at 35%. At this time, [fivethirtyeight](http://projects.fivethirtyeight.com/2016-nba-picks/) has the Warriors at 45%, Cavs at 28% and Thunder at 24%" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Blazers win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Thunder win this round: ( 41% 73% 84%) win through here: ( 41% 73% 84%)\n", + "Warriors vs Cavs win this round: ( 29% 61% 80%) win through here: ( 12% 45% 67%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 4, 1),\n", + " ('Blazers', (0.55, 0.67, 0.75), 4, 1),\n", + " ('Thunder', (0.45, 0.63, 0.70), 1, 1),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Hawks win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Raptors win this round: ( 66% 88% 96%) win through here: ( 66% 88% 96%)\n", + "Cavs vs GSW win this round: ( 20% 39% 71%) win through here: ( 13% 35% 68%)\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Hawks', (0.45, 0.60, 0.75), 4, 0),\n", + " ('Raptors', (0.50, 0.65, 0.75), 1, 0),\n", + " ('GSW', (0.35, 0.45, 0.60))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Yet!\n", + "\n", + "## 24 May 2016\n", + "\n", + "The Thunder won two in a row (first time the Warriors had lost two in a row all year), putting the Warriors down 3-1. And the Cavs are looking mortal, losing two to the Raptors. So now it looks to me like the Thunder are favorites to win it all:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Blazers win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Thunder win this round: ( 2% 17% 27%) win through here: ( 2% 17% 27%)\n", + "Warriors vs Cavs win this round: ( 29% 61% 80%) win through here: ( 0% 10% 22%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 4, 1),\n", + " ('Blazers', (0.55, 0.67, 0.75), 4, 1),\n", + " ('Thunder', (0.25, 0.55, 0.65), 1, 3),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Hawks win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Raptors win this round: ( 50% 57% 78%) win through here: ( 50% 57% 78%)\n", + "Cavs vs Thunder win this round: ( 20% 39% 71%) win through here: ( 10% 23% 56%)\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Hawks', (0.45, 0.60, 0.75), 4, 0),\n", + " ('Raptors', (0.50, 0.55, 0.70), 2, 2),\n", + " ('Thunder', (0.35, 0.45, 0.60))])" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Thunder vs Dallas win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Thunder vs Spurs win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Thunder vs Warriors win this round: ( 73% 83% 98%) win through here: ( 73% 83% 98%)\n", + "Thunder vs Cavs win this round: ( 29% 61% 80%) win through here: ( 21% 51% 79%)\n" + ] + } + ], + "source": [ + "playoffs('Thunder',\n", + " [('Dallas', (0.75, 0.83, 0.85), 4, 1),\n", + " ('Spurs', (0.30, 0.40, 0.60), 4, 2),\n", + " ('Warriors', (0.35, 0.45, 0.75), 3, 1),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# But Not Done Yet\n", + "\n", + "## 26 May 2016\n", + "\n", + "The Warriors won game 5, bringing them up from a 10% to an 18% chance of winning it all:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warriors vs Rockets win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Blazers win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Warriors vs Thunder win this round: ( 12% 30% 42%) win through here: ( 12% 30% 42%)\n", + "Warriors vs Cavs win this round: ( 29% 61% 80%) win through here: ( 4% 18% 34%)\n" + ] + } + ], + "source": [ + "playoffs('Warriors',\n", + " [('Rockets', (0.50, 0.70, 0.80), 4, 1),\n", + " ('Blazers', (0.55, 0.67, 0.75), 4, 1),\n", + " ('Thunder', (0.35, 0.55, 0.65), 2, 3),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Cavs vs Pistons win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Hawks win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Cavs vs Raptors win this round: ( 75% 80% 91%) win through here: ( 75% 80% 91%)\n", + "Cavs vs Thunder win this round: ( 20% 39% 71%) win through here: ( 15% 31% 65%)\n" + ] + } + ], + "source": [ + "playoffs('Cavs',\n", + " [('Pistons', (0.75, 0.83, 0.85), 4, 0),\n", + " ('Hawks', (0.45, 0.60, 0.75), 4, 0),\n", + " ('Raptors', (0.50, 0.55, 0.70), 3, 2),\n", + " ('Thunder', (0.35, 0.45, 0.60))])" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Thunder vs Dallas win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Thunder vs Spurs win this round: (100% 100% 100%) win through here: (100% 100% 100%)\n", + "Thunder vs Warriors win this round: ( 58% 70% 94%) win through here: ( 58% 70% 94%)\n", + "Thunder vs Cavs win this round: ( 29% 61% 80%) win through here: ( 17% 42% 75%)\n" + ] + } + ], + "source": [ + "playoffs('Thunder',\n", + " [('Dallas', (0.75, 0.83, 0.85), 4, 1),\n", + " ('Spurs', (0.30, 0.40, 0.60), 4, 2),\n", + " ('Warriors', (0.35, 0.45, 0.75), 3, 2),\n", + " ('Cavs', (0.40, 0.55, 0.65))])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "# The Finals\n", + "\n", + "## 1 June 2016\n", + "\n", + "The Warriors completed their comeback against the Thunder, putting them in a great position to win this year (and they are already established as [favorites for next year](http://www.foxsports.com/nba/story/golden-state-warriors-title-favorites-cleveland-cavaliers-odds-2016-17-053016)). Rather than update the odds after each game 0f the finals, I'll just repeat the table (with the note that I think the Warriors are somewhere in the 60% range for each game):\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "W-L | Singe Game Win Percentage\n", + " | 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80%\n", + "----+-----------------------------------------------------------------\n", + "0-3 | 0% 0% 1% 2% 3% 4% 6% 9% 13% 18% 24% 32% 41%\n", + "0-2 | 1% 2% 3% 5% 9% 13% 19% 26% 34% 43% 53% 63% 74%\n", + "0-1 | 2% 4% 7% 12% 18% 26% 34% 44% 54% 65% 74% 83% 90%\n", + "0-0 | 3% 7% 13% 20% 29% 39% 50% 61% 71% 80% 87% 93% 97%\n", + "----+-----------------------------------------------------------------\n", + "1-3 | 1% 2% 3% 4% 6% 9% 12% 17% 22% 27% 34% 42% 51%\n", + "1-2 | 3% 5% 8% 13% 18% 24% 31% 39% 48% 56% 65% 74% 82%\n", + "1-1 | 6% 10% 16% 24% 32% 41% 50% 59% 68% 76% 84% 90% 94%\n", + "1-0 | 10% 17% 26% 35% 46% 56% 66% 74% 82% 88% 93% 96% 98%\n", + "----+-----------------------------------------------------------------\n", + "2-3 | 4% 6% 9% 12% 16% 20% 25% 30% 36% 42% 49% 56% 64%\n", + "2-2 | 10% 16% 22% 28% 35% 43% 50% 57% 65% 72% 78% 84% 90%\n", + "2-1 | 18% 26% 35% 44% 52% 61% 69% 76% 82% 87% 92% 95% 97%\n", + "2-0 | 26% 37% 47% 57% 66% 74% 81% 87% 91% 95% 97% 98% 99%\n", + "----+-----------------------------------------------------------------\n", + "3-3 | 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80%\n", + "3-2 | 36% 44% 51% 58% 64% 70% 75% 80% 84% 88% 91% 94% 96%\n", + "3-1 | 49% 58% 66% 73% 78% 83% 88% 91% 94% 96% 97% 98% 99%\n", + "3-0 | 59% 68% 76% 82% 87% 91% 94% 96% 97% 98% 99% 100% 100%\n" + ] + } + ], + "source": [ + "series_table()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/dist-climb-time.csv b/pytudes/ipynb/dist-climb-time.csv new file mode 100644 index 0000000..c6f9ff8 --- /dev/null +++ b/pytudes/ipynb/dist-climb-time.csv @@ -0,0 +1 @@ +5092,20.9,1360 13902.6,50,3183 4239.4,34,1011 14146.5,71,3407 1728,0,341 9595.8,58.6,1866 49571.4,377,8491 35040.3,113,6300 30775,60,5671 10246.2,41,1976 27850.7,67,5010 38901.6,69,7097 109988,1868.4,22392 32369.6,85,5723 40331.7,81,7573 40767.3,209,7162 1325.3,1,246 18910.7,43,3471 44109.3,86,7399 72041.9,194,11428 3683.3,8,672 62921,950,12532 38522.8,81,6817 33413.1,80,5413 32539.5,63,5828 38397.7,186,6436 21211.6,54,3526 48657.5,124,8447 40202.8,71,6669 42429,151,7301 11228.3,28,1915 24194.9,69,4318 12900.4,24,2016 15412.6,120,2305 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z3>yu^_~&Is_k;gTU&)oqc%CM{+BE0xLAnTxpp?rRJvaja&l``gvPFw{UC;XSO)C&!{?jkWP7 z?%zo+gQVj)rOChtnaIG8+#PYGXdp)JKW@AaCYFWQ*QeB3nzBd1f90!f)^$h@ymTF8 z;B`LIM%369|K+alAIdBcr!bxPvcz=|Wl-4WpqNBcAKl+!s(~24pLaKaCBeU_>p1y4 zNS+ivL991ur0XDqW-Es6L}L7Vu)+u6PWTDT27bB9I||XpKW(36q$^zwj3f=z2l3V{ z+;@>jV5>?Aqe}k!N?x8WRh4eEtAXLGf!ax2<(I*0)_E`oycK-fbo#FhDe6jB1H)ef z{&hU!f9r7t_}BFt!T;XfcNC@7p_;kf->wEmfChYVuN`Gq(mp+&1^>O4(shug9=g9H vSOdPG=Ouk9;>Uvj^E)M9znZC;^!xt len(self.best):\n", + " self.best = self.left + list(self.right)\n", + " if N - self.Nshown > 1000 or N > 16000:\n", + " self.Nshown = N\n", + " print(self.report())\n", + " \n", + " def report(self):\n", + " N = len(self.best)\n", + " nwords = N + sum(self.dict[p].count(' ') for p in self.best)\n", + " nletters = sum(len(p) for p in self.best)\n", + " return ('Pal: {:6,d} phrases, {:6,d} words, {:6,d} letters ({:,d} steps, {} seconds)'\n", + " .format(N, nwords, nletters, self.i+1, round(time.time() - self.t0)))\n", + " \n", + " def applicable_actions(self):\n", + " L, R, D = self.L, self.R, self.dict\n", + " actions = []\n", + " def score(A): return D.prefixes[L+A] * D.suffixes[A+R]\n", + " if self.is_allowed(L):\n", + " actions.append(',')\n", + " if self.is_allowed(R):\n", + " actions.append(';')\n", + " for A in sorted(alphabet, key=score):\n", + " if score(A) > 0:\n", + " actions.append(A) \n", + " return actions\n", + " \n", + " def is_allowed(self, phrase): return phrase in self.dict and phrase not in self.set\n", + " \n", + " def is_palindrome(self): \n", + " \"Is this a palindrome? (Does any extra .L or .R match the other side?)\"\n", + " return ((self.L == '' and self.left[-1].endswith(self.R)) or \n", + " (self.R == '' and self.right[0].startswith(self.L)))\n", + "\n", + "alphabet = 'abcdefghijklmnopqrstuvwxyz'\n", + "cat = ''.join\n", + "UndoCommand = str\n", + "DoCommand = list\n", + " \n", + "def test2():\n", + " p1 = Panama()\n", + " assert p1.is_palindrome()\n", + " assert str(p1) == 'a man, a plan, a canal, Panama'\n", + " p2 = Panama(['aman','aplan'], 'acadd','dd', ['acanal', 'panama'])\n", + " assert not p2.is_palindrome()\n", + " p3 = Panama(['maya'], '', '', ['ayam'])\n", + " assert p3.is_palindrome()\n", + " assert str(p3) == 'Maya, a yam'\n", + " return 'ok'\n", + "\n", + "test2()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The main point of the `Panama` class is to allow the `.search()` method to search for a long palindrome. The [overall strategy](http://norvig.com/pal-alg.html#v3) is explained elsewhere. The search\n", + "adds a lett1er at a time to both left and right side, backtracking when necessary. The state of the search is represented by the four fields `.left, .L, .R, .right`, for example:\n", + " \n", + " A man, a plan, a cam, a yak, a yam, a canal, Panama\n", + " \n", + "gets encoded into the four fields like this:\n", + " \n", + " .left: ['aman', 'aplan', 'acam', 'ayak']\n", + " .L: ''\n", + " .R: 'k'\n", + " .right: ['ayam', 'acanal', 'panama']\n", + " \n", + "We always maintain the invariant:\n", + "\n", + " cat(left + [L]) == cat([R] + right)[::-1]\n", + " \n", + "The `search` method would be more straightforward if we could write it is a recursive function. But Python does not perform well when recursing to 100 thousand levels deep. So instead I manually manage a *stack* of *commands* that tell the search what to do and to undo. A command can be a `DoCommand`, which consists of a list of letters describing all the possible actions we could take at this point. Actions include letters that could be added (only the letters that make a legitimate prefix of a known phrase in `.L` and a legitimate suffix of a known phrase in `.R`). Actions can also include the character `','`, which is used to dignal that `.L` is a complete word and should be moved ontot he `.left` list, or `';'` to signal the same for `.R/.right`. A command can also be a `UndoCommand`, which consists of a single character; one that was previously chosen to be done. So the list of characters in a `DoCommand` constitutes a choice point; we first choose one, and continue deeper from there, but we put on the command stack an `UndoCommand` to reverse the effects of the action, and put back the remaining characters to try instead, if the first character doesn't work out. Note that we pop characters off the end of a `DoCommand`, so the last character is the first one tried.\n", + "\n", + "Let's see how it works:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pal: 1,001 phrases, 1,395 words, 6,246 letters (30,023 steps, 1 seconds)\n", + "Pal: 2,003 phrases, 2,802 words, 12,375 letters (112,614 steps, 3 seconds)\n", + "CPU times: user 5.61 s, sys: 17.4 ms, total: 5.63 s\n", + "Wall time: 5.65 s\n" + ] + } + ], + "source": [ + "p = Panama()\n", + "%time p.search(200000)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'Pal: 2,791 phrases, 3,876 words, 17,101 letters (200,000 steps, 4 seconds)'" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p.report()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That seemed to go ok; let's try a longer search (100 million steps):" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pal: 1,001 phrases, 1,395 words, 6,246 letters (30,023 steps, 1 seconds)\n", + "Pal: 2,003 phrases, 2,802 words, 12,375 letters (112,614 steps, 2 seconds)\n", + "Pal: 3,004 phrases, 4,162 words, 18,341 letters (227,472 steps, 5 seconds)\n", + "Pal: 4,005 phrases, 5,507 words, 24,199 letters (386,226 steps, 8 seconds)\n", + "Pal: 5,019 phrases, 6,890 words, 30,137 letters (619,790 steps, 12 seconds)\n", + "Pal: 6,021 phrases, 8,235 words, 35,931 letters (877,024 steps, 17 seconds)\n", + "Pal: 7,023 phrases, 9,568 words, 41,593 letters (1,183,926 steps, 23 seconds)\n", + "Pal: 8,024 phrases, 10,878 words, 47,259 letters (1,561,761 steps, 30 seconds)\n", + "Pal: 9,026 phrases, 12,183 words, 52,965 letters (1,947,540 steps, 38 seconds)\n", + "Pal: 10,028 phrases, 13,467 words, 58,583 letters (2,480,848 steps, 48 seconds)\n", + "Pal: 11,029 phrases, 14,730 words, 64,117 letters (3,206,870 steps, 61 seconds)\n", + "Pal: 12,030 phrases, 16,018 words, 69,588 letters (4,044,269 steps, 77 seconds)\n", + "Pal: 13,031 phrases, 17,293 words, 74,967 letters (5,272,674 steps, 99 seconds)\n", + "Pal: 14,033 phrases, 18,519 words, 80,203 letters (7,091,166 steps, 133 seconds)\n", + "Pal: 15,034 phrases, 19,753 words, 85,307 letters (10,753,057 steps, 201 seconds)\n", + "Pal: 16,003 phrases, 20,886 words, 90,015 letters (27,084,693 steps, 506 seconds)\n", + "Pal: 16,004 phrases, 20,886 words, 90,015 letters (27,149,605 steps, 508 seconds)\n", + "Pal: 16,005 phrases, 20,890 words, 90,017 letters (27,316,698 steps, 511 seconds)\n", + "Pal: 16,009 phrases, 20,896 words, 90,039 letters (27,350,925 steps, 511 seconds)\n", + "Pal: 16,010 phrases, 20,896 words, 90,039 letters (27,412,633 steps, 513 seconds)\n", + "Pal: 16,011 phrases, 20,897 words, 90,045 letters (27,427,058 steps, 513 seconds)\n", + "Pal: 16,013 phrases, 20,898 words, 90,049 letters (27,567,249 steps, 516 seconds)\n", + "Pal: 16,014 phrases, 20,898 words, 90,046 letters (27,592,882 steps, 516 seconds)\n", + "Pal: 16,016 phrases, 20,900 words, 90,055 letters (27,595,464 steps, 516 seconds)\n", + "Pal: 16,019 phrases, 20,903 words, 90,070 letters (27,616,478 steps, 517 seconds)\n", + "Pal: 16,020 phrases, 20,904 words, 90,073 letters (27,670,352 steps, 518 seconds)\n", + "Pal: 16,022 phrases, 20,908 words, 90,081 letters (27,690,556 steps, 518 seconds)\n", + "Pal: 16,024 phrases, 20,908 words, 90,096 letters (27,750,047 steps, 519 seconds)\n", + "Pal: 16,025 phrases, 20,911 words, 90,097 letters (27,902,094 steps, 522 seconds)\n", + "Pal: 16,028 phrases, 20,916 words, 90,113 letters (27,913,484 steps, 523 seconds)\n", + "Pal: 16,029 phrases, 20,916 words, 90,119 letters (28,000,410 steps, 524 seconds)\n", + "Pal: 16,030 phrases, 20,916 words, 90,115 letters (28,199,063 steps, 528 seconds)\n", + "Pal: 16,033 phrases, 20,920 words, 90,131 letters (28,207,363 steps, 528 seconds)\n", + "Pal: 16,035 phrases, 20,924 words, 90,143 letters (28,222,377 steps, 529 seconds)\n", + "Pal: 16,036 phrases, 20,924 words, 90,145 letters (28,245,911 steps, 529 seconds)\n", + "Pal: 16,038 phrases, 20,928 words, 90,155 letters (28,319,574 steps, 530 seconds)\n", + "Pal: 16,039 phrases, 20,927 words, 90,165 letters (28,357,649 steps, 531 seconds)\n", + "Pal: 16,044 phrases, 20,933 words, 90,179 letters (28,398,480 steps, 532 seconds)\n", + "Pal: 16,045 phrases, 20,936 words, 90,187 letters (28,669,877 steps, 537 seconds)\n", + "Pal: 16,046 phrases, 20,936 words, 90,193 letters (28,756,803 steps, 538 seconds)\n", + "Pal: 16,047 phrases, 20,937 words, 90,195 letters (28,951,247 steps, 542 seconds)\n", + "Pal: 16,048 phrases, 20,937 words, 90,195 letters (29,168,799 steps, 546 seconds)\n", + "Pal: 16,049 phrases, 20,939 words, 90,197 letters (29,304,707 steps, 548 seconds)\n", + "Pal: 16,050 phrases, 20,940 words, 90,200 letters (29,402,659 steps, 550 seconds)\n", + "Pal: 16,055 phrases, 20,946 words, 90,223 letters (29,483,409 steps, 552 seconds)\n", + "Pal: 16,060 phrases, 20,951 words, 90,241 letters (29,703,353 steps, 556 seconds)\n", + "Pal: 16,062 phrases, 20,951 words, 90,257 letters (29,935,767 steps, 560 seconds)\n", + "Pal: 16,065 phrases, 20,957 words, 90,261 letters (30,401,372 steps, 568 seconds)\n", + "Pal: 16,066 phrases, 20,957 words, 90,267 letters (30,488,256 steps, 570 seconds)\n", + "Pal: 16,067 phrases, 20,961 words, 90,271 letters (30,742,860 steps, 575 seconds)\n", + "Pal: 16,068 phrases, 20,961 words, 90,277 letters (30,829,744 steps, 576 seconds)\n", + "Pal: 16,069 phrases, 20,965 words, 90,279 letters (31,091,412 steps, 581 seconds)\n", + "Pal: 16,070 phrases, 20,965 words, 90,285 letters (31,178,296 steps, 583 seconds)\n", + "Pal: 16,071 phrases, 20,969 words, 90,287 letters (31,452,702 steps, 588 seconds)\n", + "Pal: 16,072 phrases, 20,969 words, 90,293 letters (31,539,586 steps, 589 seconds)\n", + "Pal: 16,075 phrases, 20,973 words, 90,299 letters (31,899,517 steps, 597 seconds)\n", + "Pal: 16,077 phrases, 20,975 words, 90,305 letters (32,079,651 steps, 600 seconds)\n", + "Pal: 16,079 phrases, 20,978 words, 90,317 letters (32,418,194 steps, 606 seconds)\n", + "Pal: 16,080 phrases, 20,977 words, 90,327 letters (32,456,269 steps, 607 seconds)\n", + "Pal: 16,085 phrases, 20,983 words, 90,341 letters (32,497,076 steps, 608 seconds)\n", + "Pal: 16,087 phrases, 20,985 words, 90,351 letters (32,651,838 steps, 611 seconds)\n", + "Pal: 16,090 phrases, 20,986 words, 90,365 letters (32,782,954 steps, 613 seconds)\n", + "Pal: 16,091 phrases, 20,988 words, 90,363 letters (33,528,985 steps, 627 seconds)\n", + "Pal: 16,093 phrases, 20,992 words, 90,375 letters (33,696,891 steps, 630 seconds)\n", + "Pal: 16,094 phrases, 20,992 words, 90,381 letters (33,783,775 steps, 631 seconds)\n", + "Pal: 16,095 phrases, 20,992 words, 90,379 letters (34,151,848 steps, 638 seconds)\n", + "Pal: 16,096 phrases, 20,995 words, 90,389 letters (34,283,539 steps, 640 seconds)\n", + "Pal: 16,098 phrases, 20,996 words, 90,397 letters (34,342,030 steps, 642 seconds)\n", + "Pal: 16,099 phrases, 20,998 words, 90,397 letters (34,699,703 steps, 648 seconds)\n", + "Pal: 16,100 phrases, 21,001 words, 90,405 letters (36,050,560 steps, 673 seconds)\n", + "Pal: 16,102 phrases, 21,002 words, 90,413 letters (36,109,051 steps, 674 seconds)\n", + "Pal: 16,103 phrases, 21,004 words, 90,413 letters (36,466,496 steps, 680 seconds)\n", + "Pal: 16,105 phrases, 21,005 words, 90,411 letters (37,036,344 steps, 691 seconds)\n", + "Pal: 16,106 phrases, 21,004 words, 90,423 letters (76,003,720 steps, 1522 seconds)\n", + "Pal: 16,107 phrases, 21,006 words, 90,423 letters (76,361,384 steps, 1530 seconds)\n", + "Pal: 16,108 phrases, 21,009 words, 90,431 letters (77,712,187 steps, 1559 seconds)\n", + "Pal: 16,110 phrases, 21,010 words, 90,439 letters (77,770,678 steps, 1560 seconds)\n", + "Pal: 16,111 phrases, 21,012 words, 90,439 letters (78,128,114 steps, 1568 seconds)\n", + "CPU times: user 33min 11s, sys: 13 s, total: 33min 24s\n", + "Wall time: 33min 38s\n" + ] + } + ], + "source": [ + "p = Panama()\n", + "%time p.search(10**8)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "\"a man, a plan, a caretaker, a moksha, Lufkin, a jacinth, Gile, Daniell, Ivanov, an odor, a negativeness, a tsarevna, melanomas, an ire, Gib, Olga, Lata Narayanan, a meld, an elecampane, an evonymus, an anatase, Rachael, an anabasis, an anaesthetics, an anamniote, an ani, DRE, Fredra, Cal, Parette, Serang, Isaacs, a ramark, IHD, a nonacademic, an obstet, Sellers, Sanalda, Erbe, Eba, an ane, Zaneski, Red, Erfurt, Sinai, Sale, Gene Roddenberry, a nonactive, Cenaean, Namangan, a mell, Everes, a nonanimal, a sanitarian, a non-American, Gat, Noman, an arista, Lattimer, a nonemendation, Eberta, Poe, LCT, an anaerobe, Ranita, Marella, an antired, ipsissima verba, a nan, a manille, Tiv, a nonet, an one, Kenney, a caret, Alon, Omar Epps, an analemma, an enami, Barents, Regen, A. H. Taub, a self, Farant, Caresse, RdAc, a nil, a nonrevocation, a melanite, Ranite, Canarese, NEbE, an allanite, Caressa, an all, IJssel, DNA, Carolee Carmello, Sara, Pareto, Oran, a mel, Dissenter, Cesare, Tema, an alt, Evslin, an alienist, anabases, a torpedoman, a meta, Garett, a csk, Cabaeus, an aloneness, Emelita, an alerion, Eleni, a cong, Ilan Adler, a keratoderma, an alg, Roe, generalities, a nonrateability, a hellebore, an anatta, Ranitta, petits, a baresark, unities, an iman, a non-Indian, a non-Israelite, Delano, Ita, Ranit, Ame, a hanaper, Tanah, an alarum, an alpha, Lacedaemonian, a tab, Cenac, an alette, Levona, an airbrasive, Lody, Nnadia Chan, a naira, an airstream, Macedon, an anatexis, an aileron, a nail, arts, UART, San, a nong, a morceau, dice, Delavan, a mete, Parent, Artemas, Esau, an ora, Hsingan, Amero, FAD, Naman, Amery, Bareilly, Hwang, Inanna, an aider, Acre, Vona, an ait, an aisle, a decare, billies, Banares, ARE, Nanakuli, codette, Lemon, a nonmember, a jaconet, an aigrette, Sang, Tanagra, Genet, a portal, an ore, Pip, a non-Uralian, Bohaty, a parent, Sikang, Amorette, Locrian, Cameron, Anna, Carole, Delaware, Temenus, an iterativeness, Enos, an aim, a danaite, Ahrens, Enarete, Mona, Marelda, an ataractic, a noise, lanais, anatexes, a noisette, Long, APS, Enalus, Omari, a natl, Usanis, an attestator, Gean, an oiliness, an oilskin, Numanus, Ari, Hellene, RCAF, a caresser, Pare, Tem, a torsel, a nat, a kokanee, LaSorella, Gipsies, Irby, an aperient, Mareld, an enallage, a decalcomania, an argali, an arbalester, an imagnableness, an arith, a nonsensitiveness, Anam, Kramer, a caress, a parens, Asel, Ujiji, Emelina, PMA, Carena, ELAS, an it's, Estella, Marela, Edana, Melba, Tsana, Mel, Bonar, a nidana, Meri, Fareham, an arum, a receivable, Gene Geter, a grammarian, Alanah, Ana, Hsian, a lenity, an aug, an oil, a decane, an arrest, Ibanez, an acosmist, an absorptance, a noisemaker, a metall, a gasser, an acuteness, Ender, an ossa, Maria, Teria, an acetal, a manilla, Marie, Benilda, Erb, a no-side, an amah, Drava, Lat, Ragan, Amer, O'Fallon, an amasser, Tai, Tini, Nanak, a nine, Leninabad, an enargite, Gilles, a benignancy, Lanam, an ami, Vanessa, LCI, Kikelia, Delamare, Terr, Efahan, a visitor, a nies, a nit, OFris, an amenorrhea, Laramie, Lipsey, an augend, Averell, a carelessness, oogoninia, Lad, a nose, Majel Barrett, an amen, AHSA, Lari, Oka, Hsi, Namara, an enate, Caren, a career, Gena, Jenna von Oy, a material, Lebanon, an abaca, an abalone, an abaser, a nebris, a benison, Aug, an osnaburg, a nosh, Tim, Selle, Baram, an aba, Hellen, a decal, a paretta, Marelya, Teri Polo, a predicate, leva, Warenne, R. Bayer, Fred Astaire, an abr, Unit, a legatee, RFA, Nananne, Kenner, Rawley, a greensand, Ronald, Barea, Benildas, an abb, inamoratas, an abuser, an illegalisation, a mess, a heller, a decapitation, a hello, Helles, Ignatia, Hsia-men, a hcl, a north, Gilda, Edan, a mesa, Barotse, Hts, an ill, a green, OPA, Ewan, a menu, Bret, epithalami, an adder, a nos, an ordainer, an adagio, Marion, a menses, a tsi, Perelman, a taker-in, Ume, Arp, an ord, a ceder, ACS, an oracy, Aneto, O'Kelley, Na-Dene, Lassell, a caramel, a derisiveness, a cudgel, an orang, Farewell, a beek, Sella, Geneva, Dela, Derian, a men, Arcadian, a meg, Rabassa, an adenoma, Gareth, Gilbart, Sandy, a hell, a mix, Elam, a danewort, an emanation, Matsys, a gala, Mario, Marilyn, a tob, an origan, a media, Sello, Cinerama, an asonia, Rania, Redeemer, an oddness, endia, Tsan, a medullation, a colin, a mee, RFD, a raft, a tsarina, Venita, an aulos, a ferret, Edna, Rgen, Alena, Idelle, Baras, an isotach, an oceanography, an orinasal, a bander, a jar, Tepic, a carabin, ANG, a mannan, A Mei, paralipses, ATC, Enola, a goner, a caracal, a spur-rowel, an agron, an oribi, an adenine, Lger, a wet, Agana, an agromania, Lehet, an oca, EdB, USAR, an ell, a veritas, an orca, Marena, Elgan, a morale, a m/s, inamoratos, a rasse, Irene, Csel, a dep, Ohara, a ballade, Paramatman, an agr, Efren, a ramie, Wenona, tubas, an ipm, a caravaner, a decanter, a nitrogen, a morn, Onalaska, a sinapine, LAC, Sellma, Lamas, an agar, Ihab, a rani, Artamas, an aga, Nana Visitor, an agnate, Lev, Lavater, Alli, paramos, a namaste, Lanae, a paretic, an orc, an anagrammatist, Ostap, an acariasis, an enemy, Carey, a let, Al Pacino, Tananarive, Lanark, an amateur, Carew, Arde, Ranie, Torp, Ate, Maren, archenia, Lai, H.P. Korver, an apse, an apery, an anarch, an octameter, Axa, Nanook, Coralie, nonolfactories, Sinatra, parastades, Behan, a mower, Italian, Sans, an orbitale, an evener, a seller, a manatee, Lana Turner, a kerogen, a leat, a monal, Emeline, an eta, Carolle, a nap, POB, Ivar, an aesc, a nip, Opalina, Braca, an aedes, a nim, a sedateness, a metal, a paregoric, a tsardom, a reserve, Freda, Elsi, Maretta, MSAE, an eremite, CAP, Sanfo, Lenin, an enema, a nae, linemen, Arch, an omnivore, Moran, a mowrah, Carola, Janetta, barotraumata, a navelwort, a nave, Tseng, a pareira, Vane, Marat Safin, a nene, Laveran, an orb, a ferule, Carol, an enol, a mane, Jenna, Iranian, an orfe, an aviator, a navarin, a raught, ansae, a negater, a nav, a heliotaxis, a nork, an ortolan, a mow, Seko, PSAT, Angara, a sell, a carapace, Sarette, Ste, Janette, LSS, an amora, laminae, an edema, Rakel, a deg, a predepletion, Rekha, Lala, Heller, Radnor, Ace, Ilse, Lenore, cicale, a metamale, a grisette, Sumerologist, a hgt, a nyala, Arcadia, Mae, Saretta, Harelda, Syr, rabatos, a vanadinite, Cam, Rep, Sarena, Eden, alae, Saree, Tenn, Osanna, Melete, an immune, Dou, Daniel Chan, a kleagle, an afar, an ugsomeness, a cud, Rego, Renita, Lapeer, an azan, a motto, an ayah, a metamer, paras, a carapa, Lamarre, Tanaka, Anaheim, an akala, Arg, Nasser, an ennobler, a notelet, a corban, a mot, a note, Lek, Sarah, Adna, Kenna, IRO, Lenora, Anaxo, Renie, Saragat, a carer, Ansar, Anu, Calan, a mol, Kenny, Lam, Meredi, a ranee, Lavery, Trammel, Asur, E.J. McShane, entea, Hare, Tell, Ibadan, an axe, Renata, Maril, a notable, a gab, a notary, an ektene, Sra, Sara Gilbert, Saipan, a mog, Ardath, Gilli, a tanager, an aortoclasia, an ajiva, an interfacing, an anapaest, Airel, an imagist, a consecrater, Alcaeus, Sinan, a monosyllabism, a rem, Meredith, Savannah, an immortal, a kerosene, MEA, Lattie, Cedarhurst, a hwan, a mara, Tak, Nev, mks units, Uru, Alan-a-dale, a gib, an ottar, an otto, Caro, Tara, Pesaro, Taro, Ball, O'Casey, a helio, Terena, Ebert, Sada, carabaos, a motor, a craniol, an anabasine, a carangid, a no-trumper, a novelese, an ironside, Elata, a metamere, Hsia, Lananna, hsien, Nor, epitra, Maris, Omarr, an ennead, an irenics, a predestitution, a cayman, tupelos, an iris-in, an irregular, an acetate, CAB, USA, an illamon, a cir, Emarie, Harod, an illative, lenos, an ovarium, Anil Kamath, an odium, an anabas, an engager, a weka, Baron, a maniac, an ileus, Sita, a nitramine, Cinelli, Kenn, a susso, an anadem, a nitrate, Let, ALP, an ova, Delisle, a greeter, a wae, Sarad, a nitre, Blane, Marra, Yetac, an italic, Artema, RFC, a net, Norford, a gov, an ovisac, an ital, Paraebius, Anita Mui, Lisa, Venite, Menard, a bene, Lanett, a pareu, a b/l, Freddi, Bred, Nun, a nov, Elena, Anita, Carolynne, Paharis, an octan, Rebeca, Rohn, a marseille, Brogle, a sanies, a car, aparejos, Aires, a ranula, Baroda, a niton, a mar, Ray Allen, a nitromannitol, an isotac, Edette, Lossa, Caravette, Lorene, Tihwa, anis, a moton, Asia, Paran, IHS, an ideal, a spp, Univ, Alfadir, a canaster, Eben, Alano, Italy, Niv, an oleate, an ide, Maregos, a noli-me-tangere, an iter, an idealiser, a bra, Benil, a sanidine, Benita, Lagasse, Nela, Maressa, Leno, T-stop, an olla, Freddy, Renate, an ips, an ignoramus, a tahsil, an acaridan, an omission, Illinoisan, an omicron, a legend, Air, an omen, Marina, Ieda, Lassa, Kenison, Eda, Nanete, a b/s, Ojai, Sarah Smith, Sarazen, a maid, Ninos, a mali, Mariken, Aloysia, Lacedaemon, a nome, a danio, Laney, an ivy, an user, a wassail, Lagash, Tol, CerE, Carolina, Nanna, Merta, Labannah, an omni, Art, Serpasil, a sri, Sell, a helipad, Arafat, a cuda, an ibex, a selectness, a nanako, Lomasi, a nib, a selamlik, a nomad, Ania, Lenox, a selah, an ihp, an ionomer, a wren, Nidaros, a vavasory, AKC, Uball, a caracara, a gems, an adermin, Amal, Caralie, Lanier, an ipr, a helix, Enone, Ugarit, Sarawak, an okay, an engr, Evert, Sass, Enid, a rage, maremme, an izard, a metacarpus, a noma, Leta, an ikan, Amata, Nanni, a trammie, Hort, Selimah, an oyelet, an odd, a barege, a nix, Elatia, Barocius, a yellow, Zenia, Colo, Helle, baronies, a carabid, Asante, Petite, Mimas, a nomarch, Nunes, a helotage, Lorena, Ewart, Serapis, an ode, Motu, an odyl, a carat, AFL, osar, Annamarie, Repeal, Lemal, an iff, Ursula, Selima, Caras, Aimee, Laroy, a dill, a helotry, Maridel, Ade, Vullo, Roca, Aniweta, robalos, a niyama, a mania, Rolanda, wares, a rfb, a rod, a noddle, Ifni, a ninetieth, Gilba, an elemi, an akela, Labors, Selig, Rani, Argo, Likasi, an adsorbate, Lamar, a nametape, an adsorbent, ACP, Italia, Terah, an imager, an anoia, Portage, Baroja, Mareah, Selia, Helli, an acarine, Ohare, an elem, a nod, a lava-lava, Zenobia, Loki, Nellie, SRO, Nanny, Leo, Jenni, Rocker, a greet, Elum, an oos, Sabaean, a helping, Ankara, a manifesto, Mari, a decan, a carafe, a lunacy, a dil, Lohse, Irena, Edessa, CSA, Ranee, Labanna, Meir, an elastin, a decade, Kip, Saros, AEF, Simah, an ideate, Selie, Nellir, Gareri, a peracid, a cranesbill, Abe, Sabatini, Nanji, Rena Komine, Maro, Faro, Tarra, Barak, a decating, a groma, labra, Kenaz, an eliminator, a secretin, an elegit, Serpens, Ian Robison, Amadas, a numen, a nemo, Lifar, an akene, Lesser, a stob, an emirate, Petit, Arany, a greed, a nematocyst, a paramo, Lapsey, a metage, Ledah, an ibid, a senility, BSE, RPO, a carucate, a gree, Tsai, Anna Bruss, Endo, Ogata, Ai Kato, Pedasus, a carder, Angarsk, Ase, Kimmie, Hellas, Salesian, Rabat, a morel, CSE, a lune, a predrawer, AWL, Ema, Nena, an eme, Jenner, Utahan, an emerald, a noon, Udelle, Barimah, an amatol, a basanite, Lemass, Ens, Selda, Oralla, Brett, Ubangi, Sedan, a madrepore, a luce, Fredie, Natalie Maines, Ajaccio, an orphan, Nahshon, a neral, an era, a nitrometer, a noodlehead, Agra, Sapporo, a camellia, Calen, Alo, BSA, Natalee, a lute, Seleucid, Emalee, Harald, an oogamy, an oomiak, an erector, a sea, Cartesian, Alroy, a dir, Fredi, Stu, Ona, an eristic, Ife, Daniele, begats, a nereis, a benne, Ill, AgE, Laver, a secret, a loo, Zaneta, an extent, Ramanujan, a tiptop, a caravan, an o-o, Ramadan, a card, Nassir, a pail, a tannage, an ess, a metabolism, a day, Elna, Tsushima, an estrade, a luge, Teri, an obsidian, Atsuko Okamoto, a cacanapa, Janeta, parodoi, Lehar, a sap, Nedrah, a laniard, an epit, a noddy, OLLA, Laband, YPSCE, Selah, Cimarosa, an earflap, an evader, a wardenry, Tsuda, Renault, a carte, Medell, Ave, RCS, an ugali, Arbela, Daniel, a jaw, Kenedy, Adi, Lohner, Aaron, Aella, Ark, an obs, Ilsedore, Morra, SECAM, a roe, Garey, Aleda, an evasion, Udella, Bac, Tarr, EST, nomas, a mob, a noble, Hell, a volatileness, Eiger, a hanap, a tamarao, Sim, Italianist, Uwton, a jaculator, an obb, Irakis, an eve, Tsuga, Biro, talli, Cavanagh, a yell, Averill, an octal, an oba, Geneina, Mede, Barram, an even, a lunate, Biton, Isaiah, Selry, Martin Amis, an obelus, PAC, a nob, a jailer, a kero, Macy, saris, Sac, Etam, Aranha, BGE, Isai, Sandra Reemer, Ahwaz, Angie, a lugsail, an edacity, Lom, salpas, Anderegg, an anorak, an editor, an opa, Carian, CMTC, a res, Seta, an ethanol, Iwo, a cipolin, a decile, Danie, tsuba, Tania, R. Carnap, an anomia, Selma, delis, a benny, Lenna, Irbil, a magnetron, a masseter, Ucalegon, an opp, interacra, a negatron, Sarid, a gassit, Rucker, a jailbird, an oxidant, a predonor, a belle, a baronetage, Rosene, Mixteco, VanAtta, RPQ, Arissa, Lanie, Tulare, Tepper, Tsui, Lenno, BAS, a cart, Apo, Elche, Paros, Serge, Raney, an oxen, an ogam, Argall, a bacteriolytic, an eelworm, a rgen, Alyda, Lab, a carotid, Artair, a neb, Ito, Martin', Kenya Moore, Delia, Genia, Codi, Lanital, an eel, a kerbaya, Latakia, Paris, Benito, Resa, a needle, a ben, an inalienableness, Egeria, Lihue, Alberti, Maria Laria, LCM, a rollaway, an ivory, Tanis, a sanbenito, Lenny, Rockel, a manit, a loe, Nelli, an etaerio, Mariah Carey, Alanna, Mahan, a tiger, a lac, Sarilda, Erastes, Sari, Apers, Idalia, Ted, an ogre, Rapallo, Ranna, MAA, Nella, Kenya, Merth, an ike, H-steel, Farah, Cananea, Carte, Peti, a warden, Nessie, Wenn, ASU, a lenis, a motet, an estragon, a siper, a llano, Issi, Meraree, Nonna, Caria, LBP, ANTA, Carin, Riksm', a roselle, Parik, a bray, Idell, Enya, Renaud, a neisseria, FFA, an ebonite, Rann, a mem, Ilsa, a help, a tsade, ABM, a sena, Bacau, a nodus, Areta, Mariam, Aney, Harappa, Natal, Liberal, Cartist, a recast, Alfreda, Elatus, Peh, Stahl, a nodule, Rosena, Morell, enigmas, Saharan, YCL, an aced, Odalys Garcia, Letsou, Kenmore, Monotremata, a nef, Ursuline, a lug, Nunu, Arber, Albania, Truc, an ogee, a lur, O'Malley, Ivette, Lahey, an anomite, a lube, Nelly, bissellia, Terrel, Peter Gacs, a robalo, Sapir, an eng, a salary, Terai, Cedar, Asare, Teide, a lub, IFS, a nylghai, a depressor, Parrott, a remainder, a jail, a reb, ILS, anmia, Rattigan, a nogg, a wase, Iraki, a pred, an enroller, Rabah, a nizamate, Lasala, a belly, Peter Clote, Mariolater, Ced, an ogle, an ejido, Lanita, Mehala, a majolica, Lauder, algae, a lulab, Arcady, Olfe, Allix, Amb, Ussuri, an ovalness, Enrika, an oregano, Martine, Gare, Tex, Enyo, Skaw, a seraph, Sarum, an enrollee, a lyre, TPN, a maharani, Ramah, anni, Jenne, Ide, moca, an orfray, a bell, Edam, an ornis, a baronet, Nata, Emalia, Trev, Lisan, a mako, Oza, barracks, a senega, an omer, Cart, a musette, Lian, an off, Ubald, Enugu, an aholt, a manic, Sercq, a rubella, Ebner, radarmen, a tuba, an omasum, a lah, Taney, Odawa, Len, a decimator, a tannate, a ripsaw, a say', Imelda, Ebn, a maestro, Peraea, Lucic, an ohm, a ria, Beniamino, a nomism, ARU, Palla, Mameluke, Ergener, a zany, a deer, Gedaliah, an oast, a rehearser, a leno, TSgt, Canaan, a losel, a dunite, lines, an oak, an o-wave, HCM, Artacia, an olio, a cirri, Barra, Mal, Kra, Marte, Tanner, Benia, Cub, Idalla, Bria, Harar, Egede, an oleaster, a batata, Ems, Redd, an anole, Marino, episedia, Ria, Teheran, Saruk, an obeah, CNO, Carie, Damali, a recitativo, Jenny, wellies, Ramses, a bat, a carol, Averi, Alla, GeV, Rehm, arcae, a rise, Delle, Basilio, Fri, an anoa, Cyler, Alf, an owner, Rad, Sem, a jai, sacra, a ha-Nasi, Trapani, Argades, Benis, a mater, a mutase, Ardys, Pel, Carib, Otaru, a sol, a gem, a now, Reddin, Assassin, a ratter, Aba, Cariocan, a milksop, an otalgia, Rct, a ramekin, an oik, an oiler, Rab, Fla, Hara, an oka, a hetaira, Vano, Isacco, NATSOPA, a nooser, a decibar, Asa, Kamerun, a manipulator, an ameer, Farand, Oberon, Aesir, a barony, a gregale, Arsippe, an ozonide, an oyer, Ambert, Sula, an okapi, HSM, a min, a named, Lahaina, Morelos, a name, Locris, Napaeae, an amowt, a barong, Isaac, an omelet, Sarre, a heth, CIF, an uta, an ultra, Had, Nilsson, a milo, Sera, Cid, Emelia, Ken, a baron, Elenore, an aniline, Dell, Edora, Madaras, Savanna, Hagen, a beretta, Marin, Nebr, Asti, RMA, an upas, a motel, Adm, ijmaa, a nude, Ardy, Helice, Cari, Ali, Heli, HCF, a radar, a spall, Ocala, a tsunami, a sedan, a cranage, Marty, Lenaea, Luci, PSS, a moil, Genie, Serov, Eddy, Ollen, a por, Parry, Tera, MDO, Orban, a mild, Ogallala, Lau, Odell, Edy, Seroka, a numskull, an aketon, Card, Nahshu, LBJ, a nudnik, a nubecula, Lapp, Estelle, Parr, an anise, ranli, Karena, Kibei, Latta, a nub, a tinea, Jenn, a sore, Arbe, Nette, L'Avare, Tali, Danilova, lapins, an amok, Ruthann, a heron, Aileen, a parade, Carrel, Tucson, a nunatak, an upset, an episode, Arbil, Annabelle, Bassein, Annamaria, Harrod, annals, a mock-up, a lovelock, a rayah, Andaman, Natie, Mart, Saba, Lanikai, a samara, an amp, Macedonia, Tanny, Lymann, a manikin, a carotin, a jarrah, Caruso, a recitative, Lahore, Mir, parts, Endres, a bed, an amylose, Arges, a crew, Olatha, Barret, an amyloid, a trend, a rad, Ligetti, Faletti, Welles, Orelee, Tsonga, Helban, an amyl, Lod, an amba, cartes, a mop, Ilene, Leiser, a vaticide, Maraj, anni mirabiles, Ufa, Laverne, Garofalo, Anniken, Arcata, Elbart, Sida, Annice, a sup, Merete, Morea, Natiha, Annorah, a rps, Amoy, MOI, Elene, Lehman, Emelun, Nip, an ambo, RDTE, Lords, a matador, annulli, atria, Harunobu, a belah, Cmdr, an octavo, Lani, Arda, Anny, Lenni, Maroney, a synod, Alec, an amir, remedies, a matelot, an animal, Orpah, Angadreme, RCMP, carli, Maros, a metic, Lacagnia, Latton, Eva, Harim, a dal, veniremen, Tupelo, Hero, Barre, HSH, Anya, Renan, Nereid, a senna, Ileane, Galena, Bab, Maroc, antennae, a recall, a ward, Nazar, a hassock, a raylet, a rank, Emelda, Lanni, Lanny, LFO, a tie, Lenee, Pete, a kerb, a saran, Nessim, a tatter, a grammar, a hanuman, a milliard, an amie, lustra, Harts, Banaras, Suharto, Ipsus, a tepal, Angi, Sarge, Raseta, Rape, Sallie, Nod, Erelia, Maritsa, Noma, Lal, a preta, E.H. Moore, Mohamed Mosbah, Antabuse, Jenilee, Barron, Karelian, an amino, Inuit, a namma, Andee, Madelon, a nymph, Barr, a barolo, Carl, Danila, Anyah, Serra, Bart, Nina Amenta, Ertha, Laina, Delos, Revere, Taran, a mire, Caryl, lenes, Lenard, Isabel, Garamas, a nye, Renado, a tress, Alcatraz, Omaha, Dannie, Lorca, Natika, Anh, a decremeter, Gelasias, ANC, a dirtfarmer, a tamara, Matteo, Parl, Gbari, Augeas, Sofer, a psalm, a senor, Tangier, an amtrac, Avo, Donall, a danny, LGk, a ratepayer, a tarata, Ergane, Mannos, a manioc, an amt, an anaemia, a tart, Salli, BEP, INS, an amuck, a repeller, Oleta, Roi, Lemar, ASM, Isadore, Asben, Arctic, Ernesto, Carrew, a taro, Serg, Ian, a carom, alcaides, Amado, a letter, a gramme, Lassie, a tar, Carrie Dobro, Tang, ERP, Minamoto, a samaj, a kerf, a kermes, a carob, a target, an ego, Mohamed, Aidan, a mir, Rebecca, Nath, Gilberte, Milli, Marabel, a tale, Matta, Geno, Tarah, Cassino, Illimani, a tpm, ARCS, a madame, lanugos, a madre, Tarcy So, a tal, a barat, an anima, Jenica, a tail, Icel, a decree, Petal, Parke, Bubalo, Soren, a coly, Marola, Vania, Massine, Delp, a manage, a meteor, Genna, Idel, an acetyl, carri, MeV, a decl, Udell, Eidson, a colitis, Opa-Locka, a pseud, Aletta, LPS, a macaroni, Artesia, Micaela, colascioni, a tremor, Carbo, Cary, Sally, Sall, a barabara, Teruel, Ossetia, Lepsius, Timi, Ruysdael, a sopor, Parhe, Lansberg, Italic, a taille, Wester, Ava, Laresa, Elaine, Jenifer, a fracas, a macro, Tait, Neto, Pan-African, Gigi Fu, Sert, Neckar, a naker, Afra, Wareing, a baraza, a tabla, nates, an airbill, a hero, Mac, Yser, a flew, an airt, Seal, a paravane, MATS, an aide, Marozas, a manner, Kellie, Broca, a taka, Renelle, a taker, a fanon, amlacra, Marou, qasidas, a pretrace, a tempo, Harte, Peta, Rip, an aide-mmoire, Bassett, Elli, a pretorian, Odab, a r-color, a tat, a yard, nattoria, Homans, Marozik, a saw, Aker, a tanna, Murtha, Laks, a heres, Semela, Carya, Tarazi, Saladin, Argyres, a malaria, Peralta, Zama, Lakeview, an anime, a harem, an animator, Ibada, Erdah, a repp, O'Callaghan, non-Muslims, a mitra, a tag, an anim, a gaseity, Ad Rock, a rissole, a tilery, a sense, Medawar, an aiglet, Silas, a miracidium, Rai, Deluc, a manness, a mib, a carrom, a carrus, a naive, USSCt, a tass, a cariama, a tassel, an acetone, carpalia, TBO, Barbe, Helbona, MMetE, Locrus, Salas, Ananias, Uhde, a belay, a tapa, Zeno, Tyra, Barb, Ansonia, Marga, a naif, Fasano, Ilan, Amida, Fred, Arapahos, an anna, Helbonnah, a rah-rah, Caz, a taw, a yelp, Pan-Arab, a belt, Sacrobosco, Damalus, Nina Brosh, a regale, a tannin, an ann, a kiva, Renell, an arteriole, Attu, Genni, Vedette, Luo, genua, Ebsen, a site, a craps, a mudslinger, autota, Serb, a ferula, a tad, a tay, a kola, Lait, a pretor, a gastronome, a herem, an art, a muser, a daren't, Rap, an arena, Mee, Zenas, Orel, an anion, a gasogene, Mayas, a muesli, a two, Carmena, Mehalek, a tav, a feria, LCL, a sop, Sid, an arcanum, a telesis, Ada, Veda, a tela, a tell, Emera, Dli, Kellia, Coralye, Welty, Lenca, Natta, Margit, a telfer, a dec, an aneroid, a lutanist, a kellet, a cor, Bard, Mocha, Laennec, a raster, Ajani, Alta, Carpaccio, a silesia, Mycah, a rath, Pahari, Massinissa, a metropolis, an arcs, an arroyo, Bel, Bat, Salahi, a saker, a gasp, a lealty, Oberg, Elara, Mada, Lvos, Salangi, Sneed, an alp, Senatobia, Rihana, Tezel, a serai, a snob, a narrater, Emmi, Wsan, Amiens, Amy, Auge, Acis, Even, a caribe, Delcina, Salazar, a loma, a tergum, Manno, ILP, a tercet, a red, Omagh, Carhart, Arakawa, Ley, Barye, TSF, Argyrol, a temper, Panini, lames, ACW, Olli, Pani, ATP, a carrot, an arak, Nassi, a negator, taros, Selassie, Genl, Imamite, a cur, Revell, ECU, Lette, Silesia, Marylyn, a tetanic, Irazu, RCP, a camelopard, Carpo, Cassel, Tamarah, a zero, Matt, a manus, a jane, a cardamom, an arbor, a maturer, Apsaras, Suhail, a rodeo, Hattie, Woking, Estell, a sarape, Hart, Cassatt, a rall, a belga, a teel, Fresnel, Faraday, Adara, Faria, Passover, a vil, Genk, Cornelle, a tee, Mlar, a lokacara, Margi, Menado, Owades, Ulla, Carpet, a recap, a carp, an annal, freemen, an arm, Isac, a carn, Emad, a rajas, a manual, a sis, an argal, a sruti, Artaud, Nihi, Ario, Marykay, a papain, Alansen, a metro, Farika, Fari, Alb, Cirenaica, Petty, Farra, Pass, Engel, Garifalia, Salema, Cassilda, Erse, Maje, a dirt, a pueblo, Carn, Omak, Arkie, Sinaloa, Petras, Lederer, Freehold, Orella, Bary, Danaus, a kat, Settera, a teff, a tanh, a carfax, a nuclein, a tef, an aryballus, a tedium, Major, a map, Utah, a darer, a fanegada, Ernest, Ramsey, a carse, a trap, settos, a metre, Benin, a carhop, Seto, Cassil, BAgSc, a kulak, an akee, Lalu, Erek, a trample, Kareem, Reval, Abakan, Amiel, Kelli, arbota, Marys, Saleme, Mary, markkaa, Lagos, Sabatier, Kellen, a gro, NATO, Pasia, Lavena, BSF, Low, a narwhal, a dBa, Heloise, Irvin, a leone, a dipole, Petra Yared, an arvo, Salita, a trawler, RADA, Lao, Karee, Nevada, Ehud, Nuba, a transudate, a din, Carma, Terti, Marko, Nassau, Qatar, a rate, Logi, Raseda, Terpstra, LCD, a remaker, a ked, an allegro, bagnios, Saber, Airy, Marc, Salim, a tremolo, Sylas, Ahlgren, an allopath, Gilford, Naseby, Gari, Algar, Alamanni, Leverett, a paraffin, Ogaden, Ralli, a spot, an al-Lat, a raj, Ugo, a bel, a saros, Secor, Pasiphae, lazarettos, a recon, Ida Lupino, Romanist, Eraste, Nodab, annates, sabalos, a rigatoni, Marks, Iberia, Mark, a carzey, Adall, OHMS, APSA, a treble, a trehalose, a diol, an alidade, a betatron, eila, Nason, a clover, Azalea, Lunn, a cark, a barred, a trope, Adai, Lehrer, Aorangi, Sven, a mesh, Tegea, Lune, Bahai, Satan, a suslik, Serena, Olaf, a nek, an alameda, Cassie, Renee, Keller, Odelet, Serene, PST, a rattener, Emil, a cargo, Gen, a sorb, Mars, FSR, a tryma, LaF, a meller, impis, SOGAT, a rustle, Marv, crania, Mert, a tinning, Ilario, Manolo, Cassirer, EHFA, Argyra, a tiller, Alameda, Clava, Cassi, a beta, Rima, Nast, a garage, Pasay, a sibyl, a denim, a till, a roc, an alarm, Benet, Erasure, Mihe, a mallee, a mall, Ezekiel, a gash, Tomsk, a senhor, Freeport, sacela, Matadi, a myriad, an ala, Daniala, Atila, a tilth, Gila, a tirade, a mela, Massimo, Olen, a sitar, a laser, Aosta, Cuyab, a sacaton, Eug, UHF, a lipase, Irl, a virelay, Ruelle, Wes, Sufu, Rennold, Arno, Cannae, Sorel, a grey, Alps, Idas, a rec, Onida, Lajoie, camerae, Bene, Legree, Salida, Freer, Gera, EKG, a bema, Garrek, a tire, Geri Halliwell, ECA, Nasho, Benni, Welcy, Cage, Manoah, Camellia, Farro, Cassy, Basseterre, IPA, Laredo, Cass, Eng, Nilla, Garrik, Salomo, Smoke, Amaral, Cann, a sushi, a damsel, a tarok, an alpaca, Leakey, a heriot, Civia, Hopeh, Catalan, Reviel, LaMee, Lareine, Dania, Morel, a tanner, Rawdin, a massivity, Oveta, Ragen, a varec, a ratio, Cadal, a sari, atlases, a barit, Sill, an alcayde, Merari, a fanega, Hynes, a canna, Hojo, Alabama, a label, a rabal, OAPC, a sard, Freeborn, Egadi, a mrem, an alkalimeter, Ossa, Marci, Mano, Iraqi, LaRue, a tiro, Manama, an enc, Orpha, Leela, Leaf, a recce, Lett, Ellerey, Alpert, Nec, an algarroba, a tirl, Atrahasis, a tor, Pasto, O'Reilly, a gremial, Casey, a kelleg, Nashe, Dray, a dotage, Petula, Salop, a time-lag, Nitro, Petua, Pelagias, an alga, Rasure, Mohammedan, EAM, an alba, Free, Shama, a titi, Veneti, LeMay, a pele, a mock, a selenide, a mucro, Tamer, Casie, Rask, a liter, Evette, Lucas, a relater, Eve, Lars, Geri, Albert, Neveda, Cranaus, a yelk, Carcas, Arella, a titter, EbS, a remark, Cuban, a myall, a tip, a canoe, an anniv, a tit, Ramsay, Alper, Evemerus, tamaraos, an alfalfa, Nelides, an alfa, Lea, Kimmi, an etalon, a tub, an acceder, Egide, Casi, Ansermet, Salot, an annotator, Telloh, Cindie, Reno, Harp, Endora, Dot, Nee, Leonardi, Setbal, Abba, Casatus, Aretta, Helot, Saida, a tiderip, a tariff, a kelebe, Dnieper, Ops, Aida, a tidemark, a sister, Rabaul, a bani, Kelis, Sima, a tid, an acc, a lamed, an ergate, Soma, Seidule, a mycetoma, a ticker, Edea, Lug, Illene, a kelep, a sales, self-ironies, a darg, a denial, a tic, a tremie, Helga, Ebro, Past, a fane, meinies, Orelia, Marge, llanos, a melodrama, Gniezno, bassi, Manassas, a tiki, Nels, a better, Alcaids, a reset, a reticule, a glade, Reina, Lema, Leucas, Rabin, a lie, Leto, Canicula, Leibniz, a bettor, a gas, Aramaic, Cotterell, Osage, Karoly, a time, Gerome, Kalbli, Asp, Otero, Farr, a tsk, a sinew, a grebe, Wales, a raker, Opal, a timer, an acarus, Nama, Lemnos, APA, Idaea, Llud, Emery, a fere, Moham, a retake, Helgeson, Kwa, Harv, Seiden, Amye, Gobat, a rumen, Akane Kanazawa, Lassus, Ratha, Lela, Lee, Neri, Alg, an attach, a ransom, a serif, a sera, Ohm, Arman, Amy Smart, Rebel, a ratal, Paske, Erbes, a lord, YHA, a tizzy, Bennu, Den, Erinna, Millar, EMU, Nash, Tamaru, a son, a titania, Modoc, an attar, a tonette, Soraya, Wat, a kelek, a tolan, Amur, Teno, BEd, Albanese, Elea, Reo, Marutani, a retaker, Omsk, a rataplan, Erda, NASD, a nanny, Lessing, Absa, Garm, Octave, a glebe, a gal, Petulah, Tarim, Azeria, Seibold, Orem, Adamsun, Amri, an angiocarp, Udela, G. de Leve, Lash, Taber, Olimbos, an att, Argyll, an anuran, a msl, Edrei, Lebanese, Nidia, Hbert, Itasca, a sin, OSA, Jenei, Danita, Salto, Rasht, a malkin, a luffa, Aharon, impalas, a ravel, Arblay, a ferv, a herd, a parol, Lepp, an anus, a native, Leslee, a girth, a razer, Olav, a last-minute, SDA, Warram, Dacey, Alkmaar, Pas, a ratoon, salts, a top, a salep, a melos, Eiffel, a canary, Patras, Names, Alberoni, Sleep, a canella, a tomato, Aoki, Ronnie, Suh, a tog, Ober, Old, Rowan, Amp, MUP, an ataraxia, Pudsey, an agal, an agamete, Magas, a rice, glassmen, Akela, Atoka, Del, a hwyl, a gaffer, an agama, Alas, an agility, Ohio, an ipecac, a token, a kop, Seiber, Odo, Efrem, a rcd, Arlen, OCTU, an ans, Oban, a mtier, a toe, LCF, Atlas, a rut, Lasko, BSME, Gerti, Lilli, Manala, Gert, Rashi, Held, Dara, a tut, Amelita, Lovash, Taos, Ardis, a tun, a denom, a lassie, Reine, Helsie, a giber, Odele, Cordy, Hanan, Nakada, Mayhew, Orcadian, a tumor, allodia, Suk, Ohl, a tot, an age, noddi, a salade, Manawyddan, Amtorg, a betel, Caniff, a waste, PPI, Tenney, a canner, Benn, a pariah, ESRO, Hanafee, Lila, Gassendi, Canada, Eliga, Levania, Marven, Egin, a lunes, Sejm, Arvada, Elayne, Goss, Idaho, Tetu, Arras, Atul, Avaria, Freida, Lady, a dye, Hanni, Lesya, Helse, Weld, Dawn, AMT, an assentor, rags, arrobas, a herb, Massie, LPG, a rasure, Dubrovnik, an acad, Arvy, Gannon, Aramean, Neper, OCD, Rahab, Arnelle, Bal, Lima, Canova, Seif, FET, Sean, Lunetta, Pet, a renege, Danika, Laski, Lefton, Karol, Yates, a herp, Map, a nagor, CST, a rue, Seabee, Lil, a grex, a wash, turtles, Sevan, Ambur, Gerda, Casavant, Sikata, Molli, Papen, a wasp, a canula, Freia, Marve, Nigel, a parrakeet, a kelt, Sarah Polley, Lesh, Warga, SbE, a gotra, Mah, Tedi, SALT, Bass, Ennis, Arm, Oct, a bai, Danava, Lula, a tug, Ras, Arva, Zena, Maida, Imalda, Elery, Tarsus, Aryn, Ice T, a riv, Elah, a ross, a melee, Perimele, a gunsel, a csc, a manuf, an aeronaut, Namtar, Com, Edrea, Gill, EGO, Adams, a treponema, Rema, Canea, Fano, ironies, OHG, a rpt, Abbasid, Alver, Oceanic, Siple, a letup, Erasme, Edroi, Reisman, a sorrel, a harim, Ida, Lvov, an assai, Marva, a tuy, Savaii, Russel, Ruhl, a colat, a maker, Ong, Isador, Maranh, a henna, elevenses, a rasp, an aedeagus, Tamarra, masses, a rcpt, KKt, a manuka, Leveroni, Lenape, Rif, an aet, Nadeen, Irisa, mukade, Mord, Nasya, Dyal, a turaco, Rea, Narew, a ngaio, an elative, a plaster, Ragg, a tabi, Daniyal, a pie, Lrida, a serum, Attenweiler, otters, Beno, braceros, Debarath, Sissel, Yablon, Gapin, Alma, Herod, a gomerel, Canter, Gerdie, denims, a jass, Erde, Raynor, castelli, Welsh, Warfore, Tarkany, Leonard, Nadabas, Alabamian, Natalie, Baranov, Eddie, Neale, a faradiser, Cant, East, Aesop, a canework, a soken, a wartime, a plucker, EGmc, Castra, Dani, Allayne, Elamite, LCVP, Minako Masumizu, a gager, Obe, Koh, Casta, Evey, a canso, Seaford, Nuri, Adim, an ass, a henry, Beng, a terbia, Bruno, Irbid, Algeria, ZANU, a fanion, OLG, an abohm, a haem, adenoids, a labarum, Ikeda, cans, a ye'se, a bet, Ariz, Ivanna, Mli, USSB, an assam, Attila, Attah, a thematic, ulta, Rus, an abo, Rosanna, MHE, Leilah, a tlo, Valaree, Hanno, Hiss, a lama, Denie, Heron, Salba, Nadab, a hallan, Ambie, Leila, Rolan, a hav, an abele, a pupa, Leda, a tchr, Heros, YMHA, Lienhard, Estel, a par, a liker, Obadias, a rim, a serving, a last, Rapp, a beret, Salbu, Patsis, Sabah, a ros, a menial, an ablator, Episc, Keli, Bomarc, sorgos, Satsuma, a tpd, an emagram, an abba, Rayna, tilak, a hen, a jam, a doit, a mgr, Alia, Benue, Jelena, Meyer, Obel, a barih, a navel, a resister, Rajab, a pret, Alsatia, Wallache, POA, Iliad, a menopause, Nada, Emden, AMLS, a lilac, a passe, Nevil, an assagai, Sab, an assorter, Rik, Salk, Dan Aykroyd, a bonehead, aerobia, Buddie, Bonilla, Denney, a merit, Tanaron, Iago, a dene, Lectra, Caetano, Iden, Airliah, Cimah, a hallah, a remake, Bernarr, A. Blass, Erdda, Nadia, Caspar, Tedra, gobos, Sura, Lebna, MEPA, Tamah, a revamp, CanF, a den, Aili, Leid, a retro, Tamaulipas, a loci, Neron, Leslie, Nero, Mag, a salad, narrows, a rev, Lasley, Addi, Manaus, Samalla, Manila, Takeo Kanade, Hazel, a bedel, Gasser, Tia, Wallas, Rett, a tasse, Neu, Gavan, Amhara, Lech, a rotary, Croce, a butter, Balarama, Rimola, Bme, Cash, Tiff, Irgun, a deli, Boma, Lezlie, Callida, Bobseine, Ewen, Ailene, Libau, an ikebana, taws, a locater, Alcaic, a repeal, LeCroy, a many, Lever, Alemanni, Ramsden, an average, Samal, a manway, an aviary, Calliope, Elsass, Erie, Hanny, Seda, Rina Tajima, Rakia, Biddie, DOP, Macareus, an avatar, Patsy, Cod, Incan, a mho, Benu, an assoc, an avenue, Frei, Lebrun, an akebi, gases, Aoede, Mic, Latif, an ahu, Wels, ilia, BBA, a reamer, Ogawa, leis, a delay, Oralia, Rayne, Ewall, a boko, a grade, Kelci, TUC, Anakim, Arela, Vener, Evania, Borel, a verb, Monagan, Samau, Gerd, Nally, tube-eyes, a baryta, Sama, a tret, Alsace, Sawyere, Ben, Aiden, Axe, Hannus, an ake, Patti, a rein, Nobell, Echemus, a lobe, Avonne, MEP, a trellis, an azote, Nome, Aia, Bertila, a renegade, Anax, a fell, Evalyn, a tahr, an emery, Beria, Zelle, Bamako, Oralie, Kelcy, Canossa, Wesermde, a refit, Orabel, Udele, Baraca, a wart, Samul, an assuror, Alcazar, Marja, Vanier, Evanne, Hegel, a kaross, Essa, Nadine, a proc, Sams, Ines, bistros, Llano, Icaria, Danella, Mitran, karos, Sucre, Patt, Argyle, a refer, Oken, a yds, Allenby, Ortegal, a code, Pater, Bataan, a dero, Leiria, Berio, Callie, Neille, a reebok, a head, Ehrsam, a handler, a reheat, a rip, Samia, Hebrew, a salal, a hallower, Oebalus, a lemma, Rozi, Marji, Herisau, an unassuredness, a luff, a warb, a sallow, Ester, grampuses, a bear, a pit, Lumen, aedegi, a pressie, Herra, Vanna, Mab, Alaska, Ewell, Eulalia, Kela, Esten, a merc, an assured, a sepal, a citadel, Sami, a lca, a rebirth, Gilletta, Basilian, a mGal, Fania, Canotas, Alber, Oyama, Riha, Loralee, Ray Romano, Iva, Nadiya, a reward, Nola, Calli, Codel, Akel, Aepyornis, a heat, a lea, CEA, NMU, Locke, Erasmo, Teddi, Vaden, Aornis, Sade, a zebrass, a cameo, Haney, Ogren, Argonne, Tamiko, a felon, IPY, Addams, a race, Nerine, Mode, Prot, a rap, Ivor, a misaim, an azine, Moe, Yetah, an embacle, a kimmer, Paten, a jalopy, advenae, Berar, Cannock, a labroid, a raga, intros, an embusqu, SAmer, Peri, a terce, Samp, Patnode, Erato, PHS, Adama, rhinaria, Jeno, Basilan, a mgt, a prodder, a zeta, Lipson, a ledger, Danete, Dustin, Samy, Gaspinsula, Kamet, Alpena, Rob, an empennage, Eddina, Economy, Tedd, Ube, a jalap, Makell, Emory, Admete, MSME, Aarau, Ganiats, an emulator, Ganny, Wallensis, Adelle, Bambie, BLA, Herr, Ottillia, Macario, Marfa, I-beam, Mame, Carboni, Roma, Nador, Minnie, Bello, Ivett, Ella, patia, Weser, an akhara, an eloper, Utu, Sassari, Ucayali, a rum, a sally, Dinan, a mwalimu, Saseno, Jal, a mateyness, Argos, Segal, a cassaba, a raki, a rakee, Lianna, MHA, Reiche, Jen, Ilesha, Lillie, Daneen, a jadedness, Naji, a roke, Cartan, Ammann, a meson, IFF, a rason, a psec, angia, Lorollas, Savage, Kelt, Subak, a leben, Illyria, Danene, EMet, a mil, canli, Kemi, Latia, Galligan, an octad, an assuager, Uno, Cath, Gil, Sasebo, a katydid, an emu, loli, Karoo, Mania, Wagner, Rabiah, Gnossus, Ainus, Massey, Eleen, Daven, a noontide, Marwin, a maya, Lorolla, Heti, Hwu, a serf, fisheyes, a passage, Mani, Albany, Lehi, Aldas, a dimer, UCCA, Miru, Patin, Losse, Iris, a ladanum, Dorena, Rist, Nady, Orth, Giraldo, Jere, Miss, a caser, Eimmart, Rabia, Kassel, a dell', Ewe, Jerome, Kaleva, Rayle, a mesolite, Irita, Rodez, an eld, Dirac, a muse, Carthal, a garote, Lacee, Limenia, Waller, Rafe, Kimmel, Sumer, Upali, a stirps, an emmenia, Wedgie, Wesa, a heme, Argovie, cargos, Okayama, a razee, Calama, Latoye, Nadda, Leif, Ferro, Callery, a dele, Difflugia, Kas, an emf, Lowery, Ted Baker, Tami, a romaji, a we'd, Lake, Calpe, mohalim, a hemmer, a mid, Alveta, Noe, NADH, Hanus, Mahalie, Neill, a tree, Basil, a del, Livenza, patios, Assamese, Napa, Jno, NADP, Panagia, Herb, Mohawk, Cataebates, Sabec, a pass, Erkan, a rupee, Loja, Loren, Ilke, catalos, Oeflein, a tantara, H-beam, Megan, a rozener, Rettig, an elbow, an elm, a hem, a lash, Cassite, Manya, Denna, Erbil, a mossie, Herc, an ilex, a kCi, Paton, Sayres, oraria, Vani, Alben, Ilmen, Ironside, Evang, a messan, Ivah, a ronde, Ercilla, Coe, Tamma, Haimes, a vario, Nereen, Daveta, Ngo, cates, summae, basisidia, Rayburn, an oocyte, FAS, an esse, nomina, a jakes, a jade, Mlaga, Amedeo, Reiko, a razor, a fanny, Wesla, Vanni, Wrekin, a brush, Cattell, a bass-bar, a hoy, Ikey, a felt, Tara Reid, Rockie, Reimer, Palau, Tiran, an eyesore, Negros, Netaji, Gery, Erevan, AWB, an enfeebler, Rafaelof, a karoo, Manresa, a baseliner, Uella, Hanratty, Peru, Tabu, Catto, Clawson, a jadder, Amie, Weinek, Camelot, Sayer, Alcina, fatsos, Nolan, an eikon, a remex, Offen, a garg, a beata, Eboh, a parasite, Nevsa, Avery, Gallico, Pales, See, Sedlik, Soracco, Romanizer, Eblis, a basis, AOU, a lip, an erron, an upside, Venola, Mallen, AMEDS, Eddi, a gude, Camarata, Tessie, Neiva, Tessi, Lemmy, Callahan, a yam, a retem, a gage, Manus, Tob, Basutos, a dammar, a mod, Nogales, Nabal, a cen, Estes, Sugar, a mogote, Nevai, Saidel, Livesay, a pun, Anetta, Latt, Albee, Luella, Dunne, PNA, Estevan, an uhlan, NAB, Russom, a romaine, a taste, Donata, Noyes, SEbS, a dart, Nessi, Rock, a loper, Uke, Cadena, Ipoh, a pastel, Laban, Aydin, IRS, a rode, Maller, a ticket, Rufe, Cad, an edifier, UAW, a see, Sayed, a robe, Denn, a grommet, Eridu, Massa, Romanov, Ebba, Aretus, an asemia, Resee, Resor, a rober, Cusanus, Llanelli, Mallet, a rogue, Masera, Emmit, Ignacia, Majlis, Nepalese, Idabel, a canzo, Pero, Mammon, Eva Larue, Caernarfon, Amoreta, Gelasius, a dahlia, Maseru, Lisa Loeb, Urania, Wollis, an eddo, Hassi, Rafat, a moss, a dragsaw, Oceania, Freyah, Tessa, Gabaon, a limes, Sejanus, Obara, Mukden, Rahel, Livy, a beer-up, an edh, Saktas, an egg, a lariat, Salado, Owena, WDC, a mCi, Mallis, Urdar, a massicot, an errata, Kelsi, Lamaist, a pasta, eyes, Silber, dreidels, Narbada, Emmott, Oballa, Dnitz, a potassa, Macapagal, a renegado, Oradea, Sivas, a casual, CVO, Ailey, a grad, a bus, an evocator, Ocnus, Yerga, Longan, Anyang, a det, a gramarye, NAACP, a rover, a cort, an evil, a megapode, Rollin, USTC, apasttra, Myca, a rove, Deny, a press, Eisen, Idona, Molossus, Sissi, Karim, Imp, a cwo, NSA, a rort, a pussy, Adda, lassos, Arie, Cretan, a zest, Napoleon, a psi, Henig, Erne, MSM, Lamus, an epagoge, Soo, Gallia, masais, Amarette, Gallas, Lawson, Imroz, a legato, Leix, a beet, Surt, an epic, Carbrey, a saliva, Cattima, a rimer, Dreeda, Loni, Weinreb, a rig, EHF, a jad, an aparejo, Bell, Iver, Billie, Talladega, Toor, a need, Rabi, a dawn, a cep, an e'en, Rahm, Ahl, Epis, a wkly, rebatos, a neep, a neuk, CMG, a lepton, races, Siusan, Ireton, a diagram, Lakin, Isidore, Tula, locos, Emmy, Sayles, Isaacson, Idalina, FFI, Tecu, a saloop, a rumour, a miter, Dr. Drew, a past, Nahama, a resurgam, a catalpa, Lotti, Osman, Iredell, Ives, Orton, Riplex, Anasazi, Reggi, Frey, a paseo, Dade, cacei, Latrell, Acta, Catt, Alpha, Lim, a ketubah, Sama-Veda, Aruba, NAAFI, a heinie, Henri, Basuto, Lamb, Cini, Alcman, Imray, a waragi, a dakoit, a pash, Conon, Airlia, MSEE, Lnos, a jaga, Lamson, Ivey, a desire, Cati, Batia, Walley, Roche, NYA, Leboff, a resumer, Duax, a ratafia, Tegan, a panatella, Caton, IPBM, a catena, Wein, a ledge, Issiah, tega, Topaze, a beef, a rub, Michael, Ramsdell, Abo, NAA, lobos, a caracole, putamina, Hocker, Reddy, Obeded, a ruse, a casino, Lamond, Orgell, Ivy, Ramey, a blab, mottos, Sitnik, an amanita, Pallas, Dahle, a jager, Gelya, Belg, a noggin, Nehru, a presa, Masan, Rapidan, a hamal, a deadener, Occam, Roch, a robot, a rpm, a slabber, gazelles, Omri, Myron, Ohaus, tubmen, a ruga, Namibia, Kato, Hamadan, Argia, Kahler, Ratib, a rasa, AAF, a rug, Este, nibs, a sable, Ikkela, a ruler, a civ, a newsreel, an eye, Nagasaki, a hallo, CATV, Bastia, WMO, Tees, Sela Ward, an effecter, Geraud, Russi, Keri, a dap, Malanie, HRIP, a he's, Sorce, Ciro, Mallon, Egham, Danni, Weir, Alcis, Ainu, a felucca, Saylor, a don, Sarkis, sargos, Caelum, Hsiang, Gader, Rumania, Weisler, a dom, a desirer, Bilac, a nebula, Lobo, Lamp, Galla, Callan, Rocray, Gamal, Adaminah, Teresina, CLU, Vasileior, Elsey, Esta, Calla, Callao, Danna, Mzi, Ewald, Omora, Karie, Kariba, Sedgemoor, Bely, a graver, Teillo, a rule, Cirri, Baker, Billi, a redan, a cultivar, Perret, Nannie, Henn, Austral, Liam Neeson, a ganger, Gel, Liva, Seely, a keno, BPI, Hasek, Oys, a snake, Cindi, a qasida, Artus, a make-work, Apl, a karakul, a yeti, a megabit, Argive, Lecia, Say, a waka, Osaka, a zila, a treillage, Eros, Nessa, Mast, tempi, Hasidim, Ardussi, Ald, Ronni, a pas, a pataca, Ido, Zasuwa, Arv, a megawatt, Alkoran, Negro, Tagalog, Nomi, Amii, Reneta, Bette, sordini, Mohave, Rika, LaBaw, Assam, a lab, Masury, Cally, a lad, Gama, Loise, Itnez, a poker, pudda, Arne, Okemah, Argus, Tubb, a cast, Tevis, Apoc, Seel, a rake-off, a qat, a hallucinosis, Sakta, Obelia, Neo, Tallulah, a rope, Calif, Luwana, Lydell, Irv, an inner, an illogic, Cassini, a meal, Lubet, a guff, Fowler, Hebron, Duster, Oba, Tallula, Loella, a panel, AFT, Sewel, Liv, a nudie, Mall, a psyllid, a leu, Massna, Morena, Odel, Liberec, an ilk, Colene, coenla, a grav, a yett, Eliot, an imagery, Pallua, Penn, Aulea, Rog, an imaret, a ganoid, Rocca, Naga, a heder, an ironer, Rodmur, a latino, Yeta, Gierek, a cash, Cufic, Circe, SBA, Loeffler, a doe, Dannel, Getter, Buatti, Minoru, Hengist, a dassie, Gesner, Orelie, Weisbart, Slyke, Cima, Nagel, Derayne, Mekka, Ethan, Iaria, Kile, Pellet, Seed, a lear, Freud, a loca, a long, Ivory, Teilo, Jeromy, Laden, Idun, a cuddle, Ifill, Abby, Ray J, Ramon, a brunet, Sirkin, Imogen, Deb, an irreg, an amalaka, a logogram, a log, Nogas, Adila, Kery, Bastrop, Saidee, Bast, Tavish, Paresh, a rozzer, Omor, eucti, Bahamas, Sereth, Cirilla, Keita, Caliban, a lob, Anissa, Heidi, a memorial, Noelle, a year, Basov, an idolater, gemses, a baby, a water, Issy, a romyko, Pall, an octet, Saito, Bett, Enalda, a vast, Tiffa, a wattage, Ray, a wee, Layard, an idlesse, Nitti, Wallie, Nono, Ibson, IWW, Ask, caballos, a lovely, a desert, Madag, a lugger, Keily, Kari, Bajan, Igerne, MSG, Igenia, Cali, Ladew, Oler, Yim, a slab, a nipa, Alodie, Cida, Ibycus, a loden, Iarbas, Sakti, Basra, Epsilon, a lollapalooza, Aloke, Cioban, Ibo, Cajun, a kennel, Osset, a boiler, Redmer, Teresita, Metsys, an iph, Reahard, Niela, KCMG, Adamina, Hokkaido, Keiko, Ocker, Demetre, Dec, a fino, Beta, Gwennie, Malayalam, Aloha, a litotes, Sibelle, Bea, Malines, Sorocaba, a lit, Seeto, Obau, a lues, a basic, a beep, an unavidness, Nelsen, Aerol, Yann, ACLU, Veno, Richara, Ozen, Iapyx, a lagena, Olsen, Ivie, Tab, a tuft, Adamik, a halavah, Sakais, Susannah, Keir, Ellata, obli, a saloon, Saied, a limacon, a keel, Artha, Lodie, CIO, Vasari, Dasya, Wanamaker, vila, Alic, Odette, Socred, a lati, Bedad, a dilemma, Heidy, Leese, Negress, OGO, Aidos, Calore, Malik Yoba, a lib, Yssel, Amadeo, Hekker, Obed, a life, Dann, a susu, Albamycin, Ibiza, necia, Malik, Iblis, Napoli, Maced, albarelli, Masry, a nurl, Limassol, a nullo, Callum, a lila, Pelles, NOP, a lily, Kei, Lacey, a memo, Sorcim, an ulu, Bezwada, a liza, Tumaco, Callas, Rusell, a desk, a pres, Algonac, Sotho, Danyluk, a beeves, Sokotra, Seem, Missi, Kevan, Kath, Gino, Tallu, Hasid, a revelry, Beall, Obaza, Pell, Imajin, IFC, a lilt, Adv, Ediva, Lomax, a minima, Alix, a trefah, Callot, Allah, Laven, Icarus, Palici, Trevah, Arri, Saiva, RRC, a placage, Tallbott, an anaspid, Nemea, Tivoli, Malena, Jerol, a gnamma, Erdei, Lennon, Nahum, Obadiah, Ally, CSC, a bandit, Oonagh, Nedi, SpEd, an ulema, Loyde, Ernie, vasa, AAAL, a macram, Ledeen, diseurs, a brute, Nissa, BASc, INH, Ceto, Ozalid, Offa, Danl, Omoo, Ramos, Narayan, a jag, a lepidolite, Olpe, crepes, SBLI, a grass, a kame, crabs, Abie, Calva, Pelagi, battels, a he'd, a lst, a ganof, Lahoma, Layamon, IMCO, Dasht-i-Lut, a tilt, a fan, a retally, Rebekah, a lupoma, Heida, a lud, a rash, Jerubbaal, Geof, a nut, a grab, a lactam, Aitken, a diam, a lye, Albi, Heigl, an udal, a redefeat, Settle, MSAM, Alfredo, Hesiod, Laveen, Katinka, Alboin, Nafis, Sulawesi, a legit, Sev, an udder, Domenic, Safar, a dak, Alsip, a task, a waratah, Calakmul, Lock, a meet, Semaleus, a gravel, Lillis, Umeko, Calia, Gab, an uhuru, an elf, Fayanne, Frear, tegmina, Zahavi, Lorens, Segner, Dugan, Elroy, a wrong, a demon, Gallup, Annora, Loy, a panier, Kev, an ogham, Otti, Brut, a seiren, Nuncia, Somalia, Leesburg, Urga, Alva, Keelin, Nejd, a doodah, Alikee, Ltd, Alhambra, battute, Cecilia, M'sieur, a rascal, Lida, Cattegat, Saiff, a demotic, Sadira, bokos, Rocco, Darees, Rafaelle, Byram, a sullen, a jasy, Layne, Knapp, an ascot, Senegal, a seignior, Gallus, Niebuhr, a dah, a surbase, retia, Kiah, a sudd, Adamok, Lewellen, a jabber, a sugar, a silicide, Nebo, Aello, remedied, Olympe, Edva, Seve, a meed, a seif, Fabri, busses, Saloma, a silex, a maremma, Hasan, Rosen, Emili, HBM, a damask, a yad, a silage, Vastah, Talia, Bates, Roddy, Catima, Dett, Erulus, Uruk, a siren, Izy, Teut, Rivalee, Regt, Sadler, Egk, a defeat, Socha, LOOM, a sennet, a sine, Curt, a sennit, seppa, Nagy, Matti, MSEM, Albay, a wye, Kati, bottegas, Bobette, Sumner, Demos, Naraka, Sokoto, Katti, lees, Sennett, a vas, a gapes, Romany, Lesli, a trey, a meekness, Ortiz, a prelim, a serpigo, Layla, Dmitri, Depew, obis, sugis, Sileas, Ruben, Ixelles, Sikes, Romaine, Guesde, Elsan, EDC, a situs, USNA, Mia, Camel, Somni, a psalmist, a watt, a wag, Igal, a rocker, Uzia, Kolomna, MSD, Nalda, Maloy, a fetter, Olson, Exod, an ameba, camisados, a sem, a jabiru, Adamo, Denise, lassoed, Ortles, Eogene, Coeus, Nakuru, a bee-eater, a grama, Lozano, Medeah, Cami, an elk, catalufa, Lugar, a daze, Curcio, Hesione, MSA, Geo, Hesse, TVA, Lugones, IMF, Fogel, Lido, a siege, Cuda, a sienna, MSL, IOF, a secular, a mama, Keelia, Bathulda, Hejaz, a halo, Rita Wilson, Idette, Susan, Nairobi, Rajiv, a necro, Fasto, Obote, Pali, a bee, Romalda, Hijaz, a gallet, Tilla, a venin, a jab, a basti, Remsen, Eth, a lust, Tips, a guddle, Iyar, a dived, a poll, a galleon, a sippet, SAA, Lukas, a guy, a catty, Ladino, Cardea, Troas, a gnu, Demo, Sonoma, a sorner, Glass, Eirene, Coimbra, Galati, Picco, Naomi, Aigneis, Alba, Tanya, Redon, Catania, Pedi, Manasseh, a soma, Ladoga, a solemnizer, Beal, Unni, Pedro, Cerell, DMSO, a cachou, Hett, Evyn, a rubasse, Nizam, a sett, Eliott, Augusta, Bia, Zadoc, a seta, Geanine, Seys, a kart, a sleet, a glia, Talien, Cmon, IUD, Laddy, Orsino, Daron, Yahata, Medea, Tadashi, Eward, Nut, a seton, a slut, a syntax, a set-off, a radiov, a sexiness, opai, a pagan, a rime, Cudlip, Ensoll, Echo, Camoens, a kalema, Hudnut, Saki, Leclair, a sego, Millais, a seeress, Ogg, a halibut, CWA, Tay, Nusku, an asb, a besom, a smokeho, Cammi, Reede, Eddas, Sabadell, Utta, OBulg, Naoma, Stephan, Munafo, Oisin, a jato, Janek, a watap, Sabin, Sabbath, a dilly, Redroe, Leeth, Saval, a cicada, Lopes, Ronny Cox, ennia, Brunelle, Sorci, Amorete, MSBA, Till, Emile, Malo, Cindee, Sabba, Bede, Pirri, cameos, a komatik, a supp, a panic, Ramiah, Tevet, Seow, a subsmile, Dillie, Vasta, Olive, Demy, a fete, MBA, Tiler, a dks, Uniat, Sochor, Geerts, a kudos, Morten, Elly, Camm, Amari, NSC, ramta, Ogpu, a jasey, Esd, Ribal, a hamaul, a prelabel, Bassano, Jeri, Fasta, Orgel, Baco, Vasti, Babel, Bactra, Cogan, ariki, a fetor, a suborner, Hamal, a far, a dkm, a damp, Fats Domino, reges, remains, a rape, Cupavo, Kval, Sango, Lobel, bags, a kraft, Silone, Alecto, Pto, Haslam, Asgard, Eddra, Haller, Rafa, Tilford, Isidor, Mensa, Mady, Ruella, Fatah, Cibis, Sorkin, Zinn, Ayo, Jerad, Rebah, a dekagram, a sub, Allys, a sfm, a demo, Toy, Mattah, Beeson, a haggard, a sully, HETP, a heeltap, a half-note, Vasos, a revel, Bambi, Raamses, Sabra, Devol, a direx, a mewl, a dirigo, Seoul, Eureka, Lalage, Raddatz, a kVA, Kid, Alves, RuPaul, Ultun, Cairo, a diva, Deva, Erny, rammi, a heed, Nary, a wailer, a sura, Gemara, Madel, BAM, a taler, Remy, a radio, Reeve, Lali, Avalon, Oval, Falla, Frau, Oboe, Macegan, Nidorf, a surplice, Caird, a hegari, Matejka, Berna, Mya, Lalo, a galliwasp, Atalee, Keele, Kalb, a divot, Siegel, Baul, a vagus, a dive, Colp, a surge, Cydippe, Pega, Tracay, a romp, a patella, Bath, Guanabara, Zomba, Hallagan, a hack, a deme, Caravaggio, Dever, Batruk, a div, Udaipur, Camus, Raddi, Keen, Nobel, Bax, Atalayah, Katt, a wail, a tango, Dari, Kuban, a hocket, Orissa, Melessa, Toru, Essy, Mewar, a moke, CBEL, Bap, a pate, Krips, a surg, Aeolia, Venu, Talos, Tejo, Tarawa, Key, UNIDO, Roberts, Aledo, Tav, Olin, New, Geer, a zap, a surd, a dibbuk, Susah, Cilix, a mew, Opelt, Tapaj, a resp, a lath, Ceb, a demy, Nagari, Hallam, Saul, USES, Runkel, a manroot, a baragnosis, Somme, Logan, a trapes, Ilione, Romains, Oby, a rock-eel, a sucrose, Illawarra, Madero, Mill, Ocko, OCDM, Salomi, Palm, Camp, Walli, Broz, a radial, Pals, Beeb, Ash, Tebet, a damfool, a fol, a groom, a kcal, Batum, a lampoon, Sausa, Yeisk, Cocke, Elgar, a bec, a fast, Topeka, RAdm, Devy, Galen, Ratisbon, Exc, a fatso, Pegu, a gallop, a demob, a lampad, Malca, Venn, AeE, Lello, yaws, a vidette, Ningal, Saud, Balla, Gaddi, a zed, a half, Eradis, padrones, Ilya, Laurel, a hewer, Caines, Semele, Signac, an omega, Laure, Messiah, Glynnis, Seth, a dagga, a delft, Sampo, Talya, Lenapes, Bee Gees, Sikh, a duo, Hallie, Matty, Darra, Edd, a path, Cilla, a waiter, Cullie, Froma, Maidy, Lely, a keen, Olia, Gahl, a roller, Evans, Susa, Tirolese, Nava, Jesse James, Ozmo, Darrell, an acacia, Lauri, Bahr, a biz, Nazler, Ocilla, Verona, Eleanor, Tammi, a massasauga, Katz, siloing, a bast, Olnee, Lauro, Bever, Overton, Eos, Avron, a titanate, Bittner, an areca, Matlock, a begar, Umea, bemata, POW, Mott, Sawyer, Roth, a mime, Jessi, Tammy, Malaya, Galway, a summa, Wall, Aggi, Reeva, a derby, Artima, Ratlam, a sumo, Cainite, Tanga, Mallory, a palais, UMT, Sakmar, Gorga, a dentil, psis, IADB, a dayan, Romeu, Gordan, a tittle, Cayla, Engud, a suite, Maisel, a gemmule, HJS, Aidin, Nepali, a demur, Bali, a fath, Sayette, Nippur, Ysabel, a keepsake, Bevash, a marbles, Sokil, a riprap, Sage, Tada, Navarro, Damal, a kalifate, Rolf, a suitor, Geez, a suit, Angil, a make, Tabor, Padriac, a sugi, Bores, Ialysus, a def, Luba, a dey, a manrope, Padegs, Aiken, Elrod, Apgar, Abruzzi, Lesly, Bissell, Artie, Weill, a venery, Padua, Balbo, Dallan, Raddy, Samoa, Halima, Jeane, Macey, a keep, Paramus, Kania, Bev, an etna, Naor, Eudora, Vlada, Ocie, Gresham, Uda, Tiu, Quar, PaD, a hom, Laue, Fayth, Gilbye, Ladin, Nedrud, a davit, a sordino, Elspet, Sami Zaiddan, a townee, Leven, Atli, Hedin, Sauk, a trad, Nipha, Luebke, Emily, Hedie, Weil, Ataliah, Pegg, Elsy, a salol, Liam, a daddy, Hali, a kali, Rycca, Rwy, Alcor, Ravenna, Edmee, Lashar, Rafi, a wake, Tayib, a satsuma, a dog-ear, BMus, AISI, a culture, Emie, fomites, Orono, Izard, Dennis, Inez, a halma, Cayuga, Trabue, Siva, Tresa, Cailean, Nairn, a supremo, Cadiz, a relic, Rambow, Safier, a sugh, a murk, Neva, Emlen, Orsini, Leal, Espy, Caia, Maisie, Tonye, Kassa, Keegan, a sillabub, a dot, a mense, I-spy, Gebler, a hdkf, Jelle, Byam, a dos-, a suet, Noella, a jay, a lect, serais, Ozkum, Raynell, Acmon, Rude, Tori, Perugino, Ripon, Obbard, a suede, Maiga, Hedi, Malin, a flu, Safi, a wanigan, Raji, AUA, Kesia, Raetic, Sibel, Pam, a cask, Comines, Olcott, Alfred, Albinoni, Ladonna, Mren, a sing, a hardy, a fen, Elreath, Cush, a tph, a pizaine, Dragon, Okla, Roma Maffia, Kasey, Bega, lepta, Kazan, a sika, a duro, kokos, Eisele, Kediri, Maiah, Kask, Costello, Capon, Kalila, Kemme, Fay, Aldan, a snow, Adur, Tekla, Weixel, a dub, rabbis, a sudor, a psocid, a mart, tumli, Elka, Orff, USRC, Cadel, a velum, a sukkah, Clo, Keyek, Cuba, a dual, a dragonet, Saxony, a caramba, Bekah, Acima, Trubow, Capp, an arc, Geb, an import, Sax, Alagez, a latah, Gal, a pipa, Adlee, Torbart, Natalya, Gardy, Hamamatsu, a copy, Hama, STOL, Faires, Yakima, Kali, Miami, Rudd, Islam, an arg, Madid, a lamina, yadim, a lebes, Urd, a dBm, alamos, Perr, udos, Lacy, Capua, a sinecure, WMC, a vapor, Dallon, Kallikak, a well, API, Verada, Epirus, a flake, Tobe, Raeburn, a gaddi, Rajkot, Rabbi, Raffin, Savadove, Jarash, a clamp, a pine, Gayleen, a maypop, a sinnet, a sinh, padres, Saw, Deniker, Gard, Doi, Riley, a jak, a sulk, a vols, a mag, a siree, Tove, Raff, a harikari, Rye, Naval, Sonora, Yesima, a maksoorah, Saturday, a basalt, an alec, Naxos, a sixain, Novara, Babette, Nibbs, Satie, Hrolf, a mort, Sava, LST, Seton, Gio, Madlen, amoles, UDC, a jawp, a modiste, Elfreda, famuli, Hamid, a veld, Diredawa, a miso, Zel, Bissau, lappilli, Faur, Biddle, Frog, Naboth, Supen, Eysk, a jowl, a pennon, Nadabb, Ullund, a category, a catnip, a sig, Ellett, Igorot, a satai, Lopez, albinos, SACEUR, Pepin, Keyte, Tova, a mimic, Slovenia, Ledda, Inigo, RDX, a satrap, a sailer, a psf, Foy, a paleontol, Paule, Idonna, Kohima, Trst, Septuagesima, Cape, Evatt, a bania, Gayelord, Algona, Clovah, Aviva, a miff, Farl, Laws, a jornada, Bayamo, Otto, Capt, Madden, a muddle, Vte, Irma, gayals, INRI, a call-up, Reeba, a mud, a sav, Ilokano, Morette, Nimrud, Nabis, USHA, Tizes, nidudi, Kneller, Rajput, Sudan, a gaffe, Ilyssa, Jed, a toll, a batter, Rabkin, Ulita, Maleki, Maddi, Legra, Malory, Teodora, Zales, a jazz, a taluk, Melany, cava, LACW, Behar, BEM, a halm, Dev, a haslock, Ajo, Rafer, Paul, Uziel, Dalenna, Jemy, a jaap, a keef, a sage, Dobro, Tavi, Titania, Gerard, disli, Greville, Rotorua, Macapa, a sago, Tarrah, Saktism, a palea, Nahtanha, Hebel, BiblHeb, a muon, a coma, Cap'n, Gary, KKK, a yak, a soliped, a trav, Nissy, Laos, Deery, Tally, Bish, Avrom, a fate, Backs, a mast, Siloa, Ostraw, Sappho, Jem, a gallon, Kegan, Maluku, Maddy, Legnica, DNB, a boa, Bayly, Leff, Ajax, a mary, Socorro, Mayence, Bezaleel, a hake, Turkey, bedemen, Mayan, Lovel, BOSS, Aymara, BTh, a vlei, Lombok, a jetted, a calabazilla, Rolfe, Lorry, Pau, a drone, Lou, Cavan, a gorget, a batta, Garber, Eckel, Sisile, Drago, Hamel, CAVU, Caves, Pocatello, Madge, Loz, an alamo, Caaba, a keek, Rudy, a battik, Rubel, Bodrogi, a coca, Idolla, Veta, Yasmine, Lowes, a circ, Augie, Lolly, Remde, Idden, a goby, a broth, a fool, a solo, Bolen, Okun, Robenia, Rollet, Timor, Ruth, a jib, a solv, a citral, Lipski, Leesa, Eph, Carissa, Tojo, titis, UNESCO, DMS, Aenea, a civet, a bile, Cabal, FAA, Toni, Laird, Naldo, Papua, Yami, Losey, Botti, Beyo, Reef, Foch, Calisa, Vidal, a dept, FOS, a sorites, Lupe, Ravel, Sikko, Okazaki, Lilla, Roer, Pape, Papp, Ansel, Bram, a crone, Macc, a lamppost, Simois, Orsola, Heda, Ern, a gob, a sori, Garbe, DEd, ADC, Magnien, oodles, Rugen, Neibart, Redleg, a maize, Nevin, Nolly, Retha, Kalahari, Jehol, a gramps, a wallet, Safavid, Volpe, LOA, Hamrah, a sorgo, Tibold, Alvarado, Daveda, Birt, a song, an alias, nuts, a sodomy, a hailer, Eck, a zakah, Sadirah, Cav, a billet, tipis, Rusel, a kibe, Limnaea, Portageville, Riff, Ezek, Ardelle, Nova, Reba, Bayer, Radha, Vonnie, Katayev, a crape, Luigino, Subway, a soot, a pawnage, Vasya, Wanonah, Stelu, Pacien, Urbanna, Islaen, a crepe, Lyris, Kall, a wallah, Sansen, Novello, Mayag, a crum, an aloe, Gaya, Rules, Lud, a sook, Nathan, Billen, Hedy, a bevel, Cacia, Majka, Oneida, Esth, Gilly, Radke, libretti, Steel, Gath, Sergo, Cabot, Moyna, Mrike, Suomi, LSM, a frock, a zimarra, Home, Siward, Raviv, a cup, a soom, a jet, Toledo, PSC, Iny, Cave, Ruyle, Seidel, Braga, Accad, a cnida, Gati, Ravi, Varese, Orsay, Garbo, Dayan, Lozar, a reverend, a key, Baalim, a kevel, Kehr, Alcott, a lpW, a hask, Cotswold, Ulm, a yeo, Reames, Word, a soil, Osmo, Hege, Iloilo, Faggi, BAA, TTY, Hrvatska, Odey, Block, a zebra, Baganda, pagnes, Bebel, PaG, a faller, Robena, Ossy, a hamlet, Seward, Riedel, Bur, a soiree, Brey, Emyle, Cicero, MTI, Debor, Pacifica, POD, Nisen, Epner, Bebe, Heep, Ulda, Garv, a grocery, a hasp, Pack, Calapan, Kalevala, Indio, Bol, Gaelic, Ody, a habu, Royette, Nansen, Nerin, Nobe, Sobel, Bekki, Luk, Ailin, a gin, Alfy, a fairy, Galer, Pepi, Paco, Ruddy, Keb, a behavior, Labe, Hebbe, Ravo, Rikki, Lupita, Mokha, Onega, SBIC, rectos, BEF, Asami Kanno, BEW, Eolic, Ludd, a fame, Lyall, a pallet, Nampa, Bagger, Gaige, a sou, Debi, Gaia, Raul, UNEF, Felic, Nancee, a cps, a cfs, senti, Wade, Mahadeva, Talyah, Star, Badoglio, Fabi, Battat, Sammy, pepla, Debs, Itys, sensa, Itagaki, Reniti, Neel, a mascot, Noby, a fuddle, Gabor, Badb, an alb, BAcc, Cauca, Valenta, Cuyp, a walla, MSSc, Idea, POGO, Laval, Cavit, a biri, Katlaps, Seigel, CIC, Safavi, Zeiler, Olnek, Cassell, OFlem, a jen, Novia, Inoue, Janeva, hamli, Fabe, Dayak, a cgs, Sorcha, Ofori, Hey, Dasht-i-Kavir, Paki, Regazzi, Pavo, Sark, Endor, Barbi, Lazar, Barbur, Bul, Edme, SbW, a papacy, Neo-Ju, a hammal, Falkner, bans, Banff, a jeer, game laws, Asoka, a hod, a hirer, Akh, Salaidh, Amalea, Jeff, Uranie, Paza, Iddo, Gibbon, Kaylil, a bun, IDP, a vodka, Oslo, Hardy, Harz, Escudero, Tatius, Gates, Erinn, auloi, Cullen, Urban, North, Camey, Cathar, Romo, Gamma, Gabo, a rarebit, a buhr, a jake, Soho, Troth, Cabral, Demakis, a jollity, a kotwal, Fawn, Nadya, Magner, a soke, Swat, a soja, Ind, Norrie, Waals, Etti, Riki, livres, Signy, Reseda, Hallel, Evy, a pallor, Reeda, Jehu, Latini, Vetter, Odom, Iams, Dan Mason, Yerkes, Epps, Esc, Stagg, Elliot, a soy, Alloa, Isus, Sofko, Baily, Xenia, Ralf, Fargo, Togo, Tupi, Luns, Sodom, OPEC, a facet, Lothar, Rumsey, Ortrud, Labuan, Hukill, Empson, Kaya, Jeuz, a keV, a calix, a natter, Rudin, Niven, Robi, Alcuin, a bod, cauli, a keblah, a bog, a dato, Crabbe, Waikiki, Luz, a lamb, CTC, Irene Wan, a gid, a maco, dues, Sokul, opuses, Surrey, a staw, Staw, Tatum, a galet, IGY, Ticino, Tadeo, a bozo, T-men, Robson, a limen, Rob Nash, Colombi, Babi, BDSA, Iain, Lyssa, Baraboo, Babur, a stool, Cressi, Vikki, Nadja, Wed, a fact, Gabbi, Gabe, Ezzo, rms, Supt, Surtsey, Weelkes, Yvor, Berosus, Seneca, Gabel, Babson, a like, SWA, Hammel, Karb, Mike Garey, a ladder, a stum, Strabo, Hals, Urfa, Illampu, Paxon, Kaine, Draco, Valry, Baird, a stg, a bezel, Tri, Kamin, Yap, a scf, a snivel, a bish, Pahlavi, Veradi, magi, a talc, Ceres, Sumo, TQ, a snap, Stoll, a batik, a billy, Daisy, a lamp, a yatter, Evered, a wadi, Laforge, Nika, a bidet, Tobago, Gambi, Baiel, Esk, Codd, a magnum, a snell, AMSW, a palpi, Dagny, Badajoz, a grig, a jole, USMC, Baber, Azariah, Tolima, Estren, Ierna, MTh, Gilder, dogs, S.S. Ravi, lobi, Romeo, Fedin, Urba, Izawa, Kuyp, a jot, a bur, a snug, a spore, Maya, Haiti, Telegu, a habbub, a blague, Jez, a masc, MFS, Eliphaz, Riti, Rollo, Cinda, wakas, siloed, Datnow, Kain, a mono, Mayor, lignes, Levey, Taegu, Urey, Datuk, a yawp, Urial, Favrot, Surinam, Harberd, Niall, Edsel, LIFO, Colan, a lobolo, BAU, a haver, Bazar, Gabi, a rapport, Tobey, Pax, a taig, a nazir, a yob, a spoor, Tarapoto, ICSH, Colby, Trask, Casady, Laith, Savill, Eudo, Cock, Campy, Taima, Jebb, a spool, Makkah, creda, Zuleika, Jeb, a gummy, Kado, Port, Sagitta, Hagi, Rosy, a sapor, Pablo, Kayla, Taimi, Ardeth, Colpoda, Rodd, Rayner, weeds, Ednie, Froh, a speer, Creel, Faxon, Nelan, Nolte, Bazil, Esdud, Abbi, Jania, Janina, Iggy, Taka, Pogany, Weed, Nudd, Rawden, Alodee, AAAA, a spy, Hayne, Edny, Borneo, Cleo, Janna, Igbo, Baxy, rectums, a sloop, Abdel, Trutko, Wake, madres, Iey, Tromp, Marc Alaimo, Ciri, Rodin, UMW, a came, Domagk, Paff, a datum, a sld, Abnaki, Pytho, Jann, Asosan, Olvan, a darby, Trocki, Reedy, Hakim, a padauk, Rutledge, Nork, a syllabub, ASW, a jog, a ragi, Waki, Ruy, a pct, Sudanic, Neses, Simms, Stover, Pepe, Takeo, Davey, Erund, Robet, Toyama, Mayo, Koy, a graze, Neruda, MIP, a guyot, a pawner, Peel, a sorbol, Gaw, a galoot, a regina, Mylo, Kahn, a glove, Nupe, NYP, a goi, Kagi, MSGM, Palos, Rusk, cubti, Roselani, Frum, Gaea, Isth, Gittle, Creek, a facsim, a reglet, Sully, Bisk, Columba, Wace, Fax, a flock, Cold, a palp, Mays, Ecua, Enlil, Hakan, Odilo, an atm, Gaekwar, Cree, FRGS, Maffa, Jany, Madras, Selena, Xerxes, Seaver, Tailor, paise, Negev, a saga, a rent, Rugg, a galop, a rennet, a goy, a gps, Elko, Ovid, a capo, OPCW, Nagoya, a kino, Mellie, Rimini, Luigi, Roraima, DOA, Laszlo, Hobey, Wear, Dex, Ellerd, a revert, a kip, a revolt, Spa, Pacific, Mellen, odds, Stow, Izmir, Gaul, UTWA, GCM, Akaba, Kapoor, Tak-Wah Lam, a job, Budd, Rogerio, Gerge, Romy, Web, a joy, a kaka, Vonny, Daddah, Croom, Xeres, Palaeozoic, Sabino, Bahia, Daub, a ballad, Narva, Jan, Relly, Kreiner, Gazzo, Crifasi, Rubio, Zebe, Dax, AFS, a knell, a dragnet, Kremer, Bajaj, Drew, a tact, Felty, Grey, Drer, Helm, Otha, Yila, a removal, a bajada, valses, Eyck, Cordell, Aeniah, Krems, Emp, Macau, a taxi, Deneb, a viremia, Jari, Waler, Taine, Tabbi, lawmen, Rubi, Niki, Brentt, Usk, Cordi, Krell, a zebu, a datto, Cidney, Takara, Gemini, Mods, Enyedy, Ettore, Dido, CNS, Edman, Raven, Rider, Ellon, Kabul, Fafnir, Eldo, Yacov, a haiku, Stijl, a bro, Havel, Charo, Beds, Euh, Puett, Emmet, SScD, FBA, Rodi, Sidur, Drugi, USPO, Happ, a kaki, Cukor, ODT, Navaho, Lillo, Temp, Mig, a reflet, a volva, Pavlodar, AFB, an adobe, digs, CBE, Diu, Greff, a zamarra, Hums, Cdiz, Zullo, Merc, a lop, a reffo, Hax, a temp, Medill, UPI, Kivu, Hao Wang, a rex, Errecart, a rhomb, a kapok, Iambe, Olnay, a lamboy, mesela, Geneseo, Janie, ZAPU, Yedo, Donn, a koko, Yeo, Vedi, Meilen, a dwarf, Furr, Elson, a pig, EAA, Robb, Edik, a saggar, Brent, Lawlor, Reece, etyma, GOP, an ado, Elazig, a waw, a rho, Bres, WOW!, a troch, coneys, Silva, Vaasa, Ynez, a magot, a trommel, Felt, Tillio, Brag, a troke, Diwali, Fars, Isbel, Krebs, OSD, NALGO, Grew, Olds, Breger, a fut, a trepanner, Taite, a hrs, Reviere, CBD, Rooke, Darby, Tacy, Todd, Nagle, Beograd, Ravid, a kago, Waupun, a vedette, Ruel, Fed, Newsom, a trike, Dud, a trf, a toom, a tort, Simpson, a villus, a fife, Dew, STD, Newel, trymata, a taj, a carabao, Meissen, a vireo, Dercy, Remmer, Elke, Gagnon, Nikki, Dahl, a gird, a mattock, Corbet, Sergu, Brew, ostrca, a caboclo, Doisy, Emily Bronte, MSBC, Irme, Femi, Holli, Rumi, Krutz, Tirrell, Etom, Leeke, Zeb, Minni, Jared Leto, Orsa, gedd, Nevski, Vespucci, Haggi, Brom, Ursel, Ludlew, ovoli, Hollah, Tacitus, Rew, Ardel, Doy, a tom-tom, a toy, Leanna, EDT, Nomura, ECG, a jinn, Enki, Brunk, a tungo, Haze, USP, Mulki, Dodona, ICJ, SMM, Ronny, Gish, Coop, a tunka, a bact, Vassily, Rorke, Zorn, a wop, a turps, Robigo, Yazd, an adnominal, Ruffi, Zed, Nilote, Mbm, Lotis, Littrow, a tuck, Corson, a welt, Nkomo, Chany, Dolli, Pepys, Sisto, Brahmsite, Codee, Braden, Urgel, dibs, RMC, SMB, Medii, a wahoo, Haynes, Lippi, Yafo, Lowl, Lark, AFM, AEng, Naples, Orsk, limli, Wafd, a yogh, Coo, Honor, Goldi, Puck, Cork, Axel, a tutee, Diahann, Alfi, Dobb, MFT, Todt, Taiwanese, Chal, Liza, Newlon, Aeria, Z-bar, a nonacid, Evoy, Minn, Osiris, EDP, Pilsner, Willi, Jadd, Ajit, Tenniel, Kroo, Bruhn, a madafu, Krupp, Pike, Popele, Gove, Pardo, Miksen, Azusa, Nollie, Paganini, Doll, a gnash, Coke, pix, Seiter, Usbeg, a detinue, Idou, Hilel, Lawes, Orlov, Ronen, Woden, WAFS, Nevile, Biegel, Kru, BSES, onaggri, Vinna, Timms, BSc, Javler, Emogene, Guest, IOU, Quill, Chad, Divali, culttelli, Wilno, Chap, Pammi, Harbin, Osyth, Crabb, Bock, Cohen, Metz, Tiny, Ruffo, Dash, Ciel, Grail, a devoir, Epiph, cippi, Vic, Grover, Trevorr, Eppie, silos, Sibiu, a maw, an ikon, Otranto, Gobi, Dotti, Wawro, Noyon, Edley, Cadmar, Gawra, Efram, Yapur, Previdi, dregs, Newell, Ewold, Lewanna, Elijah, a dew, STM, BSP, Pigs, Neff, Rech, Cu-bop, Pommard, a drawee, Oryol, ETD, NUWW, SNOBOL, Adrial, a drub, Sung, a minim, a dry, BSLM, suci, Pregl, a doom, a dorp, a doily, Culm, LLD, Lonier, SLBM, Hulbig, Posen, Ronsard, a malady, Roze, Yezd, an acid, Feb, Bobbi, Dodd, a jim, Mitzi, Fahr, Efik, Midi, Dirk, an oke, Borg, Swtz, trews, NbE, Boz, SJD, Elohim, Moth, Clim, a daud, a duel, Adnopoz, Nolitta, Rhamnes, Kreda, Duhl, Libna, a jut, Boll, Etowah, Shiah, Preble, a mural, Goren, a bahut, FGSA, Grube, Blok, Noemi, Scevo, Mohsen, Navada, ETV, Prov, a fado, Trelu, a magic, a murky, Eisk, Cop, a mug, a model, Restivo, Royo, Yassy, Letti, Polik, a morph, Clabo, Mohn, Waldo, OWI, Mims, Tuck, Roby, LSD, LRBM, a gaze, FLB, Leoni, Dorobo, Suckow, Kirkuk, Aleppo, KNP, Dibb, Arallu, Hoo, Winni, Bob, duomi, mobs, MHD, Tildi, Booz, a bawl, Monro, Chao, Korc, Levitt, Eyde, QMC, DSW, Etz, Tokyo, Bop, Gogol, a liang, a nabob, a cav, a paua, Golgi, cuffs, Moro, Coy, Hopi, Wyo, Howe, a motive, bds, MVD, NbW, Munro, a loop, a lhb, Lugo, Maxy, Rex, a pawn, WPB, an abt, Molopo, Hoye, Vig, apili, Finn, USV, FFC, CFI, Bibl, Luby, Haftarah, Vivi, Lyngi, Vivl, UFO, Pfaff, a caff, a wax, Mdm, DVS, DDT, Tiga, DFC, MGk, Stuka, Yoo, Jonah, KWOC, a prawn, Hoku, OSF, Noah Wyle, Govt, FBI, Garth, Sink, a peso, Jodi, FPC, Cluj, Lulea, Bui, Gyor, TLC, BMV, BCP, a plug, a pcf, a guv, a cpd, LHD, Guzel, Hakluyt, Diehl, Rigby, Dodds, JHVH, Yuu, ScB, BFS, NWbW, Sfc, GCB, a yew, Wolf, a knife, FIFO, Kori, Him, Rondi, Kapor, Cayey, a crop, a kid, Normi, Hiroko, Fife, Fink, a flow, Wey, ABC, GCF, SWbW, NSF, BBC, Suu, YHVH, JSD, Dody, B-girl, Heidt, Yul, Kahle, Zug, DHL, DPC, a vug, a fcp, a gulp, APC, BVM, BCL, Troy, Giuba, Elul, Jul, CCP, Fido, Josep, a knish, tragi, BFT, Vogel, YWHA, ONF, Sou, Kohn, Warp, a cow, Khano, Joo, Yakutsk, Gmc, FDA, Gitt, DDS, VDM, DMX, a waff, a caffa, FPO, Fulvi, Vigny, Livi, Vharat, Fahy, Bull, Bibi, FCC, FFV, Sunni, Filip, a give, Yoho, Polo, MTB, an abp, WNW, a pax, Eryx, a mogul, BHL, a pool, Aornum, Wbn, DVMS, DBE, Vito, Maewo, Hoy, WIPO, Hyo, Coro, MSF, fuci, Glogau, a pav, a cabob, an agnail, a logo, GPO, Boy, Kotz, Tews, DCM, QED, Yetti, Velcro, Koah, Corno, MLW, a bazoo, BID, LitD, HMS, bomi, Mou, DBO, Binni, Woo, Hull, a rabbi, DPN, Koppel, a kukri, Kwok, CUSO, Borodino, Elbl, Fez, a gamb, RLD, Sly, Bork, CUTS, Mimi, Woodlawn, Homo, Balch, PROM, a kilo, Pitt, Elyssa, Yo-Yo, Rovit, Serle, Dom, a gum, a pock, Siey, Krum, a cig, a mauler, Tod, a favor, Pvt, Eada, Vannes, Homovec, Simeon, Kolbe, Burgas, GFTU, Habanero, Glarum, Aelber, Phaih, Shaw, Otello, BTU, Jaan, Bill, Huda, Derksen, Mahratti, Lonzo, Pond, a leud, a duad, a milch, Tommi, Hole, DJS, Zobe, BNS, Wertz, TWS, Grobe, Konakri, Didi, M. Kifer, Hafiz, Timmi, Jaddo, Dib, Bobbe, FDIC, an adze, Yezo, Rydal, a madras, Norn, esopgi, Bluhm, BLS, Reinold, LLM, Lucy, Liod, a prod, a mood, Alger, Picus, MLS, Byrd, a mini, Magnus, Burd, a laird, a lobo, NSW, Wundt, Eloy, Roee, Ward, a dram, Moppo, Buch, Cerf, Fens, Gipps, BMT, Swed, a haji, Leann, a weld, Lowell, Ewens, Gerdi, Diver, Pru, Paymar, Fear, Wagram, Dacy, Elden, Oyo, Norw, a wit, to-di, Bogot, Narton, Okinawa, Maui, BIS, Solis, Eipper, Rover, Trevor, GCI, VIP, Pich, Piper, Ioved, a liar, Gleich, Sadoff, Ury, Nitz, Temne, Hock, Cobb, BArch, Tyson, Ibrahim, Mappah, conli, Willett, Lucila, Viddah, C.L. Liu, quoits, Eugene, Gomer, Elva, JCS, BSM, Mitanni, Virg, ganoses, Burkle, Geibel, Ivens, Fawne, Downe, Norvol, Rosewall, Elihu, Odie, United, a geb, sureties, Xipe, Koch, Sangallo, Dinin, a gape, Illona, Suzan, Eskimo, Drape, Vogele, Pope, Kipp, Pur, Kufa, Damanhur, Boor, Klein, Netti, Jadda, Jilli, Wrens, Lipp, Desiri, Sonni, Myo, Vedic, a non-Arab, Zairean, Olwena, Zillah, Cesena, Wiatt, Dott, FMB, Bodi, Flanna, Haidee, Tut, Alexa, Krock, Cupid, Logrono, Hooch, Goya, DFA, Wil, Milks, Rosel, Pang, Nea, MFA, Krall, Wolof, a yip, Pilsen, Yahoo, Hawaii, Demb, MSc, Mrs, Bidle, Grune, Darbee, Docetism, Harbot, Sissy, Pepillo, Dynah, Como, Knt, Lewan, Osrock, Cut, a wort, Tilsit, Olm, BMet, Olinde, Zif, Furlani, Mond, an adz, a yogi, Bors, Prut, a powan, Rozek, Rory, Lissa, VTC, a baa, Knut, a pooch, Sigyn, Norm, MSJ, Ciano, Dodi, Klump, Suez, a hognut, a knur, Bik, Nenni, JAG, Cear, Umont, Deanna, Elyot, a motmot, a yodle, drawers, Utica, Thallo, Hilo, Vowel, Dulles, Rumor, Bigg, a hiccup, Sevik, Svend, Degas, Root, Elder, a jinni, MBE, Zeke, Elmo, Teller, Ritz, Turki, Murillo, Hime, Fem, Ric, BSMet, Norby, limeys, Iodol, Cob, ACAA, CRT, Sower, Bug, Reste, Brock, Cott, a madrigal, Hadik, Kinnon, Gage, Kler, Emmery, Credo, Erivan, Essie, Moab, Aracaj, a taata, Myrtle, Wendt, Swede, FIFA, Sullivan, OSP, Mistrot, a moot, a frt, a dude, Kirt, Amos, Wende, Fleurette, Devan, UPU, a wog, a kadi, Vardar, Goebel, Gand, Doty, Caty, Brade, Koord, BCerE, Ivers, Rhaetia, Trenna, PERT, a tufa, Reger, BSD, Lower, Gog, lands, Osber, Klebs, Israfil, a wide, Kort, a garboil, Little, Flem, Mort, a toga, Maze, Nyasa, a vav, Lissy, Enoch, Cort, a wowser, Bohr, a wawa, Giza, Leod, an apogamy, Teece, Errol, Waltner, Bragg, a saki, Debbora, Aegipan, Osler, Ruff, Rawdan, Elie, Mide, Voe, Yoko Kanno, Dode, Yup, a zein, a joe, Senegalese, MYOB, Malayan, Loeb, Maikop, a kab, Mohr, a tracer, Rexer, a gnaw, Oahu, Viki, pulli, Demp, Metaxa, Hoffer, a polacre, Moll, Uzzi, DCS, Muharram, a zaffer, Guide, BCS, Gide, BOD, an abfarad, Olva, Pavlova, Telfer, a gimp, Metol, Lilo, Havant, Doro, Kucik, a kappa, hops, Uigur, Drud, Isidora, BFDC, SST, Emmett, Euphues, Deborah, Cleva, Horbal, Jit, Suki, a havoc, a yodler, Inf, a flub, a knoller, Edirne, Varna, MDES, NCO, Diderot, Teyde, Ynes, Domini, Megara, Katy, Endicott, a daube, Zaller, Kid Rock, Suttner, Bikini, Burne, MWA, Libb, a tenia, Trela, Wira, Jaime, Riva, Benedix, a tau, a camp, Mesmer, Khai, Neall, Edrock, cyeses, Lavada, Jabal, a vomer, Aaliyah, Tom Lehrer, Dyer, Gytle, FTC, a tawer, Djaja, Bremer, Kten, Gardal, Lenka, Sfax, a debe, Zoi, Buri, Safir, Cozza, Grenier, Kyl, Lerna, Jav, Randall, a babu, Adaiha, Boni, Bascio, Zoe, a lapser, Exmoor, Chadd, a dyn, Novak, a kayo, Jabe, Wymore, Gregoire, Gord, Dubbo, Jamal, Hawk, a troop, a kabaka, McGaw, Tulua, Grim, Ziwot, SSD, Donelle, MCi, FICA, Papst, Lover, a pika, Trever, Adrell, exedrae, Wye, Bohol, Zsa, Laodamia, Rori, Giulini, Mireille, Monika, a yoga, NWC, Poop, a cadi, Vookles, PGA, Yoga, Tenner, a pol, a gag, Gurtner, AAG, a save, Genesia, prolia, Treva, Essex, Rexane, Lessard, a myna, Jaffa, Msgr, Feer, Craw, Kea, GMT, an aoli, Dona, Kahlil, Neau, Cesya, MPL, a padlock, Colfax, a fec, a wab, Mulock, Sibyl, Lust, Elger, a misc, a fakeer, Celt, tights, IAEA, Gmur, finales, Orit, Bucks, Ursola, PMG, Smiga, Kioga, Pyne, Pune, Volga, NHA, Kolyma, Niger, a tool, a gaw, a glob, Rosalee, Pren, Wapato, Yuga, Pima, Durene, Zarga, Yokoyama, Mayotte, Bord, Nureyev, a doek, a tepe, Prevot, SSM, misses, Encina, Dust, CPA, Yurik, a wig, Arago, jaws, a bubal, Lys, a krone, Gdel, Turku, Adapa, Mika, Hyde, Erik, Corty, Bradan, Avlona, Sosanna, Joh, typika, NBA, DLS, a mut, a daff, a pkg, a modem, a caw, Muni, Dori, Rico, Mial, a cramp, Morty, Eiser, Damek, a wok, Turtle, DBA, pools, a smut, Ceryx, a bob, Gianna, Joel Coen, Robyn, Deenya, Hyps, AAA, AAeE, Dolan, Edward, Dundee, Wyn, a gopak, a tyg, Gianina, Jain, a jibba, duds, Elizabet, Lonna, Lennox, a fleer, creeps, a hor, Fein, Desdee, Wren, Yard, Dorado, Ploch, Ted Raimi, Atalya, Kolb, a prop, a say-so, Riga, Hatti, Gastropoda, Kym, Mugabe, Jakie, Luzader, Chak, Kamloops, Abbe, Jami, a typ, Mack, Coco, duelli, Vashtia, Lyda, Sacks, Arty, Bloch, Scioto, paratroops, a boyar, Izanagi, a tax, a pye, Bottrop, Paraiba, Graz, a breva, Hau, a bolo, Bolan, a loco, filles, Della, Indre, Brahmani, Rust, Orv, a flair, UPWA, Yakut, a dyer, Uuge, a tye, Velsen, Gilroy, a monomania, Kwon, Taddeo, Lissak, a wad, Nicol, Lori, Tirzah, piles, FMCS, a maze, Jeu, Galba, Bubba, Hauge, Letitia, Haya, Merops, a guns, a rubato, Jap, Yukawa, Zia, Bruni, Defoe, Mori, Bolivar, SSS, Godred, Lightman, Reinert, Seami, Lothair, a zareba, BCM, Suelo, Jagir, Gazo, Jada, Byng, a dipl, a paw, Smallens, a munga, Maddocks, Eleia, Bib, Magog, a botte, Diba, a kine, Grof, a lid, a wader, Everett, a yap, Malaysia, Dyl, Liba, Kit, a ballot, spans, a qto, Musser, Eccl, a taiga, Mid, a revival, Haphsiba, Levins, a fcs, a paynim, a kirtle, Zeba, GTS, Adria, Byrl, a voc, Ardenia, Knox, a pup, Mallia, frusla, Hobart, Smuts, a redd, a layerage, Kimbra, Klemm, a hawse, Kilan, OSB, a bleb, Agace, Nessus, Orebro, Vyse, Klee, wyes, Trust, Puss, Mroz, Zeeba, Gibb, a gtc, a fade, Wajda, Nikki Visser, Cloots, a rubaboo, Barabas, Sylni, Aias, DBib, a bib, Moloch, Sanborne, Milan, Osborne, MTO, Zoba, OED, a tonicity, Gitel, a gamut, a twat, swats, Ayer, Russes, Upolu, Koss, Eudoca, Madigan, a wen, Eric, TCBM, a lazuli, Kiki, a web, Barcot, a dagoba, Halbe, Kailua, Cdoba, Niu, Claiborne, Vinni, Durrett, an axil, a cave, Kazue, Jay, a knosp, Melli, Kuhnau, Baldur, Troyes, Murrah, Toltec, a face, Pomo, Doss, Nuli, Puto, Goto, Graff, Laraine, Xylia, Bok, Foss, USIA, Ollayos, a toil, Leggat, SCS, ESP, Pesek, Reynosa, MNA, DSM, Aimo, Dorette, Vinita, Luhe, Jade, Erroll, a pay, Velella, Hades, Eryn, Gisser, Vili, Kirit, Tesla, a weir, Rondnia, Jos, a tawse, Kos, a renga, Mayda, NNW, a flaw, Tokay, Tillo, Jasik, a medlar, Bach, Torto, Hose, Kajar, Huba, Tiber, a raob, a gamma, Gomorrah, Tacye, Mach, Tronna, Brunel, Lucio, Luanni, Reseta, G-suit, a tore, ducs, Ezra, Hydra, hols, Oak, DOVAP, Dinuba, Lily, a knob, Bigod, Diaz, a pein, a ruffe, Jaela, Mahdi, a lashkar, Eriha, Doha, a kos, a swale, Magree, Jaffna, BSNA, Brenk, Laflam, Mahau, Joe, NYC, a papaw, BSEM, delubrubra, Braz, a libra, Brod, Nekrasov, a pizza, Gerik, a priv, a kith, Sadye, Hiro, Foah, Cross, GCA, Kay, a deb, a film, a haven, a jeu, Onia, Ivonne, Jamel, folles, Sacken, Lorelie, Ziv, a fascicle, Giess, palta, Kiribati, Vaclav, a logopaedics, Small, a wap, Yucatnel, a vacua, CCC, a bbl, an abd, a brob, a geld, Dufay, Bontocs, a malee, Nitin, Erika, Gatias, Nessy, Tisbe, Dalpe, Pym, Mastat, Tabib, a foil, God, a brat, Shayla, Taveda, Hamed, a witness, FCA, SPCA, EEC, Nanci, Leffen, Ulu, a raia, Gibe, duos, Aegia, Gregg, a bap, Mantell, a pall, a ylem, a fad, Dulci, Loewe, Bonn, Akim, a safe, BSOT, cerci, BSAgE, Noah, Komati, pulik, Kirov, a rebbe, Heb, Alroi, Vahe, Babe, Kyd, Duroc, a pipe, prela, gyri, a fay, Flanigan, Ilia Kulik, Keble, Bose, Bonni, Rennes, Nanette, Yoruba, Hay, Docile, a globoid, Nial, a vel, a knap, a lack, Capps, a hay, Recor, Gavra, Gad, Lupee, Hebe, Bren, penes, Indo-Pacific, a probe, Ditmore, Cicely, Meyerbeer, Ios, a ruble, Deirdra, West, Elma, Hays, Soane, Borrell, a fag, a plebe, BSEng, a padnag, a barbe, Zak, Colbye, Doak, Stav, rhytta, a bigg, a folio, Liege, Homs, olios, a drowse, MAeroE, Yam, Ludlow, stocks, a haw, Platto, Clarhe, Kleve, Kamila, a bye, Kadner, Everara, Zolnay, a dobra, Gyas, Roeser, Aviv, a rit, a gad, Inca, Dacca, a garble, Diesel, Yurev, a cynic, Spode, Lotte, Jam, o-os, a puca, Viv, Ardra, Wise, Moharram, Izak, Corfam, Slim, Ouse, Kirman, yom tob, a cog, Resht, a gleet, Sitter, Bilek, Daryl, lights, Eadie, Noak, Jamaica, Cleve, Bay, Dehnel, Libnah, Tankoos, a dulse, Luray, a geol, an amurca, Gay, a moll, Evonne, Snashall, a wall, a ksi, Ryle, perca, Neal, Sianna, Brunei, Capulet, Shanon, a ways, a vegan, wapatoos, a yaw, Busoni, Giule, Parca, Vey, a take-in, Novah, Darrey, a babe, Ravonelle, Drake, Zeffirelli, Vega, Tropaean, Mile, Bikales, Ursi, Pittel, Libava, Chari, Dasha, Kazak, Cerelia, Haymo, dos, a stunsail, Anagnos, a tribade, Vadodara, Vlad, Lobito, Gros, a harm, a haole, Plovdiv, AFA, Stella, Wasp, Margalo, Hejira, Halakah, Teryl, Lonni, Venezia, Magel, dertra, Bienne, Gursel, Doone, Inga, McDade, Debra, giros, a bogan, Reade, halos, Rosio, Mists, Opp, Malacca, Menorca, Marble, Snapp, a pep, a preoral, Lili, Kaz, a kook, Kislev, a repulse, Tiros, a soft-pedal, Adivasi, Lach, Coffee, Roye, BIT, Tobye, Solim, a yaup, a pod, Landri, alinota, a flab, a celibate, vica, Aeneas, Mdoc, Senusi, Tito, jotas, Sirach, Pease, Elik, Spillar, Tica, Vlos, Abijah, Turro, Mittel, Loraine, Bornu, Kone, lobolos, a loofah, Torbay, Bogan, eddied, Meryl, Lole, Iguac, Rica, Sewole, Nims, a yate, Vallo, diacoca, Igor, Doble, Burkitt, a bay, Durkee, Kaaba, a comal, an azole, Gda, Mollet, a copse, Vacuva, Clem, a hog, Ardelis, Islek, cerebra, GATT, a bate, Grogan, a vacuole, Nordau, a pyrrole, Floral, Liz, a bal, a cadette, Jakob, Moli, Elvah, T-bar, Amyas, Soble, Volnay, a mneme, Debye, Krute, Kahaleel, a zebec, Ney, a morro, Cosyra, Maxa, Jaffe, Lyly, a baobab, NDAC, Inge, Lydda, Mukul, a mnage, Knoll, a game, Johppa, Swarts, OAO, lists, a mask, Cabet, a fam, Orvah, Sibylla, Tyree, DSO, Alyss, Invar, Tade, Pilos, a kayak, Kkyra, GNP, a camoca, Nouma, Behl, Bible, Behah, Nathanael, a pam, Sitka, Sharra, togas, AAP, a camauro, Torelli, Vergil, Siddra, Regain, a titivator, bodegas, a fee, Kapaa, Jayme, Jannel, Adlei, Zulu, a pref, a rojak, cols, a have, DML, a hame, Brahe, BWC, a lava, Cyna, Lemkul, a tazza, Jas, Elazaro, Doe, Tyrol, a marge, Lidda, Mikel, Amati, Lunik, Barrett, a ballotade, Jassy, Lief, Fagan, a dustup, Jarrell, Enkidu, Dinse, Zitah, Susi, Bandur, Minette, Romona, Kolivas, a duma, a beerpull, a cairn, Islay, a gam, Rietveld, Duma, Nedda, MTP, a cot, Toomay, Abadan, Rojas, Wallraff, Fima, Avivah, a volcano, Glad, Roley, a gain, a batt, a veep, a camise, Gaut, Pest, Srta, Miho Kanno, Dielu, a plot, Noel, a payoff, Spar, Elias, a part, a sax, Drogin, IAD, Delaine, Volsci, Mima, a vote, Tye, Knipe, Prue, cassoni, Blaze, Poliatas, a toro, Gittel, Legis, a pint, a cay, Roget, a cad, NUL, Lubba, Dannon, Nepal, Wojak, Syene, Pushto, Bangor, Feld, Dibru, a fillip, Paluas, Sible, Zosima, a wade, Riddle, Vadim, a hilum, a fader, Fleet, Sidoma, PWA, Jac, Duse, Loma, Nelda, Moigno, Test, Slav, a stroma, Flo, Rheita, SSB, Binette, Babara, Vonni, a xis, a sox, Ancel, an atlas, a baya, Dru, Tasha, Roos, Kama, a mise, Yaron, OSlav, an eyrir, Akira, Haff, a revote, Eris, Agama, Slovak, Lusaka, Jaye, lirioddra, Grekin, Ed Wasser, Daphnis, a tennis, a pop, Yama, Neely, a genipap, Malcah, Sarajevo, Dav, a sniff, a rib, Bartok, Jarid, Dagan, Rube, a rebote, Kalfas, Uri, Peadar, Evipal, Lewak, a kill, a knoll, a drop, a vac, Mweru, Cenis, AAUP, a cyc, Also, Durr, Epsom, a lambda, Druse, Bel-ami, dayanim, a la-di-da, MGr, an amal, siddurim, Aimil, a kami, Kayseri, a flotsam, a hypocaust, a mam, a hydra, Gayla, Tantra, Brote, Elda, a pipal, a ghat, a laze, Galax, a strop, Minabe, GCR, a nappa, CWO, Burta, Micah, a kebab, Maracay, Nox, a steno, Garda, Lauda, a buckeye, Kolchak, Kus, a mule, Valeda, CCR, Suffr, Oakleil, Muttra, Madi, COSPAR, Odus, a sib, Barbuda, Lexie, Walke, Truda, Wonsan, Adlay, a femme, Kalil, a knop, a collet, socks, Akhaia, miri, Dekeles, Ieso, Kokoruda, a kisan, a zakat, Pelage, byes, a kaif, FAM, a moral, Kono, Gardenia, Zipah, Ptah, Suchta, Erlene, Faydra, Hag, Nisan, Ermanno, Dali, Noni, Blader, Flatto, Close, Nimocks, a cam, a plebiscite, a raise, Kauai, Jarnagin, a waif, a sulfanilamide, hagia, Medeus, a drab, Bono, Pironi, Gur, Epirote, Durno, McAllen, Yarmuk, Zosi, a rest, Celaya, Jaal, Leonteus, a soda, Maybelle, JFK, Dhar, Elbe, Gypsies, Nematoda, Bub, Allisan, a gee, Kass, a keynote, Isia, Maia, cypselae, Linis, Ronel, Meave, Nkrumah, Gus, a reif, a swob, Marcile, Razid, a comer, Pusan, Rianna, Elia, Caserta, Viseu, Barta, Guy, a camla, Hazen, Isin, Neddra, Zion, Orose, Timofei, Meerut, Lucais, IAS, umbrae, Goda, a must, Asabi, Yate, Kawai, Farrah, Saleem, Deanne, Varro, Clay, WRAC, Cyril, a kail, a hyd, Dada, Maillol, a says, Legge, Phail, Atalie, Weide, hyli, Meek, Beulah, Pindar, Taku, a snide, Hiltan, Eveleen, Wotan, Addia, Zima, Steps, Leonid, Rosati, Vada, Dur, Denni, Daley, Blighty, a feu, Almohad, a prau, Quita, Dumah, Sergei, Coad, Alvaro, Duero, an antenave, Bain, Aksum, a rappee, Kaye, Camenae, Jamil, a haoma, Syd, Darnall, a dobl, a baud, a pyrene, Vallie, Wei, Tralles, Sibyls, Eliz, Zurbar, a gpad, Orlene, KIAS, ged, a pepo, RNA, Mayeda, Abulfeda, Susy, Laise, Robigus, a caird, a probate, Kamal, Ignatius, a zee, Grotius, a floret, a fil, a kalam, a dorr, a vanadate, Gaspar, Pirali, Kossel, Bramah, Save, Beka, Spee, Kaleb, a syrup, Pinette, Yasht, a fail, a brume, Dail, a penni, Dias, Jhelum, Megalesia, Metius, a dug, Nealy, a celt, Titan, a drogue, Mornay, a dab, Daisi, Split, Neda, a grogram, Kast, Musial, a payroll, a magnate, Tinia, Comus, a malt, a rami, Tray, Breda, a vee, Riggall, a wammus, a yawl, a gayal, a mym, Matisse, Jemimah, Torrey, Wast, Tom Wopat, amebae, Murage, Bak, Colt, a macer, an aren't, Tibetan, a titan, Orvas, Oeno, Trevor Eve, Boru, Aleen, lots, a bagnio, Liszt, a kagu, a sass, a maim, Matrona, Eleanore, Valli, Corel, Zanzibar, Habiru, a laic, a canaller, Radom, Zosema, Jesse, Javanese, Lorita, Sussna, Verel, Loral, Hagai, Lonee, Kayle, Lydia, Mamor, Feil, Lucretia, Waal, Licht, a pad, Dearr, adytta, Meill, a houdah, Kissee, Gee, BSEP, an elayl, a topmast, Fleda, Aggadah, Tessin, nylghais, Semeru, Alage, Monacan, Gisele, Messenia, Crewe, haleru, a lay, Lise, Nord, a psid, a refl, a hade, Zaid, Dagall, Abdu, a slag, Ninette, divas, Wayolle, Leeanne, Vacla, MDAP, Malabo, Meda, Poll, a gauge, Post, a fac, Xeno, BSIT, Arnel, a gyve, DMD, a rake, Potts, a facebar, a gleek, Cocks, Ieyasu, a snoop, Malamut, a blackamoor, Galofalo, OFM, a date, Bethsabee, BSL, a plaid, a razorbill, a wpm, a cml, a pimola, SMD, Cook, Collimore, Damarra, wallies, Orcus, a leek, Coray, Bosnia, Moreno, Ilise, Partan, a golem, Mossi, Song, a rabato, Orna, Malek, Nurse, Sulu, a small, Ahira, Ganymeda, Becht, a lapse, Raj, a pattle, Powe, Maxi, Lichas, Uskub, Bida, Drus, a pazaree, Gwenni, Lovato, Delastre, Borodin, Uyekawa, RATO, Jet Sol, a tune, Vail, Oeagrus, a spirket, a papable, BCE, Komara, Wemyss, Eurotas, Selemas, Sirotek, Cohan, Abukir, a dog, Natalia, Watt, a khayal, a taxable, Bonnee, Kidd, a rsum, a cru, Pia, Duvida, Kurt, a breve, Doig, Gav, a raceme, Dak, Cahan, a gall, Ahab, Mozarab, an aught, a ballet, a pap, Moray, a cartage, Peppi, Dyce, Grus, a ploce, Vida, Sug, a valuable, Geist, Ovida, Blakelee, Keel, a taps, a will, a gaol, a layman, Rebak, JET, a mirage, Hadria, Cecil, Prus, Afro, Dinnage, Cameo, Bouar, Fall, a flavonol, a vail, a levee, Roid, a ray, Merrel, a tamable, Damara, Megarus, Arelia, Way, Randee, Haim, Maryn, Reave, Davida, Oria, Cnut, Lulu, a purse, Vladikavkaz, Tadd, a regal, a lake, Ruelu, oesogi, Rida, Lwe, Max, Erida, Love, Darb, asses, Maarib, Mable, Vera Sos, a veto, NFL, a hap, Atlee, Hapte, Hyllus, a drag, Gahan, Osee, Bhatt, a myotome, Dam, FSA, Syllabus, a marga, Kedah, Aberdare, Joyann, Iznik, Rossi, Bichat, a fall, Eurydamas, Nemrod, Isidro, Flita, Farrell, a hard, Dedra, GSA, MALS, a hotpot, Celaeno, List, Farkas, Gable, Bologna, Slavkov, a puce, parasnia, Merse, Geronimo, DST, a fpm, a dam, Kdar, a fa-la, Mahren, Robus, a rote, Fai, Kiran, a go-cart, Cable, Babits, a vocable, groats, a fire, Jonas, Sable, Baler, Palua, Mahala, bird's-eyes, a jaup, Goat, Marc Snir, a mamma, Cyllene, Tromso, Dukas, Tree, Groh, Costain, Uskdar, Elita, BMetE, Fayme, Devi, Loats, a veil, Lide Li, MSBus, a woe, Steve, Thai, Marcin, a pappus, Akita, Mokas, OEM, a cirripede, Babb, a seed, Nicola, Meli, mellita, BSMetE, Romaic, Rosellen, Urbain, Nexo, Cyn, Norse, Polad, a cicala, Vashtee, Leor, Deryl, Lidah, Tabb, a snib, a spat, a waken, a jota, Janis, IOOF, a numnah, Petsamo, Angl, U-boat, Tulle, DAB, Assad, Deedee, Rimma, Cohe, Komsa, Mose, Babs, an auk, Sunyata, WCTU, Bil, a hag, Gosse, Rees, a sial, Limoges, a rial, Celik, a stun, Duhamel, a kas, Neoma, Coh, cellos, Nepil, Duce, Miran, agapai, a posse, nixes, a void, a raff, Otes, a xat, Nysa, Tulsa, notes, a tundra, Weihs, a data, edemata, Haynor, Adonis, Roydd, Alduino, McNeil, a tailgate, Elsa, Trakas, Yesenin, Aegates, a cod, a zaibatsu, Guat, toilettes, a maziness, a buran, Yvette, Huoh, cacaos, Mdlle, Recorde, pinnulae, Brezin, Melosa, a god, Alamosa, Hess, an amide, Pain, a tacnode, Raynata, Blasien, Giaimo, an occipital, a garb, Miocene, Riess, Algren, Rosa, a monosome, dungas, aortae, Draconid, a lytta, Cayugas, a kula, a step, Pisa, Noell, a gallopade, Vidar, a yield, Dugas, Pitts, Ulah, Tenes, merits, a baba, Janine, Vaal, Littell, a gaz, a jihad, Lamoree, Bail, a peto, Boots, a force, navi, Jarib, Orianna, Susette, Dino, Sliwa, Tirol, Ahaz, a jehad, Luht, a bailee, Kama-Mara, luces, a foilsman, Neisa, a duce, geisa, Odille, Goff, Miseno, Gula, Vtesse, Hoe, gasmen, Oise, Hoi, Cruce, Zadar, a gula, Ful, a tackle, Naima, Chae, Demona, Zola, Margareta, EEE, Bauru, Kansu, Eocene, Goeselt, rodeos, Salesin, Edom, a dau, Riba, James, a sod, a sima, Cabe, Manado, Xenos, Lorette, Fayola, Mad, Landsman, Molokai, Zurek, Coral, a gigawatt, a wat, Simla, Spain, Moslem, a caiman, Susu, Tisa, Cdenas, Leeds, Eugenia, Morse, Kissel, Lexine, bursae, Lissi, Gussi, Bowe, PEDir, Tim Daly, Alogi, Pres, a miler, Pazit, Rossen, Kee, Mayer, tails, Elyn, a morse, Pagas, a vat, Tennessee, Litt, a koto, Kosaka, Ransome, Dren, Musette, Bob Saget, Tobit, a keyway, a blame, Smitt, a myg, a nappe, Stinnes, a truce, Nisa, Tennes, a moolah, costae, Fedak, Gereld, a stge, Reel, a virtue, Tyzine, Risa, Kurusu, Lurette, Damita, Cyd, Dorset, a bail, a that's, a veg, Alisa, Dayaks, a madam, Bhili, Menes, Ornas, a hammer, a max, Elisa, a molasses, Subir, baffies, a dee, Maeve, Savdeep, mylodei, Demerol, Leao, Benedic, Ilisa, Ragusa, Rebba, Janelle, Welkom, a dad, Dusa, haikai, Teresa, Brusa, Hadar, Hube, Insull, a groin, Gies, a lagen, estocs, an app, Ankeny, Alysa, Janel, Lusa, Marybelle, a farseer, a doc, Corso, Kobarid, a sci, Tome, Daffi, a stag, Etta, Cadillac, Sara Rue, Ismaili, Cece, Tutt, a barb, Mahla, D.T. Lee, Kilah, a doodad, Jennilee, Kavla, a grugru, BSEE, Lail, a mosaic, nunneries, a turbit, Tomah, Gonave, Krein, a payola, Ronn, a pull, a gnome, Dag, Norway, Orlena, Gudren, Gessner, Oliva, hazanim, Getraer, Fenn, a yaffle, Nauru, Hun, Abagail, a coke, Musil, Lille, Vargas, Uel, a mestee, Mak, Collum, Kal, a chat, Arawaks, a tap, Isla, Kadar, a fascine, Modred, Dun, a vestige, Lais, Ewa, Lussi, Fanni, Obla, a knit, a knee, Val-d'Oise, Hoder, Flam, a smelt, testae, Federal, a dun, Algie, hibla, Eyla, Maidanek, Tiamat, Calabar, Gatun, a foe, Glaab, Bure, JHS, a radula, a die, Hamo, Pula, Hake, Beryl, Lateran, a fat, litatu, Lith, Sadoc, Mino, May, Alamo, Halfon, a gat, Slade, Haslett, Abigale, Pavla, ceibas, Barce, Makassar, Gail, BSSE, Perce, Ploeti, Lodi, Pelaga, Janaya, Ransom, a roo, Moln, a daffodil, a zootechnics, a bassinet, Urbas, Rue, Sidnee, Delmar, Camala, AAAS, a vein, Reed, Yola, Melun, a depside, NHG, an ootid, NABAC, Scylla, Haida, Bomu, Hannon, Nelie, Dream, Mangalore, Janela, Milo, vitae, Mendips, an anatto, BLL, a teg, a calpac, R. Ravi, a sirrah, a verticil, Apsu, Racine, Valhalla, Toll, a chafer, Taxila, a minimax, a mola, Videvdat, Lilac, Fini, Jamille, Paz, abollae, Byrle, Veradis, a hull, a tonight, a knave, Kissimmee, Sarto, Kosse, Vee, Baku, Lyn, a doh, Toscano, Glaser, Pakse, dalles, Ursal, lacoca, Mutazila, a daw, Zebulun, a microsome, Maye, Calie, Kylila, Ponselle, Palila, Mull, a collun, a loss, a millrun, a yrs, a miller, a blade, Camilo, Pansil, Bikila, Maice, Nazi, Bini, Cyma, Blau, Susann, a defilade, Borek, Kehoe, Damales, Sybila, a boy, Kila, Merola, CSO, Diao, Gosser, Genesee, Lydie, Hamm, Elidad, a debit, a lader, Cosette, Docila, a livre, Kam, an away, Sadiras, a voice, Idolah, Tralee, Kano, Camila, DEI, a snool, a sailboat, Allerie, Khanna, Sussi, a kasha, Val, a hakim, a dat, Futabatei, Vine, Sloane, Galaxy, Paine, Zoarah, Cirone, Vulcan, Naylor, Eanes, Lenssen, Div, a nun, a pee, Bacis, Abas, Eulau, a bootee, Stila, Abaco, Rosse, Nila, Maebelle, Bisset, Otila, Ahola, Malay, Alamein, Newgate, Boniface, Derte, Medrek, Cookie, Kodiak, Kohanim, a dag, McKale, Indra, Ha-erh-pin, a systematiser, Etrem, Derrel, Iobates, Solenne, KANU, Jacobina, Boice, Kola, a zool, a pal, Lola, Noli, Spears, a bit, Kassab, Raine, Dola, Sucy, Biadice, Idola, a pin, a balsam, Iyre, Lowe, Dalila, Caine, gigsmen, Regina, Jabir, a kylie, Kreg, Gulag, Adam Trese, Dayle, Vola, Soll, a backsaw, winos, Bion, Oneill, a wittiness, Eldin, a dray, a leeway, a regatta, Waaf, Fitts, a vaad, Lanette, boti, a stet, Conall, a poky, morays, Siret, a way, babas, Esme, Gretal, Odin, avos, a brae, Yael, Leon Lai, Rome, Maidie, Hassin, a bola, Nabila, Catie, Kalli, Richter, Essam, a habit, Cuero, Morez, Zorah, seraphs, Ivatts, a beedi, a sports, a byre, Kalidasa, Gongola, Margo, Gola, a kal, a manager, rin, Abednego, Mini, Kristen, Urbano, Marjy, arybballi, Field, Ducan, Udine, Dalymore, Jolie, Tyro, Vignola, a cola, Duer, fraela, Dee, Stelle, pelikai, Rainah, Teak, Kemeny, a redleg, an amice, Kylstra, BSIE, Weiler, Orense, Geis, Sadat, Signe, Huron, Imitt, Aubrette, Glenn, a deodar, Elf, Feola, BSEc, Ricci, Fuchs, a cake, Reigate, Yonit, a larum, Dorren, Orin, a rede, Haag, an accordion, a gate, Ramin, agorae, Luanne, Paull, a pyre, Gamin, a toilette, Yavar, Gaal, Neocene, Locklin, a cere, Bille, Doane, romans, Samuela, Dilly, Spalla, Mei, Dunaville, Westfalen, a paal, Leola, Lull, a taboret, Sudnor, Behre, Lwoff, Fugate, bullae, Mainis, Sacci, Gollin, a rennin, a vrille, Dylana, Wulfila, Ceporah, a lull, a toenail, E-boat, Kassi, Soni, Cull, a hat, a qaf, FOE, Karalee, Scopas, Ivetts, a cab, Butsu, Grahame, Koenraad, Dupre, Kopaz, enties, Iola, Magdala, Ylla, Cyrus, Ambala, Massawa, Balakirev, a hominid, Rosette, Baten, Eri Imai, Mongol, a gator, Gennaro, Klatt, a wage, Mavra, a wus, a zodiac, a tapas, a pain, Nord-lais, Sudra, Midis, a hip, Metts, a mass, Ensor, EEG, Allier, Taal, Izaak, a soakaway, a saice, Levi, Grati, BAgE, Maite, Yalu, Kara-Kalpak, Rowe, Kamasutra, a dis, a qaid, Nice, Kansas, yokes, a hipbone, Kaylee, Saville, Greg, Nagano, Seen, Maillart, Suanne, Hein, Nanterre, Pravit, Lucan, a derail, Libre, Kabir, Rice, Lura, Ollie, Trevar, Gayle, Broome, Gde, Sabir, a keir, a karo, Modla, Weizmann, a do-all, a calla, cat's-eyes, Leroi, Elis, a vulcaniser, Ethanim, Adala, Magyar, Cornall, a call, a gpm, a lobola, Luben, a calibre, Rise, Damodar, Elsie, Wain, a murre, Daggna, Ishmul, EACSO, Grassi, Krasnodar, Oly, a saccule, Faun, Iasi, Clarie, Winn, Admah, Genolla, Morice, Crosse, Hapi, Rhein, a lampadaire, Kiss, Urdu, a regret, CEF, Fen, a draw, a lessee, Tom Waits, a bvt, a coll, a haik, a sag, an eyen, a leer, Swen, a vicar, Elura, a lek, kielbasas, Binet, Segura, FAAAS, a rabi, Tarrel, Hakai, Granada, Maho Takai, Bim, an agura, Nembutsu, a honor, Ymir, Moselle, Zagreb, Balsam, Prato, Borah, Cormac, Corene, Daedala, Mahanadi, Parnas, a maser, Paur, Hennig, Gonagle, Bayle, Grega, Jael, Hadsall, a patin, a manakin, Tissot, Tombalbaye, Maryville, Grodno, Malonis, a caesura, Dede, Boyd, Derrek, Cohanim, a tupelo, Caracas, Obola, a no-ball, EdS, Marleah, Cimbura, Fee, Baez, a potage, Thais, Sieg, Delanie, Waneta, Camb, Pinot, a callet, an apanage, Taif, Atarax, Audre, Muse, Raffo, Belayneh, Coryell, a wait-a-bit, a cerise, Daye, vinos, Malaga, Jason Lee, Smail, Rianon, Ochs, a patio, Kadai, Garaway, Armina, McLain, ICBM, a lotus, a birne, Heinie, Haifa, an abura, a deva, Masha, Bute, Kamilah, Platt, a catcaller, Talie, cace, dadoes, a payer, Figge, Rizas, an axel, Pirnot, Roseville, Derina, M. Soittola, Plata, Camag, Ruse, Raama, Hants, a pawer, Dr. Dre, Timaru, Omura, Pool, a sauce, Tiffani, Ladinos, CAA, Sisely, a sym, mesocola, Lutero, Disini, Kalmar, Gaidano, Terina, Suisse, Carnot, Pelag, McKuen, a peen, a sot, a beryl, Kwasi, Pelham, Harneen, a pecan, Wadai, Bardeen, a rootage, Dall, a teil, Libreville, Bojer, a panada, Jaf, Hegira, Bernie, Winola, Deerdre, Mira, a mitt, a cavil, a sayer, Bracci, Pen, a trustee, Baxie, L'Otage, Lazor, Minos, Walsall, a getter, Amasias, a maill, a goosegog, a pen, a sum, almsmen, Regine, Hispano, Elo, pants, Ezana, Terceira, SOS, salad days, Supat, Rora, a snowcap, Mimir, a kiss, Issus, Soloman, Odine, Siesser, Payne, Devora, a cymar, TTS, a pact, Sunil, Loredo, Page, Mali, Ven, a trocar, Evora, PCA, an eyra, Margate, Dagna, Ynan, Agnola, Greysun, Corot, a coven, a subadar, Gaye, Liao, V. Claus, a casa, visaed, a rood, a general, a gap, a camass, a topaz, Tindall, a bottom, Mead, a bransle, Dierdre, Blisse, Yeats, a pat, Siam, a lisle, Katar, Renato, Cis, Samara, Drusilla, Micmac, Dwane, Wood, Alastair, a laggen, Asat, Kashden, a puree, Bayville, Harned, Kumar, a bosun, a jesse, Milano, a bagasse, Thayer, Faina, ECOWAS, Gardas, somata, Fariss, a hodden, a sill, Owain, a rubeola, Silures, a mail, Hadas, Uis, a legate, Romano, Fran, Reace, Ural, a venom, Mamore, Pozna, Caleb, a diesel, a pensil, Jamaican, gitim, Meares, a meu, Gora, Tella, Millen, Allsun, a sucre, Bora, Rose, Reese, Raimes, a nasute, Raab, Bevon, a morass, a mudir, Etem, Morganne, Debora, Dey, a seesaw, aurei, Fiden, a dace, Furtek, Citarella, Medora, Srini, Dyana, ballets, a paho, Piane, Dace, Kure, Polak, Coriss, entradas, Besse, Yonatan, Odets, a taenia, Mora, Moss, Urbannal, Hunan, a vet, Sean Penn, Udall, Eulee, Blatt, a latten, an upaya, Seville, Diasia, Veneto, Gomar, a gusset, Senecal, a bansela, Gondomar, Ammadas, Otus, Abbotsun, a megagamete, Ramayana, Halla, Cym, Melisse, Tavie, Neisse, Tatar, a mace, Dugaid, Desde, Manella, Malone, Vedis, Punan, Orren, a pilau, Oasis, a basil, Berezina, Mo Rocca, Roskilde, Seessel, a pocill, a gyre, Vaas, Venetis, Arapaho, beatae, BAgr, a ganef, Foxe, Merano, Kienan, Alonso, Stafani, Clarey, a stole, Mackenie, Weimar, Edda, Janos, Walcott, a cubature, PYT, Tarn, a hall, Eure, Niles, a baas, Erna, Moor, a kaf, Olea, Farrel, Bee, Fnen, a bwana, Ver, Eyre, Gij, a tensor, Gene Rose, Yenan, a ritual, a premie, Reik, Cordier, a rattle, Faye, Kiyohara, BSS, a ballett, a chs, Urbani, Kerwinn, a valse, Wynn, a faro, Zara, Okie, Roede, Maag, Almeda, Jase, Kajaani, Monessen, a safety, Coonan, Ruby, a raid, Isis, a beam, Musset, a cognate, Vadnee, Renoir, a vase, Mia Hamm, a teocalli, Creed, Norah, a vinasse, Magna, Veedis, Norine, M-line, Blain, a vair, a rosery, a snot, a pickaxe, Linacre, Heis, Somali, Breanne, Dayna, Metis, Sachs, a lame, Hamlen, a w/o, Blen, a git, Terrene, Zorana, gemmae, Bharat, Nataniel, Feosol, a tace, Kline, Rola, Jolee, Purana, Kress, a pace, Basset, a beat, a ckw, a hombre, Haig, an appd, a non-Japanese, Massasoit, A. Paz, Neville, Dalis, a beer, Tallie, Neila, Hamsun, a hhd, a neonate, Vladimar, Emme, Hamil, a homeplace, Kaldewaij, amoraim, a trek, a bde, Tyre, wolfmen, a sakai, Gulf, Fidele, Day, Rella, Corr, Effie, Ladd, an eyot, a lam, a lace, Ezara, a may, a koso, Grace, Ivo, Graeme, Haase, Weig, Dewain, Emmen, a spritsail, Apure, Muslem, Mike Farrell, a wain, Emilee, Caletor, a galah, Trace, Sumac, a riddle, Naze, Dorati, Rieti, Lose, Maely, a rave, Lakemore, Jewelle, Dales, Sakai, Bartram, Mieres, a cassimere, Jodl, a right, Royd, Antsirane, Rodmun, a dalasi, ries, Solnit, Apurimac, Cure, Midas, Adlai, Helyn, a blain, a megass, a pase, Yeh, Siffre, Sau, Whitehall, Orola, Yamani, WRA, Medit, Noonan, Evadnee, Leyes, Samsun, Iasus, Songhai, Barren, Gawain, a moor, a kilolumen, a didy, Takao, Bes, a slight, a conure, Gauss, an adat, Conan, a gill, a gait, a limekiln, a climate, Meenen, a dairy, L-line, Belak, a bustle, Keg, a vassal, Lorola, Ignace, Spanos, a raffinose, Mann, Amman, a trace, korai, Janssen, deda, Janeen, a deil, Lilah, Seline, Jeh, Cie, Rahmann, Ailee, Kara, Ikara, a bass, a cal, a gesso, Grasse, Nye, Tamala Jones, a sumi, Lawman, an idyll, a samurai, Lay, a cuirass, a suture, Pole, Naarah, Kanarese, Wait, a pallette, Violle, Bein, Nimrod, an amorino, Brace, mammae, Biafra, Moir, a camail, Lit, Torre, Halbeib, Mabelle, Dasi, Snell, a wynn, a grot, a lumen, a stain, a guar, AAE, MSMetE, M-day, Romelle, Kampala, Jae, Budde, Tymon, Oceanid, Deegan, nepmen, a borane, Plate, Makalu, snips, a gym, a snit, Sudeten, a dreg, Delanos, Pilate, Zared, Dorpat, G-man, Alis, a bone, Jair, an ihram, a dashpot, a reed, Ont, a ppm, a secretaire, Prem, a suq, submen, a sort, Niagara, Dior, Balak, Conn, a crare, Beane, V-Day, Pola, Janet, a prem, Mikael, cabmen, a hate, yeomen, Izanami, a simar, ovipara, torpedomen, Irene Cara, SMA, D-day, Pinole, FAO, Kim, a tenno, Graner, Goyen, a hoe, Macassar, Bezae, Dassin, Roane, Davidde, Toms, a reek, columnae caelatae, Hasin, Roy, Peale, Kale, Docilla, Calondra, Wera, a yid, an avion, Amory, a reel, Arola, Hiram, a yore, Blas, a ton, a cain, a flagman, Ailis, a battel, Light, Ribera, a claim, a sled, a tical, a pesade, Russ, an acre, Manet, Seale, Kaila, Luelle, Weaks, Alabaman, Navarre, Heisser, Paige, Deane, multiparae, Base, Sup, Margret, Sewoll, a sabra, Waf, Fulas, Sender, USS, an unau, a sire, Hijra, Mizoram, Melas, Ula, Beore, Woll, a halal, a sawer, Behaim, aspiratae, Hera, Reld, Nahamas, rhedae, Hako, Beera, Ellie, Neilla, Coire, Bai;, Rie, Loredana, a tabret, a pedocal, a get, Roybn, Ellas, Dyane, Kore, FERA, Ely, Gratt, a percussor, a knar, Tim Allen, Adair, a cion, all-sorts, Ibsenism, a scorpaenid, an assessor, a kale, Gehenna, Verein, a vajra, Mraz, a clar, ORuss, an alum, Astra, WAAC, Arabele, Duleba, Rotifera, EdM, Rese, Wasson, a cycle, Keil, a rook, Amabelle, Zaire, byre-men, a rhatany, Lavelle, Faxan, AEd, a genera, a litre, Baiae, Monet, Ozan, a siller, tapemen, novae, bolas, Umeh, Celle, Bonnie Raitt, a pekan, a sunn, a hexane, Diane, Berey, Waseca, Slater, Taam, a satyr, a base, Yee, Butyl, Landre, Guam, a snag, an ombre, Vale, Robaina, Verene, Valera, Mikan, a cuticle, Kedar, Gao, Koball, a weeny, a rail, a royale, Dasie, Law, a gore, Maera, Abbai, Lisle, Wuhan, a fit, Alcimede, oases, a gibe, Kananur, Belier, Feune, Van, a coss, an aune, Bohman, a cnidocyst, a prat, a van, a suer, a campodeid, Dibai, Karami, Jat, an irade, Synn, a heiress, a sleep, Oilla, Cyra, Ivan, a yawn, a malam, a segar, Evan, an eds, Marinna, Melar, Evelyn, a mayor, cellae, Pera, Cia, Clareta, Colas, Watanabe, Kinau, Abilene, Liane, weenies, Bobadilla, Ceil, Zela, Mobile, Danu, Griffiths, a cembalo, Miramar, a labret, tubae, Corcyra, Torah, Cela, Rahman, a vagueness, a tattersall, a waitress, a glede, Bale, Zahedan, a kOe, Katalin, a mallam, Assuan, a midday, Els, Alvera, Swor, Randal, a sagamore, Neils, Elnore, Nicolas, a pil, UAM, a torte, Radie, Liliane, Dafna, CPM, Avera, Ham, a tapeman, Bela, Russo, Bogarde, traps, a caid, an address, Albarran, Rebeka, Mera, Hall, a ha-ha, Michail, Riane, Dion, a teacart, Celene, Dao, Gainor, an attire, Mayenne, Dallin, Obeid, Dubai, Boreadae, Hen, Obad, York, Yan, a dkl, a skirret, Ross, an abasia, Gass, an aliveness, a paca, Lilas, Lman, Edmead, an esu, a pone, Madai, Liaopeh, Call, a wait, a slater, PABA, Jarret, Sisera, Levan, Ahir, a bale, Bore, Yemane, Lejeune, Bailar, Gmat, Iodama, Jane, Hak, a litany, a rabban, a marg, a menad, Pta, a mus, Tasso, Groscr, a mobile, KCSI, Perot, Alban, Alaine, Masorah, a bassist, a publ, a stere, BAppArts, a lag, Nivre, Samira Said, a bore, Kilar, a palet, Sedrah, Neilah, Mysore, HRH, CTA, Adela, pupae, Leban, a vahana, Loralie, Leibman, Allahabad, an abl, a snore, Heine, Damalas, Sihonn, a heer, a lavolta, Halie, Lehmann, a soroban, a surat, Lucita, Mehta, Hatta, Alitta, Mass, an abs, Suilmann, a vizirate, Baese, Yasna, Cade, Kimura, Balas, Dione, Dame, a ham, Hoban, a glonoin, a faun, a zaire, Gladi, Brion, Urbai, Bretagne, Byrne, Hassan, a midair, UNDRO, Fae, Sosna, Caye, Veats, a chokebore, Gagauzi, Musa, Mok, an impv, Cleti, Maleeny, Allain, a darts, a ccm, Gerek, culpae, Mitra, Wane, Kosak, Rowena, capos, eats, Aetna, Cresida, Rafael, Aeneid, Devon, Arabeila, tannaim, a balas, a bad, Andra, Noelyn, a krater, OFr, a whsle, willets, a crony, a redress, a jasmine, Deidre, Gretna, Clere, Mogadore, Hamlani, Pagnol, Bayless, Ishtar, a bedsore, Carbone, BSRet, Tore, Liew, Netta, Mure, Saadi, R. Leipala, Yin, a dibatag, Garret, salpae, Vitale, naoi, a gnawer, an aerocar, Uta, lay days, Andromeda, Kumasi, Rinee, Dantean, a firepan, Elinore, Vela, Kun, a mat, KKtP, crases, Samarra, Matsu, Gae, Dean, Apsarases, Neve, Leanne, Hahn, a ramrod, a signore, Kamat, a local, Hurless, Uriia, Vasyuta, Avra, Miass, an avo, Vladimir, a haler, Rosana, MSIE, Rior, Deems, a repute, Lael, piscinae, Core, Vladi, Sabbat, Prag, Hosein, Orion, a faena, cameramen, OPer, Tasm, Adao, Gelligaer, Democrat, Mantua, Norean, a fun, a mac, Scales, nugae, Lemire, Peele, Massorah, a levirate, Cinyras, USR, a tyre, Lead, Lamia Diamane, Zavras, arguta, a lulav, an adiabat, Comras, Inness, a btl, a side, Thamar, togae, BSAgr, a whse, Lyell, Oph, a rastle, Katee, Karr, a pale, Ginevra, Maier, Falun, a caps, a wane, papillomata, Kistna, Vas, a cadre, Grubman, a vessel, truths, a waxer, Galilee, BAE, Seurat, Scrogan, a pampre, Hase, Taylor, a knot, Feliks, a lakin, a degenerate, Patten, ulnae, Steffie, Savona, Camilla Belle, NRAB, a hardcore, pennae, Maranon, Nagyvrad, a canakin, VOR, Buderus, a rag, pleis, Sambre, Hasa, Borras, Garrot, Ness, an atman, Waddle, Wesle, Hayse, Linn, a heyday, Daladier, Fair, a valuta, Sarraute, Toh, a dissogeny, a lead, Avram, Jessen, Ulani, Genevra, Main, a vela, Gilead, an acidness, a galilee, Fan, a horsehair, a panne, Brenna, Cayenne, Tippets, a waf, Fina, Clete, BAg, Rotman, Addy, Wan, a medal, a said, Donegan, a total, Hokusai, Dollar, Omuta, Naida, Crowe, H. Yamada, Kannan, a hydrocele, Dore, bigae, Isle, Henie, Reis, Salamone, Danuta, Sidras, oaths, a volatile, Matuta, a raddle, HIH, Sartre, Galan, a millilitre, gemsboks, Alturas, Altaf, Cleota, Reitman, a bo's'n, a naut, Conelrad, Cramer, Feodore, BIE, Spokane, Kota, CAC, epinaoi, Hoyt, Iligan, a salaam, Agan, a ref, Fagaly, Whale, Dakota, a lekane, Mss, Algeciras, a gamete, Magan, a lagan, a yes, Dupaix, a ratan, a pumpman, a word-lore, Bogota, Husein, Noriko Aota, mota, Allen, a cape, Elsinore, Blase, Mansart, a pyran, a calef, Fiesole, Mapel, a sapota, STL, a snoot, Aras, a praam, Klaye, Cadmarr, a wadset, Uni, Mts, a lav, a lore, Zarah, trigae, Else, Levitan, a sun, an appellor, a padre, Havre, Fayal, Brale, varas, a lap, Minor, a haaf, Fulani, Klamaths, a rotl, a satin, a diene, Jason Isaacs, a titre, Bhai, Dinesen, a belier, Delsman, Arun, an ally, Grattan, a sob, Milore, baths, a level, Ed Gale, Dupr, a coign, an airman, USM, a dame, Rodl, Obie, Saire, Zamir, Athal, Ute, plagae, Belgae, Vat, Comr, a gasbag, Nisse, Lynn, an ads, an adrenal, Pat, Araks, More, Kate, Raina, Tura, Moerae, Leesen, a bladebone, Truman, a lota, Kele, Kataway, a rosette, nota, Rattan, a codomain, a titanosaur, a maths, a numeral, Limann, Irene Dunne, Byz, Zita, a hydrolase, breeks, a plat, a rale, Bertram, Syman, Amram, Hoare, Safire, Samos, Narah, Cattan, a glaire, neela, Lelah, Tarsuss, a law, Azan, a ken, a kane, Murat, a bogeyman, Edie, SVR, a hawknose, Gle, Hekate, Rama, Homere, Fayre, medullae, a diapason, Mela, Mansur, a can, a remital, a pore, Karas, Ela Weber, Gawen, Isak, Starr, a fore-topsail, Blakemore, Gemi Taylor, a keg, a solleret, Tocci, Amaras, a garotte, Bazin, Biela, Lucina, Cote, Leilani, Barsac, Uela, Melanie, red algae, Lucite, rates, Eras, Dia, Clarette, Basle, Nikita, Sassan, a miss, a bonze, Ingamar, Dole, Mason, Allegra, Mailer, Osei, Niemen, a fats, a porbeagle, Heimer, Tacita, Laine, DAgr, a dasein, Ori, Flessel, a sapele, Kaenel, ligulae, Derek, Cita, a mote, cymae, Ludie, Samoset, a grenade, Malaccan, a dita, a missile, Kinabalu, a barret, Sisak, Rame, Dita, a diaspore, PEI, Ndebele, Kaffir, a tapir, Edita, a diastole, Hatteras, Utas, a cabbala, BTE, Sidra, Noeleen Todaro, Dnepr, a hone, Reid, Nicholle, Trot, a tonn, Anatol, a stem, Resnais, a cedi, Gere, Deccan, a butanol, a tenaim, Mikaela, Flan, a sedile, Nafl, a flan, a soar, a matsu, REME, Vere, playas, Martita, Vinn, an aeon, a capital, Layman, a buckra, Meras, Beret, Tita, Alleras, a crackle, Yasu, an arcade, Ventre, Blaire, GSR, a leveret, Aleras, a culet, Tevere, tilaks, a reis, a cremator, Cumae, Dine, Lesak, comae, Lepaya, Melitene, vitita, a mahseer, Fablan, a maenad, Emma, Homerus, a raglan, a saiga, Lepaute, Portingale, Mita, Pol, a salute, Peg, a today, Ardehs, Angelle, Kayes, a claimer, Gayl, Lie, Roots, a protasis, a hartal, Rita, a bor, Raglan, a centre, Player, Ellette, Lecce, Rafaela, Leelah, Procne, Naaman, Amorita, Eur, a liq, Arion, a micra, Massorete, Mila, Klan, a mermaid, a genro, Beer, FDR, a sac, Paola Barale, Balaam, a balao, Johanna, Case, Nyhagen, a fair, a remedy, a clan, Allistir, a bases, Altair, a sal, a dacoit, a racer, a vane, Garate, Voyt, Ivis, Samanid, Warren, Natale, Romain, a denier, a lee, mallei, Vernal, a tache, Pohai, Victoire, Haye, Kaela, Caplan, a kor, a tales, Madaih, Susanna, Claramae, Komsomol, a skirr, a gallingness, a coder, Ala, Pierre, Tess, Abyss, a corr, a faille, Machaon, a megacycle, Winne, Bohs, a nacelle, Will, a hire, Gerita, Kerr, a gamebag, Keare, Greer, Fadil, a seer, Gelene, Beare, Maceio, Jala, Dinoceras, a displayer, Gale, Roseanna, Conrad, Lonne, Rufus Sewell, Euryale, rivalries, a pilaf, Huguenot, a casaba, Yucat, Soares, a lar, a tisane, Loomis, Samale, MAEd, a rita, a light, Lita, Alita, Alain, a dalan, a dairymaid, a tamale, Castro, Peer, Frohne, Saks, moths, a gale, Ike, Zellamae, Ellamae, Himerus, a retene, BMR, Alan, a corallita, MiNE, Daly, Bisayas, a peg, Aragats, an amirate, Baiss, a cavalcade, Malar, Ellita, Ary, Graaf, Here, Riss, a colon, a moir, a lignin, Nita, Tremain, a rcvr, a melt, Surat, a gossip, Mirelle, Mafala, Myrta, RSFSR, Ambrosane, Gogra, Calimere, Nett, a rat, Spener, Estele, Dorelle, Keene, Reiss, a cade, Malan, a kenaf, a loaner, Eskil, Susana, Tasia, habenulae, Gethsemane, V-sign, a roarer, Heliadae, Porta, Derr, a bakra, cannulae, Lazare, volcanos, an alienor, Tate, Baeda, Dilan, Aloidae, Sola, Herta, Elberta, a spasm, Holladay, Ezr, a cakra, Maire, Biskra, Minot, a girasol, a basset, Annaba, Donets, a retsina, Moroni, Pul, a dinoceras, Otter, Azaleah, pis, a processor, a sale, BAO, Gujarat, Allan, a topsail, Larned, a gonif, Far, a patter, Evelinn, a malar, a glair, a gybe, Sandro, Flight, a pollan, an erg, Lhasa, Lysol, Omer, Tamil, a scr, a myriare, Basso, Ingaborg, Ellan, a dekare, Kamerad, clarts, PRE, Tades, a rigolet, Ararat, a quass, an okra, Mitre, Tamra, cnidae, Tad, USN, Arta, a bundu, Head, a veneer, a koala, Darrel, Warta, a til, a sovran, a deray, Arte, Pelopidae, Noelani, Vries, Iole, Habdalah, Wran, a wolfsbane, Valais, a pot, an organelle, Kreit, a basso, Gala, Akkra, Myra, Memel, Assyr, Amato, Braille, Kleiman, a kabala, Vermeer, a kelp, Marta, Ker, Eulalee, Kanaka, Lukacs, G.A. Bliss, a cote, Spohr, a canine, Berte, Mas, Otte, Sparta, Esra, Cayes, Martsen, Read, a gen, a farer, Adaha, Tupamaro, Jammu, ideta, Sulla, Byran, a feta, Niel, Cunaxa, Fra, Cahn, a taffeta, Arette, S. Takasu, Anadyr, a baller, Odlo, Heer, Frere, Delsarte, Paola, Nisei, Krak, Amon-Ra, Colb, eupatridae, James Read, Liss, a camel, a sail, a fir, a glegness, a parr, a fytte, Pacian, Eric Blair, a fakir, a forte, manes, Nalani, a papaya, Kyra, Moirai, Hindu, a trait, Ursala, Gran, a sisal, Aun, Amasa, Jarad, Amen-Ra, caca, Simran, an emeer, Flann, an apr, a cap, a cerate, PRA, callused, a wood, an emigr, a maraca, Kolar, Almeeta, Ellen, Rockne, Glivare, Voss, a pair, a faraday, Adar, a flenser, Fleeta, Agle, Ballarat, Tass, a ctr, a hepar, a sallet, segni, Koweit, Tahoe, Doralia, Hussar, a sparer, Utamaro, Bran, a mom, a dracaena, Jasun, a mattamore, Zahara, Matless, a copra, Cdr, a pole, Macap, Cruz, a ricin, a tetany, Lyra, Maise, Lisette, Lucelle, verrucae, Tima, Milne, Geiss, a lessor, a trot, Agenais, Sankaran, a torr, a captain, a pillowcase, Malinin, a prep, Meta, Lory, Graf, Steyr, a byelaw, a karat, Rahr, a chg, a moderate, Creta, Plion, Nammu, Greta, a molar, Azal, a sanicle, Debir, a cane, vesicae, Guaymas, Neiman, a swimmeret, Arran, a bonsai, a resale, Zetana, Hirai, BOT, an esplanade, Ensign, a lasso, Vladamar, Alegre, Boyt, Laelaps, a gare, Kasai, Hal, a stableboy, Orran, a scran, a silo, Porte, Maas, Sinis, Samira, Haphtarah, a cymaise, Li-sao, ICC, APRA, Catlaina, Jaret, Saracen, Nealah, Comdr, a brocatelle, Katsina, tuladi, Oren, an ace, Dare, Fleta, Tigr, a matt, an acne, Lytle, Weyl, a rocaille, Kildare, Melleta, Aleta, a devadasi, Seleta, Mun, a cran, a disposal, Claire, Favata, Kel, a he-man, EMR, a cowtail, Seumas, a yamen, egos, a ganoin, an ale, Rosane, Zeeman, Eran, a partner, a dare, Sumatran, a mere, Haemon, orts, a garoter, Patiala, Lokayata, DATA, a lure, Fabre, Sato, Tuareg, Nils, Dumas, Parcae, tisanes, Beaune, Goulette, Devinne, guttae, Loire, Tran, Allene, Ravi Kannan, an inn, a tael, a gerah, Sorb, an insula, Madoc, Sobor, Castle, Babar, an apple, Yawata, Zachar, Harahan, Noble, Hannan, a soh, a parader, Fadiman, a lion, a saffian, AAgr, a main, Osnabr, a barytone, Zapata, Yale, BAEd, Husain, a nasal, Assur, Colet, Emma Noble, Hebr, a bobtail, Apr, a cenote, canales, sata, a mair, a cassata, TCS, Suevian, a surra, Camorra, Cabimas, Senn, a macule, Diarmuid, ICA, Rimas, a listel, Gian, a raw, a demesne, Sayre, Litae, Loss, Irak, Corday, ties, a gamin, an agata, Artimas, Mil, Sum, Nonnah, Gall, a copperah, a dread, a birota, Min, a namer, a haemin, an awe, Ive, Kala, Mazatl, a repair, a lamasery, Grani, Dal, a sizar, a tayra, Cale, Messere, Haskalah, Trumann, a tare, Kawasaki, Zora, MSN, a mohair, Ott, Andr, a ya-ta-ta, Rolo, Crab, Adonai, Roter, paillettes, Saberio, Mme, Dian, a pirate, Petr, a hop, metae, Carter, Pasadis, a quor, a marc, Almanon, a fare, Kata, Ellene, Rakata, a corbeille, Krenn, a mas, Azor, a median, a stamen, a var, a palaestrian, a welfare, Sycamore, Halli, Brian, a set, an albata, Azar, a bag, Nier, a warfare, Kanarak, Centre, Sufi, Gignac, Irfan, a potentiator, Camas, a carfare, Fine, Jeni, a leaser, a lavaret, Sewell, IATA, Cila, Tigre, BSN, a lehr, a proposal, Eads, Yuri Mitsui, Spelaites, Soleure, Tarabar, a ball, a syll, a syr, a cobra, Cromer, Taino, ICs, a locale, a cimaise, Trainor, Acamas, Platte, Ladue, Spaak, Col, a posit, Ilocanos, Dielle, Dulce, Dave Mirra, Clyte, Canale, Dianne, Groete, Maegan, a maple, Denis, Samain, a valor, Amy Locane, Rosol, Abu-Bekr, a plate, Peerce, Dale, Ciliata, a cine, Jamin, an atar, a balata, Osy, Crater, Damas, Ogun, Alem, Adamas, Cram, Ptain, a million, Issachar, a tone, Gattamelata, Lebar, a millimetre, Blight, an acce, Berriman, a diadem, a homogenate, Grata, Bor', a case, MRE, Kafre, Kaja, Masao, Tom, an impregnator, Bode, Irra, Crataeis, Salem, Margarette, Laodamas, Edi, a clamor, a canaigre, Sorata, Werra, Cotsen, Recit, Crane, BSAE, Roda, Simsar, a meliorate, Lorelle, Perak, Cuman, a snipe-bill, a strata, AIME, an anatman, a coin, a mason, Namen, a great, a rata, Rey, a pet, Arak, Glynn, a dallan, Odovacar, T-man, a reign, a trone, Saml, a spare, fossae, Guaira, Bglr, a poet, Tamara, Mata, Rem, RAF, Tridacna, Sais, Alegrete, Merce, Dahna, a kit, an acrolein, Nadaha, Mozart, a classer, Tao, Dane, Reyna, Samar, a gleba, Sidran, Elsene, Llyr, a ceriman, a rater, Eversole, Danialah, Treat, Nema, an intr, a barre, Shayna, a lin, a dlr, a color, a barr, a bhp, Myna, Nole, Dame Edna, Ammanati, Union, Iman, a nailer, a knorr, a beeline, Jesu, Batna, Hab, Som, Dem, a homeroom, Heater, palala, Monastir, a mailer, Ed O'Neill, a separates, a regr, a signal, a petasus, Piotr, a hussar, an abstr, a hart, Suleiman, a drail, Liman, a mun, a haram, Margaret, tatamis, Sennar, a sabre, Kaete, Peene, Leitao, Flynn, a linn, a ladle, Mekn, a ratel, Yarak, Cos, Sahara, Zandra, Wallace, Raeann, Etna, Cora, Mbabane, lagenae, Lianne, Sadie, Rennane, Raynah, Sherr, a borehole, Putnem, Erine, Vladamir, a have-not, Talaing, a calcite, Masora, MILR, a cpm, Cremer, Dagnah, a prolamin, Anatole, Tamas, eide, Merriman, a celadon, Ysaye, Nora, Minne, Lynna, a drain, a lovat, Conard, McHale, Baubo, Nur, a hairtail, Lunna, Rod, a tamas, Drolet, Drobman, a pinnule, Menam, Helene, leiomyomas, Praha, Ronna, a hit, an aerometer, Empusae, Cinna, a distr, a bleat, a crane, Kinna, Ola, For, a genre, Vala, Fuseli, Bari, Minna, Jara, Medici, Tavares, Ielene, lipomas, Etr, a cabman, a dollyman, an able, Hagno, Steele, Roselle, Witte, Lafitte, Gilda Radner, Tadio, Lyman, a terr, a baht, a lower-case, Grae, Solyman, a debaser, Dnestr, a primero, Halevi, Tat, Ice, Rao, Sur, a charr, a janitor, a canikin, Amann, Amy Lynn, a tain, Ode, Campman, Aara, Masai, a kin, alabastra, Meit, Annam, Adnah, a yarak, Cole, Volapuk, comas, Lanna, Dorr, a hair, a manna, Nies, Sabelle, Banna, librae, Dosi, penates, Punak, a tan, Una, Nos, Cutlerr, a cedar, a pane, Elianore, Hannah, Turkoman, Asni, pala, Volin, a dilater, a valet, Tenebrae, Rosanne, Jaen, Itabuna, Attalie, Bikaner, a kiln, a resin, an arr, a pellet, Seppala, Luce, Buna, Kin, Dunaj, Bluh, Shandra, CNote, Kanal, Luks, Muna, a kore, Sydelle, Douala, Lalla, Godliman, a broodmare, Tyrr, a propane, Lloyd Devore, Seine, gliomas, spiculae, an elytra, Meg, an arcana, Desai, Manu, Staal, a collapsar, a daraf, Chile, Hilaira, Cecile, hydrae, Duna, AAM, Jim Dale, Tomas, a puna, Amritsar, Bennir, a matte, Rebane, Gahanna, Vassar, a damar, Odelle, Deni, Lin, an aeron, Elenor, a bane, Kaile, Medicare, Soliman, OSS, Linda Hart, Luna, a tuna, Fichte, Haerr, a stele, Monaca, a signor, a batwoman, Aeaea, Pansir, Coleman, a sole, Romania, Haldeman, an imamship, a kona, a lustre, BMarE, Yona, Edin, Ozona, Epp, Israel, a ger, Gaynor, Abaris, Eanore, Bodnar, a freeman, a rot, a lupin, a manure, Makasar, a bice, Dares, Oona, a post, an occasion, a variate, Haakon, Aar, a half-barrel, Iona, Kiona, Nike, Marat, Craig, Latona, Pos, Kliman, a coir, a cabaret, Taranis, Sassanid, Derwon, a megalosaur, a tobira, clepsydrae, Satu-Mare, Tamasine, BSEd, a grain, a partisan, a haar, Casia, James Darren, Won, a flare, Lycaon, an airfoil, Isabelle, Desirae, a cram, Herve Gallaire, Valora, catabases, Marseille, Wynne, Jovita, Tice, Raila, Madeira, conchae, Bona, Kur, a snare, hetairai, Desi, Peonir, a melon, an adder's-meat, a tabaret, SAE, Lona, Ede, Gerar, a hairball, a dibucaine, Brenn, a tetra, Mark Lamarr, a birr, ICAO, Ilona, AIC, a tram, Chev, a won, a kaon, a sen, Iletin, Udale, Solana, an actg, Stone, lares, Rae, Herat, Saon, a hail, a degree-day, Nazarene, Greek, Ule, Mamallapuram, Simona, Oni, Maine, Bairam, Hon, aciculae, a report, Seaman, Beadle, Miyasawa, spirae, Tann, a tarot, a mice, Danelaw, a doyen, a thalamus, a mona, a butane, MRA, Darren, Bealle, Buraq, Crescin, a matlo, Hanau, Gun, Edla, Buffon, an ailette, Sumatra, Cremona, a gene, Sask, Carr, a bazookaman, a silvertail, a meat, Antenor, a basin, Rona, Madelle, Bayar, Frona, a comedienne, Jinnah, a marinara, Haman, pterylae, Ell, Orne, Namur, a shp, a resaw, Aksoyn, Exeter, a genit, Ramona, Gerona, a kirn, Essen, Lavona, Irus, submaxillae, Floyd, a crab, alulae, a glare, Duala, Cilo, Jamaal, a hematin, Alodi, Jena, Elgon, a decretal, OIr, a metol, Crete, Pylle, Baal, a salet, Ama, Zinah, a barrel, Lorne, Nader, Paik, Aries, a waggon, an agit, Tarai, MNAS, Liberalia, Jared, NIA, Merat, Torr, a prosser, Pedaiah, Glynas, fibulae, Dieter, Asar, a deciare, Tyr, a lasagne, Nari, Pasol, a borasca, Grete, Plerre, tailles, Sibylle, nebulae, Timon, an aye, Halette, Viyella, morulae, Egon, a curtain, a blare, Braun, ungulae, Nilus, Rufena, ATA, Merton, Omero, MNE, Kuo, stelai, Crag, Syl, a dodecanal, Cynara, Hassam, Ginelle, Romanes, Orelu, Donal, Hatshepsut, a leader, flats, a cerat, Sitra, Clare, Billat, an appar, a hyena, Mair, Amaterasu, Donau, a cabane, sambaed, a staple, Haas, Limemann, Aretino, Bena, affaires, Siena, Duane, Raynelle, Diyarbakir, Apelles, Oram, Skirnir, a catnap, Blair, a cannoneer, a remission, Allare, Pisano, Gart, Senate, Tomasine, Lausanne, Weiss, ennedra, Waite, Petra, Caen, an achar, a fleet, Shekinah, Tremayne, Kalle, Naamann, a roll, a parergon, a detail, a disrepair, assets, a read, Lir, a scalare, Gitana, Hamann, a layer, a chair, a moire, a tenaille, Neo-Latin, Amalek, Corynne, Loti, NEbn, a sasin, a tyro, Vinaya, Wal, Loram, Clair, a lair, a mitre, Blaeu, Hilaire, Gessen, Elba, Neil, an inane, Bael, Deena, a serotine, BSIR, a paik, Atalaya, Bre, Kaleena, Latin, a lidocaine, Gaile, Deroo, Mayne, Knitra, Moti Ben-Ari, a traditor, a cabala, Dylane, Gram, Row, Leena, City, Loiret, Caball, a gram, Agon, an exon, a yen, a regressor, a peh, Cleopatra, Casabonne, Liu, Strep, Peter, a lutein, a lass, Iraq, Pratt, an avocet, Ximenes, Oreg, a tenor, a bael, Lebaron, Oder, Patna, Dixon, a drib, Lia, Jarek, Curtiss, Agadir, a snort, a gena, ARC, Aret, Nippon, a nog, Ela, Curetes, Saman, Orten, Gamali, Brianne, Lynne, Basile, Damle, Saimon, an apa, NRA, Crain, a tabu, Stein, Adelice, Danilo, PICAO, Wilonah, Tena, a tesseract, McNair, a capon, a roti, Dena, Karon, an agger, Ednas, a plasmolytic, Adena, Lias, gulae, Ignaz, a whare, Meer, Ard, Nasia, Siegbahn, a ram, a tecassir, a sycamore, Karelia, Jabon, a capsule, Bon, a sim, Anitra, Myrle, Shaia, Sino-Tibetan, Ulane, Vena, Marr, a bedeman, Iene, Gabon, a lat, Conal, lire, Valle, Yahgan, a vacillator, Ibagu, Stevena, Sik, a ribbon, a rota, Luca, Janot, Wutsin, Aila, Timisoara, Matapan, a hare, Giessen, Eli, Tal, Ovalle, Helbon, abomasa, Montserrat Caballe, Dunois, a vena, a delayer, a georama, Cesar Romero, Des, Lisbon, a kraal, Leanor, Aaren, Holiday, Dene, Kwajalein, a dale, Braila, Gunas, crevalle, Demetra, CAT, Luane, Radu, Styr, Nedra, Ware, Davena, Pal, fraena, a sora, Michale, Secs, Pydna, Bala, Lloyd, Donati, Pena, Drain, a lahar, Denpasar, a heliodor, a paten, a japan, a cacao, Toma, Koo, Kustanai, Dis, Bonaire, tegulae, Dart, Sena, Ami, Hsu, Stanley Adams, ILO, Bate, Massena, Egan, Natalia Paris, Sandra, Canad, a maroon, a navar, a capot, Pitana, Jun, a martnet, Xena, a ten, a zoolater, Cesar, Eva Le Gallienne, Basie, Rena, Sta, Gebelein, a deficit, Sirena, an outsider, Friday, Orlanais, Etra, Caesar, OTC, Erena, Kai, Moon, Aym, a goon, Adlar, a heel, a medic, Uele, setulae, Elat, an asbolane, Lacaille, Macao, ROP, Pasargadae, Hel, Doon, a rete, Mor, Tina Arena, Larena, Noh, Shannah, pronaoi, CCA, Jasen, IAM, Eilat, an eider, feculae, Roper, Daman, a design, a butterball, a roadlessness, a meletin, a sabalo, Tamanaha, Mirabelle, Dunoon, Adlare, Mena, Naha, Turenne, Jemena, an enamelware, Warder, paenulae, scleromata, Barnaise, Lassalle, Heim, Mike Saks, Ragnar, Edra, casus, a depot, a kiaat, a goodness, Urbannai, a steer, Gaeta, Curacao, Presbyt, Iline, Sadi, Binah, a delegate, Mayes, Palomar, a patsy, Cot, Amena, Deer, Gayn, a ratite, Petar, Imena, Botsares, Selene, Kanara, Filomena, Nemunas, a daman, Osi, Born, Aisne, Prestige, Lena, Niter, Cesaro, Tani, Milena, Zane, Karbala, Morgagni, Tace, Dakar, a barrator, a foramen, Imo, Kane, Rijn, an init, a baseball, Ibsen, Arcadic, a repairer, a grille, Neile, setae, Dinah, a misfeasor, a spikedace, Danit, Salena, Riemann, a baleen, a rascasse, deaneries, Holliday, canulae, Fara, Canace, Daira, Mo-tse, Fin, a maar, a knag, Niple, Hanae, a bassoon, a muleteer, Garek, Corinne, Joelynn, an orseille, Nikolai, Bone, Zavala, Valadon, a melena, ERA, Hoenir, a canaille, Haile, Shaer, a major, a beg, a tropaion, an areg, a minah, a retail, a tipcat, Neb, Ros, Danae, Pate, Manara, Malet, a bros, Danais, a kilograin, Argile, SSR, Obala, lekanai, Melena, a blight, Eiten, Ina, Infield, Don, a dorab, Fraser, a wadna, Lorain, a ma'am, Ayina, Sol, a borate, Wina, a coroll, Uvedale, Dira, Myrt, Ole, Halliday, Oralee, Mia Sara, Camile, Salus, Ruffina, lamellae, Pereira, Mannar, a solfatara, Calydon, Automedon, a sip, a restr, a weaner, Oleg, a tole, Hasen, UNHCR, a monas, a mimetite, PETN, a sadi, Bar, a casein, Orabelle, Holocaine, Zwolle, Yasui, Cor, a bait, Alexina, Eger, Abaddon, a tele, Yonah, a mile, Stroheim, Martainn, an ataman, a kina, a telamon, a supr, a cate, Madra, Zina, Emmer, a megarad, Ines Sastre, Vergne, Nay, a konak, a war, a stir, a guenon, Exile, Harpina, Rein, a lei, Lara, Claman, Imre, Danas, megaara, Caracalla, buckayros, a vavasor, a dinnerware, Mon, Oina, Phina, Hale, Saxon, Elaina, Damon, a kil, Male, Sabina, Isa, Molokan, an assent, Cele, Saxe, Bina, a ducat, a farad, a pile, Halle, Sirsalis, a prestrain, Monahan, Nabala, Tremann, an anil, Ora, cerecloths, a galliass, a ware, Sunay, Vina, Yen, a loin, a daemon, a nom, Eade, Calais, Yolane, Kira, Mila Mason, Indiaman, Ezar, Ashti, MSHA, Rasia, Jos Baeten, an adenosine, Kassala, Deianira, Mnemon, Ariadne, Gelanor, Cimon, a nasion, Illinois, Simon, a nadir, a canalis, Hatasu, Maron, Gina, spinae, Tane, Rydder, Fallon, a potstone, Lasser, a maleness, a galatine, Beni, Din, a saline, Barbaresi, Lae, Dina, retinae, Reg, Nate, Milon, Aso, Ger, a medina, Eta, Elon, a vinylation, a lane, berets, an acarid, a flavin, Uppsala, Edina, Shinar, a paisano, Tomasina, a whitener, Olette, Var, a cassolette, Decato, Sina, Lot, Inn, a mor, Tina, Nell, a yarraman, Otina, a dor, a balun, a raser, Iaso, Jer, a paracasein, Asael, gorbellies, Raman, Horace, Bernat, Con, a sir, a ha'penny, Lora, Catina, an elevon, an underbidder, F.L. Bauer, a patten, Alene, Badr, an emetine, Vasiliu, Matina, Sui, Bear, a platina, Cas, Ivon, Avogadro, Frontenac, Frame, Traci, Latina, Cate, yarramen, Albertina, Dar, a seaware, Teer, Gael, Sile, Davon, a platelet, Artina, Medan, a naos, Susanne, Killen, Iceni, Martina, a tissue, Lina, Cain, a manor, a bakeware, Gagne, NASA, Ban, an amu, Idonah, Tama, Klina, Muir, Avon, a sone, Levit, Allina, Dor, a heir, Americano, Mallina, a subacetate, Canara, Luger, Rina, Nis, Irina, Sole, Putnam, Yacano, ITU, Tit, Seder, Pascin, Erina, DAE, NNE, Narra, Mosira, Marti, peronnei, Shannan, a lai, Shere, MatE, Maat, Aleedis, Norina, ESE, Levon, a rep, Murton, a dig, Nara, Caenis, a ban, an aloin, Arcaro, Tomaso, a bar, a cadastre, Beaner, Etoile, Hayes, a collaborator, a separator, a cotton, a ratton, Abigael, a dan, a laurustinus, K.M. Venkataraman, a what's, Ruhr, a deceit, Talaemenes, Ore, Kalat, Rom, Mina, Hanna, Vashti, Der, Emmeram, Sib, Allyson, Oman, an issue, a claret, Arce, Sno-Cat, Sig, a mina, Ler, IATSE, a pan, a nag, Nic, a fret, Nina, Avi, Jana, ais, Alcot, Roana, Regan, a taillight, a dragoman, a piastre, BLI, Gar, a sarsenet, Kenay, Raton, Abagael, Baton, a lira, Matane, Rexana, NAD, a billeter, a haet, Neenah, ScM, Jerusalem, Martyr, Evaleen, a raider, Emmalynne, Kloman, a lacunar, a snarer, a cat, a gar, a seine, Roxana, a rone, Lorianne, Kandahar, a skeleton, a toman, a brocatel, Eton, a rel, Bonne, nares, Sangraal, a kana, MIE, Hana, Akan, a terra, Mala, Para, Casar, a premate, Mahayana, Ottoman, Azana, Ree, Palatine, Roger-Ducasse, nemos, Gunar, a fana, Elga, Elkanah, Clein, a duodenum, minae, Telemann, a sonneteer, a sea-lane, Deaner, a spermaceti, Nida, Navasota, Barry Sadler, a hatter, a sea-maid, a craal, Aynat, Ghats, I-go, Lore, musettes, IrGael, a mate, Mael, a cicerone, Leslie Caron, Darrelle, halalah, kernoi, TEL, Peder, Pagedale, Karame, Denae, animala, Romanas, Sletten, a jet-setter, a sec, a para, Calle, Saar, a gnat, a spokeswoman, a lot, Ron, Akron, a six, a toile, Havana, Reta, genae, a snath, Guarani, Ravana, Rota, Ivana, Efron, an ain, Arianne, Jena Malone, Nalor, a celure, Fabron, an are, Valene, Nani, Fast, Aramen, a varier, a pagne, Stevana, Trow, Levana, a tam, UAR, Tor, a batten, a jalor, a charwoman, a romero, Vin, Monah, cranemen, Ileana, a mene, Nanine, Lofn, a space-time, Renae, a smatter, a misleader, Fevre, Seram, Odra, Staci, Roger, a palate, Massenet, a desaminase, Deana, a carbanil, a popinac, Seana, Ravi Boppana, Ellora, catenae, Nile, melanomata, Elane, Gore, Karen, Rutan, a leet, an amarelle, Sarene, venae, Lati, Bron, ASN, a snail, a tirewoman, a heb-sed, a tsar, a partan, Issei, ROT, CAF, Lon, Oneil, a rockoon, Anaxarete, Mat, Conah, Cran, an ayre, Pana, Espana, Rev, Rok, phialai, Neh, Craner, a metaprotein, a redrawer, a cruet, a manak, Ran, a lev, Iran, an atonic, a platelayer, a cymene, Nasi, Sair, a canap, a tsotsi, Tam, Mar, Gan, an acron, a citer, a paean, a let's, a manas, Omar, a pillaret, a valvelet, a n'gana, Roti, Sivan, a nagana, Sam, a train, a rab, a hiragana, Samala, Mlle, scaleni, Pan, Isaak, Sal, a non-Roman, Egor, Tinaret, Nace, Daren, a vara, Campinas, a butanone, Weimaraner, Fergana, Nam, Tamar, a pedal, labaara, Hopedale, sceneries, Sarasota, Roman, Ismael, a roman, a gleaner, a macron, a satire, Vallenar, a subdeaconate, Helaina, Morgana, an agateware, Glenine, Danai, Biron, an organa, Lew, Orr, Upsala, Cara, Care, Noga Alon, ectases, Pilar, a pieman, Anna Magnani, Bara, caci, Petra Jared, Nabalas, an iron, AYH, Par, Gona, Econah, Cato, Sinas, Arabelle, Diane Lane, Grande-Terre, Faso, Luana, a tine, Vanir, a statfarad, Freeman, Ilocano, Ital, Ludeman, a staidness, End, Donar, Emee, Derain, a rain, Osana, a mare, Nicolle, Saideman, a giron, a botany, Lira, Moira, Malagasy, stamnoi, Tan, a menat, Rowen, Adam Alexi-Malle, Haydn, a str, a blighter, a gamone, Dana, ASS, a bargeman, AID, a craneman, Airedale, Davene, Galle, Skee-Ball, Ewer, a fgn, Aron, a leg, Ducasse, Nevis, Iredale, Mara, Calles, Salene, Danyelle, Kootenay, Caron, a scare, Decadron, a praemunire, katana, Mler, epistases, Neman, Oira, MOIG, Adana, Reni, Adron, a sonar, Eddana, Ima, Lahti, Peter Buneman, a weaponeer, Gallinas, Thestor, a baseman, a deadlight, Ronal, Chane, Mai, Shaitan, Giselle, Holle, Hanoi, Tati, Pace, Darelle, Hasseman, Oita, Sil, a gel, Linares, Ubana, Sat, a rom, a nibbana, Sad, Line, Baer, a bdl, an ordn, a sneer, Gayel, Warrenne, Kennan, an afreet, a gelatin, Urbana, Eri, ATS, a der, Freya, Brenner, a wavelet, a cider, Paolo, Pire, Tayler, a matter, a palace, Danelle, Habana, Marabelle, Smithson, a grub, Anson, a guanosine, Basir, Benares, Abana, Eno, Labana, a cabana, Nona, Bellaire, Tamayo, Nov, Anne, Jane Greer, a caner, a cetane, Naara, Manisha Koirala, Shane, Manat, Terra, BLE, Jameson, Adalai, Nino, Goossens, Seler, a caller, Evadne, guanayes, pilei, Marala, Ehr, Rone, Mana, Sir, Fotinas, Einar, Otis, Ivanah, a ferreter, a male, Daile, Kiki Classen, a vimana, Man, a lyc, Nan, Gine, Basel, Ligeti, Grane, Nadaba, Nine, Leninakan, an initiatress, a mana, Noll, a foreman, Agartala, Vardhamana, Edison, a breadline, Beira, Mallin, a malate, Cana, Aire, Taira, Masson, a redness, ENE, Tucana, Ress, a gallate, Marek, Ames, Ion, AEC, Nat, Pros, Banat, Sims, Ocana, Zen, a bitser, Rana, Ena, Cedalion, a guanay, Tine, Lanai, Shanahan, a lanai, Ram, Margarete, Gene, Gelb, a vie, Ceram, Urana, Maher, a fireman, a dinar, a nobleman, a stableman, a dealer, a mallet, sestinas, a leaner, a campanile, Meiji, Jules Asner, a passer, a care, Mark Manasse, nevi, tis, Nes, Nonah, Tirana, SSE, Nel, Bang, a minaret, Sela, Brana, Ila, grana, Ain, a moc, Lace, Daegal, Lane, Nadler, a mtn, Eire, Panay, Briseis, Pigalle, Rosaleen, a ko-katana, Les, Rotameter, a presser, a caf, a crenelle, Hirasuna, Munniks, Lion, Assen, Ilion, an aegrotat, Set, Tana, Sin, a sultana, Ira, Mosul, an espagnolette, Sion, a sex, Etana, Sian, a lesion, a cit, Car, a tana, Adler, a manometer, an esne, Rhaetian, a damiana, Son, Essene, Vita, retinas, Une, Meter, a wale, Delora, Cannanore, Macnair, Colette, Romagna, Kistner, a payt, a hobnail, a run-on, a piperonal, Atropatene, Gargan, a tgn, a setter, Giana, Ten, Oca, Jareb, Memnon, an omelette, Docilu, Kan, an eraser, an abseil, Liberace, Dael, Siana, Tiana, an overcare, Diana, Ann, an ign, a why'll, Ier, a byre-man, Amanda Foreman, Agni, Sharon Au, a sesame, Tratner, a peteman, a vale, deciduae, Cro-Magnon, an astr, Australiana, Nore, Liana, Six, Etan, an anode, Cammaerts, Riana, Ariana, Nah, Cai, Danny Dolev, Isar, Briana, a novelette, Lana, Can, Ecbatana, Ino, Meade, Calah, Plana, Mur, Alana, Han, a trepan, a haematin, a rationale, deti, Lear, Sinon, an aid, Ninon, an aminase, Itin, Ukr, a ser, a bastite, Pattin, a rattan, an aero, Belle, Hayti, Lib, AET, Arnon, a sei, Tila, Rene, Georglana, Amr, Edo, Tare, Karel, Dan, a lignocaine, Lenoir, Elana, a tile, Messene, Nolana, Sue, a backscatter, a gateman, a mode, protases, a banat, Sine, Ilana, Nil, Svetlana, a meter, a secretness, Idleman, a rooter, a parasol, Lem, Race, Elora, Candless, Jillana, Asser, a cetin, Allana, Ebeneser, an acetin, a retina, Leman, OIt, a c/o, Vernon, a linac, a dresser, a ctn, a raffle, Sabu, a thane, Gerstner, a bimane, Naam, Melan, an asp, Per, a monolater, a cayenne, Kenon, a tenon, a vitellin, a manana, a brev, a missis, Piderit, Nana, a ller, a matin, a rebore, an anat, Cleopatre, Benoit, Adne, Menon, a remit, Tala, Tsiranana, Montagnac, Ire, Manon, an air, a tin, a salami, Nanon, a sere, Velleman, Agna, Mannaean, Ecevit, Canon, Ayr, Reb, Ned, Dorene, Gelasia, Nistru, Frederiksen, a zenana, a beebread, Lan, ASSR, Elle, Stets, bonaci, Med, a canon, a dhikr, a marasca, a sign, a resetter, a placarder, Ferdinana, ETO, Inman, an asci, Teh, Tse, an ana, Sis, a banana, Leah, Caresa, Tanana, Sumy, novenae, Nap, Mace, Len Adleman, a nay, Ara, Natala, globigerinas, a mon, a leman, Vera, Stassen, Evita, Genaro, Donavon, a villein, a delight, Nica, Janik, Fulahs, Komarek, a ter, a canal, Panama\"" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "str(p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Success! We found a palindrome that is longer than any found before. We can do about 50,000 steps per second. I'll stop here, but there are many things to try; feel free to explore on your own:\n", + "\n", + "- I order the actions by the product of the number of prefixes and number of suffixes formed. In other words, choose first the character that forms the most possible completions. But maybe, at least in the early goings, I should choose more difficult combinations of letters, to use up the \"hard\" phrases and save the \"easy\" phrases for later.\n", + "- I'm not sure when to end a word and when to try to continue to a longer word; experimentation here would be useful.\n", + "- The program is deterministic, and thus always finds the same plaindrome. that's boring; can some randomness be introduced?\n", + "- Can we make more interesting phrases? Include determiners other than \"a\" and \"an\"; include adjectives, etc.\n", + "- The counts of prefixes and suffixes include all the phrases in the dictionary. But we are not allowed to repeat a phrase, so can we modify the code to subtract one from the counts every time a phrase is used (and add onr back in when we backtrack over the phrase)?\n", + "\n", + "Perhaps you can find other areas to explore.\n", + "\n", + "# Indefinite Articles\n", + "\n", + "What if every noun phrase (except \"Panama\") has to start with an indefinite article, as in \"an X\" or \"a Y\"? Let's see:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "! [ -e anpdict-short.txt ] || curl -O http://norvig.com/anpdict-short.txt" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "DICT2 = PhraseDict(open('anpdict-short.txt'))" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pal: 1,001 phrases, 2,001 words, 5,649 letters (473,669 steps, 13 seconds)\n", + "CPU times: user 44min 43s, sys: 25.2 s, total: 45min 8s\n", + "Wall time: 46min 55s\n" + ] + }, + { + "data": { + "text/plain": [ + "'Pal: 1,237 phrases, 2,473 words, 6,787 letters (100,000,000 steps, 2816 seconds)'" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p = Panama(dict=DICT2)\n", + "%time p.search(10**8)\n", + "p.report()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "\"a man, a plan, a caret, a rec, a manana, an anabasis, a tsar, a tanager, an araban, a mat, an aromatic, an amadan, a melanoma, an anatman, an amowt, a barege, a jar, a tav, an arr, a parataxis, an amora, an agron, an ami, a caress, a paracasein, a salad, an allopath, a baronet, an all, a darer, a caravan, an alg, a ratal, an alfa, an agnate, an arg, an arcs, an arcanum, an air, an alp, a nail, a run-on, an aid, a ratan, an anabas, a pat, an ain, a baron, a manakin, a natator, a tarok, an attar, an apa, a nag, an animator, an apr, a tannin, a nap, a janitor, a carapa, an abaca, an atabal, an agal, an abb, a ratel, a salal, a harem, an anime, a hareem, an anim, a gala, a para, a maniac, an ann, a manit, a salep, a laniard, an acaridan, an aced, an adat, an abater, a lca, an amalaka, an aim, a daraf, an anion, a galliwasp, a caraway, a redan, a mow, a nae, a paretic, an avail, a guna, an iter, a nay, a daric, an aug, an origan, a mot, an orinasal, a barret, an ordn, an anil, a torc, an ord, a haram, a darts, an ani, a rater, an imaret, a rut, a sale, a taler, an orc, a nanowatt, an annot, an ore, an angina, a nit, a nos, a nonet, a nogg, a warb, an anus, a nog, a rap, a nome, a dater, a bat, a nom, a let, an ottar, an oil, a tale, a balata, an imam, a rate, a harim, an alapa, a nim, a lar, a cort, an oca, a nil, a saliva, an ips, an oxen, a nod, a rat, an alarum, an oak, an ital, a caracara, a hallah, a nipa, an elem, a nip, a latah, an isallobar, a core, an alias, an inner, a nib, a saloop, a nies, a carol, a varec, a radiov, an emagram, an etalon, a tuba, an evader, a nett, a parol, a jam, a lama, a net, a carob, a tamis, an egg, a lati, an alif, a neep, an eel, a ballot, an alley, an eyalet, a corban, a minah, a regal, a cariama, a nork, a nek, a wallaba, a nomad, an omasum, a lac, an ecad, an ogam, a lame, a haloid, a neb, an esu, a halo, a gallop, a nef, an uta, an okay, a radar, a fanegada, a var, a civ, a nunatak, a zap, an acarid, an upas, a pariah, an udal, a colat, a rabal, a cedar, a gallet, a nub, a retail, a kalam, an alegar, a geb, a retem, a gem, a redd, an alt, an alb, an attabal, a tepal, a timer, a redleg, a repp, an atlas, a ballup, a rep, a carioca, a nut, a resaw, a sal, a tip, a carrot, a resp, a lambda, a tat, a bal, a tot, a resin, a tob, a res, a radula, a tam, a tamas, an amatol, a removal, a sis, a rem, a gall, a carpus, a revel, a rev, a rad, a canalis, a bani, a rps, a recap, a rennet, a reed, a reel, a reek, a fanon, a canikin, a manioc, a reflet, a refl, a dep, a ref, a wall, a cerat, a tub, a reward, a reb, a saros, a vav, a rein, a pannus, a rex, a wanigan, a myriad, a rag, an amah, a rail, a rank, a raob, a rota, a tag, an amurca, a tass, a canoe, an assam, a catalpa, a tad, a room, a rood, a roll, a palais, a rod, a rim, a roc, a rial, a rip, a tapa, a jad, a catnap, a rub-a-dub, a tarp, a tanga, a tenaim, a rani, a tapis, a taps, a taka, a teff, a tap, a lanai, a snob, a tax, a taw, a tennis, a tew, a teg, a teel, a trapan, a mrem, a tram, a trad, a trot, a troop, a trid, a trf, a topaz, a galiot, a topsail, a manuf, a top, a catnip, a tool, a galop, a toom, a tonk, a tom-tom, a tog, a manway, a today, a rom, a titan, a trap, a tid, an assent, a pall, a mar, a bec, a fan, a lad, a til, a tum, a gal, a noma, a tef, a tug, a tufa, a tolan, a rasa, a margay, a datum, a tsi, a waterfall, a far, a mac, a jass, a lag, a batik, a tpd, a sard, a matins, a sav, a samaj, a tabard, a saga, a mallam, a dam, a sakai, a rum, a sari, a palikar, a misaim, a kalema, a mam, a sima, a mag, an assoc, a sumac, a lila, a molar, a peh, a sum, a ramrod, a supp, a pataca, a moc, a matt, a wadi, a matsu, a haeres, a sup, a subah, a lap, a calix, an ass, a pastel, a sepal, a mahaleb, a tabu, a dat, a cuda, a mob, a sex, an ashcan, a rub, a jasey, a strops, a stob, a sora, a minimax, a satsuma, a mix, a mass, a sadi, a ragi, a tab, a lulav, a lay, a wad, a cyc, a sorb, a soda, a mud, a sop, a snug, a slag, a scf, a lack, a laic, a fats, a cassaba, a recast, a hwan, a cep, a laud, a lev, a rayah, a leek, a vat, a gam, a slab, a leg, a baas, a camaca, a ruse, a camoca, a rug, an asb, an aery, an agnail, a lex, an abac, a leud, a liard, a lip, a lied, a lid, a loofah, a loom, a loca, a ripsaw, a swob, a lob, a lub, a bayard, a lyc, a nabob, a cadi, a sag, a dagoba, a lek, an app, a yapok, a dargah, a mib, a daud, a dap, a dab, a dig, a draw, an actg, a drib, a drub, a def, a deb, a dewan, a diam, a dopa, a lune, a papaya, a lug, a doom, a dorp, a dom, a doh, a dog, a doc, a duc, a marga, a liza, a capa, a cup, a marc, a madrigal, a pipa, a babassu, a gad, a dak, an oka, a belga, a grub, a maya, a gib, a map, a mesa, a goy, a mug, a misc, a fat, a qadi, a cay, a sap, a papaw, a myg, a mpg, a pagan, a gob, a powan, a wog, a pika, a pup, a pig, a proc, a peek, a plug, a pcf, a cav, a caf, a cig, a may, a tagrag, a garb, a gaw, a guv, a bob, a kabaka, a dis, a qaid, a kaki, a pay, a bai, a law, a rab, a ways, a jag, a gab, a jak, a yak, a boyar, a halavah, a boob, a haik, a raff, a caw, a pav, an away, a breva, a waw, a bubal, a brev, a flow, a wey, a kCi, a hag, a fay, a jaw, a hap, a baff, a wax, a maw, a dah, a doodad, a duo, a named, an anadem, an aoudad, a doodah, a daw, a max, a waff, a bap, a haw, a jay, a fag, a haick, a yew, a wolf, a verbal, a bub, a wawa, a verb, a yaw, a nav, a paw, a caff, a raki, a haboob, a hav, a lahar, a yob, a kayak, a jab, a gag, a jasy, a wab, a raw, a lai, a bay, a paik, a kadi, a qasida, a kab, a kabob, a vug, a wag, a brag, a garg, a tay, a magic, a fac, a vac, a fcp, a gulp, a keep, a corp, a gip, a pupa, a kip, a gowan, a wop, a bogan, a gap, a gpm, a gym, a wap, a pap, a say', a caid, a qat, a facsim, a gum, a yoga, a sem, a pam, a biga, a yam, a burga, a gleba, a konak, a dad, a gauss, a baba, a pipal, a gird, a macram, a puca, a paca, a zila, a gram, a cud, a cod, a god, a hod, a mod, a prod, a mood, a gula, a yap, a paenula, a pod, a maidan, a we'd, a bed, a fed, a burd, a bird, a gtc, an award, a gid, a bad, a pad, a duad, a bimah, a grad, a kop, a yapp, an akela, a bog, a dag, a said, a cabob, an acyl, a dray, a babul, a bol, a bowsaw, a spira, a col, a moolah, a fool, a dil, a deil, a pil, a drail, a duel, a cab, an axel, a liang, an ayre, an abs, an agura, a com, a caesura, a cam, a casa, a bagel, a balsam, a gat, a vakeel, a hay, a ravel, a dual, a pecan, a what's, a cera, a bass, a cast, a facial, a kcal, a fcs, a gals, a guns, a pos, a duma, a dos-, a bros, a cycad, a way, a lav, a lulab, a taig, a raid, a sass, a maxima, a must, a sax, a minima, a ros, a bots, a sports, a yes, a jaburan, a chs, an axes, a boma, a ducat, a daub, a tabel, a hamal, a pes, a let's, a pass, an axil, a cap, a lah, a bus, a pus, a sere, a haust, a maid, a watt, a macoma, a cat, a pappus, a dorm, a ramus, a hepar, a loma, a lilac, a mus, a coss, an agama, a mis, a mama, a mel, a kami, a simar, a kil, a pair, a samurai, a kas, a madam, a llama, a gas, a drab, a taj, a mas, a vas, a snit, a madras, a dpt, a kit, a bag, a lass, a jacamar, a fall, a fret, a waist, a mut, a day, a grama, a saran, a lota, a fut, a gut, a feta, a monal, a gamut, a lit, a dalan, a facebar, a mall, a patness, an adit, a partan, a tit, a moray, a dot, a yawn, a magot, a motmot, a knot, a moot, a pol, a galoot, a pint, a capot, a fun, a mali, a spot, a toil, a gaz, a pot, a frt, a dirt, a poort, a tort, a dart, a mart, a merman, a part, a leet, a get, a wet, a sinnet, a wat, a xat, a bonsai, an alap, a taffeta, a kat, a spat, a sip, a tain, a rami, an eta, a gnat, a prat, a bud, a bur, a pant, a cad, a jaap, a tapir, a lair, a cor, a mirador, a sial, a pallor, a door, a moor, a data, a plat, a camass, an aeon, a cassata, a crum, an agata, a tor, a boar, a knar, a liar, a ham, an agar, a dairyman, a gin, a waxer, a sunn, a panier, a vavasor, a saber, a drawer, a butat, a recall, a wafer, a pedalfer, a telfer, a coin, a manikin, a canon, a fakeer, a leer, a deer, a tenner, a pacer, a sprain, a basil, an acad, a raver, a lever, a supr, a call, a gamer, a sisal, a vomer, a lot, a manas, a mata-mata, a lud, a raser, a botaniser, a total, a batata, a dBm, a lapser, a torr, a capital, a saw, a ser, a tuna, a coir, a caper, a pull, a basalt, a napper, a gelder, a remital, a petal, a batt, an abl, a natl, an adder, a megameter, a begar, a gel, an amal, a kali, a ter, a bun, a tell, a gar, a decal, a barat, a local, a dun, a hair, a pas, a pun, a dir, a canap, a zakat, a nun, a vicar, a vaad, a gen, a farad, a ray, a kona, a tun, a fen, a poll, a gaol, a hausen, a ben, a diol, a haem, a lam, a gonad, a cen, a calamus, a monad, a mona, a ball, a waken, a krona, a mair, a cal, a gerah, an iman, a brocatel, a yen, a yell, an atoll, a baleen, a peen, a fil, an ait, a laggen, a sim, a tabor, a catena, a malam, a jalor, a patten, a red, a vena, a butanol, a ten, a marg, a men, a void, a racer, a valor, a casein, a pool, a sabin, a rennin, a sail, an aerocar, a boll, a sin, a hat, a lapin, a melena, a pin, a hall, a haar, a caracal, a tin, a kaon, a mural, a nat, a radon, an exon, a spina, a vil, a salina, a con, a trocar, a lamina, a pal, an amir, a haet, a ram, a mina, a tal, a bael, a talion, a ratton, a telamon, a tabaret, a daemon, a paragon, a sun, an abr, a waggon, a tenon, a sonatina, an ign, an aeron, a tonn, an att, a won, an acron, a rel, a tael, a saturater, a minaret, a rain, an astr, a damar, a hadron, a crotalin, an andron, a terr, a balas, an iron, a toman, a giron, a guan, a cir, a dayan, a retina, an ugali, a van, a citer, a paean, a woman, a deray, a war, a caps, a will, a ganoin, an afar, a damiana, a kal, a mana, a claret, a banat, a dan, a decan, a nadir, a can, a drain, a lapel, a satin, a mannan, a cain, a maar, a paal, a gamin, an ameer, a haemin, a namer, a halal, a salet, a rabban, a lagan, a lab, a tana, a cabana, a par, a carotin, a japan, an inn, a tarpan, a rot, a min, a nagana, a pan, a rattan, a kor, a tarot, a tan, an ikan, a manor, a banian, a tapas, a ban, an anat, a radian, a non-Uralian, a planarian, a mun, a cran, a scr, an agr, an aet, a n'gana, a flan, a lat, a raglan, a navar, a carer, a dallan, a tenor, a baht, a pollan, a dal, a sanies, a car, a passer, a caiman, an organa, a roman, a six, a tar, a parr, an avatar, a jaeger, a batwoman, an amt, an ana, a mon, a leman, a daman, a cit, a mor, an ataman, a bar, an areg, an atar, a stasis, a banana, a nan, a macerater, a canal, Panama\"" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "str(p)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.3" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/pytudes/ipynb/xkcd1313-part2.ipynb b/pytudes/ipynb/xkcd1313-part2.ipynb new file mode 100644 index 0000000..63302a6 --- /dev/null +++ b/pytudes/ipynb/xkcd1313-part2.ipynb @@ -0,0 +1,3706 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "xkcd 1313: Regex Golf (Part 2: Infinite Problems)\n", + "====\n", + "\n", + "

Peter Norvig
with Stefan Pochmann
Feb 2014
revised Nov 2015

\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "This Again?\n", + "----\n", + "\n", + "Last month I demonstrated [a simple Regex Golf program](http://nbviewer.ipython.org/url/norvig.com/ipython/xkcd1313.ipynb?create=1). I thought that was the end of the topic, but [Stefan Pochmann](http://www.stefan-pochmann.info/spocc/) sent me a series of emails suggesting some impressive improvements. ([Davide Canton](https://plus.sandbox.google.com/108324296451294887432/posts) and [Thomas Breuel](https://plus.google.com/118190679520611168174/posts) also had good suggestions.) So this post is an exploration of some of Stefan's new ideas, and some of my own. It's a story about regex golf, and about using exploratory programming to test out ideas.\n", + "\n", + "To review, here's the program from [part 1](http://nbviewer.ipython.org/url/norvig.com/ipython/xkcd1313.ipynb?create=1), with some minor modifications:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "import matplotlib\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from __future__ import division, print_function" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from collections import Counter, defaultdict\n", + "import re\n", + "import itertools\n", + "import random \n", + "\n", + "Set = frozenset # Data will be frozensets, so they can't be mutated.\n", + "\n", + "def words(text):\n", + " \"All space-separated words in text.\"\n", + " return Set(text.split())\n", + "\n", + "def phrases(text, sep='/'): \n", + " \"All sep-separated phrases in text, uppercased and stripped.\"\n", + " return Set(p.upper().strip() for p in text.split(sep))\n", + "\n", + "def mistakes(regex, winners, losers):\n", + " \"The set of mistakes made by this regex in classifying winners and losers.\"\n", + " return ({\"Should have matched: \" + W \n", + " for W in winners if not re.search(regex, W)} |\n", + " {\"Should not have matched: \" + L \n", + " for L in losers if re.search(regex, L)})\n", + "\n", + "def findregex(winners, losers, k=4):\n", + " \"Find a regex that matches all winners but no losers (sets of strings).\"\n", + " # Make a pool of regex parts, then pick from them to cover winners.\n", + " # On each iteration, add the 'best' part to 'solution',\n", + " # remove winners covered by best, and keep in 'pool' only parts\n", + " # that still match some winner.\n", + " pool = regex_parts(winners, losers)\n", + " solution = []\n", + " def score(p): return k * len(matches(p, winners)) - len(p)\n", + " while winners:\n", + " best = max(pool, key=score)\n", + " solution.append(best)\n", + " winners = winners - matches(best, winners)\n", + " pool = {p for p in pool if matches(p, winners)}\n", + " return OR(solution)\n", + "\n", + "def matches(regex, strings):\n", + " \"Return a set of all the strings that are matched by regex.\"\n", + " return {s for s in strings if re.search(regex, s)}\n", + "\n", + "OR = '|'.join # Join a sequence of strings with '|' between them\n", + "cat = ''.join # Join a sequence of strings with nothing between them\n", + "\n", + "def regex_parts(winners, losers):\n", + " \"Return parts that match at least one winner, but no loser.\"\n", + " wholes = {'^' + w + '$' for w in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " return wholes | {p for p in parts if not matches(p, losers)}\n", + "\n", + "def subparts(word):\n", + " \"Return a set of subparts of word: consecutive characters up to length 4.\"\n", + " return set(word[i:i+n] for i in range(len(word)) for n in (1, 2, 3, 4)) \n", + " \n", + "def dotify(part):\n", + " \"Return all ways to replace a subset of chars in part with '.'.\"\n", + " choices = map(replacements, part)\n", + " return {cat(chars) for chars in itertools.product(*choices)}\n", + "\n", + "def replacements(c): \n", + " \"All ways to replace character c with something interesting: for now, 'c' or '.'.\"\n", + " return c if c in '^$' else c + '.'\n", + "\n", + "def report(winners, losers):\n", + " \"Find a regex to match A but not B, and vice-versa. Print summary.\"\n", + " solution = findregex(winners, losers)\n", + " assert not mistakes(solution, winners, losers)\n", + " print('Chars: {}, ratio: {:.1f}, inputs: {}:{}'.format(\n", + " len(solution), len(trivial(winners)) / len(solution) , len(winners), len(losers)))\n", + " return solution\n", + "\n", + "def trivial(winners): return '^(' + OR(winners) + ')$'" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here are some \"arbitrary lists\" (see panel two of the comic) which we will be using to test out the code. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "winners = words('''washington adams jefferson jefferson madison madison monroe \n", + " monroe adams jackson jackson van-buren harrison polk taylor pierce buchanan \n", + " lincoln lincoln grant grant hayes garfield cleveland harrison cleveland mckinley\n", + " mckinley roosevelt taft wilson wilson harding coolidge hoover roosevelt \n", + " roosevelt roosevelt roosevelt truman eisenhower eisenhower kennedy johnson nixon \n", + " nixon carter reagan reagan bush clinton clinton bush bush obama obama''')\n", + "losers = words('''clinton jefferson adams pinckney pinckney clinton king adams \n", + " jackson adams clay van-buren van-buren clay cass scott fremont breckinridge \n", + " mcclellan seymour greeley tilden hancock blaine cleveland harrison bryan bryan \n", + " parker bryan roosevelt hughes cox davis smith hoover landon wilkie dewey dewey \n", + " stevenson stevenson nixon goldwater humphrey mcgovern ford carter mondale \n", + " dukakis bush dole gore kerry mccain romney''') - winners\n", + "\n", + "boys = words('jacob mason ethan noah william liam jayden michael alexander aiden')\n", + "girls = words('sophia emma isabella olivia ava emily abigail mia madison elizabeth')\n", + "\n", + "pharma = words('lipitor nexium plavix advair ablify seroquel singulair crestor actos epogen')\n", + "cities = words('paris trinidad capetown riga zurich shanghai vancouver chicago adelaide auckland')\n", + "\n", + "foo = words('''afoot catfoot dogfoot fanfoot foody foolery foolish fooster footage foothot footle footpad footway \n", + " hotfoot jawfoot mafoo nonfood padfoot prefool sfoot unfool''')\n", + "bar = words('''Atlas Aymoro Iberic Mahran Ormazd Silipan altared chandoo crenel crooked fardo folksy forest \n", + " hebamic idgah manlike marly palazzi sixfold tarrock unfold''')\n", + "\n", + "nouns = words('''time year people way day man thing woman life child world school \n", + " state family student group country problem hand part place case week company \n", + " system program question work government number night point home water room \n", + " mother area money story fact month lot right study book eye job word business \n", + " issue side kind head house service friend father power hour game line end member \n", + " law car city community name president team minute idea kid body information \n", + " back parent face others level office door health person art war history party result \n", + " change morning reason research girl guy moment air teacher force education''')\n", + "adverbs = words('''all particularly just less indeed over soon course still yet before \n", + " certainly how actually better to finally pretty then around very early nearly now \n", + " always either where right often hard back home best out even away enough probably \n", + " ever recently never however here quite alone both about ok ahead of usually already \n", + " suddenly down simply long directly little fast there only least quickly much forward \n", + " today more on exactly else up sometimes eventually almost thus tonight as in close \n", + " clearly again no perhaps that when also instead really most why ago off \n", + " especially maybe later well together rather so far once''') - nouns \n", + "verbs = words('''ask believe borrow break bring buy can be able cancel change clean\n", + " comb complain cough count cut dance draw drink drive eat explain fall\n", + " fill find finish fit fix fly forget give go have hear hurt know learn\n", + " leave listen live look lose make do need open close shut organise pay\n", + " play put rain read reply run say see sell send sign sing sit sleep\n", + " smoke speak spell spend stand start begin study succeed swim take talk\n", + " teach tell think translate travel try turn off turn on type understand\n", + " use wait wake up want watch work worry write''') - nouns\n", + "\n", + "randoms = Set(vars(random))\n", + "builtins = Set(vars(__builtin__)) - randoms\n", + "\n", + "starwars = phrases('''The Phantom Menace / Attack of the Clones / Revenge of the Sith /\n", + " A New Hope / The Empire Strikes Back / Return of the Jedi''')\n", + "startrek = phrases('''The Wrath of Khan / The Search for Spock / The Voyage Home /\n", + " The Final Frontier / The Undiscovered Country / Generations / First Contact /\n", + " Insurrection / Nemesis''')\n", + "\n", + "dogs = phrases(''''Labrador Retrievers / German Shepherd Dogs / Golden Retrievers / Beagles / Bulldogs / \n", + " Yorkshire Terriers / Boxers / Poodles / Rottweilers / Dachshunds / Shih Tzu / Doberman Pinschers / \n", + " Miniature Schnauzers / French Bulldogs / German Shorthaired Pointers / Siberian Huskies / Great Danes / \n", + " Chihuahuas / Pomeranians / Cavalier King Charles Spaniels / Shetland Sheepdogs / Australian Shepherds / \n", + " Boston Terriers / Pembroke Welsh Corgis / Maltese / Mastiffs / Cocker Spaniels / Havanese / \n", + " English Springer Spaniels / Pugs / Brittanys / Weimaraners / Bernese Mountain Dogs / Vizslas / Collies / \n", + " West Highland White Terriers / Papillons / Bichons Frises / Bullmastiffs / Basset Hounds / \n", + " Rhodesian Ridgebacks / Newfoundlands / Russell Terriers / Border Collies / Akitas / \n", + " Chesapeake Bay Retrievers / Miniature Pinschers / Bloodhounds / St. Bernards / Shiba Inu / Bull Terriers / \n", + " Chinese Shar-Pei / Soft Coated Wheaten Terriers / Airedale Terriers / Portuguese Water Dogs / Whippets / \n", + " Alaskan Malamutes / Scottish Terriers / Australian Cattle Dogs / Cane Corso / Lhasa Apsos / \n", + " Chinese Crested / Cairn Terriers / English Cocker Spaniels / Dalmatians / Italian Greyhounds / \n", + " Dogues de Bordeaux / Samoyeds / Chow Chows / German Wirehaired Pointers / Belgian Malinois / \n", + " Great Pyrenees / Pekingese / Irish Setters / Cardigan Welsh Corgis / Staffordshire Bull Terriers / \n", + " Irish Wolfhounds / Old English Sheepdogs / American Staffordshire Terriers / Bouviers des Flandres / \n", + " Greater Swiss Mountain Dogs / Japanese Chin / Tibetan Terriers / Brussels Griffons / \n", + " Wirehaired Pointing Griffons / Border Terriers / English Setters / Basenjis / Standard Schnauzers / \n", + " Silky Terriers / Flat-Coated Retrievers / Norwich Terriers / Afghan Hounds / Giant Schnauzers / Borzois / \n", + " Wire Fox Terriers / Parson Russell Terriers / Schipperkes / Gordon Setters / Treeing Walker Coonhounds''')\n", + "cats = phrases('''Abyssinian / Aegean cat / Australian Mist / American Curl / American Bobtail / \n", + " American Polydactyl / American Shorthair / American Wirehair / Arabian Mau / Asian / Asian Semi-longhair / \n", + " Balinese / Bambino / Bengal / Birman / Bombay / Brazilian Shorthair / British Shorthair / British Longhair / \n", + " Burmese / Burmilla / California Spangled Cat / Chantilly/Tiffany / Chartreux / Chausie / Cheetoh / \n", + " Colorpoint Shorthair / Cornish Rex / Cymric / Cyprus cat / Devon Rex / Donskoy or Don Sphynx / Dragon Li / \n", + " Dwelf / Egyptian Mau / European Shorthair / Exotic Shorthair / German Rex / Havana Brown / Highlander / \n", + " Himalayan-Colorpoint Persian / Japanese Bobtail / Javanese / Khao Manee / Korat / Korn Ja / \n", + " Kurilian Bobtail / LaPerm / Maine Coon / Manx / Mekong bobtail / Minskin / Munchkin / Nebelung / Napoleon / \n", + " Norwegian Forest Cat / Ocicat / Ojos Azules / Oregon Rex / Oriental Bicolor / Oriental Shorthair / \n", + " Oriental Longhair / Persian / Peterbald / Pixie-bob / Ragamuffin / Ragdoll / Russian Blue / Russian Black / \n", + " Sam Sawet / Savannah / Scottish Fold / Selkirk Rex / Serengeti cat / Serrade petit / Siamese / Siberian / \n", + " Singapura / Snowshoe / Sokoke / Somali / Sphynx / Swedish forest cat / Thai / Tonkinese / Toyger / \n", + " Turkish Angora / Turkish Van / Ukrainian Levkoy / York Chocolate Cat''')\n", + "\n", + "movies = phrases('''Citizen Kane / The Godfather / Vertigo / 2001: A Space Odyssey / The Searchers / Sunrise / \n", + " Singin’ in the Rain / Psycho / Casablanca / The Godfather Part II / The Magnificent Ambersons / Chinatown / \n", + " North by Northwest / Nashville / The Best Years of Our Lives / McCabe & Mrs Miller / The Gold Rush / \n", + " City Lights / Taxi Driver / Goodfellas / Mulholland Drive / Greed / Annie Hall / The Apartment / \n", + " Do the Right Thing / Killer of Sheep / Barry Lyndon / Pulp Fiction / Raging Bull / Some Like It Hot / \n", + " A Woman Under the Influence / The Lady Eve / The Conversation / The Wizard of Oz / Double Indemnity / \n", + " Star Wars / Imitation of Life / Jaws / The Birth of a Nation / Meshes of the Afternoon / Rio Bravo / \n", + " Dr Strangelove / Letter from an Unknown Woman / Sherlock Jr / The Man Who Shot Liberty Valance / \n", + " It’s a Wonderful Life / Marnie / A Place in the Sun / Days of Heaven / His Girl Friday / Touch of Evil / \n", + " The Wild Bunch / Grey Gardens / Sunset Boulevard / The Graduate / Back to the Future / Crimes and Misdemeanors / \n", + " The Shop Around the Corner / One Flew Over the Cuckoo’s Nest / Blue Velvet / Eyes Wide Shut / The Shining / \n", + " Love Streams / Johnny Guitar / The Right Stuff / Red River / Modern Times / Notorious / Koyaanisqatsi / \n", + " The Band Wagon / Groundhog Day / The Shanghai Gesture / Network / Forrest Gump / \n", + " Close Encounters of the Third Kind / The Empire Strikes Back / Stagecoach / Schindler’s List / \n", + " The Tree of Life / Meet Me in St Louis / Thelma & Louise / Raiders of the Lost Ark / Bringing Up Baby / \n", + " Deliverance / Night of the Living Dead / The Lion King / Eternal Sunshine of the Spotless Mind / \n", + " West Side Story / In a Lonely Place / Apocalypse Now / ET: The Extra-Terrestrial / The Night of the Hunter / \n", + " Mean Streets / 25th Hour / Duck Soup / The Dark Knight / Gone With the Wind / Heaven’s Gate / 12 Years a Slave / \n", + " Ace in the Hole''')\n", + "tv = phrases('''The Abbott and Costello Show / ABC’s Wide World of Sports / Alfred Hitchcock Presents /\n", + " All in the Family / An American Family / American Idol / Arrested Development / Battlestar Galactica /\n", + " The Beavis and Butt-Head Show / The Bob Newhart Show / Brideshead Revisited / Buffalo Bill /\n", + " Buffy the Vampire Slayer / The Carol Burnett Show / The CBS Evening News with Walter Cronkite /\n", + " A Charlie Brown Christmas / Cheers / The Cosby Show / The Daily Show / Dallas / The Day After / \n", + " Deadwood / The Dick Van Dyke Show / Dragnet / The Ed Sullivan Show / The Ernie Kovacs Show /\n", + " Felicity / Freaks and Geeks / The French Chef / Friends / General Hospital /\n", + " The George Burns and Gracie Allen Show / Gilmore Girls / Gunsmoke / Hill Street Blues /\n", + " Homicide: Life on the Street / The Honeymooners / I, Claudius / I Love Lucy / King of the Hill /\n", + " The Larry Sanders Show / Late Night with David Letterman / Leave It to Beaver / Lost /\n", + " Married with Children / Mary Hartman, Mary Hartman / The Mary Tyler Moore Show / MASH / The Monkees /\n", + " Monty Python’s Flying Circus / Moonlighting / My So-Called Life / Mystery Science Theater 3000 /\n", + " The Odd Couple / The Office / The Oprah Winfrey Show / Pee Wee’s Playhouse / Playhouse 90 /\n", + " The Price Is Right / Prime Suspect / The Prisoner / The Real World / Rocky and His Friends / Roots /\n", + " Roseanne / Sanford and Son / Saturday Night Live / Second City Television / See It Now / Seinfeld /\n", + " Sesame Street / Sex and the City / The Shield / The Simpsons / The Singing Detective / Six Feet Under /\n", + " 60 Minutes / Soap / The Sopranos / South Park / SpongeBob SquarePants / SportsCenter / Star Trek /\n", + " St Elsewhere / The Super Bowl / Survivor / Taxi /The Tonight Show Starring Johnny Carson /\n", + " 24 / The Twilight Zone / Twin Peaks / The West Wing / What’s My Line / WKRP in Cincinnati /\n", + " The Wire / Wiseguy / The X-Files''')\n", + "\n", + "stars = phrases('''Humphrey Bogart / Cary Grant / James Stewart / Marlon Brando / Fred Astaire / Henry Fonda / \n", + " Clark Gable / James Cagney / Spencer Tracy / Charlie Chaplin / Gary Cooper / Gregory Peck / John Wayne / \n", + " Laurence Olivier / Gene Kelly / Orson Welles / Kirk Douglas / James Dean / Burt Lancaster / Marx Brothers / \n", + " Buster Keaton / Sidney Poitier / Robert Mitchum / Edward G. Robinson / William Holden / Katharine Hepburn / \n", + " Bette Davis / Audrey Hepburn / Ingrid Bergman / Greta Garbo / Marilyn Monroe / Elizabeth Taylor / Judy Garland / \n", + " Marlene Dietrich / Joan Crawford / Barbara Stanwyck / Claudette Colbert / Grace Kelly / Ginger Rogers / \n", + " Mae West / Vivien Leigh / Lillian Gish / Shirley Temple / Rita Hayworth / Lauren Bacall / Sophia Loren / \n", + " Jean Harlow / Carole Lombard / Mary Pickford / Ava Gardner''')\n", + "scientists = phrases('''Alain Aspect / Martin Karplus / David Baltimore / Donald Knuth / Allen Bard / \n", + " Robert Marks II / Timothy Berners-Lee / Craig Mello / John Tyler Bonner / Luc Montagnier / Dennis Bray / \n", + " Gordon Moore / Sydney Brenner / Kary Mullis / Pierre Chambon / C Nüsslein-Volhard / Simon Conway Morris / \n", + " Seiji Ogawa / Mildred Dresselhaus / Jeremiah Ostriker / Gerald M Edelman / Roger Penrose / Ronald Evans / \n", + " Stanley Prusiner / Anthony Fauci / Henry F Schaefer III / Anthony Fire / Thomas Südhof / Jean Frechet / \n", + " Jack Szostak / Margaret Geller / James Tour / Jane Goodall / Charles Townes / Alan Guth / Harold Varmus / \n", + " Lene Vestergaard Hau / Craig Venter / Stephen Hawking / James Watson / Peter Higgs / Steven Weinberg / \n", + " Leroy Hood / George Whitesides / Eric Kandel / Edward Wilson / Andrew Knoll / Edward Witten / Charles Kao / \n", + " Shinya Yamanaka''')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "And here we show how it works:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "' T|E.P|OP'" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution = findregex(starwars, startrek)\n", + "solution" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "not mistakes(solution, starwars, startrek) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Plan of Attack\n", + "----\n", + "\n", + "To improve the program, I'll take the following steps:\n", + "\n", + "- *Profiling:* Figure out where the program spends its time.\n", + "- *Speedup:* Make the program faster.\n", + "- *Benchmarking:* Run the program over pairs of arbitrary lists to see how fast it is and how short the solutions are. \n", + "- *Analyzing:* Learn something by looking at the benchmark results.\n", + "- *Searching:* Introduce a better search algorithm.\n", + "- *Eliminating Parts:* Get rid of parts that can't possibly be part of an optimal solution.\n", + "- *Adding Parts:* Add new types of parts to allow new, shorter solutions.\n", + "- *Randomizing Search:* Randomness allows us to explore different parts of the search space.\n", + "- *Speculating:* Think about what we could do next.\n", + "\n", + "Profiling \n", + "----\n", + "\n", + "Let's time how long it takes to separate the top 100 adverbs from top 100 nouns:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 5.4 s per loop\n" + ] + } + ], + "source": [ + "%timeit findregex(adverbs, nouns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "On my computer it was 4 seconds. I have some ideas for how to make this faster, but I know that I shouldn't waste effort trying to speed up parts of a program that [don't take much of the total time](http://en.wikipedia.org/wiki/Amdahl's_law). I'll use the [`cProfile`](http://docs.python.org/2/library/profile.html#module-cProfile) module to see where the time goes:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 12220085 function calls in 7.748 seconds\n", + "\n", + " Ordered by: cumulative time\n", + "\n", + " ncalls tottime percall cumtime percall filename:lineno(function)\n", + " 1 0.000 0.000 7.748 7.748 {built-in method builtins.exec}\n", + " 1 0.000 0.000 7.748 7.748 :1()\n", + " 1 0.001 0.001 7.748 7.748 :23(findregex)\n", + " 54424 0.051 0.000 7.652 0.000 :39(matches)\n", + " 54424 1.052 0.000 7.601 0.000 :41()\n", + " 2841615 1.347 0.000 6.549 0.000 re.py:170(search)\n", + " 2841615 1.482 0.000 4.016 0.000 re.py:278(_compile)\n", + " 41 0.015 0.000 3.584 0.087 {built-in method builtins.max}\n", + " 25445 0.033 0.000 3.569 0.000 :31(score)\n", + " 41 0.021 0.001 3.335 0.081 :36()\n", + " 45055 0.223 0.000 2.459 0.000 sre_compile.py:531(compile)\n", + " 45055 0.169 0.000 1.206 0.000 sre_parse.py:819(parse)\n", + " 2841615 1.186 0.000 1.186 0.000 {method 'search' of '_sre.SRE_Pattern' objects}\n", + " 45055 0.080 0.000 0.911 0.000 sre_compile.py:516(_code)\n", + " 1 0.000 0.000 0.825 0.825 :46(regex_parts)\n", + " 45055 0.098 0.000 0.821 0.000 sre_parse.py:429(_parse_sub)\n", + " 1 0.003 0.003 0.809 0.809 :50()\n", + " 45055 0.281 0.000 0.660 0.000 sre_parse.py:491(_parse)\n", + " 45055 0.263 0.000 0.650 0.000 sre_compile.py:412(_compile_info)\n", + " 172941 0.076 0.000 0.246 0.000 sre_parse.py:247(get)\n", + " 217996 0.212 0.000 0.212 0.000 sre_parse.py:226(__next)\n", + " 45055 0.159 0.000 0.196 0.000 sre_parse.py:167(getwidth)\n", + " 45055 0.141 0.000 0.177 0.000 sre_compile.py:64(_compile)\n", + " 916825 0.129 0.000 0.129 0.000 {method 'append' of 'list' objects}\n", + " 45055 0.074 0.000 0.122 0.000 sre_parse.py:217(__init__)\n", + " 172941 0.067 0.000 0.091 0.000 sre_parse.py:165(append)\n", + " 28890 0.078 0.000 0.082 0.000 sre_compile.py:391(_generate_overlap_table)\n", + " 574427 0.058 0.000 0.058 0.000 {built-in method builtins.len}\n", + " 45055 0.046 0.000 0.054 0.000 sre_parse.py:797(fix_flags)\n", + " 90110 0.040 0.000 0.051 0.000 sre_compile.py:513(isstring)\n", + " 135163 0.050 0.000 0.050 0.000 {built-in method builtins.min}\n", + " 45055 0.048 0.000 0.048 0.000 {built-in method _sre.compile}\n", + " 225275 0.043 0.000 0.043 0.000 {built-in method builtins.isinstance}\n", + " 90110 0.032 0.000 0.042 0.000 sre_parse.py:75(groups)\n", + " 45055 0.041 0.000 0.041 0.000 sre_parse.py:70(__init__)\n", + " 45055 0.026 0.000 0.031 0.000 sre_parse.py:276(tell)\n", + " 45055 0.029 0.000 0.029 0.000 sre_parse.py:105(__init__)\n", + " 88 0.020 0.000 0.020 0.000 {method 'clear' of 'dict' objects}\n", + " 57782 0.017 0.000 0.017 0.000 {method 'extend' of 'list' objects}\n", + " 1 0.002 0.002 0.016 0.016 :49()\n", + " 45055 0.014 0.000 0.014 0.000 sre_parse.py:242(match)\n", + " 119455 0.013 0.000 0.013 0.000 {built-in method builtins.ord}\n", + " 2131 0.005 0.000 0.012 0.000 :56(dotify)\n", + " 45055 0.008 0.000 0.008 0.000 {method 'items' of 'dict' objects}\n", + " 2131 0.004 0.000 0.005 0.000 :59()\n", + " 14684 0.003 0.000 0.003 0.000 {method 'get' of 'dict' objects}\n", + " 11135 0.002 0.000 0.002 0.000 {method 'join' of 'str' objects}\n", + " 98 0.001 0.000 0.002 0.000 :52(subparts)\n", + " 4921 0.001 0.000 0.001 0.000 :61(replacements)\n", + " 2874 0.001 0.000 0.001 0.000 :54()\n", + " 1 0.000 0.000 0.000 0.000 :48()\n", + " 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}\n", + "\n", + "\n" + ] + } + ], + "source": [ + "import cProfile\n", + "\n", + "cProfile.run('findregex(adverbs, nouns)', sort='cumulative')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "About 99% of the time was spent in `matches`. And most of the time in `matches` goes to `re.search`. So my thoughts are: \n", + " \n", + "+ Can we make each call to `matches` run faster? \n", + "+ Can we make fewer calls to `matches`?\n", + "+ Can we use `re.search` more effectively? \n", + "+ Nothing else matters. 99% of the time is in `matches`; don't waste effort speeding up anything else.\n", + "\n", + "# Speedup: Faster `matches` by Compiling Regexes\n", + "\n", + "\n", + "The `re` package uses strings to specify regular expressions, but internally, when we call `re.search` on a string, that string is compiled, with the function `re.compile`, into an object that has a `search` method. If you need to search many times with the same regex, then it is faster to call `re.compile` once, and then call the `search` method of the compiled object, rather than calling `re.search` each time.\n", + "\n", + "Another trick: use the builtin function `filter` rather than a set comprehension. Builtins, written in C, are often faster." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def matches(regex, strings):\n", + " \"Return a set of all the strings that are matched by regex.\"\n", + " searcher = re.compile(regex).search\n", + " return set(filter(searcher, strings))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "One thing to be careful about: the `re` module manages a cache of recent compilations. I call `re.purge()` before each timing, to make sure that I'm not re-using any work that was done before the timing started." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 2.95 s per loop\n" + ] + } + ], + "source": [ + "re.purge()\n", + "\n", + "%timeit findregex(adverbs, nouns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "*That was almost twice as fast!* Not bad for changing two lines. \n", + "\n", + "# Speedup: Fewer `matches` Against Losers" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "In `regex_parts`, for each part, `p`, we test `if not matches(p, losers)`. This applies `searcher` to every loser and builds up a set of all those that match. It would be faster if we could *exit early*: as soon as we find one loser that matches, we don't need to apply `searcher` to the remaining losers. Stefan Pochmann came up with a great way to do this. If we concatenate the list of losers together into one big string, then we only need one call to `re.search` for each part `p`. If a part matches the big string anywhere, the call will return immediately, and we will know the part is no good. \n", + "\n", + "There is one catch: we have to make sure that the start of each loser matches `'^'` and the end matches `'$'`. We can do that by concatenating together the losers with a newline between them, and by using the `re.MULTILINE` option. (See the [`re` module documentation](http://docs.python.org/2/library/re.html) if this is unfamiliar.)\n", + "\n", + "Here is the change, with timing before and after:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 271 ms per loop\n" + ] + } + ], + "source": [ + "re.purge()\n", + "\n", + "%timeit regex_parts(adverbs, nouns)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def regex_parts(winners, losers):\n", + " \"Return parts that match at least one winner, but no loser.\"\n", + " losers_str = '\\n'.join(losers)\n", + " def no_losers(part): return not re.compile(part, re.MULTILINE).search(losers_str)\n", + " wholes = {'^' + w + '$' for w in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " return wholes | set(filter(no_losers, parts))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10 loops, best of 3: 171 ms per loop\n" + ] + } + ], + "source": [ + "re.purge()\n", + "\n", + "%timeit regex_parts(adverbs, nouns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We've made `regex_parts` almost two times faster.\n", + "\n", + "# Speedup: Fewer `matches` Against Winners\n", + "\n", + "Here's what `findregex` currently looks like:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, k=4):\n", + " \"Find a regex that matches all winners but no losers (sets of strings).\"\n", + " # Make a pool of regex parts, then pick from them to cover winners.\n", + " # On each iteration, add the 'best' part to 'solution',\n", + " # remove winners covered by best, and keep in 'pool' only parts\n", + " # that still match some winner.\n", + " pool = regex_parts(winners, losers)\n", + " solution = []\n", + " def score(p): return k * len(matches(p, winners)) - len(p)\n", + " while winners:\n", + " best = max(pool, key=score)\n", + " solution.append(best)\n", + " winners = winners - matches(best, winners)\n", + " pool = {p for p in pool if matches(p, winners)}\n", + " return OR(solution)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Notice that we call `matches` twice (once within `score`) for every part in the pool on every iteration of the main loop. If there are 50 iterations of the loop, and 1000 parts, that's 100,000 calls to `matches`. Instead of repeating all these calls, I propose that, for each part in the pool, we limit ourselves to this:\n", + "\n", + "- One `re.compile`.\n", + "- One `re.search` against each of the winners.\n", + "- One `re.search` against the big string of losers.\n", + "- Some cache lookups as needed.\n", + "\n", + "During initialization, we create a dict, called `covers`, that will serve as a cache: `covers[p]` is the set of all winners that match the part `p`. The new function `regex_covers` replaces the old function `regex_parts`. Here is the new `findregex`, with timing before and after:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 2.85 s per loop\n" + ] + } + ], + "source": [ + "re.purge()\n", + "\n", + "%timeit findregex(adverbs, nouns)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, k=4):\n", + " \"Find a regex that matches all winners but no losers (sets of strings).\"\n", + " # Initialize covers = {regex: {winner,...}} for a large set of regex components.\n", + " # On each iteration, add the 'best' component to 'solution',\n", + " # remove winners covered by best, and keep in 'pool' only components\n", + " # that still match some winner.\n", + " covers = regex_covers(winners, losers)\n", + " pool = list(covers)\n", + " solution = [] \n", + " def score(p): return k * len(covers[p] & winners) - len(p)\n", + " while winners:\n", + " best = max(pool, key=score)\n", + " solution.append(best)\n", + " winners = winners - covers[best]\n", + " pool = [p for p in pool \n", + " if not covers[p].isdisjoint(winners)]\n", + " return OR(solution)\n", + "\n", + "def regex_covers(winners, losers):\n", + " \"\"\"Generate regex parts and return a dict of {regex: {winner,...}}.\n", + " Each regex matches at least one winner and no loser.\"\"\"\n", + " losers_str = '\\n'.join(losers)\n", + " wholes = {'^' + w + '$' for w in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " pool = wholes | parts\n", + " searchers = {p: re.compile(p, re.MULTILINE).search for p in pool}\n", + " return {p: Set(filter(searchers[p], winners)) \n", + " for p in pool\n", + " if not searchers[p](losers_str)}" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 251 ms per loop\n" + ] + } + ], + "source": [ + "re.purge()\n", + "\n", + "%timeit findregex(adverbs, nouns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "*Wow!* That's a dozen times faster! But I don't want to draw too many conclusions from just this one example." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Benchmarking\n", + "\n", + "We will benchmark the program on a suite of 22 different problems (11 examples, run in both directions). The function `benchmark` finds a solution to each problem and prints the number of characters in the solution, and some other information. In the end it prints the total number of characters, and if we use the `%time` magic, we can see how long it took." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "EXAMPLES = [ex for example in [\n", + " (winners, 'win', 'lose', losers),\n", + " (boys, 'boy', 'girl', girls),\n", + " (pharma, 'drug', 'city', cities),\n", + " (foo, 'foo', 'bar', bar),\n", + " (starwars, 'wars', 'trek', startrek),\n", + " (nouns, 'noun', 'adj', adverbs),\n", + " (nouns, 'noun', 'verb', verbs),\n", + " (randoms, 'rand', 'built', builtins),\n", + " (dogs, 'dog', 'cat', cats),\n", + " (movies, 'movie', 'tv', tv),\n", + " (scientists, 'sci', 'star', stars)]\n", + " for ex in (example, example[::-1])] # Do each example both ways\n", + "\n", + "SOLUTION = {} # A cached table of solutions; SOLUTION[W, L] will hold a regex\n", + " \n", + "def benchmark(examples=EXAMPLES): \n", + " \"Run examples; print summaries; return total of solution lengths.\"\n", + " totalchars = 0\n", + " for (W, Wname, Lname, L) in examples:\n", + " re.purge()\n", + " solution = SOLUTION[W, L] = findregex(W, L)\n", + " assert not mistakes(solution, W, L)\n", + " legend = '{}({}):{}({})'.format(Wname, len(W), Lname, len(L))\n", + " print('{:20} {:3}: \"{}\"'.format(legend, len(solution), truncate(solution, 50)))\n", + " totalchars += len(solution)\n", + " print('Total characters: {:6}'.format(totalchars))\n", + " return totalchars\n", + "\n", + "def truncate(text, nchars, ellipsis=' ...'):\n", + " \"Return whole string, or version truncated to nchars.\"\n", + " return text if len(text) < nchars else text[:nchars-len(ellipsis)] + ellipsis" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 54: \"a.a|i..n|j|li|a.t|a..i|bu|oo|ay.|n.e|r.e$|ru|l ...\"\n", + "lose(34):win(34) 59: \"^d|^s|r.$|^.re|cc|hu|ld.|nd.|l.i|n.y|ya|ss|pa| ...\"\n", + "boy(10):girl(10) 11: \"e.$|a.$|a.o\"\n", + "girl(10):boy(10) 10: \"a$|^..i|is\"\n", + "drug(10):city(10) 15: \"o.$|x|ir|f|q|^e\"\n", + "city(10):drug(10) 11: \"ri|an|ca|id\"\n", + "foo(21):bar(21) 3: \"f.o\"\n", + "bar(21):foo(21) 28: \"r..$|k|.m|^..l|ld|c..n|id|or\"\n", + "wars(6):trek(9) 9: \" T|E.P|W \"\n", + "trek(9):wars(6) 15: \"TI|R.. |Y|RA|IS\"\n", + "noun(100):adj(98) 170: \"m.n|a.e$|m$|in.$|en.$|ch.|^w.r|id|^g|io|s.n|o. ...\"\n", + "adj(98):noun(100) 155: \"a.l|^..$|st$|et|re$|tl|en$|^al|ver$|nl|^a.o|ui ...\"\n", + "noun(100):verb(94) 174: \"m.n|er$|am|es|^.ar|ho|.on|or.$|id|f.c|o.l|..h. ...\"\n", + "verb(94):noun(100) 177: \"^..l|ak|ve$|^..$|s..n|a.n|^fi|^tr|ut$|.pe|o.g| ...\"\n", + "rand(58):built(147) 76: \"ia|and|^_.e|_s|_.o|.G|e_|P.$|_e|ets|lti|^_.c|^ ...\"\n", + "built(147):rand(58) 138: \"ro|Wa|as|^d|^i|r..i|li|^o|te.$|a.s$|m..$|up|tr ...\"\n", + "dog(100):cat(91) 73: \"E.S$|O.S$|DS|.AS|.HI|RD|.D.E|ANS|IES|G.S|N.S$| ...\"\n", + "cat(91):dog(100) 113: \"AI.$|T$|AN$|EX|A$|L$|Y$|A..B|NX|M.I|H$|R$|R.G| ...\"\n", + "movie(100):tv(97) 157: \"GO| . |^N|HIN|S O|E IN|A.NI|.A.C|TIO|RIV|U.K|E ...\"\n", + "tv(97):movie(100) 148: \"H.W|.CI|PR|R..$|D .E|A.ER|O..I|PE|^SE|^RO|T.C| ...\"\n", + "sci(50):star(50) 70: \"AL..|T..N|R.S|.KA|NN|VE|-|MU|^P|OD|OS|L.O|W.I| ...\"\n", + "star(50):sci(50) 77: \"CA|T. |LI..|F..D|GR|BU| GA|LO.|R..Y|UM| R| ST| ...\"\n", + "Total characters: 1743\n", + "CPU times: user 5.98 s, sys: 19.1 ms, total: 6 s\n", + "Wall time: 6 s\n" + ] + }, + { + "data": { + "text/plain": [ + "1743" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time benchmark()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "In 5 seconds we solved 22 problems, getting a score of 1749 for the total number of characters in all the solutions. \n", + "\n", + "(**Note:** if you run this, you might get a slightly different answer. Why? The algorithm has no random parts in it; shouldn't it return the same result every time? It will return the same results if you run it twice in the same Python. But when `findregex` evaluates `max(pool, key=score)` and two components are tied for the best score, Python chooses the one that comes first in the iteration of `pool`. And different versions of Python can iterate over `pool` in different orders.)\n", + "\n", + "# Analyzing\n", + "\n", + "What can we do to understand the program better? Let's start by analyzing what the regex parts look like. We cached the solutions in `SOLUTION`, and we can start to examine the solutions and the parts they are made of. For example, how long are the parts that appears in solutions?" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Counter({1: 17, 2: 192, 3: 179, 4: 84, 7: 1, 10: 1})" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "parts = [p for regex in SOLUTION.values() for p in regex.split('|')]\n", + "lengths = [len(p) for p in parts]\n", + "Counter(lengths)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This says that there are 17 parts of length 1, 198 parts of length 2, etc. There's also one part of length 10; that's such an outlier, I wonder if it is an error? " + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'^HAVANESE$'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(parts, key=len)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I happen to own [a Havanese](http://pn.smugmug.com/Family/Dobby-Idgie/i-2JPzBkL/A), but I don't think the program knew that. Rather, the issue is that in the set of `cats` we have `'HAVANA BROWN'` and `'JAVANESE'`, which means that any 4-letter-or-less subsequence of `'HAVANESE'` matches one of these two. So the only component that doesn't match one of these two cats is the whole, `'^HAVANESE$'`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "What about the individual characters that make up the parts? Which ones are popular? We can see:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('.', 205),\n", + " ('$', 71),\n", + " ('a', 58),\n", + " ('^', 54),\n", + " ('e', 48),\n", + " ('r', 46),\n", + " ('o', 44),\n", + " ('t', 37),\n", + " ('i', 37),\n", + " ('n', 37),\n", + " ('l', 35),\n", + " ('O', 31),\n", + " ('E', 31),\n", + " ('A', 30),\n", + " ('s', 28),\n", + " ('R', 27),\n", + " ('S', 26),\n", + " ('N', 24),\n", + " ('u', 23),\n", + " ('I', 23)]" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(cat(parts)).most_common(20)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "I wonder if there are parts that appear in many solutions?" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('id', 4),\n", + " ('ru', 3),\n", + " ('hu', 3),\n", + " ('f.c', 2),\n", + " ('oo', 2),\n", + " ('f$', 2),\n", + " ('lt', 2),\n", + " ('m.n', 2),\n", + " ('vi', 2),\n", + " ('Y', 2),\n", + " ('^..$', 2),\n", + " ('N.S$', 2),\n", + " ('rc', 2),\n", + " ('^u', 2),\n", + " ('a$', 2),\n", + " ('j', 2),\n", + " ('ls', 2),\n", + " ('UG', 2),\n", + " ('^..l', 2),\n", + " ('YN', 2)]" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(parts).most_common(20)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Most parts appear in only 2 solutions or less.\n", + "\n", + "# Analyzing: Set Cover Theory\n", + "\n", + "Now I want to think about this as a [set cover problem](http://en.wikipedia.org/wiki/Set_cover_problem). Wikipedia shows this diagram to explain set cover:\n", + " \n", + "\n", + "\n", + "The idea is that each blue dot in set $u$ on the left represents a regex component, and each green dot in set $v$ represents a winner that is matched by the regex component. The problem is to pick some blue dots such that all the green dots are covered. In this example, we can see that picking the blue dots that are second and third from the top will do it.\n", + "\n", + "But in general, what do our graphs look like? How many blue and green dots are there? How many links between them? Let's build a little tool to find out. We'll list the $N$ \"most popular\" blue and green dots—the ones with the most links to the other side. Then we'll show histograms of all the nodes and their numbers of links.\n", + "\n", + "But first some explanation: I use the term *multimap* for a dictionary, like `covers = {regex: {winner,...}}`, that maps keys to collections. Then `invert_multimap(covers)` is of the form `{winner: {regex, ...}}`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def show(W, L, N=10):\n", + " \"Summarize the links between the set of winners, W, and its parts.\"\n", + " covers = regex_covers(W, L)\n", + " inv = invert_multimap(covers)\n", + " for ((n1, w), (n2, r)) in zip(top(N, covers), top(N, inv)):\n", + " print(\"{:8} {:2} | {:3}| {}\".format(w, n1, n2, r))\n", + " print(\"TOTAL %5d | %3d TOTAL\" % (len(covers), len(W)))\n", + " plt.subplot(1, 2, 1); histmm(covers, \"parts\", \"winners\")\n", + " plt.subplot(1, 2, 2); histmm(inv, \"winners\", \"parts\")\n", + " \n", + "def top(N, multimap): \n", + " \"The top N longest items in a dict of {key: {val,...})\"\n", + " return sorted([(len(vals), key) for (key, vals) in multimap.items()], reverse=True)[:N]\n", + "\n", + "def histmm(multimap, key, val): \n", + " \"Display a histogram of how many values each key has.\"\n", + " plt.rcParams['figure.figsize'] = (8.0, 4.0)\n", + " plt.hist([len(v) for v in multimap.values()])\n", + " plt.xlabel('set size of {' + val + ',...}')\n", + " plt.ylabel('number of ' + key + ' mapping to that size')\n", + "\n", + "def invert_multimap(multimap):\n", + " \"Covert {key: {val,...}} to {val: [key,...]}.\"\n", + " result = defaultdict(set)\n", + " for key in multimap:\n", + " for val in multimap[key]:\n", + " result[val].add(key)\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "i..n 4 | 110| van-buren\n", + "a.a 4 | 98| washington\n", + "a..i 4 | 93| jefferson\n", + "r.i. 3 | 93| eisenhower\n", + "r.i 3 | 81| garfield\n", + "oo.. 3 | 78| roosevelt\n", + "oo. 3 | 72| buchanan\n", + "oo 3 | 61| obama\n", + "ma 3 | 61| kennedy\n", + "li.. 3 | 59| jackson\n", + "TOTAL 1615 | 34 TOTAL\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(winners, losers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "What does this say? First the table says that there are only three regexes that have 4 winners; all the rest have 3 or fewer winners. So the links going left-to-right are rather sparse. There are more links going the other direction; 110 to `van-buren`, for example. The histograms give the whole picture mapping set sizes to the number of keys that have that set size. So, on the left we see that over 1400 regexes have a set size of one winner, and 100 or fewer have set sizes of 2 and 3, and we saw that only 3 regexes have a set size of 4 winners. On the right, the histogram shows a wide spread of winners that have set sizes between 1 and 110 regexes.\n", + "\n", + "From looking at this I get two ideas:\n", + " \n", + "+ I notice that both `'oo..'` and `'oo.'` happen to match 3 winners. But even if I didn't know how many they matched, I would know that the winners matched by `'oo..'` must be a subset of the winners matched by `'oo.'` (remember that a set is a subset of itself). Furthermore, `'oo.'` is shorter. This suggests that we would *never* want to use `'oo..'` in a solution, because we could always make the solution one character shorter (and cover at least all the same winners) by substituting `'oo.'`. We say that * part A dominates B* if *A* is shorter and matches a superset of winners. We might as well throw out all dominated parts right at the start.\n", + "\n", + "+ It might be a good idea to pay special attention to the characters, like `'-'`, that appear in the winners but not the losers.\n", + "\n", + "Let's look at another example:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "E.S$ 41 | 186| SOFT COATED WHEATEN TERRIERS\n", + "RS$ 34 | 184| STAFFORDSHIRE BULL TERRIERS\n", + "ERS$ 34 | 175| GREATER SWISS MOUNTAIN DOGS\n", + ".RS$ 34 | 162| TREEING WALKER COONHOUNDS\n", + "IE.S 22 | 157| CAVALIER KING CHARLES SPANIELS\n", + "E.RI 21 | 149| AMERICAN STAFFORDSHIRE TERRIERS\n", + "T..R 20 | 147| WEST HIGHLAND WHITE TERRIERS\n", + "IER. 19 | 146| STANDARD SCHNAUZERS\n", + "IER 19 | 146| FLAT-COATED RETRIEVERS\n", + "I.R. 19 | 146| CHESAPEAKE BAY RETRIEVERS\n", + "TOTAL 4570 | 100 TOTAL\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(dogs, cats)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "My immediate reaction to this is \"there are a lot of retrievers and terriers.\" All ten of the parts in the table recognize this fact, but the left-hand histogram shows that almost all the parts match fewer than 5 dog breeds. In contrast, the right-hand histogram shows that most of the dog breeds have 9 or more parts that match them.\n", + "\n", + "Let's look at one more example:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a.l 12 | 94| especially\n", + "a.ly 11 | 83| eventually\n", + "a.l. 11 | 74| particularly\n", + ".a.l 11 | 67| actually\n", + "ll 9 | 65| quickly\n", + "^..$ 9 | 65| exactly\n", + ".ll 9 | 65| directly\n", + "..ll 8 | 63| certainly\n", + "all 7 | 61| usually\n", + "st$ 6 | 57| recently\n", + "TOTAL 2049 | 98 TOTAL\n" + ] + }, + { + "data": { + "image/png": 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011AvoEcAJH2WKi+e1mhUETFuoxYAJK1EVSW/exfe+7W2fydpfWC2pDtbd9q2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\nkyRtYHsf4DHbO9hu9zxtGsv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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show(adverbs, nouns)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The pattern looks similar here. Almost all the parts match only one winner, but most of the winners are matched by many parts. What can I conclude from this?\n", + "\n", + "+ It would be good to think of new types of parts that match more winners.\n", + "+ Most parts are 2 or 3 characters long and most match just 1 or 2 winners. That suggests that often we will have a tie in the `score` function, and greedy search will arbitrarily pick the one that comes first. But I'm worried that another choice might be better. Maybe we should replace greedy search with something that considers more than one choice.\n", + "\n", + "Given all we've seen, I will shift my attention to understanding the search algorithm we have, and thinking about how to improve it." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Analyzing: Understanding Greedy vs. Exhaustive Search\n", + "\n", + "`findregex` is a *greedy search* algorithm. In general, greedy search is used when you are trying to find a solution that is composed of parts. On each iteration you choose a part that looks good, and you never reconsider that choice; you just keep on adding parts until you get a complete solution. \n", + "\n", + "The pseudo-code for a general `greedy_search`, described as a recursive function, is given below. It takes two arguments: a set of parts, and a partial solution indicating parts that have previously been chosen. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "# Pseudocode \n", + "def greedy_search(parts, partial_solution=None):\n", + " if is_complete(partial_solution):\n", + " return partial_solution\n", + " else:\n", + " best = max(parts, key=score)\n", + " return greedy_search(parts - {best}, partial_solution + best)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "An *exhaustive search* considers *every* possible choice of parts, and selects the best solution. On each iteration exhaustive search picks a part (just like greedy search), but then it considers *both* using the part and not using the part. You can see that exhaustive search is almost identical to greedy search, except that it has *two* recursive calls (on lines 7 and 8) instead of *one* (on line 7). (*If you are viewing this in a iPython notebook, not just a web page, you can toggle line numbers by pressing 'ctrl-M L' within a cell.*) How do we choose between the results of the two calls? We need a cost function that we are trying to minimize. (For regex golf the cost of a solution is the length of the string.)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "# Pseudocode\n", + "def exhaustive_search(parts, partial_solution=None):\n", + " if is_complete(partial_solution):\n", + " return partial_solution\n", + " else:\n", + " best = max(parts, key=score)\n", + " return min(exhaustive_search(parts - {best}, partial_solution + best),\n", + " exhaustive_search(parts - {best}, partial_solution),\n", + " key=cost)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Here's an interesting piece of trivia: the first thing that exhaustive search does is a greedy search! Think about it: on each recursive call, `exhaustive_search` selects the best part, and then calls itself recursively with `best` chosen as part of the partial solution. It keeps going until it reaches a complete solution. That's exactly what greedy search does. But then exhaustive search does more: It also considers all the cases where it *didn't* choose the best part.\n", + "\n", + "Here's something else to ponder: why should we bother with selecting the \"best\" part? If we're going to explore *all* possibilities, wouldn't it be the same if we just selected *any* part, not the \"best\" one?\n", + "\n", + "# Searching: Computational Complexity of Greedy and Exhaustive Search\n", + "\n", + "\n", + "Greedy search only considers one path towards the goal of finding a solution. Exhaustive search considers two paths on *every* iteration. How much work is that all together? If there are *P* parts, then there are $2^P$ subsets of parts. Now, we don't have to consider every one of these subsets, because the search ends when we cover all the winners. If there are $W$ winners, than an upper bound on the number of combinations we have to consider is the number of ways we can pick $W$ parts from a pool of $P$, which in math we write as ($P$ choose $W$). For the presidential candidates $W$, is 34, and $P$ is 1615.\n", + "\n", + "So exhaustive search would have to consider roughly [(1615 choose 34)](https://www.google.com/search?q=1615+choose+34) = $10^{70}$ combinations, which is clearly too many. Don't even think about dogs versus cats, where $W$ = 100 and $P$ = 4570, so [(4570 choose 100)](https://www.google.com/search?q=4570+choose+100) = $10^{207}$. Fortunately, there is another way.\n", + "\n", + "# Searching: Branch and Bound Search\n", + "\n", + "[*Branch and bound*](http://en.wikipedia.org/wiki/Branch_and_bound) is a search strategy that gets the same answer as exhaustive search, but runs faster because it avoids considering many combinations that could not possibly lead to an optimal solution. Here's how and why it works:\n", + "\n", + "- The *branch* part of the name means that, just like exhaustive search, on each iteration it picks a part, and considers two branches, one where the part is in the solution, and one where it is not. \n", + "- The *bound* part of the name means that the algorithm continually keeps track of the lowest-cost solution it has found so far. This serves as a *bound* on what the optimal solution can be.\n", + "- The *trick* is to notice that the cost of a partial solution always *increases* as we add more parts to it. Therefore, if we ever get to a partial solution whose cost is more than the lowest-cost solution we have found so far, then we can *immediately* discard the partial solution, and *never consider* all the other combinations that would have come from continuing the partial solution. If there are $MP$ parts left to consider, that means we just eliminated $2^P$ potential combinations all at once. \"Eliminating potential combinations\" is also called \"pruning the search tree\"—\"[pruning](https://www.google.com/search?q=pruning)\" means cutting off unwanted branches.\n", + "\n", + "The pseudocode below uses a global variable called `CHEAPEST` to hold the lowest-cost solution found so far. Note that the two branches (two recursive calls in lines 7 and 8) communicate through this global variable. If the first branch sets `CHEAPEST` to an improved solution, then the second branch will see it. That is why it is important to choose good \"best\" parts—it means we are more likely to find a good solution early on, which makes it more likely that we can prune away branches. " + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "# Pseudocode\n", + "def branch_and_bound_search(parts, partial_solution=None):\n", + " if is_complete(partial_solution):\n", + " CHEAPEST = min(CHEAPEST, partial_solution, key=cost)\n", + " elif cost(partial_solution) < cost(CHEAPEST):\n", + " best = select_best(parts)\n", + " branch_and_bound_search(parts - {best}, partial_solution + best)\n", + " branch_and_bound_search(parts - {best}, partial_solution)\n", + " return CHEAPEST" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "# Searching: Anytime Branch and Bound Search\n", + "\n", + "Even with all this pruning, we still may be presented with problems that require trillions of recursive calls. [Who's got that kind of time?](http://www.gocomics.com/calvinandhobbes/1995/08/17#.UvSJImSwI8g) But if we stop the algorithm at any time, we still have our best solution stored in `CHEAPEST`. Algorithms that have the property that an answer is always available are called [*anytime algorithms*](http://en.wikipedia.org/wiki/Anytime_algorithm); let's do that.\n", + "\n", + "I can think of two easy ways to allow early stopping. We could use the [`threading.Timer`](http://docs.python.org/2/library/threading.html#timer-objects) class to run the search for a given number of seconds, then stop. Or we could have a counter which gets decremented every time we make a call, and when it hits zero, stop. I'll use the second approach.\n", + "\n", + "Enough pseudocode—here is a real implementation. Since global variables are [considered bad style](https://google.github.io/styleguide/pyguide.html#Global_variables), I decided to use a class, `BranchBound`, to hold the lowest-cost solution and the number of calls remaining. The class provides one method, `search`, which does the work." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "class BranchBound(object):\n", + " \"Hold state information for a branch and bound search.\"\n", + " def __init__(self, winners, max_num_calls, k=4):\n", + " self.cheapest = trivial(winners)\n", + " self.calls = max_num_calls\n", + " self.k = k\n", + " \n", + " def search(self, covers, partial=None):\n", + " \"\"\"Recursively extend partial regex until it matches all winners in covers.\n", + " Try all reasonable combinations until we run out of calls.\"\"\"\n", + " if self.calls <= 0: \n", + " return self.cheapest\n", + " self.calls -= 1\n", + " covers, partial = simplify_covers(covers, partial)\n", + " if not covers: # Nothing left to cover; solution is complete\n", + " self.cheapest = min(partial, self.cheapest, key=len)\n", + " elif len(OR(partial, min(covers, key=len))) < len(self.cheapest):\n", + " def score(p): return self.k * len(covers[p]) - len(p)\n", + " best = max(covers, key=score) # Best part\n", + " covered = covers[best] # Set of winners covered by best\n", + " covers.pop(best)\n", + " # Try with and without the greedy-best part\n", + " self.search({c:covers[c]-covered for c in covers}, OR(partial, best))\n", + " self.search(covers, partial)\n", + " return self.cheapest" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Simplifying Covers\n", + "\n", + "There's a new function introduced above, `simplify_covers`. The idea is that you pass it a `covers` dict and a partial regex, and it does a triage process to divide the components in `covers` into three categories:\n", + "\n", + "- *Useless components*: could never appear in an optimal solution.\n", + "- *Necessary components*: must appear in any solution (because no other component covers some winner).\n", + "- *Remaining components*: neither useless nor necessary.\n", + " \n", + "The necessary components are joined to the partial regex that is passed in, to yield a new partial regex that the function returns. The useless components are eliminated, and the remaining ones are returned in a new `covers` dict. \n", + "\n", + "`simplify_covers` works by first eliminating useless components, and then selecting necessary components. We keep repeating this process of eliminating and selecting until there are no more changes to `covers`:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def simplify_covers(covers, partial=None):\n", + " \"Eliminate dominated regexes, and select ones that uniquely cover a winner.\"\n", + " previous = None\n", + " while covers != previous:\n", + " previous = covers\n", + " covers = eliminate_dominated(covers)\n", + " covers, necessary = select_necessary(covers)\n", + " partial = OR(partial, necessary)\n", + " return covers, partial" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "For convenience we modified the function `OR` slightly; we made it work just like the function `max` in that you can call it two ways: either with a single argument, which is a collection of components, or with 2 or more arguments, each a component. We also made it ignore components that are `None`, so that `OR(None, 'a')` equals `'a'`, but `OR('a', 'b')` equals `'a|b'`, as does `OR(['a', 'b'])`" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def OR(*regexes):\n", + " \"\"\"OR together component regexes. Ignore 'None' components.\n", + " Allows both OR(a, b, c) and OR([a, b, c]), similar to max.\"\"\"\n", + " if len(regexes) == 1: \n", + " regexes = regexes[0]\n", + " return '|'.join(r for r in regexes if r)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Simplifying Covers: Eliminating Dominated Components\n", + "\n", + "We defined the notion of a regex being *dominated* if there is some other regex that is shorter (or at least not longer) and covers a superset of winners. How can we efficiently compute which parts are dominated? Here's one simple approach: go through each regex part, `p`, and every time we find one that is not dominated by any another regex part `p2`, add `p` (and its winners) to a new dict that we are building up. This approach works, but it is $O(n^2)$.\n", + "\n", + "Here's an alternative that is faster: First, sort all the regexes so that the ones that match more winners come first (in case of tie, put the shorter ones first). (In other words, \"best\" first.) Initialize a new dict to empty, and go through the sorted regexes, `p`, one at a time. For each `p`, compare it only to the regexes, `p2`, that we have already added to the new dict; if none of them dominate `p`, then add `p`. This is still $O(n^2)$, but if, say, 99 out of 100 regexes are eliminated, we will only need $n^2/100$ comparisons.\n", + "\n", + "The code for `eliminate_dominated` is a slight variant on the [version](https://github.com/pochmann/regex-golf) by Stefan Pochmann (because his version turned out to be better than my first version). Note that the function `signature` represents a regex as a pair of numbers, the negative of the number of winners and the length in characters. The smaller (in lexicographical order) this pair is, the \"better\" the regex is. Why is it important to put the regexes in sorted order? So that we know that the only possible dominators are the ones that came *before*, not ones that come after. Note that, as we are going through the component regexes, `p`, in sorted order, if we ever hit a `p` that covers no winners, then we know that all the remaining `p` will also cover no winners (because we're going in best-first order), so we can break out of the loop immediately. And one more thing: the expression `covers[p2] >= covers[p]` asks if `p2` covers a superset of the winners that `p` covers." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def eliminate_dominated(covers):\n", + " \"\"\"Given a dict of {regex: {winner...}}, make a new dict with only the regexes\n", + " that are not dominated by any others. A regex part p is dominated by p2 if p2 covers \n", + " a superset of the matches covered by p, and rp is shorter.\"\"\"\n", + " newcovers = {}\n", + " def signature(p): return (-len(covers[p]), len(p))\n", + " for p in sorted(covers, key=signature):\n", + " if not covers[p]: break # All remaining r must not cover anything\n", + " # r goes in newcache if it is not dominated by any other regex\n", + " if not any(covers[p2] >= covers[p] and len(p2) <= len(p) \n", + " for p2 in newcovers):\n", + " newcovers[p] = covers[p]\n", + " return newcovers" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Simplifying Covers: Selecting Necessary Components\n", + "\n", + "\n", + "If some winner is covered by only one part, then we know that part must be part of the solution. The function `select_necessary` finds all such parts, `OR`s them together, and returns that, along with a dict of the remaining covers, after removing the necessary parts (and removing all the winners that are covered by the neccessary parts)." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def select_necessary(covers):\n", + " \"\"\"Select winners covered by only one part; remove from covers.\n", + " Return a pair of (covers, necessary).\"\"\"\n", + " counts = Counter(w for p in covers for w in covers[p])\n", + " necessary = {p for p in covers if any(counts[w] == 1 for w in covers[p])}\n", + " if necessary:\n", + " covered = {w for p in necessary for w in covers[p]}\n", + " covers = {p: covers[p] - covered \n", + " for p in covers if p not in necessary}\n", + " return covers, OR(necessary)\n", + " else:\n", + " return covers, None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Testing and Benchmarking: Branch and Bound\n", + "\n", + "Let's make up a test suite (showing some examples of how these functions work). Then let's see if `findregex` works with the new branch and bound search. " + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'test_bb passes'" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_bb():\n", + " assert OR(['a', 'b', 'c']) == OR('a', 'b', 'c') == 'a|b|c'\n", + " assert OR(['a|b', 'c|d']) == OR('a|b', 'c|d') == 'a|b|c|d'\n", + " assert OR(None, 'c') == 'c'\n", + " covers1 = {'a': {'ann', 'abe'}, 'ab': {'abe'}}\n", + " assert eliminate_dominated(covers1) == {'a': {'ann', 'abe'}}\n", + " assert simplify_covers(covers1) == ({}, 'a')\n", + " covers2 = {'a': {'abe', 'cab'}, 'b': {'abe', 'cab', 'bee'}, \n", + " 'c': {'cab', 'cee'}, 'c.': {'cab', 'cee'}, 'abe': {'abe'},\n", + " 'ab': {'abe', 'cab'}, '.*b': {'abe', 'cab', 'bee'}, \n", + " 'e': {'abe', 'bee', 'cee'}, 'f': {}, 'g': {}}\n", + " assert eliminate_dominated(covers2) == simplify_covers(covers2)[0] == {\n", + " 'c': {'cab', 'cee'}, 'b': {'cab', 'abe', 'bee'}, 'e': {'cee', 'abe', 'bee'}}\n", + " covers3 = {'1': {'w1'}, '.1': {'w1'}, '2': {'w2'}}\n", + " assert eliminate_dominated(covers3) == {'1': {'w1'}, '2': {'w2'}}\n", + " assert simplify_covers(covers3) in (({}, '2|1'), ({}, '1|2'))\n", + " covers, nec = select_necessary({'a': {'abe'}, 'c': {'cee'}})\n", + " assert covers == {} and (nec == 'c|a' or nec == 'a|c')\n", + " assert {0, 1, 2} >= {1, 2}\n", + " assert {1, 2} >= {1, 2}\n", + " assert not ({1, 2, 4} >= {1, 3})\n", + " return 'test_bb passes'\n", + "\n", + "test_bb()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's investigate how much the cover simplification process is helping:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1615" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers = regex_covers(winners, losers)\n", + "len(covers)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "49" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers2, partial = simplify_covers(covers)\n", + "len(covers2)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.9696594427244583" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1 - len(covers2)/len(covers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see that `simplify_covers` gives us a 97% reduction in the number of parts! What do the remaining covers look like?" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "({'-': frozenset({'van-buren'}),\n", + " '.b': frozenset({'obama', 'van-buren'}),\n", + " '.f': frozenset({'garfield', 'taft'}),\n", + " '.h.n': frozenset({'buchanan', 'washington'}),\n", + " '.se': frozenset({'eisenhower', 'roosevelt'}),\n", + " 'a..i': frozenset({'garfield', 'harding', 'harrison', 'washington'}),\n", + " 'a.a': frozenset({'adams', 'buchanan', 'obama', 'reagan'}),\n", + " 'a.t': frozenset({'carter', 'grant', 'taft'}),\n", + " 'ad': frozenset({'adams', 'madison'}),\n", + " 'am': frozenset({'adams', 'obama'}),\n", + " 'an.$': frozenset({'cleveland', 'grant'}),\n", + " 'ay.': frozenset({'hayes', 'taylor'}),\n", + " 'bu': frozenset({'buchanan', 'bush', 'van-buren'}),\n", + " 'di': frozenset({'harding', 'madison'}),\n", + " 'ed': frozenset({'kennedy'}),\n", + " 'el.$': frozenset({'garfield', 'roosevelt'}),\n", + " 'g..n': frozenset({'grant', 'washington'}),\n", + " 'ga': frozenset({'garfield', 'reagan'}),\n", + " 'h..e': frozenset({'eisenhower', 'hayes'}),\n", + " 'ho': frozenset({'eisenhower', 'hoover'}),\n", + " 'i..n': frozenset({'eisenhower', 'harrison', 'madison', 'nixon'}),\n", + " 'i..o': frozenset({'clinton', 'lincoln', 'wilson'}),\n", + " 'i.l': frozenset({'garfield', 'mckinley'}),\n", + " 'i.o': frozenset({'harrison', 'madison', 'nixon'}),\n", + " 'ie.': frozenset({'garfield', 'pierce'}),\n", + " 'is.': frozenset({'eisenhower', 'harrison', 'madison'}),\n", + " 'li': frozenset({'clinton', 'coolidge', 'lincoln'}),\n", + " 'ls': frozenset({'wilson'}),\n", + " 'm..i': frozenset({'madison', 'mckinley'}),\n", + " 'ma': frozenset({'madison', 'obama', 'truman'}),\n", + " 'n..o': frozenset({'nixon', 'washington'}),\n", + " 'n.e': frozenset({'kennedy', 'mckinley'}),\n", + " 'nl': frozenset({'mckinley'}),\n", + " 'oe': frozenset({'monroe'}),\n", + " 'oo': frozenset({'coolidge', 'hoover', 'roosevelt'}),\n", + " 'r..s': frozenset({'harrison', 'roosevelt'}),\n", + " 'r.e$': frozenset({'monroe', 'pierce'}),\n", + " 'r.i': frozenset({'garfield', 'harding', 'harrison'}),\n", + " 'r.n': frozenset({'grant', 'van-buren'}),\n", + " 'ra': frozenset({'grant'}),\n", + " 'rc': frozenset({'pierce'}),\n", + " 'rt': frozenset({'carter'}),\n", + " 'sh': frozenset({'bush', 'washington'}),\n", + " 'ta': frozenset({'taft', 'taylor'}),\n", + " 'to': frozenset({'clinton', 'washington'}),\n", + " 'u..n': frozenset({'truman', 'van-buren'}),\n", + " 'vel': frozenset({'cleveland', 'roosevelt'}),\n", + " 'xo': frozenset({'nixon'}),\n", + " 'ye': frozenset({'hayes'})},\n", + " 'j|po')" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simplify_covers(covers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + " Now let's benchmark branch and bound. I'm going to introduce a modified version of `benchmark`, called `bbenchmark`, to print the number of calls taken. The easiest way to do that is to introduce a new version of `findregex`, called `bb_findregex`, that returns the `BranchBound` object it creates, rather than returning the solution. (In general, I tend to introduce a new function when I change the call/return signature, but not when I just improve the mechanism.)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def bbenchmark(examples=EXAMPLES, calls=10**4): \n", + " \"Run these data sets; print summaries; return total of solution lengths.\"\n", + " totalchars = 0\n", + " for (W, Wname, Lname, L) in examples: # Do both ways\n", + " re.purge()\n", + " bb = bb_findregex(W, L, calls)\n", + " SOLUTION[W, L] = bb.cheapest\n", + " assert not mistakes(bb.cheapest, W, L)\n", + " legend = '{}({}):{}({})'.format(Wname, len(W), Lname, len(L))\n", + " print('{:20} {:6} calls, {:3}: \"{}\"'.format(\n", + " legend, (calls - bb.calls), len(bb.cheapest), truncate(bb.cheapest, 45)))\n", + " totalchars += len(bb.cheapest)\n", + " return totalchars\n", + "\n", + "def bb_findregex(winners, losers, calls=10**4):\n", + " \"Return a BranchBound object which contains the shortest regex that covers winners but not losers.\"\n", + " bb = BranchBound(winners, calls)\n", + " bb.search(regex_covers(winners, losers))\n", + " return bb\n", + "\n", + "def findregex(winners, losers): return bb_findregex(winners, losers).cheapest" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Remember, the old benchmark took about 5 seconds and totaled 1749 characters. Let's see how the branch and bound benchmark compares:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 1000 calls, 52: \"j|po|a.a|a..i|bu|ma|li|ls|a.t|vel|ho|xo|a ...\"\n", + "lose(34):win(34) 1000 calls, 58: \"^s|ox|ss|^ki|^d|go|^.re|hu|ry|ai|k..$|n.y ...\"\n", + "boy(10):girl(10) 9 calls, 11: \"de|a.$|c|as\"\n", + "girl(10):boy(10) 13 calls, 10: \"a$|a.i|e.i\"\n", + "drug(10):city(10) 3 calls, 15: \"ir|^e|o.$|f|x|q\"\n", + "city(10):drug(10) 17 calls, 11: \"ri|an|h|a.e\"\n", + "foo(21):bar(21) 1 calls, 3: \"f.o\"\n", + "bar(21):foo(21) 205 calls, 24: \"k|ld|b|...n|ah|ar|or|z|A\"\n", + "wars(6):trek(9) 21 calls, 9: \" T|E..H|B\"\n", + "trek(9):wars(6) 9 calls, 13: \"IS|Y|RA|CT| F\"\n", + "noun(100):adj(98) 1000 calls, 167: \"f.t|^hea|aw$|^g|jo|rty|rt$|ot$|^wa|o.y|el ...\"\n", + "adj(98):noun(100) 721 calls, 146: \"r.t|re$|f$|st$|at$|rse|b.t|a.l|ui|far|u.h ...\"\n", + "noun(100):verb(94) 1000 calls, 168: \"am|er$|t.t|ir|po|ot|.as|^ar|^en|gu|.ne|ac ...\"\n", + "verb(94):noun(100) 1000 calls, 170: \"c.n|p.y|sw|r.ad|^tr|ru|^fi|un.$|it$|b.y|^ ...\"\n", + "rand(58):built(147) 1000 calls, 73: \"ia|_p|a.p|ee|_e|and|ets|^u|lti|^_.e|_s|_. ...\"\n", + "built(147):rand(58) 1000 calls, 130: \"^i|se.$|^range$|Y|..E|xe|Wa|bo|ev|w$|xt|^ ...\"\n", + "dog(100):cat(91) 1000 calls, 69: \"^HAVANESE$|E.S$|O.S$|N.S$|.AS|GS|.HI|RD|B ...\"\n", + "cat(91):dog(100) 539 calls, 104: \"J.V|NX|H$|AN$|EX|OE|BAL|^TH|Y$|T$|R$|MES| ...\"\n", + "movie(100):tv(97) 1000 calls, 154: \"^GR|R W|LAD|^CI|GO| . |AP.|^N|^RA|HIN|NC. ...\"\n", + "tv(97):movie(100) 1000 calls, 146: \"MAS|^.OS|WIR|EER|OAP|4|H.W|6|.CI|X.$|.MO| ...\"\n", + "sci(50):star(50) 1000 calls, 67: \"AL..|T..N|R.S| TO|.KA|KN|OS|MU|VE|NN|Ü|LE ...\"\n", + "star(50):sci(50) 1000 calls, 76: \"UM|WES|CA|T. | ST|YN|LI..|F..D|GR|BU| GA| ...\"\n", + "CPU times: user 8.05 s, sys: 23.4 ms, total: 8.07 s\n", + "Wall time: 8.07 s\n" + ] + }, + { + "data": { + "text/plain": [ + "1676" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This is encouraging! We took about 2 seconds longer, but improved on the total number of characters by about 4%. For 10 of the 22 cases we didn't reach the cutoff of 1000 calls, which means that we searched every feasible combination of the parts we have. Let's try with 10,000 calls:" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 1707 calls, 52: \"j|po|a.a|a..i|bu|ma|li|ls|a.t|vel|ho|xo|a ...\"\n", + "lose(34):win(34) 3075 calls, 57: \"^s|ox|ss|^ki|i.$|go|^f|de|br|hu|ker|le$|e ...\"\n", + "boy(10):girl(10) 9 calls, 11: \"de|a.$|c|as\"\n", + "girl(10):boy(10) 13 calls, 10: \"a$|a.i|e.i\"\n", + "drug(10):city(10) 3 calls, 15: \"ir|^e|o.$|f|x|q\"\n", + "city(10):drug(10) 17 calls, 11: \"ri|an|h|a.e\"\n", + "foo(21):bar(21) 1 calls, 3: \"f.o\"\n", + "bar(21):foo(21) 205 calls, 24: \"k|ld|b|...n|ah|ar|or|z|A\"\n", + "wars(6):trek(9) 21 calls, 9: \" T|E..H|B\"\n", + "trek(9):wars(6) 9 calls, 13: \"IS|Y|RA|CT| F\"\n", + "noun(100):adj(98) 2009 calls, 167: \"f.t|^hea|aw$|^g|jo|rty|rt$|ot$|^wa|o.y|el ...\"\n", + "adj(98):noun(100) 721 calls, 146: \"r.t|re$|f$|st$|at$|rse|b.t|a.l|ui|far|u.h ...\"\n", + "noun(100):verb(94) 10000 calls, 168: \"am|er$|t.t|ir|po|ot|.as|^ar|^en|gu|.ne|ac ...\"\n", + "verb(94):noun(100) 3285 calls, 170: \"c.n|p.y|sw|r.ad|^tr|ru|^fi|un.$|it$|b.y|^ ...\"\n", + "rand(58):built(147) 1427 calls, 73: \"ia|_p|a.p|ee|_e|and|ets|^u|lti|^_.e|_s|_. ...\"\n", + "built(147):rand(58) 10000 calls, 130: \"^i|se.$|^range$|Y|ro|Wa|bo|ev|w$|xt|^d|^o ...\"\n", + "dog(100):cat(91) 10000 calls, 69: \"^HAVANESE$|E.S$|O.S$|N.S$|.AS|GS|.HI|RD|B ...\"\n", + "cat(91):dog(100) 539 calls, 104: \"J.V|NX|H$|AN$|EX|OE|BAL|^TH|Y$|T$|R$|MES| ...\"\n", + "movie(100):tv(97) 10000 calls, 153: \"^GR|R W|LAD|^CI|GO| . |AP.|^N|^RA|HIN|NC. ...\"\n", + "tv(97):movie(100) 10000 calls, 146: \"MAS|^.OS|WIR|EER|OAP|4|H.W|6|.CI|X.$|.MO| ...\"\n", + "sci(50):star(50) 10000 calls, 67: \"AL..|T..N|R.S| TO|.KA|KN|OS|MU|NN|W.I|IG. ...\"\n", + "star(50):sci(50) 10000 calls, 76: \"UM|WES|CA|T. | ST|YN|F..D|GR| GA|H.P|LO.| ...\"\n", + "CPU times: user 20.2 s, sys: 40.4 ms, total: 20.3 s\n", + "Wall time: 20.3 s\n" + ] + }, + { + "data": { + "text/plain": [ + "1674" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=10000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We doubled the time and gained a few characters. How about 100,000 calls?" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 1707 calls, 52: \"j|po|a.a|a..i|bu|ma|li|ls|a.t|vel|ho|xo|a ...\"\n", + "lose(34):win(34) 3075 calls, 57: \"^s|ox|ss|^ki|i.$|go|^f|de|br|hu|ker|le$|e ...\"\n", + "boy(10):girl(10) 9 calls, 11: \"de|a.$|c|as\"\n", + "girl(10):boy(10) 13 calls, 10: \"a$|a.i|e.i\"\n", + "drug(10):city(10) 3 calls, 15: \"ir|^e|o.$|f|x|q\"\n", + "city(10):drug(10) 17 calls, 11: \"ri|an|h|a.e\"\n", + "foo(21):bar(21) 1 calls, 3: \"f.o\"\n", + "bar(21):foo(21) 205 calls, 24: \"k|ld|b|...n|ah|ar|or|z|A\"\n", + "wars(6):trek(9) 21 calls, 9: \" T|E..H|B\"\n", + "trek(9):wars(6) 9 calls, 13: \"IS|Y|RA|CT| F\"\n", + "noun(100):adj(98) 2009 calls, 167: \"f.t|^hea|aw$|^g|jo|rty|rt$|ot$|^wa|o.y|el ...\"\n", + "adj(98):noun(100) 721 calls, 146: \"r.t|re$|f$|st$|at$|rse|b.t|a.l|ui|far|u.h ...\"\n", + "noun(100):verb(94) 100000 calls, 167: \"am|er$|t.t|ir|po|ot|.as|^ar|^en|gu|.ne|ac ...\"\n", + "verb(94):noun(100) 3285 calls, 170: \"c.n|p.y|sw|r.ad|^tr|ru|^fi|un.$|it$|b.y|^ ...\"\n", + "rand(58):built(147) 1427 calls, 73: \"ia|_p|a.p|ee|_e|and|ets|^u|lti|^_.e|_s|_. ...\"\n", + "built(147):rand(58) 94795 calls, 127: \"^i|se.$|^range$|Y|ro|Wa|bo|ev|w$|xt|^d|^o ...\"\n", + "dog(100):cat(91) 100000 calls, 69: \"^HAVANESE$|E.S$|O.S$|N.S$|.AS|GS|.HI|RD|B ...\"\n", + "cat(91):dog(100) 539 calls, 104: \"J.V|NX|H$|AN$|EX|OE|BAL|^TH|Y$|T$|R$|MES| ...\"\n", + "movie(100):tv(97) 100000 calls, 153: \"^GR|R W|LAD|^CI|GO| . |AP.|^N|^RA|HIN|NC. ...\"\n", + "tv(97):movie(100) 100000 calls, 146: \"MAS|^.OS|WIR|EER|OAP|4|H.W|6|.CI|X.$|.MO| ...\"\n", + "sci(50):star(50) 100000 calls, 67: \"AL..|T..N|I$|.KA|KN|OS|VE|I.O| TO| .RE|LE ...\"\n", + "star(50):sci(50) 100000 calls, 75: \"UM|WES|CA|GR|LO.|F..D|^B|DEA| GA|H.P|I.L| ...\"\n", + "CPU times: user 3min 8s, sys: 333 ms, total: 3min 8s\n", + "Wall time: 3min 8s\n" + ] + }, + { + "data": { + "text/plain": [ + "1669" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=100000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We're slowly decreasing the total number of characters, but at the expense of increasing run time. I think if we want to make more progress, it is time to stop worrying about the search algorithm, and start worrying about what we're searching over.\n", + "\n", + "# New Parts: Repetition Characters\n", + "\n", + "Following a suggestion by Stefan Pochmann, I will generate two new classes of parts that use the repetition characters `'*'`, `'+'`, and `'?'`:\n", + "\n", + "- **pairs**: parts of the form `'A.*B'` where `'A'` and `'B'` are any two non-special characters that appear anywhere in any winner, the dot is always the second character, and the third character is one of the repetition characters. \n", + "\n", + "- **reps**: given a part such as `'a.c'`, insert any repetition character after any character in the part (yielding, for example, `'a*.c'`).\n", + "Don't insert after `'^'` or `'$'`, and don't allow redundant parts like `'..*c'`.\n", + "\n", + "\n", + "Here is a new version of `regex_covers` that adds the new parts:" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def regex_covers(winners, losers):\n", + " \"\"\"Generate regex components and return a dict of {regex: {winner...}}.\n", + " Each regex matches at least one winner and no loser.\"\"\"\n", + " losers_str = '\\n'.join(losers)\n", + " wholes = {'^'+winner+'$' for winner in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " reps = {r for p in parts for r in repetitions(p)}\n", + " pool = wholes | parts | pairs(winners) | reps \n", + " searchers = {p:re.compile(p, re.MULTILINE).search for p in pool}\n", + " return {p: Set(filter(searchers[p], winners)) \n", + " for p in pool\n", + " if not searchers[p](losers_str)}\n", + "\n", + "def pairs(winners, special_chars=Set('*+?^$.[](){}|\\\\')):\n", + " chars = Set(cat(winners)) - special_chars\n", + " return {A+'.'+q+B \n", + " for A in chars for B in chars for q in '*+?'}\n", + "\n", + "def repetitions(part):\n", + " \"\"\"Return a set of strings derived by inserting a single repetition character\n", + " ('+' or '*' or '?'), after each non-special character. \n", + " Avoid redundant repetition of dots.\"\"\"\n", + " splits = [(part[:i], part[i:]) for i in range(1, len(part)+1)]\n", + " return {A + q + B \n", + " for (A, B) in splits\n", + " # Don't allow '^*' nor '$*' nor '..*' nor '.*.'\n", + " if not (A[-1] in '^$')\n", + " if not A.endswith('..')\n", + " if not (A.endswith('.') and B.startswith('.'))\n", + " for q in '*+?'}" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'test_new_parts passes'" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def test_new_parts():\n", + " assert repetitions('a') == {'a+', 'a*', 'a?'}\n", + " assert repetitions('ab') == {'a+b', 'a*b', 'a?b', \n", + " 'ab+', 'ab*', 'ab?'}\n", + " assert repetitions('a.c') == {'a+.c', 'a*.c', 'a?.c',\n", + " 'a.c+', 'a.*c', 'a.?c',\n", + " 'a.+c', 'a.c*', 'a.c?'}\n", + " assert repetitions('^a..d$') == {'^a+..d$', '^a*..d$', '^a?..d$', \n", + " '^a..d+$', '^a..d*$', '^a..d?$'}\n", + " assert pairs({'ab', 'c'}) == {\n", + " 'a.*a', 'a.*b', 'a.*c',\n", + " 'a.+a', 'a.+b', 'a.+c',\n", + " 'a.?a', 'a.?b', 'a.?c',\n", + " 'b.*a', 'b.*b', 'b.*c',\n", + " 'b.+a', 'b.+b', 'b.+c',\n", + " 'b.?a', 'b.?b', 'b.?c',\n", + " 'c.*a', 'c.*b', 'c.*c',\n", + " 'c.+a', 'c.+b', 'c.+c',\n", + " 'c.?a', 'c.?b','c.?c'}\n", + " assert len(pairs({'1...2...3', '($2.34)', '42', '56', '7-11'})) == 8 * 8 * 3\n", + " covers = regex_covers({'one', 'on'}, {'won', 'wuan', 'juan'})\n", + " assert (eliminate_dominated(covers) == {'e': {'one'}, '^o': {'on', 'one'}})\n", + " return 'test_new_parts passes'\n", + "\n", + "test_new_parts()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's take our new parts out for a spin and see what they can do:" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "' T|P.*E'" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "findregex(starwars, startrek)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Awesome!** \n", + "\n", + "Remember, Randall had a ten character regex in the strip (see below); we previously got it down to nine, but we now have it down to **seven** with `' T|P.*E'`!\n", + "\n", + "\n", + "\n", + "**Update(Nov 2015)**: There are two new movies in the works; let's see what they do to our golf score:" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "' T|P.*E|KE'" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "starwars = starwars | {'THE FORCE AWAKENS'}\n", + "startrek = startrek | {'BEYOND'}\n", + "\n", + "findregex(starwars, startrek)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Too bad; back to ten characters.\n", + "\n", + "How much more work are we doing with these additional parts? Before, `regex_covers(winners, losers)` gave 1615 regexes, which were reduced to 49 by `simplify_covers`. Now:" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "13200" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers = regex_covers(winners, losers)\n", + "len(covers)" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "90" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers2, partial = simplify_covers(covers)\n", + "len(covers2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "So the total number of regexes is increased almost 10-fold, but after simplification the number is only double what it was before. (To put it another way, `simplify_covers` eliminated 99.3% of the parts.) That's not too bad; let's add *more* components.\n", + "\n", + "# New Parts: Longer Ones\n", + "\n", + "Previously we generated parts of length up to 4 characters. Why not say \"[we're doing 5](http://www.theonion.com/articles/fuck-everything-were-doing-five-blades,11056/)\"? The implementation is easy:\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "SUBPARTS = 5 # Maximum length of a subpart\n", + "\n", + "def subparts(word):\n", + " \"Return a set of subparts of word, consecutive characters up to length 5.\"\n", + " return set(word[i:i+1+s] for i in range(len(word)) for s in range(SUBPARTS)) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "But how many more regex components does this give us?" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "39537" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers = regex_covers(winners, losers)\n", + "len(covers)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "112" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "covers2, partial = simplify_covers(covers)\n", + "len(covers2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "In the end the longer parts add only 22 new components, rejecting nearly 40,000 other parts. It is time to benchmark again. Remember our previous best was Branch and Bound with 100,000 calls, which yielded 1669 total characters in 170 seconds." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 1000 calls, 47: \"i.+o|o.*o|a.a|po|a.t|j|bu|ce|ay.|ma|r.i|n ...\"\n", + "lose(34):win(34) 1000 calls, 56: \"r.*y|i.e*$|^s|go|d..e|^f|n.*k|k.+g|hu|rk| ...\"\n", + "boy(10):girl(10) 29 calls, 11: \"a.$|de|c|as\"\n", + "girl(10):boy(10) 23 calls, 9: \"a$|^m*..i\"\n", + "drug(10):city(10) 85 calls, 15: \"o.$|x|ir|f|q|^e\"\n", + "city(10):drug(10) 45 calls, 11: \"ri|a.+e|h|k\"\n", + "foo(21):bar(21) 1 calls, 3: \"foo\"\n", + "bar(21):foo(21) 1000 calls, 23: \"^...a|k|...n|ld|b|ar|or\"\n", + "wars(6):trek(9) 23 calls, 7: \" T|P.*E\"\n", + "trek(9):wars(6) 169 calls, 12: \"I.?S|RA| F|Y\"\n", + "noun(100):adj(98) 1000 calls, 161: \"^wa|l.v|m.+n|me?$|.i.*d|....o|an*.e$|..k$ ...\"\n", + "adj(98):noun(100) 1000 calls, 140: \"e.+y|^..l*$|l.*s|rs?e$|a.l|ei?t|st$|en$|f ...\"\n", + "noun(100):verb(94) 1000 calls, 168: \"h.+g|mp*.n|p.*r|..h.|mb*e|ea?s|^k?i|.ne|. ...\"\n", + "verb(94):noun(100) 1000 calls, 162: \"rr|tar|o.b|^..p?l|^f?..$|buy|f$|^fi|as*k| ...\"\n", + "rand(58):built(147) 1000 calls, 72: \"ee|^_.*n|a.p|ia|an*d.|^_.?e|tst|e._+$|o.c ...\"\n", + "built(147):rand(58) 1000 calls, 130: \"^rang|r...$|c.*t|ra*.i|^l*i|al*s|ug|^m?a| ...\"\n", + "dog(100):cat(91) 1000 calls, 43: \"E.+S$|I.*S$|H.*N.S|.HI|G.?S|TES|.SO|W |O.D.\"\n", + "cat(91):dog(100) 1000 calls, 105: \"J.V|RA*$|R.*A.$|LD?$|N.*X|M$|M...$|E.*O.$ ...\"\n", + "movie(100):tv(97) 1000 calls, 148: \" TH.+N| A*. |R...R|GR?O|IS?.$|A.C*E$|^GR| ...\"\n", + "tv(97):movie(100) 1000 calls, 148: \"4|HT?.W|..CH*I|XI$|PO*R|R..AN|MAS|..AY.|O ...\"\n", + "sci(50):star(50) 1000 calls, 71: \"AN?L..|T.V?.N|RL?.S|N.*RE|.S.+H|LER|.KA|G ...\"\n", + "star(50):sci(50) 1000 calls, 74: \"U.*R.|GR|LO.|F.+D|I.Y*N| T*R|G.*Y|LES?$|E ...\"\n", + "CPU times: user 4min 23s, sys: 2 s, total: 4min 25s\n", + "Wall time: 4min 25s\n" + ] + }, + { + "data": { + "text/plain": [ + "1616" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We reduced the total characters by about 4%, although it did take longer, even with only 1,000 calls. And notice we no longer need `'^HAVANESE$'`; instead we have `'H.*N.S'`, which saves 4 characters, and, look how many breeds it matches:" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'AFGHAN HOUNDS',\n", + " 'BASSET HOUNDS',\n", + " 'BLOODHOUNDS',\n", + " 'CHINESE CRESTED',\n", + " 'CHINESE SHAR-PEI',\n", + " 'DACHSHUNDS',\n", + " 'HAVANESE',\n", + " 'IRISH WOLFHOUNDS',\n", + " 'ITALIAN GREYHOUNDS',\n", + " 'TREEING WALKER COONHOUNDS'}" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "matches('H.*N.S', dogs)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's continue benchmarking:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 10000 calls, 46: \"i.+o|j|bu|oo|a.t|n.o*e|ma|po|ie.|ay.|e.?a ...\"\n", + "lose(34):win(34) 10000 calls, 55: \"r.*y|i.e*$|^s|go|de|do|^f|la.$|al|n.*k|k. ...\"\n", + "boy(10):girl(10) 29 calls, 11: \"a.$|de|c|as\"\n", + "girl(10):boy(10) 23 calls, 9: \"a$|^m*..i\"\n", + "drug(10):city(10) 85 calls, 15: \"o.$|x|ir|f|q|^e\"\n", + "city(10):drug(10) 45 calls, 11: \"ri|a.+e|h|k\"\n", + "foo(21):bar(21) 1 calls, 3: \"foo\"\n", + "bar(21):foo(21) 6151 calls, 23: \"^...a|k|...n|ld|b|ar|or\"\n", + "wars(6):trek(9) 23 calls, 7: \" T|P.*E\"\n", + "trek(9):wars(6) 169 calls, 12: \"I.?S|RA| F|Y\"\n", + "noun(100):adj(98) 10000 calls, 160: \"^wa|l.v|m.+n|me?$|.i.*d|....o|an*.e$|..k$ ...\"\n", + "adj(98):noun(100) 10000 calls, 136: \"e.+y|^..l*$|l.*s|rs?e$|a.l|ei?t|st$|en$|f ...\"\n", + "noun(100):verb(94) 10000 calls, 167: \"h.+g|mp*.n|p.*r|..h.|mb*e|ea?s|^k?i|.ne|. ...\"\n", + "verb(94):noun(100) 10000 calls, 162: \"rr|tar|o.b|^..p?l|^f?..$|buy|f$|^fi|as*k| ...\"\n", + "rand(58):built(147) 10000 calls, 69: \"ee|^_.*n|a.p|ia|an*d.|^_.?e|tst|_s|.G|_.o ...\"\n", + "built(147):rand(58) 10000 calls, 124: \"^rang|r...$|c.*t|ra*.i|^l*i|al*s|ug|^m?a| ...\"\n", + "dog(100):cat(91) 10000 calls, 43: \"E.+S$|I.*S$|H.*N.S|.HI|G.?S|TES|.SO|W |O.D.\"\n", + "cat(91):dog(100) 10000 calls, 104: \"J.V|RA*$|R.*A.$|LD?$|N.*X|M$|M...$|E.*O.$ ...\"\n", + "movie(100):tv(97) 10000 calls, 148: \" TH.+N| A*. |R...R|GR?O|IS?.$|A.C*E$|^GR| ...\"\n", + "tv(97):movie(100) 10000 calls, 148: \"4|HT?.W|..CH*I|XI$|PO*R|R..AN|MAS|..AY.|O ...\"\n", + "sci(50):star(50) 10000 calls, 70: \"AN?L..|T.V?.N|RL?.S|N.*RE|.S.+H|LER|.KA|P ...\"\n", + "star(50):sci(50) 10000 calls, 73: \"U.*R.|GR|LO.|F.+D|I.Y*N| T*R|G.*Y|AE?.W|E ...\"\n", + "CPU times: user 4min 38s, sys: 2 s, total: 4min 40s\n", + "Wall time: 4min 40s\n" + ] + }, + { + "data": { + "text/plain": [ + "1596" + ] + }, + "execution_count": 55, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=10000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We're making good progress. What next? We now have so many parts, that many of the searches do not complete. Suppose one of our first choices was wrong, and the search took a part that does not belong in an optimal solution. We might well spend all our calls on the half of the search tree that keeps the part, never exploring a part of the tree without it. I'd like to alter the search algorithm to get us out of that rut.\n", + "\n", + "# Searching: Random Restart\n", + "\n", + "\n", + "One way out of the rut is to run the search for a while, then stop it, and run a different search, that explores a different part of the search space. This is called a *random restart search*. How do we get a *different* search when we restart? I can think of two easy things to vary:\n", + " \n", + "+ The '4' in the `score` function. That is, vary the tradeoff between number of winners matched and number of characters in a regex.\n", + "+ The tie-breaker. In case of a tie on `max(covers, key=score)`, Python always picks the first component. Let's make it choose a different one each time.\n", + "\n", + "The first of these is easy; we can use the `random.choice` function to choose an integer, K, to serve as the tradeoff factor. The second is easy too. We could write an alternative to the `max` function, say `max_random_tiebreaker`. That would work, but an easier approach is to build the tiebreaker into the `score` function. In addition to awarding points for matching winners, and subtracting a point for each character in the solution, we will have `score` add in a random number. We'll call this the \"fuzz factor\" and use the variable `F` to determine how big it is. If the fuzz factor is a random number between 0 and 1, then all it does is serve as a tiebreaker. But if it is a random number that can be larger than 1, then sometimes it will cause `max` to pick a best part that does not have quite the best score. We're not sure how much randomness is best, so we'll let the values of `K` and `F` vary from one choice to the next." + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def bb_findregex(winners, losers, calls=10000, restarts=10):\n", + " \"Find the shortest disjunction of regex components that covers winners but not losers.\"\n", + " bb = BranchBoundRandomRestart(winners, calls)\n", + " covers = eliminate_dominated(regex_covers(winners, losers))\n", + " for _ in range(restarts):\n", + " bb.calls = calls\n", + " bb.search(covers.copy())\n", + " if bb.calls > 0: # If search was not cut off, we have optimal solution\n", + " return bb \n", + " return bb\n", + "\n", + "class BranchBoundRandomRestart(BranchBound):\n", + " def search(self, covers, partial=None):\n", + " \"\"\"Recursively extend partial regex until it matches all winners in covers.\n", + " Try all reasonable combinations until we run out of calls.\"\"\"\n", + " if self.calls <= 0: \n", + " return partial, covers\n", + " self.calls -= 1\n", + " covers, partial = simplify_covers(covers, partial)\n", + " if not covers: # Nothing left to cover; solution is complete\n", + " self.cheapest = min(partial, self.cheapest, key=len)\n", + " elif len(OR(partial, min(covers, key=len))) < len(self.cheapest):\n", + " # Try with and without the greedy-best component\n", + " K = random.choice((2, 3, 4, 4, 4, 5, 6))\n", + " F = random.choice((0.1, 0.1, 2.0))\n", + " def score(c): return K * len(covers[c]) - len(c) + random.uniform(0., F)\n", + " best = max(covers, key=score) # Best component\n", + " covered = covers[best] # Set of winners covered by r\n", + " covers.pop(best)\n", + " self.search({c:covers[c]-covered for c in covers}, OR(partial, best))\n", + " self.search(covers, partial)\n", + " return self.cheapest" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 100 calls, 49: \"i.+o|o.*o|.f|ce|a.a|po|bu|ay.|ma|n.e|j|an ...\"\n", + "lose(34):win(34) 100 calls, 52: \"r.*y|^d|^s|go|m.+a|^f|....k|^.?la|ki*..$| ...\"\n", + "boy(10):girl(10) 29 calls, 11: \"a.$|c|de|as\"\n", + "girl(10):boy(10) 21 calls, 9: \"a$|^m*..i\"\n", + "drug(10):city(10) 91 calls, 15: \"o.$|x|ir|f|q|^e\"\n", + "city(10):drug(10) 49 calls, 11: \"ri|h|a.+e|k\"\n", + "foo(21):bar(21) 1 calls, 3: \"foo\"\n", + "bar(21):foo(21) 100 calls, 23: \"..r..|^...a|k|A|ld|...n\"\n", + "wars(6):trek(9) 23 calls, 7: \" T|P.*E\"\n", + "trek(9):wars(6) 100 calls, 12: \"I.?S|TI|H |Y\"\n", + "noun(100):adj(98) 100 calls, 160: \"^wa|l.v|m.+n|me?$|....o|.i.*d|ar*c.$|wo|. ...\"\n", + "adj(98):noun(100) 100 calls, 128: \"e.+y|^o*..$|l.*s|ll|rs?e$|ei?t|en$|st$|fa ...\"\n", + "noun(100):verb(94) 100 calls, 163: \"h.+g|mo?.n|p.*r|..h.|mb*e|t.*o|.ne|^k?i|f ...\"\n", + "verb(94):noun(100) 100 calls, 161: \"rr|tar|o.b|^..p?l|^s*..$|f$|buy|as*k|r.ad ...\"\n", + "rand(58):built(147) 100 calls, 69: \"ee|^_.*n|a.p|ia|an*d.|^_.?e|tst|_s|_a?.o| ...\"\n", + "built(147):rand(58) 100 calls, 119: \"^rang|r...$|c.*t|Wa|^d?i|al*s|ug|^m?a|o.* ...\"\n", + "dog(100):cat(91) 100 calls, 43: \"E.+S$|I.*S$|H.*N.S|.HI|G.?S|.SO|W |TES|O.D.\"\n", + "cat(91):dog(100) 100 calls, 97: \"J.V|RA*$|T$|LI*$|AN?$|N.*X|M$|F$|S.+E$|E. ...\"\n", + "movie(100):tv(97) 100 calls, 144: \" TH.+N|R...R| A*. |GO|UC*. |^N|A.C*E$|^GR ...\"\n", + "tv(97):movie(100) 100 calls, 148: \"4|HT?.W|..CH*I|XI$|PO*R|R..AN|MAS| .E.?E| ...\"\n", + "sci(50):star(50) 100 calls, 67: \"AN?L..|T.V?.N|.S.+H|.KA|IL?.O|N.*RE|OS|LE ...\"\n", + "star(50):sci(50) 100 calls, 73: \"U.*R.|GR|LO.|F.+D|I.Y*N| T*R|G.*Y| M*.T|E ...\"\n", + "CPU times: user 4min 39s, sys: 2.33 s, total: 4min 41s\n", + "Wall time: 4min 41s\n" + ] + }, + { + "data": { + "text/plain": [ + "1564" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=100) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Remember, when it says \"100 calls\" here, it really means 1,000 calls, because we are doing 10 random restarts. This looks very promising; even with only 100 calls per restart, we're doing better than 100,000 calls without restarts. Let's continue:" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 1000 calls, 46: \"i.+o|o.*o|bu|a.t|j|ma|po|ie.|n.e|ay.|ar*d ...\"\n", + "lose(34):win(34) 1000 calls, 55: \"r.*y|i.e*$|^s|go|de|^f|do|la.$|al|k.+g|hu ...\"\n", + "boy(10):girl(10) 31 calls, 11: \"a.$|de|c|as\"\n", + "girl(10):boy(10) 21 calls, 9: \"a$|^m*..i\"\n", + "drug(10):city(10) 89 calls, 15: \"o.$|x|ir|f|q|^e\"\n", + "city(10):drug(10) 41 calls, 11: \"ri|a.+e|h|k\"\n", + "foo(21):bar(21) 1 calls, 3: \"foo\"\n", + "bar(21):foo(21) 1000 calls, 23: \"^...a|k|...n|ld|b|or|ar\"\n", + "wars(6):trek(9) 33 calls, 7: \" T|P.*E\"\n", + "trek(9):wars(6) 153 calls, 12: \"I.?S|RA| F|Y\"\n", + "noun(100):adj(98) 1000 calls, 159: \"^wa|l.v|m.+n|me?$|....o|.i.*d|an*.e$|..k$ ...\"\n", + "adj(98):noun(100) 1000 calls, 128: \"e.+y|^o*..$|l.*s|ll|rs?e$|ei?t|st$|en$|fa ...\"\n", + "noun(100):verb(94) 1000 calls, 162: \"h.+g|mp*.n|p.*r|..h.|mb*e|^k?i|.ne|or.?$| ...\"\n", + "verb(94):noun(100) 1000 calls, 159: \"rr|tar|o.b|^..p?l|^s*..$|f$|buy|as*k|r.ad ...\"\n", + "rand(58):built(147) 1000 calls, 69: \"ee|ia|^_.*n|a.p|an*d.|^_.?e|tst|_a?.o|ga| ...\"\n", + "built(147):rand(58) 1000 calls, 119: \"^rang|r...$|c.*t|Wa|^d?i|al*s|ug|o.*p..|Y ...\"\n", + "dog(100):cat(91) 1000 calls, 43: \"E.+S$|I.*S$|H.*N.S|.HI|G.?S|TES|.SO|W |O.D.\"\n", + "cat(91):dog(100) 1000 calls, 96: \"J.V|RA*$|T$|LD?$|AN?$|N.*X|M$|Y$|S.+E$|M. ...\"\n", + "movie(100):tv(97) 1000 calls, 139: \" TH.+N| A*. |R...R|GO|UC*. |^N|NC.$|A.NI| ...\"\n", + "tv(97):movie(100) 1000 calls, 148: \"4|HT?.W|..CH*I|XI$|PO*R|..AY.|O.+L.$|R..A ...\"\n", + "sci(50):star(50) 1000 calls, 67: \"AN?L..|T.V?.N|.S.+H|.KA|IL?.O|N.*RE|OS|NN ...\"\n", + "star(50):sci(50) 1000 calls, 73: \"U.*R.|GR|LO.|F.+D|I.+H$| T*R|G.*NE| M*.T| ...\"\n", + "CPU times: user 4min 56s, sys: 3.13 s, total: 4min 59s\n", + "Wall time: 4min 59s\n" + ] + }, + { + "data": { + "text/plain": [ + "1554" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "win(34):lose(34) 10000 calls, 46: \"i.+o|o.*o|bu|a.t|j|ma|po|n.e|ay.|ar*d|e.? ...\"\n", + "lose(34):win(34) 10000 calls, 52: \"^d|r.*y|^s|go|m.+a|^f|^.?la|....k|ki*..$| ...\"\n", + "boy(10):girl(10) 29 calls, 11: \"a.$|de|c|as\"\n", + "girl(10):boy(10) 21 calls, 9: \"a$|^m*..i\"\n", + "drug(10):city(10) 105 calls, 15: \"x|o.$|ir|f|q|^e\"\n", + "city(10):drug(10) 39 calls, 11: \"ri|a.+e|h|k\"\n", + "foo(21):bar(21) 1 calls, 3: \"foo\"\n", + "bar(21):foo(21) 6049 calls, 23: \"^...a|k|...n|ld|b|ar|or\"\n", + "wars(6):trek(9) 23 calls, 7: \" T|P.*E\"\n", + "trek(9):wars(6) 147 calls, 12: \"I.?S|TI|H |Y\"\n", + "noun(100):adj(98) 10000 calls, 158: \"^wa|l.v|m.+n|me?$|....o|.i.*d|a.e$|..k$|^ ...\"\n", + "adj(98):noun(100) 10000 calls, 128: \"e.+y|^o*..$|ll|l.*s|rs?e$|ei?t|en$|i..l|l ...\"\n", + "noun(100):verb(94) 10000 calls, 163: \"h.+g|mp*.n|p.*r|..h.|mb*e|^k?i|.ne|.t.*y| ...\"\n", + "verb(94):noun(100) 10000 calls, 157: \"rr|tar|o.b|^..p?l|^s*..$|f$|buy|as*k|r.ad ...\"\n", + "rand(58):built(147) 10000 calls, 67: \"ee|ia|^_.*n|a.p|and|^_.?e|tst|_a?.o|ga|.G ...\"\n", + "built(147):rand(58) 10000 calls, 121: \"^rang|r...$|c.*t|Wa|al*s|ug|^l*i|o.*p..|Y ...\"\n", + "dog(100):cat(91) 10000 calls, 43: \"E.+S$|I.*S$|H.*N.S|.HI|G.?S|TES|.SO|W |O.D.\"\n", + "cat(91):dog(100) 10000 calls, 96: \"J.V|RA*$|T$|LD?$|AN?$|N.*X|M$|M...$|Y$|M. ...\"\n", + "movie(100):tv(97) 10000 calls, 141: \" TH.+N| A*. |R...R|GR?O|UC*. |A.C*E$|^GR| ...\"\n", + "tv(97):movie(100) 10000 calls, 148: \"4|HT?.W|..CH*I|XI$|PO*R|..AY.|R..AN|MAS|O ...\"\n", + "sci(50):star(50) 10000 calls, 67: \"AN?L..|T.V?.N|.S.+H|.KA|OS|NN|I.O|OD|^P|N ...\"\n", + "star(50):sci(50) 10000 calls, 72: \"U.*R.|GR|LO.|I.+H$|F.+D| T*R|G.*Y|YN|^B|I ...\"\n", + "CPU times: user 8min 3s, sys: 11.9 s, total: 8min 15s\n", + "Wall time: 8min 15s\n" + ] + }, + { + "data": { + "text/plain": [ + "1550" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "%time bbenchmark(calls=10000)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Just One More Thing: Negative Lookahead\n", + "----\n", + "\n", + "In the `foo` versus `bar` example, we have a big asymmetry in the solution lengths: three letter for `'foo'` compared to 23 characters in the other direction. But if you are a real [regular expression superhero](https://xkcd.com/208/), then you might know about [*negative lookahead assertions*](http://docs.python.org/2/howto/regex.html#lookahead-assertions) and you could solve `bar` versus `foo` like this: " + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "not_foo = '^(?!.*foo)'\n", + "not mistakes(not_foo, bar, foo)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Whoa—what just happened there? The form `'^(?!.*foo)'` means \"starting from the beginning of the line, look ahead for `'.*foo'` (that is, any number of characters followed by `'foo'`). If it is there, then fail, else succeeed.\" That's just what we need to match all the non-foo strings in the `bar` collection. Let's apply this idea to the complete benchmark and see how many characters we save. We'll use the `SOLUTION` dict that was compiled by the previous call to `benchmark`:" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CPU times: user 15.8 ms, sys: 291 µs, total: 16.1 ms\n", + "Wall time: 16 ms\n" + ] + }, + { + "data": { + "text/plain": [ + "1429" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def consider_negative_lookahead(W, L): \n", + " \"Return either SOLUTION[W, L] or negative lookup of SOLUTION[L, W], whichever is shorter.\"\n", + " solution = min(SOLUTION[W, L], '^(?!.*(' + SOLUTION[L, W] + '))',\n", + " key=len)\n", + " assert not mistakes(solution, W, L)\n", + " return solution\n", + " \n", + "%time sum(len(consider_negative_lookahead(W, L)) for (W, _, _, L) in EXAMPLES)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Very nice! Almost a 10% improvement, and it took almost no additional time at all. \n", + "\n", + "# Summary of Results\n", + "\n", + "Here is a plot of results. Note that every time you re-run this notebook, the timing and the exact number of characters will vary a little; these numbers reflect rrsults from a previous run.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "image/png": 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E3AdMK8m+c8WNjmNLRJ4Tdy5/2BKxhVp9a8HAYipZBvSg0DriRsex+IPFRVZx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\n/2WqusYJtrouBaqaAWwA2mB17EsdgUec+VxWAF1FZBlWxz6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Algorithm Style Times Total character counts\n", + "DATA = [('Greedy', 'gD-', [6], [1740]),\n", + " ('BB (1/10/100K)', 'bo-', [8, 21, 196], [1676, 1674, 1669]),\n", + " ('BB + Parts (1/10K)', 'kd-', [272, 288], [1595, 1587]),\n", + " ('BB Restart (1/10/100K)', 'rs-', [289, 303, 493], [1560, 1556, 1547]),\n", + " ('BB Restart NegLook (100K)','m*-', [493], [1426])]\n", + "\n", + "def display(data=DATA):\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111)\n", + " for (label, line, times, counts) in data:\n", + " plt.plot(times, counts, line, label=label)\n", + " x, y = times[-1], counts[-1]\n", + " offset = (-22, -15) if line in ('rs-', 'm*-') else (10, -5)\n", + " ax.annotate(str(y), xy=(x, y), xytext=offset, textcoords='offset points')\n", + " plt.xlabel('Time (seconds)'); plt.ylabel('Solution size (total chars)')\n", + " plt.legend(loc='lower left');\n", + "\n", + "display()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We've made great strides, decreasing the total solution length by 20%. (It is up to you whether that 20% improvement is worth the increase in time from 6 seconds to 8 minutes.)\n", + "\n", + "# Profiling Again\n", + "\n", + "Now where does the time go? Let's check again:" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 59623899 function calls (59278679 primitive calls) in 36.067 seconds\n", + "\n", + " Ordered by: cumulative time\n", + "\n", + " ncalls tottime percall cumtime percall filename:lineno(function)\n", + " 1 0.000 0.000 36.067 36.067 {built-in method builtins.exec}\n", + " 1 0.000 0.000 36.067 36.067 :1()\n", + " 1 0.002 0.002 36.067 36.067 :21(findregex)\n", + " 1 0.072 0.072 36.066 36.066 :1(bb_findregex)\n", + "100178/10 0.781 0.000 24.877 2.488 :13(search)\n", + " 100000 0.593 0.000 20.145 0.000 :1(simplify_covers)\n", + " 209152 2.074 0.000 11.561 0.000 :1(eliminate_dominated)\n", + " 1 0.007 0.007 10.413 10.413 :1(regex_covers)\n", + " 4047977 2.941 0.000 8.916 0.000 {built-in method builtins.any}\n", + " 1 0.104 0.104 8.110 8.110 :9()\n", + " 209151 0.747 0.000 8.080 0.000 :1(select_necessary)\n", + " 89666 0.043 0.000 8.006 0.000 re.py:222(compile)\n", + " 89666 0.533 0.000 7.963 0.000 re.py:278(_compile)\n", + " 89666 0.449 0.000 7.330 0.000 sre_compile.py:531(compile)\n", + " 18054570 4.510 0.000 4.745 0.000 :10()\n", + " 89666 0.335 0.000 3.693 0.000 sre_parse.py:819(parse)\n", + " 209151 0.801 0.000 3.453 0.000 __init__.py:505(__init__)\n", + " 209151 1.187 0.000 3.322 0.000 :5()\n", + " 89666 0.161 0.000 2.947 0.000 sre_compile.py:516(_code)\n", + " 89666 0.187 0.000 2.930 0.000 sre_parse.py:429(_parse_sub)\n", + " 50084 0.587 0.000 2.783 0.000 {built-in method builtins.max}\n", + " 209152 1.339 0.000 2.649 0.000 {built-in method builtins.sorted}\n", + " 209151 0.408 0.000 2.626 0.000 __init__.py:574(update)\n", + " 89666 1.184 0.000 2.626 0.000 sre_parse.py:491(_parse)\n", + " 636500 0.910 0.000 2.196 0.000 :26(score)\n", + " 1 1.683 1.683 2.164 2.164 :10()\n", + " 89666 0.472 0.000 1.407 0.000 sre_compile.py:412(_compile_info)\n", + "171350/89666 0.873 0.000 1.369 0.000 sre_compile.py:64(_compile)\n", + " 426948 0.469 0.000 1.331 0.000 :1(OR)\n", + " 2167485 0.983 0.000 1.311 0.000 :6(signature)\n", + " 209151 0.622 0.000 1.310 0.000 {built-in method _collections._count_elements}\n", + " 4734318 1.287 0.000 1.287 0.000 :5()\n", + " 636500 1.118 0.000 1.180 0.000 random.py:342(uniform)\n", + " 1147585 0.351 0.000 1.049 0.000 {built-in method builtins.isinstance}\n", + "11387014/11305330 0.956 0.000 0.980 0.000 {built-in method builtins.len}\n", + " 444972 0.606 0.000 0.818 0.000 {method 'join' of 'str' objects}\n", + " 209151 0.416 0.000 0.698 0.000 abc.py:178(__instancecheck__)\n", + " 2988397 0.688 0.000 0.688 0.000 :4()\n", + "253034/171350 0.566 0.000 0.684 0.000 sre_parse.py:167(getwidth)\n", + " 480786 0.209 0.000 0.605 0.000 sre_parse.py:247(get)\n", + " 89666 0.481 0.000 0.481 0.000 {method 'search' of '_sre.SRE_Pattern' objects}\n", + " 490104 0.334 0.000 0.478 0.000 sre_parse.py:157(__getitem__)\n", + " 570452 0.474 0.000 0.474 0.000 sre_parse.py:226(__next)\n", + " 532234 0.368 0.000 0.368 0.000 {built-in method builtins.min}\n", + " 2239948 0.317 0.000 0.317 0.000 {method 'append' of 'list' objects}\n", + " 418302 0.282 0.000 0.282 0.000 _weakrefset.py:70(__contains__)\n", + " 100168 0.097 0.000 0.270 0.000 random.py:250(choice)\n", + " 76784 0.248 0.000 0.248 0.000 :8()\n", + " 81684 0.148 0.000 0.241 0.000 sre_compile.py:386(_simple)\n", + " 399102 0.153 0.000 0.234 0.000 sre_parse.py:165(append)\n", + " 89666 0.145 0.000 0.233 0.000 sre_parse.py:217(__init__)\n", + " 1102830 0.213 0.000 0.213 0.000 :6()\n", + " 50084 0.195 0.000 0.195 0.000 :30()\n", + " 100168 0.111 0.000 0.164 0.000 random.py:220(_randbelow)\n", + " 89666 0.098 0.000 0.111 0.000 sre_parse.py:797(fix_flags)\n", + " 1 0.018 0.018 0.109 0.109 :7()\n", + " 171350 0.107 0.000 0.107 0.000 sre_parse.py:105(__init__)\n", + " 171350 0.088 0.000 0.107 0.000 sre_parse.py:276(tell)\n", + " 89666 0.102 0.000 0.102 0.000 {built-in method _sre.compile}\n", + " 245052 0.080 0.000 0.102 0.000 sre_parse.py:153(__len__)\n", + " 38126 0.095 0.000 0.100 0.000 sre_compile.py:391(_generate_overlap_table)\n", + " 179332 0.076 0.000 0.096 0.000 sre_compile.py:513(isstring)\n", + " 7902 0.016 0.000 0.091 0.000 :19(repetitions)\n", + " 89666 0.085 0.000 0.085 0.000 sre_parse.py:70(__init__)\n", + " 179332 0.064 0.000 0.082 0.000 sre_parse.py:75(groups)\n", + " 636500 0.062 0.000 0.062 0.000 {method 'random' of '_random.Random' objects}\n", + " 7902 0.047 0.000 0.061 0.000 :24()\n", + " 171350 0.048 0.000 0.048 0.000 sre_parse.py:242(match)\n", + " 76784 0.047 0.000 0.047 0.000 :7()\n", + " 123976 0.042 0.000 0.042 0.000 {method 'getrandbits' of '_random.Random' objects}\n", + " 246020 0.028 0.000 0.028 0.000 {built-in method builtins.ord}\n", + " 81684 0.023 0.000 0.023 0.000 sre_parse.py:161(__setitem__)\n", + " 1 0.003 0.003 0.022 0.022 :6()\n", + " 76384 0.022 0.000 0.022 0.000 {method 'extend' of 'list' objects}\n", + " 2433 0.006 0.000 0.016 0.000 :56(dotify)\n", + " 89666 0.016 0.000 0.016 0.000 {method 'items' of 'dict' objects}\n", + " 7902 0.014 0.000 0.014 0.000 :23()\n", + " 61211 0.012 0.000 0.012 0.000 {method 'endswith' of 'str' objects}\n", + " 100168 0.011 0.000 0.011 0.000 {method 'bit_length' of 'int' objects}\n", + " 50084 0.009 0.000 0.009 0.000 {method 'pop' of 'dict' objects}\n", + " 49204 0.009 0.000 0.009 0.000 {method 'get' of 'dict' objects}\n", + " 2433 0.006 0.000 0.009 0.000 :59()\n", + " 176 0.008 0.000 0.008 0.000 {method 'clear' of 'dict' objects}\n", + " 98 0.001 0.000 0.002 0.000 :3(subparts)\n", + " 9029 0.002 0.000 0.002 0.000 {method 'startswith' of 'str' objects}\n", + " 6431 0.002 0.000 0.002 0.000 :61(replacements)\n", + " 3568 0.001 0.000 0.001 0.000 :5()\n", + " 1 0.000 0.000 0.001 0.001 :14(pairs)\n", + " 1 0.001 0.001 0.001 0.001 :16()\n", + " 10 0.000 0.000 0.000 0.000 {method 'copy' of 'dict' objects}\n", + " 1 0.000 0.000 0.000 0.000 :3(__init__)\n", + " 1 0.000 0.000 0.000 0.000 :73(trivial)\n", + " 1 0.000 0.000 0.000 0.000 :5()\n", + " 1 0.000 0.000 0.000 0.000 weakref.py:102(remove)\n", + " 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}\n", + "\n", + "\n" + ] + } + ], + "source": [ + "cProfile.run('findregex(adverbs, nouns)', sort='cumulative')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We see that the majority of the time is in `simplify_covers`, and within that, half the time goes to `eliminate_dominated`. That gives us some ideas of where speedups could be made, but gains will be harder now than before." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "# Speculating: Other Ideas\n", + "\n", + "I'm going to stop here, but I'll briefly mention some other ideas that I didn't get to investigate. Perhaps you can play with some of these, or with other ideas.\n", + "\n", + "- *Completely different approach*: [Thomas Breuel](https://plus.google.com/118190679520611168174/posts) suggested doing [minimization](http://en.wikipedia.org/wiki/DFA_minimization) of [weighted finite state transducers](http://nbviewer.ipython.org/url/nlpa.iupr.com/resources/nlpa-openfst.ipynb?attredirects=0&create=1).\n", + "- *Character classes*: We never considered character classes, such as `'[abc]'`. It is not obvious they would help, but it is possible. Consider the fragment `'ld|la'`, which shows up in one of the solutions. We could replace that with a single component, `'l[da]'`. But we haven't gained anything; both are 5 characters long. If we had had `'l.d|l.c|l.b|l.a'` then the replacement `'l.[a-d]'` would save 8 characters, but I don't see many opportunities like that. It might also be possible to use *negative* character classes, like `l[^y]` to explicitly avoid something in the losers set.\n", + "\n", + "- *Prefilter parts*: Currently, `regex_covers` generates a huge set of components, then eliminates the ones that match losers (or don't match winners), and then eliminates the ones that are dominated. We could make `regex_covers` faster by not generating components that can't possibly contribute. Suppose we're considering a subpart, say `'ab'`. If it matches no losers, then there is no reason to extend it to a longer subpart, such as `'abc'`, because we know that `'abc'` is dominated by `'ab'`. By filtering out dominated parts before we have to check them, I estimate we should be able to cut the time for `regex_covers` in half, maybe better.\n", + "- *Better component choice*: We pick the \"best\" component based on how many winners it covers and how many characters it takes. Maybe we could have a better measure; perhaps taking into account whether it covers winners that are \"easy\" to cover by other regexes, or \"hard\" to cover.\n", + "- *Tuning*: We have the two parameters `K` and `F`, which are randomly chosen from a fairly arbitrary distribution. We could measure which values of the parameters perform better and pick those values more often.\n", + "- *Post-editing*: We concentrated on the task of generating a solution from scratch; another task is to improve an existing solution. For example, take the set of components in a solution, and see if one component could be dropped—it is possible that all the winners covered by that component might accidentally have been covered by other components, making it unnecessary. Or take all pairs of components, and see if they could be replaced by a shorter set of components.\n", + "- *Better bounds*: Branch and Bound search works best if the bounds are tight. If we can recognize early that the path we are on cannot possibly be as good as the best solution found so far then we can cut off search early and save time. But the bound estimate we are using now is a poor one. We estimate the cost of a solution as the cost of the partial solution plus the cost of the shortest component remaining. We use this estimate because all we know for sure is that we need at least one more component. Here's one way to get a better bound by recognizing that in many cases we will need more than one more component. We'll define the following quantities:\n", + "\n", + " + *P* = the length of the partial solution, plus the \"|\", if needed. So if the partial solution is `None`, then *P* = 0, else *P* is the length plus 1.\n", + " + *S* = the length of the shortest regex component in `covers`.\n", + " + *W* = the number of winners still in `covers`.\n", + " + *C* = the largest number of winners covered by any regex in `covers`.\n", + " \n", + " The current estimate is *P* + *S*. We can see that a better estimate is *P* + *S* × ceil(*W* / *C*).\n", + "\n", + "\n", + "I hope you had fun seeing how I (and Stefan) attacked this problem; now go out and solve some problems of your own." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "
\n", + "[*Peter Norvig*](http://norvig.com), Feb. 2014" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/xkcd1313.ipynb b/pytudes/ipynb/xkcd1313.ipynb new file mode 100644 index 0000000..aba9c4d --- /dev/null +++ b/pytudes/ipynb/xkcd1313.ipynb @@ -0,0 +1,1220 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# xkcd 1313: Regex Golf\n", + "\n", + "

Peter Norvig
January 2014
revised November 2015

\n", + "\n", + "I ♡ [xkcd](http://xkcd.com)! It reliably provides top-rate [insights](http://xkcd.com/285/), [humor](http://xkcd.com/612/), or [both](http://xkcd.com/627/). I was thrilled when I got to [introduce Randall Monroe](http://www.youtube.com/watch?v=zJOS0sV2a24) for a talk in 2007. But in [xkcd #1313](http://xkcd.com/1313), \n", + "\n", + "\n", + "\n", + "I found that the hover text, \"/bu|[rn]t|[coy]e|[mtg]a|j|iso|n[hl]|[ae]d|lev|sh|[lnd]i|[po]o|ls/ matches the last names of elected US presidents but not their opponents\", contains a confusing contradiction. I'm old enough to remember that Jimmy Carter won one term and lost a second. No regular expression could both match and not match \"Carter\". \n", + "\n", + "But this got me thinking: can I come up with an algorithm to match or beat Randall's regex golf scores? The game is on.\n", + "\n", + "# Presidents\n", + " \n", + "I started by finding a [listing](http://www.anesi.com/presname.htm) of presidential elections, giving me these winners and losers:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "from __future__ import division, print_function\n", + "import re\n", + "import itertools\n", + "\n", + "def words(text): return set(text.split())\n", + "\n", + "winners = words('''washington adams jefferson jefferson madison madison monroe \n", + " monroe adams jackson jackson van-buren harrison polk taylor pierce buchanan \n", + " lincoln lincoln grant grapartnt hayes garfield cleveland harrison cleveland mckinley\n", + " mckinley roosevelt taft wilson wilson harding coolidge hoover roosevelt \n", + " roosevelt roosevelt roosevelt truman eisenhower eisenhower kennedy johnson nixon \n", + " nixon carter reagan reagan bush clinton clinton bush bush obama obama''')\n", + "\n", + "losers = words('''clinton jefferson adams pinckney pinckney clinton king adams \n", + " jackson adams clay van-buren van-buren clay cass scott fremont breckinridge \n", + " mcclellan seymour greeley tilden hancock blaine cleveland harrison bryan bryan \n", + " parker bryan roosevelt hughes cox davis smith hoover landon willkie dewey dewey \n", + " stevenson stevenson nixon goldwater humphrey mcgovern ford carter mondale \n", + " dukakis bush dole gore kerry mccain romney''')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We can see that there are multiple names that are both winners and losers:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'adams',\n", + " 'bush',\n", + " 'carter',\n", + " 'cleveland',\n", + " 'clinton',\n", + " 'harrison',\n", + " 'hoover',\n", + " 'jackson',\n", + " 'jefferson',\n", + " 'nixon',\n", + " 'roosevelt',\n", + " 'van-buren'}" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "winners & losers" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Clinton? He won both his elections, didn't he? Yes, *Bill* Clinton did, but *George* Clinton (the Revolutionary War leader, not the Funkadelic leader) was a losing opponent in 1792 and 1812. To avoid the contradiction, I decided to eliminate all winners from the set of losers (and in fact Randall later confirmed that that was his intent):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "losers = losers - winners" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Defining the Problem\n", + "\n", + "\n", + "Let's be clear exactly what we're trying to achieve. We're looking for a Python regular expression which, when used with the `re.search` function, will match all of the winners but none of the losers. We can define the function `mistakes` to return a set of misclassifications; if `mistakes` is empty then the regular expression is verified correct:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def mistakes(regex, winners, losers):\n", + " \"The set of mistakes made by this regex in classifying winners and losers.\"\n", + " return ({\"Should have matched: \" + W \n", + " for W in winners if not re.search(regex, W)} |\n", + " {\"Should not have matched: \" + L \n", + " for L in losers if re.search(regex, L)})\n", + "\n", + "def verify(regex, winners, losers): \n", + " assert not mistakes(regex, winners, losers)\n", + " return True" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Let's check the xkcd regex:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Should not have matched: fremont'}" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "xkcd = \"bu|[rn]t|[coy]e|[mtg]a|j|iso|n[hl]|[ae]d|lev|sh|[lnd]i|[po]o|ls\"\n", + "\n", + "mistakes(xkcd, winners, losers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The xkcd regex incorrectly matches `\"fremont\"`, representing John C. Frémont, the Republican candidate who lost to James Buchanan in 1856. Could Randall Monroe have made an error? Is someone **[wrong](http://xkcd.com/386/)** on the Internet? Investigating the [1856 election](http://en.wikipedia.org/wiki/United_States_presidential_election,_1856), I see that Randall must have had Millard Fillmore, the third-party candidate, as the opponent. Fillmore is more famous, having served as the 13th president (although he never won an election; he became president when Taylor died in office). But Fillmore only got 8 electoral votes in 1856 while Fremont got 114, so I will stick with Fremont in *my* list of losers. \n", + "\n", + "We can verify that Randall got it right under the interpretation that Fillmore, not Fremont, was the loser: " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alternative_losers = {'fillmore'} | losers - {'fremont'}\n", + "\n", + "verify(xkcd, winners, alternative_losers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Strategy for Finding a Regex\n", + "\n", + "\n", + "We need a strategy to find a regex that matches all the winners but none of the losers. I came up with this approach:\n", + " \n", + "- Generate a pool of regex *parts*: small regexes of a few characters, such as `\"bu\"` or `\"r.e$\"` or `\"j\"`.\n", + "- Consider only parts that match at least one winner, but no losers.\n", + "- Our solution will be formed by \"or\"-ing together some of these parts (e.g. `\"bu|n.e|j\"`).\n", + "- This is a [set cover problem](http://en.wikipedia.org/wiki/Set_cover_problem): pick some of the parts so that they cover all the winners.\n", + "- Set cover is an NP-hard problem, so I feel justified in using an approximation approach that finds a small but not necessarily smallest solution.\n", + "- For many NP-hard problems a good approximation can be had with a [greedy algorithm](http://en.wikipedia.org/wiki/Greedy_algorithm): Pick the \"best\" part first (the one that covers the most winners with the fewest characters), and repeat, choosing the \"best\" each time until there are no more winners to cover.\n", + "- To guarantee that we will find a solution, make sure that each winner has at least one part that matches it.\n", + "\n", + "There are three ways this strategy can fail to find the shortest possible regex:\n", + "\n", + "- The shortest regex might not be a disjunction. Our strategy can only find disjunctions (of the form `\"a|b|c|...\"`). \n", + "- The shortest regex might be a disjunction formed with different parts. For example, `\"[rn]t\"` is not in our pool of parts.\n", + "- The greedy algorithm isn't guaranteed to find the shortest solution. We might have all the right parts, but pick the wrong ones.\n", + "\n", + "The algorithm is below. Our pool of parts is a set of strings created with `regex_parts(winners, losers)`. We accumulate parts into the list `solution`, which starts empty. On each iteration choose the best part: the one with a maximum score. (I decided by default to score 4 points for each winner matched, minus one point for each character in the part.) We then add the best part to `solution`, and remove from winners all the strings that are matched by `best`. Finally, we update the pool, keeping only those parts that still match one or more of the remaining winners. When there are no more winners left, OR together all the solution parts to give the final regular expression string." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, k=4):\n", + " \"Find a regex that matches all winners but no losers (sets of strings).\"\n", + " # Make a pool of regex parts, then pick from them to cover winners.\n", + " # On each iteration, add the 'best' part to 'solution',\n", + " # remove winners covered by best, and keep in 'pool' only parts\n", + " # that still match some winner.\n", + " pool = regex_parts(winners, losers)\n", + " solution = []\n", + " def score(part): return k * len(matches(part, winners)) - len(part)\n", + " while winners:\n", + " best = max(pool, key=score)\n", + " solution.append(best)\n", + " winners = winners - matches(best, winners)\n", + " pool = {r for r in pool if matches(r, winners)}\n", + " return OR(solution)\n", + "\n", + "def matches(regex, strings):\n", + " \"Return a set of all the strings that are matched by regex.\"\n", + " return {s for s in strings if re.search(regex, s)}\n", + "\n", + "OR = '|'.join # Join a sequence of strings with '|' between them" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Glossary\n", + "\n", + "\n", + "Just to be clear, I define the terms I will be using:\n", + "\n", + "- *winners:* A set of strings; our solution is required to match each of them.\n", + "- *losers:* A set of strings; our solution is not allowed to match any of them.\n", + "- *part:* A small regular expression, a string, such as `'bu'` or `'a.a'`.\n", + "- *pool:* A set of parts from which we will pick a subset to form the solution.\n", + "- *regex:* A [regular expression](http://docs.python.org/2/library/re.html); a pattern used to match against a string. \n", + "- *solution:* A regular expression that matches all winners but no losers.\n", + "- *whole:* A part that matches a whole word (and nothing else): `'^word$'`\n", + "\n", + " \n", + "# Regex Parts\n", + "\n", + "\n", + "\n", + "Now we need to define what the `regex_parts` are. Here's what I came up with:\n", + "\n", + "- For each winner, include a regex that matches the entire string exactly. I call this regex a *whole*.\n", + "
Example: for `'word'`, include `'^word$'`\n", + "- For each whole, generate *subparts* consisting of 1 to 4 consecutive characters.\n", + "
Example: `subparts('^it$')` == `{'^', 'i', 't', '$', '^i', 'it', 't$', '^it', 'it$', '^it$'}`\n", + "- For each subpart, generate all ways to replace any of the letters with a dot (the \"match any\" character).\n", + "
Example: `dotify('it')` == `{'it', 'i.', '.t', '..'}`\n", + "- Keep only the dotified subparts that do not match any of the losers.\n", + "\n", + "Note that I only used a few of the regular expression mechanisms: `'.'`, `'^'`, and `'$'`. I didn't try to use character classes (`[a-z]`), nor any of the repetition operators, nor other advanced mechanisms. Why? I thought that the advanced features usually take too many characters. For example, I don't allow the part `'[rn]t'`, but I can achieve the same effect with the same number of characters by combining two parts: `'rt|nt'`. I could add more complicated mechanisms later, but for now, [YAGNI](https://en.wikipedia.org/wiki/You_aren%27t_gonna_need_it). Here is the code:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "def regex_parts(winners, losers):\n", + " \"Return parts that match at least one winner, but no loser.\"\n", + " wholes = {'^' + w + '$' for w in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " return wholes | {p for p in parts if not matches(p, losers)}\n", + "\n", + "def subparts(word, N=4):\n", + " \"Return a set of subparts of word: consecutive characters up to length N (default 4).\"\n", + " return set(word[i:i+n+1] for i in range(len(word)) for n in range(N)) \n", + " \n", + "def dotify(part):\n", + " \"Return all ways to replace a subset of chars in part with '.'.\"\n", + " choices = map(replacements, part)\n", + " return {cat(chars) for chars in itertools.product(*choices)}\n", + "\n", + "def replacements(c): return c if c in '^$' else c + '.'\n", + "\n", + "cat = ''.join" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Our program is complete! We can run `findregex`, verify the solution, and compare the length of our solution to Randall's:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(53, 'a.a|i..n|j|oo|a.t|i..o|a..i|bu|n.e|ay.|r.e$|po|ma|nd$')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "solution = findregex(winners, losers)\n", + "verify(solution, winners, losers)\n", + "\n", + "len(solution), solution" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(63, 'bu|[rn]t|[coy]e|[mtg]a|j|iso|n[hl]|[ae]d|lev|sh|[lnd]i|[po]o|ls')" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(xkcd), xkcd" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Our regex is 15% shorter than Randall's—success!\n", + "\n", + "# Tests\n", + "\n", + "Here's a test suite to give us more confidence in (and familiarity with) our functions:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'tests pass'" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def tests():\n", + " assert subparts('^it$') == {'^', 'i', 't', '$', '^i', 'it', 't$', '^it', 'it$', '^it$'}\n", + " assert subparts('this') == {'t', 'h', 'i', 's', 'th', 'hi', 'is', 'thi', 'his', 'this'}\n", + " subparts('banana') == {'a', 'an', 'ana', 'anan', 'b', 'ba', 'ban', 'bana', \n", + " 'n', 'na', 'nan', 'nana'}\n", + " \n", + " assert dotify('it') == {'it', 'i.', '.t', '..'}\n", + " assert dotify('^it$') == {'^it$', '^i.$', '^.t$', '^..$'}\n", + " assert dotify('this') == {'this', 'thi.', 'th.s', 'th..', 't.is', 't.i.', 't..s', 't...',\n", + " '.his', '.hi.', '.h.s', '.h..', '..is', '..i.', '...s', '....'}\n", + " assert regex_parts({'win'}, {'losers', 'bin', 'won'}) == {\n", + " '^win$', '^win', '^wi.', 'wi.', 'wi', '^wi', 'win$', 'win', 'wi.$'}\n", + " assert regex_parts({'win'}, {'bin', 'won', 'wine', 'wit'}) == {'^win$', 'win$'}\n", + " regex_parts({'boy', 'coy'}, \n", + " {'ahoy', 'toy', 'book', 'cook', 'boycott', 'cowboy', 'cod', 'buy', 'oy', \n", + " 'foil', 'coyote'}) == {'^boy$', '^coy$', 'c.y$', 'coy$'}\n", + " \n", + " assert matches('a|b|c', {'a', 'b', 'c', 'd', 'e'}) == {'a', 'b', 'c'}\n", + " assert matches('a|b|c', {'any', 'bee', 'succeed', 'dee', 'eee!'}) == {\n", + " 'any', 'bee', 'succeed'}\n", + " \n", + " assert OR(['a', 'b', 'c']) == 'a|b|c'\n", + " assert OR(['a']) == 'a'\n", + " \n", + " assert words('this is a test this is') == {'this', 'is', 'a', 'test'}\n", + " \n", + " assert findregex({\"ahahah\", \"ciao\"}, {\"ahaha\", \"bye\"}) == 'a.$'\n", + " assert findregex({\"this\", \"that\", \"the other\"}, {\"one\", \"two\", \"here\", \"there\"}) == 'h..$'\n", + " assert findregex({'boy', 'coy', 'toy', 'joy'}, {'ahoy', 'buy', 'oy', 'foil'}) == '^.oy'\n", + " \n", + " assert not mistakes('a|b|c', {'ahoy', 'boy', 'coy'}, {'joy', 'toy'})\n", + " assert not mistakes('^a|^b|^c', {'ahoy', 'boy', 'coy'}, {'joy', 'toy', 'kickback'})\n", + " assert mistakes('^.oy', {'ahoy', 'boy', 'coy'}, {'joy', 'ploy'}) == {\n", + " \"Should have matched: ahoy\", \n", + " \"Should not have matched: joy\"}\n", + " return 'tests pass'\n", + "\n", + "tests()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Regex Golf with Arbitrary Lists\n", + "\n", + "Let's move on to arbitrary lists. I define `report`, to call `findregex`, verify the solution, and print the number of characters in the solution, the number of parts, the *competitive ratio* (the ratio between the lengths of a trivial solution and the actual solution), and the number of winners and losers." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 53, Parts: 14, Competitive ratio: 5.2, Winners: 35, Losers: 34\n" + ] + }, + { + "data": { + "text/plain": [ + "'a.a|i..n|j|oo|a.t|i..o|a..i|bu|n.e|ay.|r.e$|po|ma|nd$'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def report(winners, losers):\n", + " \"Find a regex to match A but not B, and vice-versa. Print summary.\"\n", + " solution = findregex(winners, losers)\n", + " verify(solution, winners, losers)\n", + " trivial = '^(' + OR(winners) + ')$'\n", + " print('Characters: {}, Parts: {}, Competitive ratio: {:.1f}, Winners: {}, Losers: {}'.format(\n", + " len(solution), solution.count('|') + 1, len(trivial) / len(solution) , len(winners), len(losers)))\n", + " return solution\n", + "\n", + "report(winners, losers)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The top 10 [boys and girls names](http://www.ssa.gov/oact/babynames/) for 2012:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 11, Parts: 3, Competitive ratio: 6.4, Winners: 10, Losers: 10\n" + ] + }, + { + "data": { + "text/plain": [ + "'e.$|a.$|a.o'" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "boys = words('jacob mason ethan noah william liam jayden michael alexander aiden')\n", + "girls = words('sophia emma isabella olivia ava emily abigail mia madison elizabeth')\n", + "\n", + "report(boys, girls)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This is interesting because `'a.$|e.$|a.o'` is an example of something that could be re-written in a shorter form if we allowed more complex parts. The following would save one character:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "verify('[ae].(o|$)', boys, girls)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "We have now fulfilled panel two of the strip. Let's try another example, separating \n", + "the top ten best-selling drugs from the top 10 cities to visit:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 15, Parts: 6, Competitive ratio: 5.3, Winners: 10, Losers: 10\n" + ] + }, + { + "data": { + "text/plain": [ + "'o.$|x|ir|q|f|po'" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "drugs = words('lipitor nexium plavix advair ablify seroquel singulair crestor actos epogen')\n", + "cities = words('paris trinidad capetown riga zurich shanghai vancouver chicago adelaide auckland')\n", + "\n", + "report(drugs, cities)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "\n", + "\n", + "We can answer the challenge from panel one of the strip:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 9, Parts: 3, Competitive ratio: 13.0, Winners: 6, Losers: 9\n" + ] + }, + { + "data": { + "text/plain": [ + "' T|E.P|OP'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def phrases(text, sep='/'): return {line.upper().strip() for line in text.split(sep)}\n", + "\n", + "starwars = phrases('''The Phantom Menace / Attack of the Clones / Revenge of the Sith /\n", + " A New Hope / The Empire Strikes Back / Return of the Jedi''')\n", + "\n", + "startrek = phrases('''The Wrath of Khan / The Search for Spock / The Voyage Home /\n", + " The Final Frontier / The Undiscovered Country / Generations / \n", + " First Contact / Insurrection / Nemesis''')\n", + "\n", + "report(starwars, startrek)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Neat—our solution is one character shorter than Randall's. We can verify that Randall's solution is also correct:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "verify('M | [TN]|B', starwars, startrek)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "**Update (Nov 2015): There are two new movies in the works! **\n", + "\n", + "
\n", + "\n", + "\n", + "\n", + "
\n", + "\n", + "Let's add them:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "' T|CE| ..P'" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "starwars.add('THE FORCE AWAKENS')\n", + "startrek.add('BEYOND')\n", + "\n", + "findregex(starwars, startrek)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The two movies cost us one more character.\n", + "\n", + "There are lots of examples to play with over at [regex.alf.nu](http://regex.alf.nu), like this one:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 3, Parts: 1, Competitive ratio: 53.7, Winners: 21, Losers: 21\n" + ] + }, + { + "data": { + "text/plain": [ + "'foo'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "foo = words('''afoot catfoot dogfoot fanfoot foody foolery foolish fooster \n", + " footage foothot footle footpad footway hotfoot jawfoot mafoo nonfood padfoot \n", + " prefool sfoot unfool''')\n", + "\n", + "bar = words('''Atlas Aymoro Iberic Mahran Ormazd Silipan altared chandoo crenel \n", + " crooked fardo folksy forest hebamic idgah manlike marly palazzi sixfold \n", + " tarrock unfold''')\n", + "\n", + "report(foo, bar)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "The answer varies with different runs; sometimes it is `'foo'` and sometimes `'f.o'`. Both have 3 characters, but `'f.o'` is smaller in terms of the total amount of ink/pixels needed to render it. (How can the answer vary, when there are no calls to any `random` function? Because when `max` iterates over a set and several elements have the same best score, it is *unspecified* which one will be selected.)\n", + "\n", + "Of course, we can run any of these examples in the other direction:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 26, Parts: 8, Competitive ratio: 6.0, Winners: 21, Losers: 21\n" + ] + }, + { + "data": { + "text/plain": [ + "'r..$|k|.m|...n|ld|la|dg|or'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "report(bar, foo)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# What To Do Next? \n", + "\n", + "I see two options:\n", + "\n", + "- Stop here and declare victory! *Yay!*\n", + "- Try to make the program faster and capable of finding shorter regexes. \n", + "\n", + "My first inclination was \"stop here\", and that's what this notebook will shortly do. But several correspondents offered very interesting suggestions, so I returned to the problem in [a second notebook](http://nbviewer.ipython.org/url/norvig.com/ipython/xkcd1313-part2.ipynb?create=1). \n", + "\n", + "I was asked whether Randall was **[wrong](http://xkcd.com/386/)** to come up with \"only\" a 10-character Star Wars regex, whereas I showed there is a 9-character version. I would say that, given his role as a cartoonist, author, public speaker, educator, and entertainer, he has [chosen ... wisely](https://www.youtube.com/watch?v=puo1Enh9h5k&feature=youtu.be&t=294). He wrote a program that was good enough to allow him to make a great webcomic. A 9-character regex would not improve the comic. Randall stated that he used a genetic algorithm to find his regexes, and it has been said that genetic algorithms are often the second (or was it the third?) best method to solve any problem, and that's all he needed. But if you consider that in addition to all those roles, Randall is also still a practicing computer scientist, you could say\n", + "[he chose ... poorly](https://www.youtube.com/watch?v=Ubw5N8iVDHI). Genetic algorithms are good when you want to combine the structure of two solutions to yield a better solution, so they would work well if the best regexes had a complicated tree structure. But they don't! The best solutions are disjunctions of small parts. So the genetic algorithm is trying to combine the first half of one disjunction with the second half of another—but that isn't useful, because the components of a disjunction are unordered; imposing an ordering on them doesn't help.\n", + "\n", + "# Summary\n", + "\n", + "That was fun! I hope this page gives you an idea of how to think about problems like this. Let's review what we did:\n", + "\n", + "- Found an interesting problem (in a comic strip) and realized that it would not be hard to program a solution.\n", + "- Wrote the function `mistakes` to prove that we really understand exactly what the problem is.\n", + "- Came up with an approach: create lots of regex parts, and \"or\" together a subset of them.\n", + "- Realized that this is an instance of a known problem, *set cover*.\n", + "- Since set cover is computationally expensive, decide to use a *greedy algorithm*, which will be efficient (although not optimal).\n", + "- Decided what goes into the pool of regex parts.\n", + "- Implemented an algorithm to greedily pick parts from the pool (the function `findregex`).\n", + "- Tried the algorithm on some examples.\n", + "- Declared victory!\n", + "\n", + " \n", + "# Thanks!\n", + "\n", + "\n", + "Thanks especially to [Randall Monroe](http://xkcd.com/) for inspiring me to do this, to [regex.alf.nu](http://regex.alf.nu) for inspiring Randall, to Sean Lip for correcting \"Wilkie\" to \"Willkie,\" and to [Davide Canton](https://plus.sandbox.google.com/108324296451294887432/posts), [Thomas Breuel](https://plus.google.com/118190679520611168174/posts), and [Stefan Pochmann](http://www.stefan-pochmann.info/spocc/) for providing suggestions to improve my code.\n", + "\n", + "\n", + "\n", + "
\n", + "[*Peter Norvig*](http://norvig.com), Jan. 2014" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Characters: 44, Parts: 12, Competitive ratio: 4.8, Winners: 21, Losers: 21\n" + ] + }, + { + "data": { + "text/plain": [ + "'.17|4.2|1.4|06|55|009|37|0.2|00$|191|015|003'" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "report(words(\"\"\" 000000000\n", + " 000000003\n", + " 000000006\n", + " 000000009\n", + " 000000012\n", + " 000000015\n", + " 066990060\n", + " 140091876\n", + " 173655750\n", + " 312440187\n", + " 321769005\n", + " 368542278\n", + " 390259104\n", + " 402223947\n", + " 443512431\n", + " 714541758\n", + " 747289572\n", + " 819148602\n", + " 878531775\n", + " 905586303\n", + " 9537348\"\"\"), words(\"\"\"000000005\n", + " 000000008\n", + " 000000010\n", + " 000000011\n", + " 000000014\n", + " 018990130\n", + " 112057285\n", + " 159747125\n", + " 176950268\n", + " 259108903\n", + " 333162608\n", + " 388401457\n", + " 477848777\n", + " 478621693\n", + " 531683939\n", + " 704168662\n", + " 759282218\n", + " 769340942\n", + " 851936815\n", + " 973816159\n", + " 979204403\"\"\"))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "button": false, + "collapsed": true, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/ipynb/xkxd-part3.ipynb b/pytudes/ipynb/xkxd-part3.ipynb new file mode 100644 index 0000000..e2388b4 --- /dev/null +++ b/pytudes/ipynb/xkxd-part3.ipynb @@ -0,0 +1,428 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def partition(covers):\n", + " # covers: {w: {r,...}}\n", + " # invcovers: {r: {w,...}}\n", + " pass\n", + "\n", + "def connected(w, covers, invcovers, result):\n", + " if w not in result:\n", + " result.add(w)\n", + " for r in covers[w]:\n", + " for w2 in invcovers[r]:\n", + " connected(w2, covers, invcovers, result)\n", + " return result\n", + "\n", + "for (W, L, legend) in ALL:\n", + " covers = eliminate_dominated(regex_covers(W, L))\n", + " invcovers = invert_multimap(covers)\n", + " start = list(covers)[2]\n", + " P = connected(start, covers, invcovers, set())\n", + " print legend, len(P), len(covers), len(covers)-len(P)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finding Shorter Regexes: Trying Multiple Times\n", + "----\n", + " \n", + "Why run just two versions of `findregex`? Why not run 1000 variations, and then pick the best solution? Of course, I don't want to write 1000 different functions by hand; I want an automated way of varying each run. I can think of three easy things to vary:\n", + " \n", + "* The number '4' in the `score` function. That is, vary the tradeoff between number of winners matched and number of characters.\n", + "* The tie-breaker. In case of a tie, Python's `max` function always picks the first one. Let's make it choose a different 'best' regex from among all those that tie.\n", + "* The greediness. Don't be so greedy (picking the best) every time. Occasionally pick a not-quite-best component, and see if that works out better.\n", + " \n", + "The first of these is easy; we just use the `random.choice` function to choose an integer, `K`, to serve as the tradeoff factor. \n", + "\n", + "The second is easy too. We could write an alternative to the `max` function, say `max_random_tiebreaker`. That would work, but an easier approach is to build the tiebreaker into the `score` function. In addition to awarding points for matching winners and the number of characters, we will have add in a tiebreaker: a random number between 0 and 1. Since all the scores are otherwise integers, this will not change the order of the scores, but it will break ties.\n", + "\n", + "The third we can accomplish by allowing the random factor to be larger than 1 (allowing us to pick a component that is not the shortest) or even larger than `K` (allowing us to pick a component that does not cover the most winners). \n", + " \n", + "I will factor out the function `greedy_search` to do a single computation oof a covering regex, while keeping the name `findregex` for the top level function that now calls `greedy_search` 1000 times and chooses the best (shortest length) result." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "def findregex(winners, losers, tries=1000):\n", + " \"Find a regex that matches all winners but no losers (sets of strings).\"\n", + " # Repeatedly call 'findregex1' the given number of tries; pick the shortest result\n", + " covers = regex_covers(winners, losers)\n", + " results = [greedy_search(winners, covers) for _ in range(tries)]\n", + " return min(results, key=len)\n", + "\n", + "def greedy_search(winners, covers):\n", + " # On each iteration, add the 'best' component in covers to 'result',\n", + " # remove winners covered by best, and remove from 'pool' any components\n", + " # that no longer match any remaining winners.\n", + " winners = set(winners) # Copy input so as not to modify it.\n", + " pool = set(covers)\n", + " result = []\n", + " \n", + " def matches(regex, strings): return {w for w in covers[regex] if w in strings}\n", + " \n", + " K = random.choice((2, 3, 4, 4, 5, 6))\n", + " T = random.choice((1., 1.5, 2., K+1., K+2.))\n", + " def score(c): \n", + " return K * len(matches(c, winners)) - len(c) + random.uniform(0., T)\n", + " \n", + " while winners:\n", + " best = max(pool, key=score)\n", + " result.append(best)\n", + " winners -= covers[best]\n", + " pool -= {c for c in pool if covers[c].isdisjoint(winners)}\n", + " return OR(result)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def factorial1(n):\n", + " if (n <= 1):\n", + " return 1\n", + " else:\n", + " return n * factorial1(n-1)\n", + "\n", + "def factorial2(n, partial_solution=1):\n", + " if (n <= 1):\n", + " return partial_solution\n", + " else:\n", + " return factorial2(n-1, n * partial_solution)\n", + " \n", + "assert factorial1(6) == factorial2(6) == 720" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, calls=100000):\n", + " \"Find the shortest disjunction of regex components that covers winners but not losers.\"\n", + " covers = regex_covers(winners, losers)\n", + " best = '^(' + OR(winners) + ')$'\n", + " state = Struct(best=best, calls=calls)\n", + " return bb_search('', covers, state).best\n", + "\n", + "def bb_search(regex, covers, state):\n", + " \"\"\"Recursively build a shortest regex from the components in covers.\"\"\"\n", + " if state.calls > 0:\n", + " state.calls -= 1\n", + " regex, covers = simplify_covers(regex, covers)\n", + " if not covers:\n", + " state.best = min(regex, state.best, key=len)\n", + " elif len(OR2(regex, min(covers, key=len))) < len(state.best):\n", + " # Try with and without the greedy-best component\n", + " def score(c): return 4 * len(covers[c]) - len(c)\n", + " best = max(covers, key=score)\n", + " covered = covers[best]\n", + " covers.pop(best)\n", + " bb_search(OR2(regex, best), {c:covers[c]-covered for c in covers}, state)\n", + " bb_search(regex, covers, state)\n", + " return state\n", + "\n", + "class Struct(object):\n", + " \"A mutable structure with specified fields and values.\"\n", + " def __init__(self, **kwds): vars(self).update(kwds)\n", + " def __repr__(self): return '<%s>' % vars(self)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, calls=100000):\n", + " \"Find the shortest disjunction of regex components that covers winners but not losers.\"\n", + " covers = regex_covers(winners, losers)\n", + " solution = '^(' + OR(winners) + ')$'\n", + " solution, calls = bb_search('', covers, solution, calls)\n", + " return solution\n", + "\n", + "def bb_search(regex, covers, solution, calls):\n", + " \"\"\"Recursively build a shortest regex from the components in covers.\"\"\"\n", + " if calls > 0:\n", + " calls -= 1\n", + " regex, covers = simplify_covers(regex, covers)\n", + " if not covers: # Solution is complete\n", + " solution = min(regex, solution, key=len)\n", + " elif len(OR2(regex, min(covers, key=len))) < len(solution):\n", + " # Try with and without the greedy-best component\n", + " def score(c): return 4 * len(covers[c]) - len(c)\n", + " r = max(covers, key=score) # Best component\n", + " covered = covers[r] # Set of winners covered by r\n", + " covers.pop(r)\n", + " solution, calls = bb_search(OR2(regex, r), \n", + " {c:covers[c]-covered for c in covers}, \n", + " solution, calls)\n", + " solution, calls = bb_search(regex, covers, solution, calls)\n", + " return solution, calls" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def findregex(winners, losers, calls=100000):\n", + " \"Find the shortest disjunction of regex components that covers winners but not losers.\"\n", + " global SOLUTION, CALLS\n", + " SOLUTION = '^(' + OR(winners) + ')$'\n", + " CALLS = calls\n", + " return bb_search(None, regex_covers(winners, losers))\n", + "\n", + "def bb_search(regex, covers):\n", + " \"\"\"Recursively build a shortest regex from the components in covers.\"\"\"\n", + " global SOLUTION, CALLS\n", + " CALLS -= 1\n", + " regex, covers = simplify_covers(regex, covers)\n", + " if not covers: # Solution is complete\n", + " SOLUTION = min(regex, SOLUTION, key=len)\n", + " elif CALLS >= 0 and len(OR(regex, min(covers, key=len))) < len(SOLUTION):\n", + " # Try with and without the greedy-best component\n", + " def score(c): return 4 * len(covers[c]) - len(c)\n", + " r = max(covers, key=score) # Best component\n", + " covered = covers[r] # Set of winners covered by r\n", + " covers.pop(r)\n", + " bb_search(OR(regex, r), {c:covers[c]-covered for c in covers})\n", + " bb_search(regex, covers)\n", + " return SOLUTION\n", + " \n", + "def OR(*regexes):\n", + " \"OR together regexes. Ignore 'None' components.\"\n", + " return '|'.join(r for r in regexes if r is not None)\n", + "\n", + "\n", + "def invert_multimap(multimap):\n", + " result = collections.defaultdict(list)\n", + " for key in multimap:\n", + " for val in multimap[key]:\n", + " result[val].append(key)\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "## For debugging\n", + "\n", + "def findregex(winners, losers, calls=100000):\n", + " \"Find the shortest disjunction of regex components that covers winners but not losers.\"\n", + " solution = '^(' + OR(winners) + ')$'\n", + " covers = regex_covers(winners, losers)\n", + " b = BranchBound(solution, calls)\n", + " b.search(None, covers)\n", + " print b.calls, 'calls', len(b.solution), 'len'\n", + " return b.solution\n", + "\n", + "\n", + "def triage_covers(partial, covers):\n", + " \"Simplify covers by eliminating dominated regexes, and picking ones that uniquely cover a winner.\"\n", + " previous = None\n", + " while covers != previous:\n", + " previous = covers\n", + " # Eliminate regexes that are dominated by another regex\n", + " covers = eliminate_dominated(covers) # covers = {regex: {winner,...}}\n", + " coverers = invert_multimap(covers) # coverers = {winner: {regex,...}}\n", + " # For winners covered by only one component, move winner from covers to regex\n", + " singletons = {coverers[w][0] for w in coverers if len(coverers[w]) == 1}\n", + " if singletons:\n", + " partial = OR(partial, OR(singletons))\n", + " covered = {w for c in singletons for w in covers[c]}\n", + " covers = {c:covers[c]-covered for c in covers if c not in singletons}\n", + " return partial, covers\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ", and to , who suggested looking at [WFSTs](http://www.openfst.org/twiki/bin/view/FST/WebHome)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def regex_covers(winners, losers):\n", + " \"\"\"Generate regex components and return a dict of {regex: {winner...}}.\n", + " Each regex matches at least one winner and no loser.\"\"\"\n", + " losers_str = '\\n'.join(losers)\n", + " wholes = {'^'+winner+'$' for winner in winners}\n", + " parts = {d for w in wholes for p in subparts(w) for d in dotify(p)}\n", + " chars = set(cat(winners))\n", + " pairs = {A+'.'+rep_char+B for A in chars for B in chars for rep_char in '+*?'}\n", + " reps = {r for p in parts for r in repetitions(p)}\n", + " pool = wholes | parts | pairs | reps \n", + " searchers = [re.compile(c, re.MULTILINE).search for c in pool]\n", + " covers = {r: set(filter(searcher, winners)) \n", + " for (r, searcher) in zip(pool, searchers)\n", + " if not searcher(losers_str)}\n", + " covers = eliminate_dominated(covers)\n", + " return covers\n", + " return add_character_class_components(covers)\n", + "\n", + "def add_character_class_components(covers):\n", + " for (B, Ms, E) in combine_splits(covers):\n", + " N = len(Ms)\n", + " or_size = N*len(B+'.'+E) + N-1 # N=3 => 'B1E|B2E|B3E'\n", + " class_size = len(B+'[]'+E) + N # N=3 => 'B[123]E'\n", + " winners = {w for m in Ms for w in Ms[m]}\n", + " if class_size < or_size:\n", + " covers[B + make_char_class(Ms) + E] = winners\n", + " return covers\n", + "\n", + "def split3(word):\n", + " \"Splits a word into 3 parts, all ways, with middle part having 0 or 1 character.\"\n", + " return [(word[:i], word[i:i+L], word[i+L:]) \n", + " for i in range(len(word)+1) for L in (0, 1)\n", + " if not word[i:i+L].startswith(('.', '+', '*', '?'))]\n", + "\n", + "def combine_splits(covers):\n", + " \"Convert covers = {BME: {w...}} into a list of [(B, {M...}, E, {w...}].\"\n", + " table = collections.defaultdict(dict) # table = {(B, E): {M: {w...}}}\n", + " for r in covers:\n", + " for (B, M, E) in split3(r):\n", + " table[B, E][M] = covers[r]\n", + " return [(B, Ms, E) for ((B, E), Ms) in table.items()\n", + " if len(Ms) > 1]\n", + "\n", + "def make_char_class(chars):\n", + " chars = set(chars)\n", + " return '[%s]%s' % (cat(chars), ('?' if '' in chars else ''))\n", + "\n", + "covers = regex_covers(boys, girls)\n", + "old = set(covers)\n", + "print len(covers)\n", + "covers = add_character_class_components(covers)\n", + "print len(covers)\n", + "print set(covers) - old\n", + "\n", + "print dict(combine_splits({'..a': {1,2,3}, '..b': {4,5,6}, '..c':{7}}))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the two components `'..a'` and `'..b'`. If we wanted to cover all the winners that both of these match, we could use `'..a|..b'`, or we could share the common prefix and introduce a *character class* to get `'..[ab]'`. Since the former is 7 characters and the later is only 6, the later would be preferred. It would be an even bigger win to replace `'..az|..bz|..cz'` with `'..[abc]z'`; that reduces the count from 14 to 8. Similarly, replacing `'..az|..bz|..z'` with `'..[ab]?z'` saves 5 characters.\n", + "\n", + "There seems to be potential savings with character classes. But how do we know which characters from which components to combine into classes? To keep things from getting out of control, I'm going to only look at components that are left after we eliminate dominated. That is not an ideal approach—there may well be some components that are dominated on their own, but could be part of an optimal solution when combined with other components into a character class. But I'm going to keep it simple." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Searching: Better Bounds\n", + "----\n", + "\n", + "Branch and bound prunes the search tree whenever it is on a branch that is guaranteed to result in a solution that is no better than the best solution found so far. Currently we estimate the best possible solution along the current branch by taking the length of the partial solution and adding the length of the shortest component in `covers`. We do that because we know for sure that we need at least one component, but we don't know for sure how many components we'll need (nor how long each of them will be. So our estimate is often severely underestimates the true answer, which means we don't cut off search some places where we could, if only we had a better estimate.\n", + " \n", + "Here's one way to get a better bound. We'll define the following quantities:\n", + "\n", + "+ *P* = the length of the partial solution, plus the \"|\", if needed. So if the partial solution is `None`, then *P* will be zero, otherwise *P* is the length plus 1.\n", + "+ *S* = the length of the shortest regex component in `covers`.\n", + "+ *W* = the number of winners still in `covers`.\n", + "+ *C* = the largest number of winners covered by any regex in `covers`.\n", + "\n", + "If we assume The current estimate is *P* + *S*. We can see that a better estimate is *P* + *S* × ceil(*W* / *C*)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import math\n", + "\n", + "class BranchBound(object):\n", + " \"Hold state information for a branch and bound search.\"\n", + " def __init__(self, solution, calls):\n", + " self.solution, self.calls = solution, calls\n", + " \n", + " def search(self, covers, partial=None):\n", + " \"Recursively extend partial regex until it matches all winners in covers.\"\n", + " if self.calls <= 0: \n", + " return self.solution\n", + " self.calls -= 1\n", + " covers, partial = simplify_covers(covers, partial)\n", + " if not covers: # Nothing left to cover; solution is complete\n", + " self.solution = min(partial, self.solution, key=len)\n", + " else:\n", + " P = 0 if not partial else len(partial) + 1\n", + " S = len(min(covers, key=len))\n", + " C = max(len(covers[r]) for r in covers)\n", + " W = len(set(w for r in covers for w in covers[r]))\n", + " if P + S * math.ceil(W / C) < len(self.solution):\n", + " # Try with and without the greedy-best component\n", + " def score(r): return 4 * len(covers[r]) - len(r)\n", + " r = max(covers, key=score) # Best component\n", + " covered = covers[r] # Set of winners covered by r\n", + " covers.pop(r)\n", + " self.search({c:covers[c]-covered for c in covers}, OR(partial, r))\n", + " self.search(covers, partial)\n", + " return self.solution" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/pytudes/py/SET.py b/pytudes/py/SET.py new file mode 100644 index 0000000..5349c4c --- /dev/null +++ b/pytudes/py/SET.py @@ -0,0 +1,134 @@ +import random +import collections +import itertools + +""" +Game of Set (Peter Norvig 2010-2015) + +How often do sets appear when we deal an array of cards? +How often in the course of playing out the game? + +Here are the data types we will use: + + card: A string, such as '3R=0', meaning "three red striped ovals". + deck: A list of cards, initially of length 81. + layout: A list of cards, initially of length 12. + set: A tuple of 3 cards. + Tallies: A dict: {12: {True: 33, False: 1}}} means a layout of size 12 + tallied 33 sets and 1 non-set. +""" + +#### Cards, dealing cards, and defining the notion of sets. + +CARDS = [number + color + shade + symbol + for number in '123' + for color in 'RGP' + for shade in '@O=' + for symbol in '0SD'] + +def deal(n, deck): + "Deal n cards from the deck." + return [deck.pop() for _ in range(n)] + +def is_set(cards): + "Are these 3 cards a set? No if any feature has 2 values." + for f in range(4): + values = {card[f] for card in cards} + if len(values) == 2: + return False + return True + +def find_set(layout): + "Return a set found from this layout, if there is one." + for cards in itertools.combinations(layout, 3): + if is_set(cards): + return cards + return () + +#### Tallying set:no-set ratio + +def Tallies(): + "A data structure to keep track, for each size, the number of sets and no-sets." + return collections.defaultdict(lambda: {True: 0, False: 0}) + +def tally(tallies, layout): + "Record that a set was found or not found in a layout of given size; return the set." + s = find_set(layout) + tallies[len(layout)][bool(s)] += 1 + return s + +#### Three experiments + +def tally_initial_layout(N, sizes=(12, 15)): + "Record tallies for N initial deals." + tallies = Tallies() + deck = list(CARDS) + for deal in range(N): + random.shuffle(deck) + for size in sizes: + tally(tallies, deck[:size]) + return tallies + +def tally_initial_layout_no_prior_sets(N, sizes=(12, 15)): + """Simulate N initial deals for each size, keeping tallies for Sets and NoSets, + but only when there was no set with 3 fewer cards.""" + tallies = Tallies() + deck = list(CARDS) + for deal in range(N): + random.shuffle(deck) + for size in sizes: + if not find_set(deck[:size-3]): + tally(tallies, deck[:size]) + return tallies + +def tally_game_play(N): + "Record tallies for the play of N complete games." + tallies = Tallies() + for game in range(N): + deck = list(CARDS) + random.shuffle(deck) + layout = deal(12, deck) + while deck: + s = tally(tallies, layout) + # Pick up the cards in the set, if any + for card in s: layout.remove(card) + # Deal new cards + if len(layout) < 12 or not s: + layout += deal(3, deck) + return tallies + +def experiments(N): + show({12: [1, 33], 15: [1, 2500]}, + 'the instruction booklet') + show(tally_initial_layout(N), + 'initial layout') + show(tally_game_play(N // 25), + 'game play') + show(tally_initial_layout_no_prior_sets(N), + 'initial layout, but no sets before dealing last 3 cards') + + +def show(tallies, label): + "Print out the counts." + print() + print('Size | Sets | NoSets | Set:NoSet ratio for', label) + print('-----+--------+--------+----------------') + for size in sorted(tallies): + y, n = tallies[size][True], tallies[size][False] + ratio = ('inft' if n==0 else int(round(float(y)/n))) + print('{:4d} |{:7,d} |{:7,d} | {:4}:1' + .format(size, y, n, ratio)) + +def test(): + assert len(CARDS) == 81 == len(set(CARDS)) + assert is_set(('3R=O', '2R=S', '1R=D')) + assert not is_set(('3R=0', '2R=S', '1R@D')) + assert find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R=D']) == ('3R=0', '2R=S', '1R=D') + assert not find_set(['1PO0', '2G=D', '3R=0', '2R=S', '1R@D']) + photo = '2P=0 3P=D 2R=0 3GO0 2POD 3R@D 2RO0 2ROS 1P@S 2P@0 3ROS 2GOD 2P@D 1GOD 3GOS'.split() + assert not find_set(photo) + assert set(itertools.combinations([1, 2, 3, 4], 3)) == {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)} + print('All tests pass.') + +test() +experiments(100000) diff --git a/pytudes/py/beal.py b/pytudes/py/beal.py new file mode 100644 index 0000000..ebe4dd8 --- /dev/null +++ b/pytudes/py/beal.py @@ -0,0 +1,159 @@ +"""Search for counterexamples to Beal's conjecture +See http://norvig.com/beal.html and http://www.bealconjecture.com""" + +from __future__ import division, print_function +from math import log +from itertools import combinations, product +from collections import defaultdict +try: + from math import gcd # For Python 3.6 and up +except ImportError: + from fractions import gcd # For older versions (works in 2.7 as well) + +def beal(max_A, max_x): + """See if any A ** x + B ** y equals some C ** z, with gcd(A, B) == 1. + Consider any 1 <= A,B <= max_A and x,y <= max_x, with x,y prime or 4.""" + Apowers = make_Apowers(max_A, max_x) + Czroots = make_Czroots(Apowers) + for (A, B) in combinations(Apowers, 2): + if gcd(A, B) == 1: + for (Ax, By) in product(Apowers[A], Apowers[B]): + Cz = Ax + By + if Cz in Czroots: + C = Czroots[Cz] + x, y, z = exponent(Ax, A), exponent(By, B), exponent(Cz, C) + print('{} ** {} + {} ** {} == {} ** {} == {}' + .format(A, x, B, y, C, z, C ** z)) + +def make_Apowers(max_A, max_x): + "A dict of {A: [A**3, A**4, ...], ...}." + exponents = exponents_upto(max_x) + return {A: [A ** x for x in (exponents if (A != 1) else [3])] + for A in range(1, max_A+1)} + +def make_Czroots(Apowers): return {Cz: C for C in Apowers for Cz in Apowers[C]} + +def exponents_upto(max_x): + "Return all odd primes up to max_x, as well as 4." + exponents = [3, 4] if max_x >= 4 else [3] if max_x == 3 else [] + for x in range(5, max_x, 2): + if not any(x % p == 0 for p in exponents): + exponents.append(x) + return exponents + +def exponent(Cz, C): + """Recover z such that C ** z == Cz (or equivalently z = log Cz base C). + For exponent(1, 1), arbitrarily choose to return 3.""" + return 3 if (Cz == C == 1) else int(round(log(Cz, C))) + +############################################################################## + +def tests(): + assert make_Apowers(6, 10) == { + 1: [1], + 2: [8, 16, 32, 128], + 3: [27, 81, 243, 2187], + 4: [64, 256, 1024, 16384], + 5: [125, 625, 3125, 78125], + 6: [216, 1296, 7776, 279936]} + + assert make_Czroots(make_Apowers(5, 8)) == { + 1: 1, 8: 2, 16: 2, 27: 3, 32: 2, 64: 4, 81: 3, + 125: 5, 128: 2, 243: 3, 256: 4, 625: 5, 1024: 4, + 2187: 3, 3125: 5, 16384: 4, 78125: 5} + Czroots = make_Czroots(make_Apowers(100, 100)) + assert 3 ** 3 + 6 ** 3 in Czroots + assert 99 ** 97 in Czroots + assert 101 ** 100 not in Czroots + assert Czroots[99 ** 97] == 99 + + assert exponent(10 ** 5, 10) == 5 + assert exponent(7 ** 3, 7) == 3 + assert exponent(1234 ** 999, 1234) == 999 + assert exponent(12345 ** 6789, 12345) == 6789 + assert exponent(3 ** 10000, 3) == 10000 + assert exponent(1, 1) == 3 + + assert exponents_upto(2) == [] + assert exponents_upto(3) == [3] + assert exponents_upto(4) == [3, 4] + assert exponents_upto(40) == [3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37] + assert exponents_upto(100) == [ + 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, + 67, 71, 73, 79, 83, 89, 97] + + assert gcd(3, 6) == 3 + assert gcd(3, 7) == 1 + assert gcd(861591083269373931, 94815872265407) == 97 + assert gcd(2*3*5*(7**10)*(11**12), 3*(7**5)*(11**13)*17) == 3*(7**5)*(11**12) + return 'tests pass' + +############################################################################## + +def beal_modp(max_A, max_x, p=2**31-1): + """See if any A ** x + B ** y equals some C ** z (mod p), with gcd(A, B) == 1. + If so, verify that the equation works without the (mod p). + Consider any 1 <= A,B <= max_A and x,y <= max_x, with x,y prime or 4.""" + assert p >= max_A + Apowers = make_Apowers_modp(max_A, max_x, p) + Czroots = make_Czroots_modp(Apowers) + for (A, B) in combinations(Apowers, 2): + if gcd(A, B) == 1: + for (Axp, x), (Byp, y) in product(Apowers[A], Apowers[B]): + Czp = (Axp + Byp) % p + if Czp in Czroots: + lhs = A ** x + B ** y + for (C, z) in Czroots[Czp]: + if lhs == C ** z: + print('{} ** {} + {} ** {} == {} ** {} == {}' + .format(A, x, B, y, C, z, C ** z)) + + +def make_Apowers_modp(max_A, max_x, p): + "A dict of {A: [(A**3 (mod p), 3), (A**4 (mod p), 4), ...]}." + exponents = exponents_upto(max_x) + return {A: [(pow(A, x, p), x) for x in (exponents if (A != 1) else [3])] + for A in range(1, max_A+1)} + +def make_Czroots_modp(Apowers): + "A dict of {C**z (mod p): [(C, z),...]}" + Czroots = defaultdict(list) + for A in Apowers: + for (Axp, x) in Apowers[A]: + Czroots[Axp].append((A, x)) + return Czroots + +############################################################################## + +def simpsons(bases, powers): + """Find the integers (A, B, C, n) that come closest to solving + Fermat's equation, A ** n + B ** n == C ** n. + Let A, B range over all pairs of bases and n over all powers.""" + equations = ((A, B, iroot(A ** n + B ** n, n), n) + for A, B in combinations(bases, 2) + for n in powers) + return min(equations, key=relative_error) + +def iroot(i, n): + "The integer closest to the nth root of i." + return int(round(i ** (1./n))) + +def relative_error(equation): + "Error between LHS and RHS of equation, relative to RHS." + (A, B, C, n) = equation + LHS = A ** n + B ** n + RHS = C ** n + return abs(LHS - RHS) / RHS + +if __name__ == '__main__': + print(tests()) + print("Searching beal(500, 100)") + print(beal(500, 100)) + print("Finding Simpson-esque near-solutions to Fermat's Equation") + def s(b, p): print('{0}^{3} + {1}^{3} = {2}^{3}'.format(*simpsons(b, p))) + s(range(1000, 2000), [11, 12, 13]) + s(range(3000, 5000), [12]) + print("Searching beal_modp(500, 100)") + print(beal_modp(500, 100)) + + diff --git a/pytudes/py/docex.py b/pytudes/py/docex.py new file mode 100644 index 0000000..cbffe2a --- /dev/null +++ b/pytudes/py/docex.py @@ -0,0 +1,238 @@ +"""A framework for running unit tests and examples, written in docstrings. + +This lets you write "Ex: sqrt(4) ==> 2; sqrt(-1) raises ValueError" in a +docstring, and then execute the examples as unit tests. + +This functionality is similar to the doctest module. The major +differences between docex and doctest are: + +(1) Brevity. With docex you write the one-line comment + "Ex: len('abc') ==> 3; len([]) ==> 0; len(5) raises TypeError" + With doctest you would need 9 lines for the same thing: + '''>>> len('abc') + 3 + >>> len([]) + 0 + >>> len(5)) + Traceback (most recent call last): + ... + TypeError: len() of unsized object + ''' + +(2) Docex handles both examples and unit tests. + It took me a while to recognize this distinction: when I write + "sqrt(4) ==> 2" it has two purposes -- to serve as a unit test + and to serve as an example of how to use the sqrt function. + When I write "random.choice('abc')" it serves as an example of + how to use the choice function, but it is not a unit test. + docex lets you do both; doctest only supports tests. Of course + you can coerce this into a test in doctest, with something like + >>> random.choice('abc') in 'abc' + True + +(3) Eval-based rather than string-comparison based. The docex string + "dict(zip([1,4,9], [1,2,3])) ==> {1: 1, 4: 2, 9: 3}" works even + when a different version of Python decides to print the dict as + "{9: 3, 4: 2, 1: 1}" because docex evals the right-hand-side and + checks to see if it is equal. That's good for dicts, its good for + writing "1+1==2 ==> True" and having it work in versions of Python + where True prints as "1" rather than as "True", and so on, + but doctest has the edge if you want to compare against something + that doesn't have an eval-able output, or if you want to test + printed output. + +(4) Doctest has many more features, and is better supported. + I wrote docex before doctest was an official part of Python, but + with the refactoring of doctest in Python 2.4, I decided to switch + my code over to doctest, even though I prefer the brevity of docex. + I still offer docex for those who want it. + +From Python, when you want to test modules m1, m2, ... do: + docex.Docex([m1, m2, ...]) +From the shell, when you want to test files *.py, do: + python docex.py [log-file] *.py +If log file ends in .htm or .html, it will be written in HTML. +If log file is -, or if it is missing, then standard output is used. + +For each module, Docex looks at the __doc__ and _docex strings of the +module itself, and of each member, and recursively for each member +class. If a line in a docstring starts with r'^\s*Ex: ' (a line with +blanks, then 'Ex: '), then the remainder of the string after the colon +is treated as examples. Each line of the examples should conform to +one of the following formats: + + (1) Blank line or a comment; these just get echoed verbatim to the log. + (2) Of the form example1 ; example2 ; ... + (3) Of the form 'x ==> y' for any expressions x and y. + x is evaled and assigned to _, then y is evaled. + If x != y, an error message is printed. + (4) Of the form 'x raises y', for any statement x and expression y. + First y is evaled to yield an exception type, then x is execed. + If x doesn't raise the right exception, an error msg is printed. + (5) Of the form 'statement'. Statement is execed for side effect. + (6) Of the form 'expression'. Expression is evaled for side effect. +""" + +import re, sys, types + +class Docex: + """A class to run test examples written in docstrings or in _docex.""" + + def __init__(self, modules=None, html=0, out=None, + title='Docex Example Output'): + if modules is None: + modules = sys.modules.values() + self.passed = self.failed = 0; + self.dictionary = {} + self.already_seen = {} + self.html = html + try: + if out: sys.stdout = out + self.writeln(title, '

', '

')
+            for module in modules:
+                self.run_module(module)
+            self.writeln(str(self), '
\n

', '

\n') + finally: + if out: + sys.stdout = sys.__stdout__ + out.close() + + def __repr__(self): + if self.failed: + return ('' + % (self.failed, self.passed)) + else: + return '' % self.passed + + def run_module(self, object): + """Run the docstrings, and then all members of the module.""" + if not self.seen(object): + self.dictionary.update(vars(object)) # import module into self + name = object.__name__ + self.writeln('## Module %s ' % name, + '\n

' % name, + '

')
+            self.run_docstring(object)
+            names = object.__dict__.keys()
+            names.sort()
+            for name in names:
+                val = object.__dict__[name]
+                if isinstance(val, types.ClassType):
+                    self.run_class(val)
+                elif isinstance(val, types.ModuleType):
+                    pass
+                elif not self.seen(val):
+                    self.run_docstring(val)
+
+    def run_class(self, object):
+        """Run the docstrings, and then all members of the class."""
+        if not self.seen(object):
+            self.run_docstring(object)
+            names = object.__dict__.keys()
+            names.sort()
+            for name in names:
+                self.run_docstring(object.__dict__[name])
+
+    def run_docstring(self, object, search=re.compile(r'(?m)^\s*Ex: ').search):
+        "Run the __doc__ and _docex attributes, if the object has them."
+        if hasattr(object, '__doc__'):
+            s = object.__doc__
+            if isinstance(s, str):
+                match = search(s)
+                if match: self.run_string(s[match.end():])
+        if hasattr(object, '_docex'):
+                self.run_string(object._docex)
+        
+    def run_string(self, teststr):
+        """Run a test string, printing inputs and results."""
+        if not teststr: return
+        teststr = teststr.strip()
+        if teststr.find('\n') > -1:
+            map(self.run_string, teststr.split('\n'))
+        elif teststr == '' or teststr.startswith('#'):
+            self.writeln(teststr)
+        elif teststr.find('; ') > -1:
+            for substr in teststr.split('; '): self.run_string(substr)
+        elif teststr.find('==>') > -1:
+            teststr, result = teststr.split('==>')
+            self.evaluate(teststr, result)
+        elif teststr.find(' raises ') > -1:
+            teststr, exception = teststr.split(' raises ')
+            self.raises(teststr, exception)
+        else: ## Try to eval, but if it is a statement, exec
+            try:
+                self.evaluate(teststr)
+            except SyntaxError:
+                exec teststr in self.dictionary
+
+    def evaluate(self, teststr, resultstr=None):
+        "Eval teststr and check if resultstr (if given) evals to the same."
+        self.writeln('>>> ' +  teststr.strip())
+        result = eval(teststr, self.dictionary)
+        self.dictionary['_'] = result
+        self.writeln(repr(result))
+        if resultstr == None:
+          return
+        elif result == eval(resultstr, self.dictionary):
+          self.passed += 1
+        else:
+          self.fail(teststr, resultstr)
+    
+    def raises(self, teststr, exceptionstr):
+        teststr = teststr.strip()
+        self.writeln('>>> ' + teststr)
+        except_class = eval(exceptionstr, self.dictionary)
+        try:
+            exec teststr in self.dictionary
+        except except_class:
+            self.writeln('# raises %s as expected' % exceptionstr)
+            self.passed += 1
+            return
+        self.fail(teststr, exceptionstr)
+
+    def fail(self, teststr, resultstr):
+        self.writeln('###### ERROR, TEST FAILED: expected %s for %s' 
+                     % (resultstr, teststr),
+                     '', '')
+        self.failed += 1
+
+    def writeln(self, s, before='', after=''):
+        "Write s, html escaped, and wrapped with html code before and after."
+        s = str(s)
+        if self.html:
+            s = s.replace('&','&').replace('<','<').replace('>','>')
+            print '%s%s%s' % (before, s, after)
+        else:
+            print s
+
+    def seen(self, object):
+        """Return true if this object has been seen before.
+        In any case, record that we have seen it."""
+        result = self.already_seen.has_key(id(object))
+        self.already_seen[id(object)] = 1
+        return result
+
+def main(args):
+    """Run Docex.  args should be a list of python filenames.  
+    If the first arg is a non-python filename, it is taken as the
+    name of a log file to which output is written.  If it ends in
+    ".htm" or ".html", then the output is written as html.  If the
+    first arg is "-", then standard output is used as the log file."""
+    import glob
+    out = None
+    html = 0
+    if args[0] != "-" and not args[0].endswith(".py"):
+        out = open(args[0], 'w')
+        if args[0].endswith(".html") or args[0].endswith(".htm"):
+            html = 1
+    modules = []
+    for arg in args:
+        for file in glob.glob(arg):
+            if file.endswith('.py'):
+                modules.append(__import__(file[:-3]))
+    print Docex(modules, html=html, out=out)
+
+if __name__ == '__main__':
+    main(sys.argv[1:])
+
+
diff --git a/pytudes/py/ibol.py b/pytudes/py/ibol.py
new file mode 100644
index 0000000..d2490a6
--- /dev/null
+++ b/pytudes/py/ibol.py
@@ -0,0 +1,193 @@
+from collections import defaultdict
+
+def get_genomes(fname="byronbayseqs.fas.txt"):
+    "Return a list of genomes, and a list of their corresponding names."
+    import re
+    names, species, genomes = [], [], []
+    for name, g in re.findall('>(.*?)\r([^\r]*)\r*', file(fname).read()):
+        names.append(name)
+        species.append(name.split('|')[-1])
+        genomes.append(g)
+    return names, species, genomes
+
+def get_neighbors(fname="editdistances.txt"):
+    "Return dict: neighbors[i][j] = neighbors[j][i] = d means i,j are d apart."
+    ## Read the data pre-computed from the Java program
+    neighbors = dict((i, {}) for i in range(n))
+    for line in file(fname):
+        i,j,d = map(int, line.split())
+        neighbors[i][j] = neighbors[j][i] = d
+    return neighbors
+        
+def cluster(neighbors, d, dc):
+    """Return a list of clusters, each cluster element is within d of another
+    and within dc of every other cluster element."""
+    unclustered = set(neighbors) ## set of g's not yet clustered
+    return [closure(g, set(), unclustered, d, dc)
+            for g in neighbors if g in unclustered]
+
+def closure(g, s, unclustered, d, dc):
+    "Accumulate in set s the transitive closure of 'near', starting at g"
+    if g not in s and g in unclustered and near(g, s, d, dc):
+        s.add(g); unclustered.remove(g)
+        for g2 in neighbors[g]:
+            closure(g2, s, unclustered, d, dc)
+    return s
+
+def dist(i, j):
+    "Distance between two genomes."
+    if i == j: return 0
+    return neighbors[min(i, j)].get(max(i, j), max_distance)
+
+def near(g, cluster, d, dc):
+    "Is g within d of some member of c, and within dc of every member of c?"
+    distances = [dist(g, g2) for g2 in cluster] or [0]
+    return min(distances) <= d and max(distances) <= dc
+
+def diameter(cluster):
+    "The largest distance between two elements of the cluster"
+    return max([dist(i, j) for i in cluster for j in cluster] or [0])
+
+def margin(cluster):
+    "The distance from a cluster to the nearest g2 outside this cluster."
+    return min([d for g in cluster for g2,d in neighbors[g].items()
+                if g2 not in cluster] or [max_distance])
+
+################################################################ Analysis
+
+def pct(num, den):
+    "Return a string representing the percentage. "
+    if '__len__' in dir(den): den = len(den)
+    if num==den: return ' 100%'
+    return '%.1f%%' % (num*100.0/den)
+
+def histo(items):
+    "Make a histogram from a sequence of items or (item, count) tuples."
+    D = defaultdict(int)
+    for item in items:
+        if isinstance(item, tuple): D[item[0]] += item[1]
+        else: D[item] += 1
+    return D
+
+def showh(d):
+    "Show a histogram"
+    if not isinstance(d, dict): d = histo(d)
+    return ' '.join('%s:%s' % i for i in sorted(d.items()))
+
+def greport(genomes):
+    print "Number of genomes: %d (%d distinct)" % (len(genomes), len(set(genomes)))
+    G = dict((g, set()) for g in genomes)
+    for i in range(n):
+        G[genomes[i]].add(species[i])
+    print "Multi-named genomes:", (
+        len([s for s in G.values() if len(s) > 1]))
+    lens = map(len, genomes)
+    print "Genome lengths: min=%d, max=%d" % (min(lens), max(lens))
+    print "Character counts: ", showh(c for g in genomes for c in g)
+    
+def nreport(neighbors):
+    NN, NumN = defaultdict(int), defaultdict(int) ## Nearest, Number of neighbors
+    for n in neighbors:
+        nn = min(neighbors[n].values() or ['>25'])
+        NN[nn] += 1
+        for d2 in neighbors[n].values():
+            NumN[d2] += 1 
+    print
+    print "Nearest neighbor counts:", showh(NN)
+    print "Number of neighbors at each distance:", showh(NumN)
+
+def nspecies(c): return len(set(species[g] for g in c))
+
+def showc(c):
+    return "N=%d, D=%d, M=%d: %s %s" % (
+        len(c), diameter(c), margin(c), list(c), showh(species[g] for g in c))
+
+def creport(drange, dcrange):
+    def table(what, fn):
+        print "\n" + what
+        print ' '*8, ' '.join([' '+pct(dc, glen) for dc in dcrange])
+        for d in drange:
+            print '%s (%2d)' % (pct(d, glen), d),
+            for dc in dcrange:
+                print '%5s' % fn(cluster(neighbors, d, dc)),
+            print
+    print '\nNearest neighbor must be closer than this percentage (places). '
+    print 'Each column: all genomes in cluster within this percentage of each other.'
+    table("Number of clusters", len)
+    cluster1 = cluster(neighbors, 8, 15) ## splits Cleora
+    print '\nNumber of clusters of different sizes:', showh(len(c) for c in cluster1)
+    M, T = defaultdict(int), defaultdict(int)
+    for c in cluster1:
+        M[margin(c)] += 1; T[margin(c)] += len(c)
+    for x in M: print '%d\t%d\t%d'% (x,M[x],T[x])
+    print '\nMargins', showh(M)
+    for c in cluster1:
+        if margin(c) <= 16:
+            print showc(c)
+    print '\nScatter plot of cluster diameter vs. margin.'
+    for c in cluster1:
+        if diameter(c) > 0:
+            pass
+            #print '%d\t%d' % (diameter(c), margin(c))
+    print '\nDifference from cluster(neighbors, 11, 14):'
+    #table(lambda cl: pct(len(cluster1)-compare(cluster1, cl),max(len(cluster1),len(cl))))
+    print '\nNumber of clusters witth more than one species name:'
+    #table(lambda cl: sum(nspecies(c) > 1 for c in cl))
+    def pct_near_another(clusters, P=1.25):
+        total = 0
+        for c in clusters:
+            d = diameter(c)
+            for g in c:
+                for g2 in neighbors[g]:
+                    if g2 not in c and dist(g, g2) < P*d:
+                        total += 1
+        return pct(total, n)
+    def f(P):
+        print '\nPercent of individuals within %.2f*diameter of another cluster.'%P
+        table(lambda cl: pct_near_another(cl, P))
+    #map(f, [1.2, 1.33, 1.5])
+
+def sreport(species):
+    SS = defaultdict(int)
+    print
+    for s in set(species):
+        c = [g for g in range(n) if species[g] == s]
+        d = diameter(c)
+        if d > 14:
+            if d==glen: d = '>25'
+            print 'diameter %s for %s (%d elements)' % (d, s, len(c))
+        SS[d] += 1
+    print 'Diameters of %d labeled clusters: %s' % (len(set(species)), showh(SS))
+    
+def compare(cl1, cl2):
+    "Compare two lists of clusters"
+    return sum(c1==c2 or 0.5*(abs(len(c1)-len(c2))==1 and
+                              (c1.issubset(c2) or c2.issubset(c1)))
+               for c1 in cl1 for c2 in cl2)
+
+def unit_tests():
+    assert set(len(g) for g in genomes) == set([glen])
+    clusters = cluster(neighbors, 11, 11)
+    assert sum(len(c) for c in clusters) == len(genomes)
+    assert len(set(g for c in clusters for g in c)) == len(genomes)
+    assert dist(17, 42) == dist(42, 17)
+    assert diameter(set()) == 0
+    assert diameter([17, 42]) == dist(17, 42)
+    assert pct(1, 2) == '50.0%'
+    print '\nAll tests pass.\n'
+
+    
+
+################################################################ Main body
+ 
+max_distance = 26
+names, species, genomes = get_genomes() ## genomes = ['ACT...', ...]
+n = len(genomes)
+glen = len(genomes[0])
+neighbors = get_neighbors() ## neighbor[g] = {g2:d2, g3:g3, ...}
+greport(genomes)
+nreport(neighbors)
+creport(range(6, 15), [glen,16,15,14,13, 12, 11])
+#sreport(species)
+
+unit_tests()
diff --git a/pytudes/py/lettercount.py b/pytudes/py/lettercount.py
new file mode 100644
index 0000000..3c6db88
--- /dev/null
+++ b/pytudes/py/lettercount.py
@@ -0,0 +1,443 @@
+"""
+Code to support http://norvig.com/mayzner.html
+Read files in the Google Books ngram format, and convert them to a simpler format.
+The original format looks like this:
+
+    word     \t year \t word_count \t book_count
+    word_POS \t year \t word_count \t book_count
+
+for example,
+
+    accreted_VERB	1846	7	4
+    accreted_VERB	1847	1	1
+    accreted_VERB	1848	1	1
+
+The function 'read_year_file' will convert a file of this form into a dict of
+{WORD: count} pairs, where the WORD is uppercased, and the count is the total
+over all years (you have the option to specify a starting year) and all
+capitalizations.  Then 'read_dict' and 'write_dict' convert between a dict and
+an external file format that looks like this:
+
+    ACCRETED	9
+
+"""
+
+from __future__ import division
+from collections import Counter, defaultdict
+
+#### Read files in Books-Ngram format; convert to a dict
+
+def read_year_file(filename, dic=None):
+    """Read a file of 'word year word_count book_count' lines and convert to a dict
+    {WORD: totalcount}. Uppercase all words, and only include all-alphabetic words."""
+    if dic is None: dic = {}
+    for line in file(filename):
+        word, year, c1, c2 = line.split('\t')
+        if '_' in word:
+            word = word[:word.index('_')]
+        if word.isalpha():
+            word = word.upper()
+            dic[word] = dic.get(word, 0) + int(c1)
+    return dic
+
+#### Read and write files of the form 'WORD \t count \n'
+
+def write_dict(dic, filename):
+    "Write a {word:count} dict as 'word \t count' lines in filename."
+    out = file(filename, 'w')
+    for key in sorted(dic):
+        out.write('%s\t%s\n' % (key, dic[key]))
+    return out.close()
+        
+def read_dict(filename, sep='\t'):
+    "Read 'word \t count' lines from file and make them into a dict of {word:count}."
+    pairs = (line.split(sep) for line in file(filename))
+    return {word: int(count) for (word, count) in pairs}
+
+#### Convert a bunch of year files into dict file format.
+
+def convert_files(filenames, mincount=1e5):
+    def report(filename, D, adj):
+        import time
+        N = len(D)
+        W = sum(v for v in D.itervalues())
+        print '%s: %s %s words (%s tokens) at %s' % (
+            filename, adj, format(W, ',d'), format(N, ',d'),
+            time.strftime("%H:%M:%S", time.gmtime()))
+    for f in filenames:
+        report(f, {}, 'starting')
+        D = read_year_file(f)
+        report(f, D, 'total')
+        for key in list(D):
+            if D[key] < mincount:
+                del D[key]
+        write_dict(D, 'WORD-' + f[-1].upper())
+        report(f, D, 'popular')
+
+def load(filename='top-words.txt'):
+    "Load file of 'word \t count' lines into D (a dict), W (length of D) and M (total number of words)."
+    global D, W, M
+    D = read_dict(filename)
+    W = len(D)
+    M = sum(D.values())
+    
+#### Compute letter counts and save as HTML files.
+
+def histogram(items):
+    "Return a Counter of the number of times each key occurs in (key, val) pairs."
+    C = Counter()
+    for (key, val) in items:
+        C[key] += val
+    return C
+
+def end(name): return '/' + name
+
+def tag(name, **kwds): return '<' + name + keywords(kwds) + '>'
+
+def row(cells, **kwds):
+    return '' + ''
+    
+def ngram_tables(dic, N, pos=[0, 1, 2, 3, 4, -5, -4, -3, -2, -1]):
+    """Return three dicts of letter N-grams of length N: counts, counts1, counts2.
+    counts is a dict of {'AB': 123} that counts how often 'AB' occurs.
+    counts1[i] is a dict of {'AB': 123} that counts how often 'AB' occurs at position i.
+    counts2[i][j] is a dict of {'AB': 123} that counts how often 'AB' occurs at position i."""
+    L = len(max(D, key=len))
+    counts = Counter()
+    counts1 = [Counter() for _ in range(L)]
+    counts2 = [[Counter() for i in range(L)]]
+
+def counter(pairs):
+    "Make a Counter from an iterable of (value, count) pairs."
+    c = Counter()
+    for (value, count) in pairs:
+        c[value] += count
+    return c
+
+def ngrams(word, N):
+    return [word[i:i+N] for i in range(len(word)+1-N)]
+
+
+import glob
+#convert_files(glob.glob('book?'))
+              
+#DB = [[letter_counts() for length in range(length)] for length in range(maxlen)]
+      
+
+## Unused ???
+
+def letter_counts(wc):
+    """From word_counts dictionary wc, Create a dictionary of {(s, i, L): count}
+    where s is a letter n-gram, i is the starting position, and L is the length
+    of the word in which it appears."""
+    result = defaultdict(int)
+    for (word, count) in wc.iteritems():
+        for p in pieces(word):
+            result[p] += count
+    return result
+
+def pieces(word):
+    "Yield the 1- and 2-letter grams in (s, i, L) format."
+    L = len(word)
+    for i in range(L):
+        yield (word[i], i, L)
+        if i+1 < L:
+            yield (word[i:i+2], i, L)
+
+def getcount(counts, s, pos, length):
+    """The count for letter sequence s (one or two letters) starting at
+    position i of words of length length.  If any argument is all, sum them up."""
+    if length == all:
+        return sum(getcount(counts, s, pos, L) for L in all_lengths)
+    elif pos == all:
+        return sum(getcount(counts, s, i, length) for i in range(length))
+    else:
+        return counts[s, pos, length]
+
+
+print 'start'
+#wc = word_counts('count_100K.txt')
+#counts = letter_counts(wc)
+print 'end'
+
+
+
+def test():
+    D = {'the': 100, 'of': 70, 'and': 60, 'to': 50, 'a': 40}
+
+def num(ch):
+    "Translate 'a' or 'A' to 0, ... 'z' or 'Z' to 25."
+    return 'abcdefghijklmnopqrstuvwxyz'.index(ch.lower())
+    
+
+def stats(D, NS = (1, 2, 3, 4, 5, 6)):
+    counts = {n: Counter() for n in NS}
+    print 'words ' + ' '.join('   %d-grams  ' % n for n in NS)
+    for (i, word) in enumerate(sortedby(D), 1):
+        for n in NS:
+            for ng in ngrams(word, n):
+                counts[n][ng] += 1
+        if i % 5000 == 0 or i == len(D):
+            print "%4dK" % (i/1000),
+            for n in NS:
+                c = len(counts[n])
+                field = "%5d (%d%%)" % (c, int(round(c*100/(26**n))))
+                print '%12s' % field,
+            print
+
+letters = 'ETAOINSRHLDCUMFPGWYBVKXJQZ'
+alphabet = ''.join(sorted(letters))
+
+from itertools import cycle, izip
+
+colors = 'ygobp'
+
+def bar(text, color, count, N, pixels, height=16):
+    width = int(round(pixels * count / N))
+    if width < 2: width = 3
+    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
+    return '%s' % (
+        title, color, height, width, -width+2, text) # -int(width/2+5)
+
+def letter_bar(LC, N=None, factor='', pixels=700):
+    if N is None: N = sum(LC.values())
+    #divisor = {'':1., 'K':1e3, 'M':1e6, 'B':1e9}[factor]
+    return ''.join(
+        bar(L.lower(), color, LC[L], N, pixels)
+        for (L, color) in izip(letters, cycle(colors)))
+        
+
+def singleton(x): return [x]
+
+positions = [0, 1, 2, 3, 4, 5, 6, -7, -6, -5, -4, -3, -2, -1]
+
+def substr(word, pos, length):
+    """Return the substr of word of given length starting/ending at pos; or None."""
+    W = len(word)
+    if pos >= 0 and pos+length <= W:
+        return word[pos:pos+length]
+    elif pos < 0 and abs(pos)+length-1 <= W:
+        return word[W+pos+1-length:W+pos+1]
+    else:
+        return None
+        
+def lettercount(D, pos):
+    LC = histogram((substr(w, pos, 1), D[w]) for w in D)
+    del LC[None]
+    print LC
+    pos_name = (str(pos)+'+' if isinstance(pos, tuple) else
+                pos if pos < 0 else
+                pos+1)
+    return '\n
\n%-3s %s' % (pos_name, letter_bar(LC))
+
+def ngramcount(D, n=2):
+    return histogram((ng, D[w]) for w in D for ng in ngrams(w, n))
+
+def twograms(D2):
+    N = sum(D2.values())
+    header = ''
+    rows = [tr([cell(A+B, D2, N) for A in alphabet]) for B in alphabet]
+    return '\n'.join([header] + rows + ['
'])
+
+def cell(text, D2, N, height=16, maxwidth=25, scale=27):
+    count = D2.get(text, 0)
+    width = int(round(maxwidth * count * scale * 1. / N))
+    if width < 1: width = 1
+    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
+    return '%s' % (
+        title, height, width, -width+2, text)
+
+def cell(text, D2, N, height=16, maxwidth=25, scale=27):
+    count = D2.get(text, 0)
+    width = int(round(maxwidth * count * scale * 1. / N))
+    if width < 1: width = 1
+    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
+    return '%s' % (
+        title, height, width, text) 
+
+def tr(cells):
+    return '' + ''.join(cells)
+
+def comma(n): return '{:,}'.format(n)
+
+def ngram_stats(D, n, k=5):
+    DN = ngramcount(D, n)
+    topk = ', '.join(sortedby(DN)[:k])
+    return '%d-grams%s%scounts-%d.csvcounts-%d.html%s' % (
+        n, comma(len(DN)), comma(sum(DN.values())), n, n, n, n, topk)
+
+#### Tables
+
+def sortedby(D):
+    return sorted(D, key=lambda x: -D[x])
+
+ANY = '*'
+
+wordlengths = range(1, 10)
+
+def col(*args): return args
+
+def columns(n, wordlengths=wordlengths):
+    lengths = [k for k in wordlengths if k >= n]
+    return ([col(ANY, ANY)]
+            + [col(k, ANY) for k in lengths]
+            + [col(k, start, start+n-1) for k in lengths for start in range(1, 2+k-n)]
+            + [col(ANY, start, start+n-1) for start in wordlengths]
+            + [col(ANY, -k, -k+n-1) for k in reversed(lengths) if -k+n-1 < 0])
+
+def colname(col):
+    fmt = '%s/%s' if (len(col) == 2) else '%s/%d:%d'
+    return  fmt % col
+
+def csvline(first, rest):
+    return '\t'.join([first] + map(str, rest))
+
+def makecsv(n, D=D):
+    out = file('ngrams%d.csv' % n, 'w')
+    cols = columns(n)
+    Dng = defaultdict(lambda: defaultdict(int))
+    for w in D:
+        for (start, ng) in enumerate(ngrams(w, n), 1):
+            entry = Dng[ng]
+            N = D[w]
+            wlen = len(w)
+            entry[ANY, ANY] += N
+            entry[wlen, ANY] += N
+            if start <= 9:
+                entry[wlen, start, start+n-1] += N
+                entry[ANY, start, start+n-1] += N
+            from_end = wlen-start+1
+            if from_end <= 9:
+                entry[ANY, -from_end, -from_end+n-1] += N
+        # enumerate ngrams from word and increment counts for each one
+    print >> out, csvline('%d-gram' % n,  map(colname, cols))
+    for ng in sorted(Dng, key=lambda ng: -Dng[ng][(ANY, ANY)]):
+        print >> out, csvline(ng, [Dng[ng].get(col, 0) for col in cols])
+    out.close()
+    return Dng
+
+### Tests
+
+"""
+>>> for w in words:
+    print '%-6s %6.2f B (%4.2f%%) ' % (w.lower(), D[w]/1e9, D[w]*100./N, int(round(D[w]*4000./N)))
+... 
+the     53.10 B (7.14%) 
+of      30.97 B (4.16%) 
+and     22.63 B (3.04%) 
+to      19.35 B (2.60%) 
+in      16.89 B (2.27%) 
+a       15.31 B (2.06%) 
+is       8.38 B (1.13%) 
+that     8.00 B (1.08%) 
+for      6.55 B (0.88%) 
+it       5.74 B (0.77%) 
+as       5.70 B (0.77%) 
+was      5.50 B (0.74%) 
+with     5.18 B (0.70%) 
+be       4.82 B (0.65%) 
+by       4.70 B (0.63%) 
+on       4.59 B (0.62%) 
+not      4.52 B (0.61%) 
+he       4.11 B (0.55%) 
+i        3.88 B (0.52%) 
+this     3.83 B (0.51%) 
+are      3.70 B (0.50%) 
+or       3.67 B (0.49%) 
+his      3.61 B (0.49%) 
+from     3.47 B (0.47%) 
+at       3.41 B (0.46%) 
+which    3.14 B (0.42%) 
+but      2.79 B (0.38%) 
+have     2.78 B (0.37%) 
+an       2.73 B (0.37%) 
+had      2.62 B (0.35%) 
+they     2.46 B (0.33%) 
+you      2.34 B (0.31%) 
+were     2.27 B (0.31%) 
+their    2.15 B (0.29%) 
+one      2.15 B (0.29%) 
+all      2.06 B (0.28%) 
+we       2.06 B (0.28%) 
+can      1.67 B (0.22%) 
+her      1.63 B (0.22%) 
+has      1.63 B (0.22%) 
+there    1.62 B (0.22%) 
+been     1.62 B (0.22%) 
+if       1.56 B (0.21%) 
+more     1.55 B (0.21%) 
+when     1.52 B (0.20%) 
+will     1.49 B (0.20%) 
+would    1.47 B (0.20%) 
+who      1.46 B (0.20%) 
+so       1.45 B (0.19%) 
+no       1.40 B (0.19%) 
+
+>>> for n in sorted(H):
+    print '%2d %9.2f M (%6.3f%%)  %d' % (n, H[n]/1e6, H[n]*100./NN, H[n]*3000./NN, n)
+... 
+ 1  22301.22 M ( 2.998%)  1
+ 2 131293.85 M (17.651%)  2
+ 3 152568.38 M (20.511%)  3
+ 4 109988.33 M (14.787%)  4
+ 5  79589.32 M (10.700%)  5
+ 6  62391.21 M ( 8.388%)  6
+ 7  59052.66 M ( 7.939%)  7
+ 8  44207.29 M ( 5.943%)  8
+ 9  33006.93 M ( 4.437%)  9
+10  22883.84 M ( 3.076%)  10
+11  13098.06 M ( 1.761%)  11
+12   7124.15 M ( 0.958%)  12
+13   3850.58 M ( 0.518%)  13
+14   1653.08 M ( 0.222%)  14
+15    565.24 M ( 0.076%)  15
+16    151.22 M ( 0.020%)  16
+17     72.81 M ( 0.010%)  17
+18     28.62 M ( 0.004%)  18
+19      8.51 M ( 0.001%)  19
+20      6.35 M ( 0.001%)  20
+21      0.13 M ( 0.000%)  21
+22      0.81 M ( 0.000%)  22
+23      0.32 M ( 0.000%)  23
+
+>>> NL = sum(LC.values())
+
+>>> for L in sorted(LC, key=lambda L: -LC[L]):
+    print '%s %8.1f B (%5.2f%%) ' % (L, LC[L]/1e9, LC[L]*100./NL, LC[L]*3000./NL)
+...
+E    445.2 B (12.49%) 
+T    330.5 B ( 9.28%) 
+A    286.5 B ( 8.04%) 
+O    272.3 B ( 7.64%) 
+I    269.7 B ( 7.57%) 
+N    257.8 B ( 7.23%) 
+S    232.1 B ( 6.51%) 
+R    223.8 B ( 6.28%) 
+H    180.1 B ( 5.05%) 
+L    145.0 B ( 4.07%) 
+D    136.0 B ( 3.82%) 
+C    119.2 B ( 3.34%) 
+U     97.3 B ( 2.73%) 
+M     89.5 B ( 2.51%) 
+F     85.6 B ( 2.40%) 
+P     76.1 B ( 2.14%) 
+G     66.6 B ( 1.87%) 
+W     59.7 B ( 1.68%) 
+Y     59.3 B ( 1.66%) 
+B     52.9 B ( 1.48%) 
+V     37.5 B ( 1.05%) 
+K     19.3 B ( 0.54%) 
+X      8.4 B ( 0.23%) 
+J      5.7 B ( 0.16%) 
+Q      4.3 B ( 0.12%) 
+Z      3.2 B ( 0.09%) 
+
+>>> D2 = ngramcount(D, 2)
+
+>>> for ng in sorted(D2, key=lambda L: -D2[L])[:50]: print '%s %8.1f B (%5.2f%%) ' % (ng, D2[ng]/1e9, D2[ng]*100./N2, D2[ng]*15000./N2)
+
+def doit(k=25):
+    counts = [sortedby(ngramcount(D, n))[:k] for n in range(2, 10)]
+    for i in range(k):
+        print ('     '.join(count[i] for count in counts)).lower()
+"""
diff --git a/pytudes/py/lis.py b/pytudes/py/lis.py
new file mode 100644
index 0000000..2d031ad
--- /dev/null
+++ b/pytudes/py/lis.py
@@ -0,0 +1,145 @@
+################ Lispy: Scheme Interpreter in Python
+
+## (c) Peter Norvig, 2010-16; See http://norvig.com/lispy.html
+
+from __future__ import division
+import math
+import operator as op
+
+################ Types
+
+Symbol = str          # A Lisp Symbol is implemented as a Python str
+List   = list         # A Lisp List is implemented as a Python list
+Number = (int, float) # A Lisp Number is implemented as a Python int or float
+
+################ Parsing: parse, tokenize, and read_from_tokens
+
+def parse(program):
+    "Read a Scheme expression from a string."
+    return read_from_tokens(tokenize(program))
+
+def tokenize(s):
+    "Convert a string into a list of tokens."
+    return s.replace('(',' ( ').replace(')',' ) ').split()
+
+def read_from_tokens(tokens):
+    "Read an expression from a sequence of tokens."
+    if len(tokens) == 0:
+        raise SyntaxError('unexpected EOF while reading')
+    token = tokens.pop(0)
+    if '(' == token:
+        L = []
+        while tokens[0] != ')':
+            L.append(read_from_tokens(tokens))
+        tokens.pop(0) # pop off ')'
+        return L
+    elif ')' == token:
+        raise SyntaxError('unexpected )')
+    else:
+        return atom(token)
+
+def atom(token):
+    "Numbers become numbers; every other token is a symbol."
+    try: return int(token)
+    except ValueError:
+        try: return float(token)
+        except ValueError:
+            return Symbol(token)
+
+################ Environments
+
+def standard_env():
+    "An environment with some Scheme standard procedures."
+    env = Env()
+    env.update(vars(math)) # sin, cos, sqrt, pi, ...
+    env.update({
+        '+':op.add, '-':op.sub, '*':op.mul, '/':op.truediv, 
+        '>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq, 
+        'abs':     abs,
+        'append':  op.add,  
+        'apply':   apply,
+        'begin':   lambda *x: x[-1],
+        'car':     lambda x: x[0],
+        'cdr':     lambda x: x[1:], 
+        'cons':    lambda x,y: [x] + y,
+        'eq?':     op.is_, 
+        'equal?':  op.eq, 
+        'length':  len, 
+        'list':    lambda *x: list(x), 
+        'list?':   lambda x: isinstance(x,list), 
+        'map':     map,
+        'max':     max,
+        'min':     min,
+        'not':     op.not_,
+        'null?':   lambda x: x == [], 
+        'number?': lambda x: isinstance(x, Number),   
+        'procedure?': callable,
+        'round':   round,
+        'symbol?': lambda x: isinstance(x, Symbol),
+    })
+    return env
+
+class Env(dict):
+    "An environment: a dict of {'var':val} pairs, with an outer Env."
+    def __init__(self, parms=(), args=(), outer=None):
+        self.update(zip(parms, args))
+        self.outer = outer
+    def find(self, var):
+        "Find the innermost Env where var appears."
+        return self if (var in self) else self.outer.find(var)
+
+global_env = standard_env()
+
+################ Interaction: A REPL
+
+def repl(prompt='lis.py> '):
+    "A prompt-read-eval-print loop."
+    while True:
+        val = eval(parse(raw_input(prompt)))
+        if val is not None: 
+            print(lispstr(val))
+
+def lispstr(exp):
+    "Convert a Python object back into a Lisp-readable string."
+    if isinstance(exp, List):
+        return '(' + ' '.join(map(lispstr, exp)) + ')' 
+    else:
+        return str(exp)
+
+################ Procedures
+
+class Procedure(object):
+    "A user-defined Scheme procedure."
+    def __init__(self, parms, body, env):
+        self.parms, self.body, self.env = parms, body, env
+    def __call__(self, *args): 
+        return eval(self.body, Env(self.parms, args, self.env))
+
+################ eval
+
+def eval(x, env=global_env):
+    "Evaluate an expression in an environment."
+    if isinstance(x, Symbol):      # variable reference
+        return env.find(x)[x]
+    elif not isinstance(x, List):  # constant literal
+        return x                
+    elif x[0] == 'quote':          # (quote exp)
+        (_, exp) = x
+        return exp
+    elif x[0] == 'if':             # (if test conseq alt)
+        (_, test, conseq, alt) = x
+        exp = (conseq if eval(test, env) else alt)
+        return eval(exp, env)
+    elif x[0] == 'define':         # (define var exp)
+        (_, var, exp) = x
+        env[var] = eval(exp, env)
+    elif x[0] == 'set!':           # (set! var exp)
+        (_, var, exp) = x
+        env.find(var)[var] = eval(exp, env)
+    elif x[0] == 'lambda':         # (lambda (var...) body)
+        (_, parms, body) = x
+        return Procedure(parms, body, env)
+    else:                          # (proc arg...)
+        proc = eval(x[0], env)
+        args = [eval(exp, env) for exp in x[1:]]
+        return proc(*args)
\ No newline at end of file
diff --git a/pytudes/py/lispy.py b/pytudes/py/lispy.py
new file mode 100644
index 0000000..08923c1
--- /dev/null
+++ b/pytudes/py/lispy.py
@@ -0,0 +1,318 @@
+################ Scheme Interpreter in Python
+
+## (c) Peter Norvig, 2010; See http://norvig.com/lispy2.html
+
+################ Symbol, Procedure, classes
+
+from __future__ import division
+import re, sys, StringIO
+
+class Symbol(str): pass
+
+def Sym(s, symbol_table={}):
+    "Find or create unique Symbol entry for str s in symbol table."
+    if s not in symbol_table: symbol_table[s] = Symbol(s)
+    return symbol_table[s]
+
+_quote, _if, _set, _define, _lambda, _begin, _definemacro, = map(Sym, 
+"quote   if   set!  define   lambda   begin   define-macro".split())
+
+_quasiquote, _unquote, _unquotesplicing = map(Sym,
+"quasiquote   unquote   unquote-splicing".split())
+
+class Procedure(object):
+    "A user-defined Scheme procedure."
+    def __init__(self, parms, exp, env):
+        self.parms, self.exp, self.env = parms, exp, env
+    def __call__(self, *args): 
+        return eval(self.exp, Env(self.parms, args, self.env))
+
+################ parse, read, and user interaction
+
+def parse(inport):
+    "Parse a program: read and expand/error-check it."
+    # Backwards compatibility: given a str, convert it to an InPort
+    if isinstance(inport, str): inport = InPort(StringIO.StringIO(inport))
+    return expand(read(inport), toplevel=True)
+
+eof_object = Symbol('#') # Note: uninterned; can't be read
+
+class InPort(object):
+    "An input port. Retains a line of chars."
+    tokenizer = r"""\s*(,@|[('`,)]|"(?:[\\].|[^\\"])*"|;.*|[^\s('"`,;)]*)(.*)"""
+    def __init__(self, file):
+        self.file = file; self.line = ''
+    def next_token(self):
+        "Return the next token, reading new text into line buffer if needed."
+        while True:
+            if self.line == '': self.line = self.file.readline()
+            if self.line == '': return eof_object
+            token, self.line = re.match(InPort.tokenizer, self.line).groups()
+            if token != '' and not token.startswith(';'):
+                return token
+
+def readchar(inport):
+    "Read the next character from an input port."
+    if inport.line != '':
+        ch, inport.line = inport.line[0], inport.line[1:]
+        return ch
+    else:
+        return inport.file.read(1) or eof_object
+
+def read(inport):
+    "Read a Scheme expression from an input port."
+    def read_ahead(token):
+        if '(' == token: 
+            L = []
+            while True:
+                token = inport.next_token()
+                if token == ')': return L
+                else: L.append(read_ahead(token))
+        elif ')' == token: raise SyntaxError('unexpected )')
+        elif token in quotes: return [quotes[token], read(inport)]
+        elif token is eof_object: raise SyntaxError('unexpected EOF in list')
+        else: return atom(token)
+    # body of read:
+    token1 = inport.next_token()
+    return eof_object if token1 is eof_object else read_ahead(token1)
+
+quotes = {"'":_quote, "`":_quasiquote, ",":_unquote, ",@":_unquotesplicing}
+
+def atom(token):
+    'Numbers become numbers; #t and #f are booleans; "..." string; otherwise Symbol.'
+    if token == '#t': return True
+    elif token == '#f': return False
+    elif token[0] == '"': return token[1:-1].decode('string_escape')
+    try: return int(token)
+    except ValueError:
+        try: return float(token)
+        except ValueError:
+            try: return complex(token.replace('i', 'j', 1))
+            except ValueError:
+                return Sym(token)
+
+def to_string(x):
+    "Convert a Python object back into a Lisp-readable string."
+    if x is True: return "#t"
+    elif x is False: return "#f"
+    elif isa(x, Symbol): return x
+    elif isa(x, str): return '"%s"' % x.encode('string_escape').replace('"',r'\"')
+    elif isa(x, list): return '('+' '.join(map(to_string, x))+')'
+    elif isa(x, complex): return str(x).replace('j', 'i')
+    else: return str(x)
+
+def load(filename):
+    "Eval every expression from a file."
+    repl(None, InPort(open(filename)), None)
+
+def repl(prompt='lispy> ', inport=InPort(sys.stdin), out=sys.stdout):
+    "A prompt-read-eval-print loop."
+    sys.stderr.write("Lispy version 2.0\n")
+    while True:
+        try:
+            if prompt: sys.stderr.write(prompt)
+            x = parse(inport)
+            if x is eof_object: return
+            val = eval(x)
+            if val is not None and out: print >> out, to_string(val)
+        except Exception as e:
+            print '%s: %s' % (type(e).__name__, e)
+
+################ Environment class
+
+class Env(dict):
+    "An environment: a dict of {'var':val} pairs, with an outer Env."
+    def __init__(self, parms=(), args=(), outer=None):
+        # Bind parm list to corresponding args, or single parm to list of args
+        self.outer = outer
+        if isa(parms, Symbol): 
+            self.update({parms:list(args)})
+        else: 
+            if len(args) != len(parms):
+                raise TypeError('expected %s, given %s, ' 
+                                % (to_string(parms), to_string(args)))
+            self.update(zip(parms,args))
+    def find(self, var):
+        "Find the innermost Env where var appears."
+        if var in self: return self
+        elif self.outer is None: raise LookupError(var)
+        else: return self.outer.find(var)
+
+def is_pair(x): return x != [] and isa(x, list)
+def cons(x, y): return [x]+y
+
+def callcc(proc):
+    "Call proc with current continuation; escape only"
+    ball = RuntimeWarning("Sorry, can't continue this continuation any longer.")
+    def throw(retval): ball.retval = retval; raise ball
+    try:
+        return proc(throw)
+    except RuntimeWarning as w:
+        if w is ball: return ball.retval
+        else: raise w
+
+def add_globals(self):
+    "Add some Scheme standard procedures."
+    import math, cmath, operator as op
+    self.update(vars(math))
+    self.update(vars(cmath))
+    self.update({
+     '+':op.add, '-':op.sub, '*':op.mul, '/':op.div, 'not':op.not_, 
+     '>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq, 
+     'equal?':op.eq, 'eq?':op.is_, 'length':len, 'cons':cons,
+     'car':lambda x:x[0], 'cdr':lambda x:x[1:], 'append':op.add,  
+     'list':lambda *x:list(x), 'list?': lambda x:isa(x,list),
+     'null?':lambda x:x==[], 'symbol?':lambda x: isa(x, Symbol),
+     'boolean?':lambda x: isa(x, bool), 'pair?':is_pair, 
+     'port?': lambda x:isa(x,file), 'apply':lambda proc,l: proc(*l), 
+     'eval':lambda x: eval(expand(x)), 'load':lambda fn: load(fn), 'call/cc':callcc,
+     'open-input-file':open,'close-input-port':lambda p: p.file.close(), 
+     'open-output-file':lambda f:open(f,'w'), 'close-output-port':lambda p: p.close(),
+     'eof-object?':lambda x:x is eof_object, 'read-char':readchar,
+     'read':read, 'write':lambda x,port=sys.stdout:port.write(to_string(x)),
+     'display':lambda x,port=sys.stdout:port.write(x if isa(x,str) else to_string(x))})
+    return self
+
+isa = isinstance
+
+global_env = add_globals(Env())
+
+################ eval (tail recursive)
+
+def eval(x, env=global_env):
+    "Evaluate an expression in an environment."
+    while True:
+        if isa(x, Symbol):       # variable reference
+            return env.find(x)[x]
+        elif not isa(x, list):   # constant literal
+            return x                
+        elif x[0] is _quote:     # (quote exp)
+            (_, exp) = x
+            return exp
+        elif x[0] is _if:        # (if test conseq alt)
+            (_, test, conseq, alt) = x
+            x = (conseq if eval(test, env) else alt)
+        elif x[0] is _set:       # (set! var exp)
+            (_, var, exp) = x
+            env.find(var)[var] = eval(exp, env)
+            return None
+        elif x[0] is _define:    # (define var exp)
+            (_, var, exp) = x
+            env[var] = eval(exp, env)
+            return None
+        elif x[0] is _lambda:    # (lambda (var*) exp)
+            (_, vars, exp) = x
+            return Procedure(vars, exp, env)
+        elif x[0] is _begin:     # (begin exp+)
+            for exp in x[1:-1]:
+                eval(exp, env)
+            x = x[-1]
+        else:                    # (proc exp*)
+            exps = [eval(exp, env) for exp in x]
+            proc = exps.pop(0)
+            if isa(proc, Procedure):
+                x = proc.exp
+                env = Env(proc.parms, exps, proc.env)
+            else:
+                return proc(*exps)
+
+################ expand
+
+def expand(x, toplevel=False):
+    "Walk tree of x, making optimizations/fixes, and signaling SyntaxError."
+    require(x, x!=[])                    # () => Error
+    if not isa(x, list):                 # constant => unchanged
+        return x
+    elif x[0] is _quote:                 # (quote exp)
+        require(x, len(x)==2)
+        return x
+    elif x[0] is _if:                    
+        if len(x)==3: x = x + [None]     # (if t c) => (if t c None)
+        require(x, len(x)==4)
+        return map(expand, x)
+    elif x[0] is _set:                   
+        require(x, len(x)==3); 
+        var = x[1]                       # (set! non-var exp) => Error
+        require(x, isa(var, Symbol), "can set! only a symbol")
+        return [_set, var, expand(x[2])]
+    elif x[0] is _define or x[0] is _definemacro: 
+        require(x, len(x)>=3)            
+        _def, v, body = x[0], x[1], x[2:]
+        if isa(v, list) and v:           # (define (f args) body)
+            f, args = v[0], v[1:]        #  => (define f (lambda (args) body))
+            return expand([_def, f, [_lambda, args]+body])
+        else:
+            require(x, len(x)==3)        # (define non-var/list exp) => Error
+            require(x, isa(v, Symbol), "can define only a symbol")
+            exp = expand(x[2])
+            if _def is _definemacro:     
+                require(x, toplevel, "define-macro only allowed at top level")
+                proc = eval(exp)       
+                require(x, callable(proc), "macro must be a procedure")
+                macro_table[v] = proc    # (define-macro v proc)
+                return None              #  => None; add v:proc to macro_table
+            return [_define, v, exp]
+    elif x[0] is _begin:
+        if len(x)==1: return None        # (begin) => None
+        else: return [expand(xi, toplevel) for xi in x]
+    elif x[0] is _lambda:                # (lambda (x) e1 e2) 
+        require(x, len(x)>=3)            #  => (lambda (x) (begin e1 e2))
+        vars, body = x[1], x[2:]
+        require(x, (isa(vars, list) and all(isa(v, Symbol) for v in vars))
+                or isa(vars, Symbol), "illegal lambda argument list")
+        exp = body[0] if len(body) == 1 else [_begin] + body
+        return [_lambda, vars, expand(exp)]   
+    elif x[0] is _quasiquote:            # `x => expand_quasiquote(x)
+        require(x, len(x)==2)
+        return expand_quasiquote(x[1])
+    elif isa(x[0], Symbol) and x[0] in macro_table:
+        return expand(macro_table[x[0]](*x[1:]), toplevel) # (m arg...) 
+    else:                                #        => macroexpand if m isa macro
+        return map(expand, x)            # (f arg...) => expand each
+
+def require(x, predicate, msg="wrong length"):
+    "Signal a syntax error if predicate is false."
+    if not predicate: raise SyntaxError(to_string(x)+': '+msg)
+
+_append, _cons, _let = map(Sym, "append cons let".split())
+
+def expand_quasiquote(x):
+    """Expand `x => 'x; `,x => x; `(,@x y) => (append x y) """
+    if not is_pair(x):
+        return [_quote, x]
+    require(x, x[0] is not _unquotesplicing, "can't splice here")
+    if x[0] is _unquote:
+        require(x, len(x)==2)
+        return x[1]
+    elif is_pair(x[0]) and x[0][0] is _unquotesplicing:
+        require(x[0], len(x[0])==2)
+        return [_append, x[0][1], expand_quasiquote(x[1:])]
+    else:
+        return [_cons, expand_quasiquote(x[0]), expand_quasiquote(x[1:])]
+
+def let(*args):
+    args = list(args)
+    x = cons(_let, args)
+    require(x, len(args)>1)
+    bindings, body = args[0], args[1:]
+    require(x, all(isa(b, list) and len(b)==2 and isa(b[0], Symbol)
+                   for b in bindings), "illegal binding list")
+    vars, vals = zip(*bindings)
+    return [[_lambda, list(vars)]+map(expand, body)] + map(expand, vals)
+
+macro_table = {_let:let} ## More macros can go here
+
+eval(parse("""(begin
+
+(define-macro and (lambda args 
+   (if (null? args) #t
+       (if (= (length args) 1) (car args)
+           `(if ,(car args) (and ,@(cdr args)) #f)))))
+
+;; More macros can also go here
+
+)"""))
+
+if __name__ == '__main__':
+    repl()
+
diff --git a/pytudes/py/lispytest.py b/pytudes/py/lispytest.py
new file mode 100644
index 0000000..bed5307
--- /dev/null
+++ b/pytudes/py/lispytest.py
@@ -0,0 +1,121 @@
+
+################ Tests for lis.py and lispy.py
+
+lis_tests = [
+    ("(quote (testing 1 (2.0) -3.14e159))", ['testing', 1, [2.0], -3.14e159]),
+    ("(+ 2 2)", 4),
+    ("(+ (* 2 100) (* 1 10))", 210),
+    ("(if (> 6 5) (+ 1 1) (+ 2 2))", 2),
+    ("(if (< 6 5) (+ 1 1) (+ 2 2))", 4),
+    ("(define x 3)", None), ("x", 3), ("(+ x x)", 6),
+    ("(begin (define x 1) (set! x (+ x 1)) (+ x 1))", 3),
+    ("((lambda (x) (+ x x)) 5)", 10),
+    ("(define twice (lambda (x) (* 2 x)))", None), ("(twice 5)", 10),
+    ("(define compose (lambda (f g) (lambda (x) (f (g x)))))", None),
+    ("((compose list twice) 5)", [10]),
+    ("(define repeat (lambda (f) (compose f f)))", None),
+    ("((repeat twice) 5)", 20), ("((repeat (repeat twice)) 5)", 80),
+    ("(define fact (lambda (n) (if (<= n 1) 1 (* n (fact (- n 1))))))", None),
+    ("(fact 3)", 6),
+    ("(fact 50)", 30414093201713378043612608166064768844377641568960512000000000000),
+    ("(define abs (lambda (n) ((if (> n 0) + -) 0 n)))", None),
+    ("(list (abs -3) (abs 0) (abs 3))", [3, 0, 3]),
+    ("""(define combine (lambda (f)
+    (lambda (x y)
+      (if (null? x) (quote ())
+          (f (list (car x) (car y))
+             ((combine f) (cdr x) (cdr y)))))))""", None),
+    ("(define zip (combine cons))", None),
+    ("(zip (list 1 2 3 4) (list 5 6 7 8))", [[1, 5], [2, 6], [3, 7], [4, 8]]),
+    ("""(define riff-shuffle (lambda (deck) (begin
+    (define take (lambda (n seq) (if (<= n 0) (quote ()) (cons (car seq) (take (- n 1) (cdr seq))))))
+    (define drop (lambda (n seq) (if (<= n 0) seq (drop (- n 1) (cdr seq)))))
+    (define mid (lambda (seq) (/ (length seq) 2)))
+    ((combine append) (take (mid deck) deck) (drop (mid deck) deck)))))""", None),
+    ("(riff-shuffle (list 1 2 3 4 5 6 7 8))", [1, 5, 2, 6, 3, 7, 4, 8]),
+    ("((repeat riff-shuffle) (list 1 2 3 4 5 6 7 8))",  [1, 3, 5, 7, 2, 4, 6, 8]),
+    ("(riff-shuffle (riff-shuffle (riff-shuffle (list 1 2 3 4 5 6 7 8))))", [1,2,3,4,5,6,7,8]),
+    ]
+
+lispy_tests = [
+    ("()", SyntaxError), ("(set! x)", SyntaxError), 
+    ("(define 3 4)", SyntaxError),
+    ("(quote 1 2)", SyntaxError), ("(if 1 2 3 4)", SyntaxError), 
+    ("(lambda 3 3)", SyntaxError), ("(lambda (x))", SyntaxError),
+    ("""(if (= 1 2) (define-macro a 'a) 
+     (define-macro a 'b))""", SyntaxError),
+    ("(define (twice x) (* 2 x))", None), ("(twice 2)", 4),
+    ("(twice 2 2)", TypeError),
+    ("(define lyst (lambda items items))", None),
+    ("(lyst 1 2 3 (+ 2 2))", [1,2,3,4]),
+    ("(if 1 2)", 2),
+    ("(if (= 3 4) 2)", None),
+    ("(define ((account bal) amt) (set! bal (+ bal amt)) bal)", None),
+    ("(define a1 (account 100))", None),
+    ("(a1 0)", 100), ("(a1 10)", 110), ("(a1 10)", 120),
+    ("""(define (newton guess function derivative epsilon)
+    (define guess2 (- guess (/ (function guess) (derivative guess))))
+    (if (< (abs (- guess guess2)) epsilon) guess2
+        (newton guess2 function derivative epsilon)))""", None),
+    ("""(define (square-root a)
+    (newton 1 (lambda (x) (- (* x x) a)) (lambda (x) (* 2 x)) 1e-8))""", None),
+    ("(> (square-root 200.) 14.14213)", True),
+    ("(< (square-root 200.) 14.14215)", True),
+    ("(= (square-root 200.) (sqrt 200.))", True),
+    ("""(define (sum-squares-range start end)
+         (define (sumsq-acc start end acc)
+            (if (> start end) acc (sumsq-acc (+ start 1) end (+ (* start start) acc))))
+         (sumsq-acc start end 0))""", None),
+    ("(sum-squares-range 1 3000)", 9004500500), ## Tests tail recursion
+    ("(call/cc (lambda (throw) (+ 5 (* 10 (throw 1))))) ;; throw", 1),
+    ("(call/cc (lambda (throw) (+ 5 (* 10 1)))) ;; do not throw", 15),
+    ("""(call/cc (lambda (throw) 
+         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 (escape 3)))))))) ; 1 level""", 35),
+    ("""(call/cc (lambda (throw) 
+         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 (throw 3)))))))) ; 2 levels""", 3),
+    ("""(call/cc (lambda (throw) 
+         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 1))))))) ; 0 levels""", 1005),
+    ("(* 1i 1i)", -1), ("(sqrt -1)", 1j),
+    ("(let ((a 1) (b 2)) (+ a b))", 3),
+    ("(let ((a 1) (b 2 3)) (+ a b))", SyntaxError),
+    ("(and 1 2 3)", 3), ("(and (> 2 1) 2 3)", 3), ("(and)", True),
+    ("(and (> 2 1) (> 2 3))", False),
+    ("(define-macro unless (lambda args `(if (not ,(car args)) (begin ,@(cdr args))))) ; test `", None),
+    ("(unless (= 2 (+ 1 1)) (display 2) 3 4)", None),
+    (r'(unless (= 4 (+ 1 1)) (display 2) (display "\n") 3 4)', 4),
+    ("(quote x)", 'x'), 
+    ("(quote (1 2 three))", [1, 2, 'three']), 
+    ("'x", 'x'),
+    ("'(one 2 3)", ['one', 2, 3]),
+    ("(define L (list 1 2 3))", None),
+    ("`(testing ,@L testing)", ['testing',1,2,3,'testing']),
+    ("`(testing ,L testing)", ['testing',[1,2,3],'testing']),
+    ("`,@L", SyntaxError),
+    ("""'(1 ;test comments '
+     ;skip this line
+     2 ; more ; comments ; ) )
+     3) ; final comment""", [1,2,3]),
+    ]
+
+def test(tests, name=''):
+    "For each (exp, expected) test case, see if eval(parse(exp)) == expected."
+    fails = 0
+    for (x, expected) in tests:
+        try:
+            result = eval(parse(x))
+            print x, '=>', to_string(result)
+            ok = (result == expected)
+        except Exception as e:
+            print x, '=raises=>', type(e).__name__, e
+            ok = issubclass(expected, Exception) and isinstance(e, expected)
+        if not ok:
+            fails += 1
+            print 'FAIL!!!  Expected', expected
+    print '%s %s: %d out of %d tests fail.' % ('*'*45, name, fails, len(tests))
+
+if __name__ == '__main__':
+    from lis import *
+    test(lis_tests, 'lis.py')
+    from lispy import *
+    test(lis_tests+lispy_tests, 'lispy.py')
+
diff --git a/pytudes/py/pal.py b/pytudes/py/pal.py
new file mode 100644
index 0000000..db8f509
--- /dev/null
+++ b/pytudes/py/pal.py
@@ -0,0 +1,154 @@
+import string, random, os, re, bisect
+
+"""Produce Panama-ish Palindromes. Copyright (C) 2002, Peter Norvig.
+See http://www.norvig.com/license.html and http://www.norvig.com/pal-alg.html"""
+
+def is_panama(p):
+    "Test if p is a Panama-ish palindrome."
+    def is_unique(seq): return len(seq) == len(dict(zip(seq, seq)))
+    return (p.endswith('Panama') and is_palindrome(p)
+	    and is_unique([s.strip() for s in p.split(',')]))
+
+def is_palindrome(phrase):
+    "Test if a phrase is a palindrome."
+    cphrase = canonical(phrase)
+    return cphrase == reverse(cphrase)
+
+def canonical(word, sub=re.compile('[^A-Za-z0-9]').sub):
+    "The canonical form for comparing: lowercase alphanumerics."
+    return sub('', word).lower()
+
+def read_dict(filename='npdict.txt'):
+    "Read the file into global variables _fw and _bw and _truename."
+    global _fw, _bw, _truename
+    _fw, _bw, _truename = [], [], {'': ''}
+    for word in open(filename).read().splitlines():
+        w = canonical(word)
+        _fw.append(w)
+        _bw.append(reverse(w))
+        _truename[w] = word
+    _fw.sort(); _bw.sort()
+    return len(_fw), len(_bw), len(_truename)
+
+def update(obj, **entries): obj.__dict__.update(entries); return obj
+
+class PalDict:
+    """A dictionary from which you can find canonical words that start or end
+    with a given canonical substring, and find the true name of a
+    canonical word."""
+    def __init__(self, fw=None, bw=None, truename=None):
+        update(self, fw=fw or _fw, bw=bw or _bw, truename=truename or _truename)
+
+    def startswith(self, prefix, k=100):
+        """Return up to k canonical words that start with prefix.
+        If there are more than k, choose from them at random."""
+        return k_startingwith(k, self.fw, prefix)
+
+    def endswith(self, suffix, k=100):
+        """Return up to k canonical words that end with suffix.
+        If there are more than k, choose from them at random.
+        Both the suffix and the word returned are reversed."""
+        return k_startingwith(k, self.bw, suffix)
+
+def k_startingwith(k, words, prefix):
+    """Choose up to k words that match the prefix (choose randomly if > k)."""
+    start = bisect.bisect(words, prefix)
+    end = bisect.bisect(words, prefix + 'zzzz')
+    n = end - start
+    if k >= n:
+        results = words[start:end]
+        random.shuffle(results)
+    else: # Should really try to avoid duplicates
+        results = [words[random.randrange(start, end)] for i in range(k)]
+    return results
+
+class Panama:
+    def __init__(self, L='A man, a plan', R='a canal, Panama', dict=None):
+        left = [canonical(w) for w in L.split(', ')]
+        right = [canonical(reverse(w)) for w in reverse(R.split(', '))]
+        update(self, left=left, right=right, dict=dict or PalDict(), best=0, 
+               seen={}, diff=len(''.join(left)) - len(''.join(right)))
+        for word in left + map(reverse, right):
+            self.seen[word] = 1
+
+    def missing(self, k=20):
+        """Return the substring that is missing, and candidate words."""
+        if self.diff >= 0: # Left is longer, missing on right
+            substr =  self.left[-1][-self.diff:]
+            return substr, self.dict.endswith(substr, k)
+        else: # Right is longer, missing on left
+            substr =  self.right[-1][self.diff:]
+            return substr, self.dict.startswith(substr, k)
+
+    def search(self, k=200):
+        "Search for palindromes; consider at most k words at each level."
+        self.stack = [self.missing(k)]
+        while self.stack:
+            substr, words = self.stack[-1]
+            if is_palindrome(substr):
+                self.report()
+            if words:
+                self.extend(words.pop(), k)
+            elif not self.backtrack():
+                return
+
+    def extend(self, word, k):
+        "Add a new word (unless we've already seen it)."
+        if self.diff >= 0: # Left is longer, add to right
+            fword = reverse(word)
+            if fword in self.seen: return
+            self.diff -= len(fword)
+            self.seen[fword] = 1
+            self.right.append(word)
+            self.stack.append(self.missing(k))
+        else: # Right is longer, add to left
+            if word in self.seen: return
+            self.diff += len(word)
+            self.seen[word] = 1
+            self.left.append(word)
+            self.stack.append(self.missing(k))
+
+    def backtrack(self):
+        "Remove the last word added; return 0 if can't backtrack"
+        if self.diff >= 0: # Left is longer, pop from left
+            if not self.left: return 0
+            word = self.left.pop()
+            self.diff -= len(word)
+            del self.seen[word]
+        else: # Right is longer, pop from right
+            if not self.right: return 0
+            word = self.right.pop()
+            self.diff += len(word)
+            del self.seen[reverse(word)]
+        self.stack.pop()
+        return 1
+
+    def report(self):
+        "Write current state to log file."
+        if len(self) > self.best + 200:
+            self.best = len(self)
+            print self.best
+            self.bestphrase = str(self)
+            assert is_panama(self.bestphrase)
+            f = open('pallog%d.txt' % os.getpid(), 'w')
+            f.write(self.bestphrase + '\n')
+            f.close()
+
+    def __len__(self):
+        return len(self.left) + len(self.right)
+
+    def __str__(self):
+        truename = self.dict.truename
+        lefts = [truename[w] for w in self.left]
+        rights = [truename[reverse(w)] for w in reverse(self.right[:])]
+        return ', '.join(lefts + ['*****'] + rights)
+
+def reverse(x):
+    "Reverse a list or string."
+    if type(x) == type(''):
+        return ''.join(reverse(list(x)))
+    else:
+        x.reverse()
+        return x
+
+if __name__ == '__main__': read_dict(); p = Panama(); p.search()
diff --git a/pytudes/py/pal2.py b/pytudes/py/pal2.py
new file mode 100644
index 0000000..9436ead
--- /dev/null
+++ b/pytudes/py/pal2.py
@@ -0,0 +1,262 @@
+import random, re, bisect, time
+
+"""Produce Panama-ish Palindromes. Copyright (C) 2002-2008, Peter Norvig."""
+
+################ Checking for Palindromes
+
+def is_panama(s):
+    "Test if string s is a Panama-ish palindrome."
+    return is_palindrome(s) and is_unique(phrases(s))
+
+def is_palindrome(s):
+    "Test if a string is a palindrome."
+    s1 = canonical(s)
+    return s1 == reversestr(s1)
+
+def phrases(s):
+    "Break a string s into comma-separated phrases."
+    return [phrase.strip() for phrase in s.split(',')]
+
+def canonical(word, sub=re.compile('''[-* \t\n\r.,;!?:()`"']''').sub):
+    "The canonical form for comparing: lowercase, no blanks or punctuation."
+    return sub('', word).lower()
+
+################ Utilities
+
+def reversestr(x):
+    "Reverse a string."
+    return x[::-1]
+
+def is_unique(seq):
+    "Return true if seq has no duplicate elements."
+    return len(seq) == len(set(seq))
+
+def update(obj, **entries):
+    "Change attributes of obj, according to the keyword args."
+    obj.__dict__.update(entries)
+    return obj
+
+################ Reading in a dictionary
+
+class PalDict:
+    """A dictionary from which you can find canonical words that start or end
+    with a given canonical substring, and find the true name of a
+    canonical word with d.truename[canonicalword]."""
+    
+    def __init__(self, k=1000, filename='npdict.txt'):
+        words, rwords, truename = [], [], {'': '', 'panama': 'Panama!'}
+        for tword in open(filename).read().splitlines():
+            word = canonical(tword)
+            words.append(word)
+            rwords.append(reversestr(word))
+            truename[word] = tword
+        words.sort()
+        rwords.sort()
+        update(self, k=k, words=words, rwords=rwords, truename=truename,
+               reversibles={}, rangek=range(k), tryharder=False)
+
+    def startswith(self, prefix):
+        """Return up to k canonical words that start with prefix.
+        If there are more than k, choose from them at random."""
+        return self._k_startingwith(self.words, prefix)
+
+    def endswith(self, rsuffix):
+        """Return up to k canonical words that end with the reversed suffix.
+        If you want words ending in 'ing', ask for d.endswith('gni').
+        If there are more than k, choose from them at random."""
+        return map(reversestr, self._k_startingwith(self.rwords, rsuffix))
+
+    def __contains__(self, word):
+        return word in self.truename
+
+    def reversible_words(self):
+        "Find words that have a reverse in the dict, like {'Camus': 'Sumac'}"
+        if not self.reversibles:
+            reversibles = self.reversibles
+            for rw in self.rwords:
+                if rw in self:
+                    w = reversestr(rw)
+                    if w != rw and w not in reversibles:
+                        reversibles[w] = rw
+            self.reversibles = reversibles
+        return self.reversibles
+
+    def _k_startingwith(self, words, prefix):
+        start = bisect.bisect_left(words, prefix)
+        end = bisect.bisect(words, prefix + 'zzzz')
+        n = end - start
+        if self.k >= n: # get all the words that start with prefix
+            results = words[start:end]
+        else: # sample from words starting with prefix 
+            indexes = random.sample(xrange(start, end), self.k)
+            results = [words[i] for i in indexes]
+        random.shuffle(results)
+        ## Consider words that are prefixes of the prefix.
+        ## This is very slow, so don't use it until late in the game.
+        if self.tryharder:
+            for i in range(3, len(prefix)):
+                w = prefix[0:i]
+                if ((words == self.words and w in self.truename) or
+                    (words == self.rwords and reversestr(w) in self.truename)):
+                    results.append(w)
+        return results
+
+paldict = PalDict() 
+
+def anpdictshort():
+    "Find the words that are valid when every phrase must start with 'a'"
+    def segment(word):  return [s for s in word.split('a') if s]
+    def valid(word): return all(reversestr(s) in segments for s in segment(word))
+    words = map(canonical, file('anpdict.txt'))
+    segments = set(s for w in words for s in segment(canonical(w)))
+    valid_words = [paldict.truename[w] for w in words if valid(w)]
+    file('anpdict-short.txt', 'w').write('\n'.join(valid_words))
+
+################ Search for a palindrome
+
+class Panama:
+    def __init__(self, L='A man, a plan', R='a canal, Panama', dict=paldict):
+        ## .left and .right hold lists of canonical words
+        ## .diff holds the number of characters that are not matched,
+        ##  positive for words on left, negative for right.
+        ## .stack holds (action, side, arg) tuples
+        update(self, left=[], right=[], best=0, seen={}, diff=0, stack=[],
+               used_reversibles=False, starttime=time.clock(), dict=dict)
+        for word in L.split(','):
+            self.add('left', canonical(word))
+        for rword in reversestr(R).split(','):
+            self.add('right', canonical(reversestr(rword)))
+        self.consider_candidates()
+        
+    def search(self, steps=50000000):
+        "Search for palindromes."
+        for _ in xrange(steps):
+            if not self.stack:
+                return 'done'
+            action, dir, substr, arg = self.stack[-1]
+            if action == 'added': # undo the last word added
+                self.remove(dir, arg)
+            elif action == 'trying' and arg: # try the next word if there is one
+                self.add(dir, arg.pop()) and self.consider_candidates()
+            elif action == 'trying' and not arg: # otherwise backtrack
+                self.stack.pop()
+            else:
+                raise ValueError(action)
+
+    def add(self, dir, word):
+        "add a word"
+        if word in self.seen:
+            return False
+        else:
+            getattr(self, dir).append(word)
+            self.diff += factor[dir] * len(word)
+            self.seen[word] = True
+            self.stack.append(('added', dir, '?', word))
+            return True
+
+    def remove(self, dir, word):
+        "remove a word"
+        oldword = getattr(self, dir).pop()
+        assert word == oldword
+        self.diff -= factor[dir] * len(word)
+        del self.seen[word]
+        self.stack.pop()
+        
+    def consider_candidates(self):
+        """Push a new state with a set of candidate words onto stack."""
+        if self.diff > 0: # Left is longer, consider adding on right
+            dir = 'right'
+            substr =  self.left[-1][-self.diff:]
+            candidates = self.dict.endswith(substr)
+        elif self.diff < 0: # Right is longer, consider adding on left
+            dir = 'left'
+            substr =  reversestr(self.right[-1][0:-self.diff])
+            candidates = self.dict.startswith(substr)
+        else: # Both sides are same size
+            dir = 'left'
+            if not self.used_reversibles:
+                self.report()
+                self.add_reversibles()
+            substr = ''
+            candidates = self.dict.startswith('')
+        if substr == reversestr(substr):
+            self.report()
+        self.stack.append(('trying', dir, substr, candidates))
+
+    def add_reversibles(self):
+        "Add in reversible words."
+        print 'using reversibles ...'
+        for (word, rword) in self.dict.reversible_words().items():
+            if word not in self.seen and rword not in self.seen:
+                self.add('left', word)
+                self.add('right', rword)
+        self.used_reversibles = True
+        self.stack = []
+        print '...done'
+                
+    def report(self):
+        "Report a new palindrome to log file (if it is sufficiently big)."
+        N = len(self)
+        if N > 13333:
+            self.dict.tryharder = True
+        if N > self.best and (N > 12500 or N > self.best+500):
+            self.best = len(self)
+            self.bestphrase = str(self)
+            print '%5d phrases (%5d words) in %3d seconds' % (
+                self.best, self.bestphrase.count(' ')+1, time.clock() - self.starttime)
+            assert is_panama(self.bestphrase)
+            f = open('pallog%d.txt' % (id(self) % 10000), 'w')
+            f.write(self.bestphrase + '\n')
+            f.close()
+
+    def __len__(self):
+        return len(self.left) + len(self.right)
+
+    def __str__(self):
+        truename = self.dict.truename
+        lefts = [truename[w] for w in self.left]
+        rights =[truename[w] for w in self.right]
+        return ', '.join(lefts + rights[::-1])
+
+factor = {'left': +1, 'right': -1}
+
+# Note that we only allow one truename per canonical name.  Occasionally
+# this means we miss a good word (as in "a node" vs. "an ode"), but there
+# are only 665 of these truename collisions, and most of them are of the
+# form "a mark-up" vs. "a markup" so it seemed better to disallow them.
+
+################ Unit Tests
+ 
+def tests(p=Panama()):
+    assert is_panama('A man, a plan, a canal, Panama.')
+    assert is_panama('''A (man),     a   plan,,;, a ```canal?'' -- Panama!''')
+    assert not is_panama('A man, a plan, a radar, a canal, Panama.')
+    assert is_palindrome('A man, a plan, a canal, Panama.')
+    assert is_palindrome('radar, radar? radar!')
+    assert not is_palindrome('radars')
+    assert phrases('A man, a plan, Panama') == ['A man', 'a plan', 'Panama']
+    assert canonical('A man, a plan, a canal, Panama') == 'amanaplanacanalpanama'
+    assert reversestr('foo') == 'oof'
+    assert is_unique([1, 2, 3])
+    assert not is_unique([1, 2, 2])
+    d = p.dict
+    def sameset(a, b): return set(a) == set(b)
+    assert 'panama' in d
+    assert d.words[0] in d
+    assert d.words[-1] in d
+    assert sameset(d.startswith('aword'), ['awording', 'awordbreak',
+        'awordiness', 'awordage', 'awordplay', 'awordlore', 'awordbook',
+        'awordlessness', 'aword', 'awordsmith'])
+    assert sameset(d.endswith('ytisob'), ['aglobosity', 'averbosity',
+        'asubglobosity', 'anonverbosity', 'agibbosity'])
+    d.tryharder = True
+    assert sameset(d.startswith('oklahoma'), ['oklahoma', 'okla'])
+    d.tryharder = False
+    assert d.startswith('oklahoma') == ['oklahoma']
+    assert d.startswith('fsfdsfdsfds') == []
+    print 'all tests pass'
+
+if __name__ == '__main__': 
+    p = Panama();
+    tests(p)
+    p.search()
diff --git a/pytudes/py/pal3.py b/pytudes/py/pal3.py
new file mode 100644
index 0000000..89e8571
--- /dev/null
+++ b/pytudes/py/pal3.py
@@ -0,0 +1,170 @@
+from collections import Counter, deque
+import re
+
+class PhraseDict(dict):
+    """A dictionary of {letters: phrase}, such as {'donaldeknuth': 'Donald E. Knuth'}, with:
+    .prefixes: Counter of {'pre': n} where n is the number of keys that start with 'pre'
+    .suffixes: Counter of {'xes': n} where n is the number of keys that end with 'xes'"""
+    def __init__(self, phrases):
+        for phrase in phrases:
+            phrase = phrase.strip()
+            self[letters(phrase)] = phrase
+        self.prefixes = Counter(x for p in self for x in prefixes(p))
+        self.suffixes = Counter(x for p in self for x in suffixes(p))
+        
+def prefixes(phrase): return [phrase[:i] for i in range(1, len(phrase) + 1)]
+
+def suffixes(phrase): return [phrase[-i:] for i in range(1, len(phrase) + 1)]
+
+def letters(phrase, sub=re.compile(r'[\W]+').sub):
+    "Remove all the non-letters from phrase; return lowercase version."
+    return sub('', phrase).lower()
+
+DICT = PhraseDict(open('npdict.txt'))
+
+class Panama:
+    """Panama represents a palindrome, or a state in searching for one.
+    It has .left and .right to hold the phrases that are chosen,
+    and .L and .R to hold the current partial phrases in the middle (still working on these).
+    Also, a .set of all complete phrases, and the .dict of allowable phrases to choose from."""
+    
+    def __init__(self, left=['aman', 'aplan'], L='aca', R='', right=['acanal', 'panama'], dict=DICT):
+        assert cat(left + [L]) == cat([R] + right)[::-1]
+        self.left   = list(left)        # list of complete phrases on left
+        self.L      = L                 # an incomplete phrase on left
+        self.R      = R                 # an incomplete phrase on right
+        self.right  = deque(right)      # deque of complete phrases on right
+        self.dict   = dict              # a {letters: actual_phrase} mapping
+        self.set    = set(left + right) # a set of all complete phrases in palindrome
+        self.best   = []                # list of phrases in longest palindrome found
+        self.Nshown = 0                 # the number of phrases shown in the previous printout
+        self.i      = 0                 # the number of steps taken in the search
+        self.check()
+
+    def __str__(self): return self.original_phrases(self.best)
+    
+    def original_phrases(self, phrases): return ', '.join(self.dict[phrase] for phrase in phrases)
+
+    def search(self, steps=10**5):
+        """Depth-first search for palindromes. From the current state, find all applicable actions.
+        Do the first one, and put on the stack reminders to undo it and try the others,
+        but first search deeper from the result of the first action."""
+        stack = [self.applicable_actions()]
+        for self.i in range(steps):
+            if not stack: 
+                return
+            command = stack.pop()
+            if isinstance(command, UndoCommand):
+                self.undo(command)
+            elif command:
+                act = command.pop()
+                self.do(act)
+                self.check()
+                stack.extend([command, UndoCommand(act), self.applicable_actions()])
+                
+    def do(self, act):
+        "Modify the current state by adding a letter, or finishing a phrase."
+        if act == ',': # finish phrase on left
+            self.set.add(self.L)
+            self.left.append(self.L)
+            self.L = ''
+        elif act == ';': # finish phrase on right
+            self.set.add(self.R)
+            self.right.appendleft(self.R)
+            self.R = ''
+        else: # add a letter
+            self.L = self.L + act 
+            self.R = act + self.R
+    
+    def undo(self, act):
+        "Modify the current state by undoing an action that was previously done."
+        if act == ',': # unfinish phrase on left
+            assert self.L == ''
+            self.L = self.left.pop()
+            self.set.remove(self.L)
+        elif act == ';': # unfinish phrase on right
+            assert self.R == ''
+            self.R = self.right.popleft()
+            self.set.remove(self.R)
+        else: # remove a letter
+            self.L = self.L[:-1]
+            self.R = self.R[1:]
+            
+    def check(self):
+        "Check to see if current state is a palindrome, and if so, record it and maybe print."
+        if not self.is_palindrome(): return
+        N = len(self.left) + len(self.right) 
+        if N > len(self.best):
+            self.best = self.left + list(self.right)
+            if N - self.Nshown > 1000 or (N > 14000 and N - self.Nshown > 100) or N > 14500:
+                self.Nshown = N
+                print(self.report())
+            
+    def report(self):
+        N = len(self.best)
+        nwords = N + sum(self.dict[p].count(' ') for p in self.best)
+        nletters = sum(len(p) for p in self.best)
+        return ('Pal: {:6,d} phrases, {:6,d} words, {:6,d} letters (at step {:,d})'
+                .format(N, nwords, nletters, self.i+1))
+        
+    def applicable_actions(self):
+        L, R, D = self.L, self.R, self.dict
+        actions = []
+
+        def score(A): return D.prefixes[L+A] * D.suffixes[A+R]
+        if self.is_allowed(L):
+            actions.append(',')
+        if self.is_allowed(R):
+            actions.append(';')
+        for A in sorted(alphabet, key=score):
+            if score(A) > 0:
+                actions.append(A)    
+
+        return actions
+ 
+    def is_allowed(self, phrase): return phrase in self.dict and phrase not in self.set
+        
+    def is_palindrome(self): 
+        "Is this a palindrome? (Does any extra .L or .R match the other side?)"
+        return ((self.L == '' and self.left[-1].endswith(self.R)) or 
+                (self.R == '' and self.right[0].startswith(self.L)))
+
+alphabet    = 'abcdefghijklmnopqrstuvwxyz'
+cat         = ''.join
+UndoCommand = str
+DoCommand   = list
+                      
+################ Unit Tests
+
+def test1():
+    assert prefixes('hello') == ['h', 'he', 'hel', 'hell', 'hello']
+    assert suffixes('hello') == ['o', 'lo', 'llo', 'ello', 'hello']
+    assert letters('a man') == 'aman'
+    assert letters('an elk') == 'anelk'
+    assert letters('Mr. T') == 'mrt'
+    assert letters('Donald E. Knuth') == 'donaldeknuth'
+    assert len(DICT) == 125512
+    assert 'panama' in DICT
+    assert 'aman' in DICT
+    assert 'threemen' not in DICT
+    assert DICT['acanal'] == 'a canal'
+    return 'ok'
+
+def test2():
+    p1 = Panama()
+    assert p1.is_palindrome()
+    assert str(p1) == 'a man, a plan, a canal, Panama'
+    p2 = Panama(['aman','aplan'], 'acadd','dd', ['acanal', 'panama'])
+    assert not p2.is_palindrome()
+    p3 = Panama(['maya'], '', '', ['ayam'])
+    assert p3.is_palindrome()
+    assert str(p3) == 'Maya, a yam'
+    return 'ok'
+
+if __name__ == '__main__': 
+    p = Panama();
+    test1()
+    test2()
+    p.search(10**6)
+    print(p.report())
+    print(str(p))
diff --git a/pytudes/py/parse.py b/pytudes/py/parse.py
new file mode 100644
index 0000000..8c7e4ea
--- /dev/null
+++ b/pytudes/py/parse.py
@@ -0,0 +1,52 @@
+grammar = {
+  'Noun': ['stench', 'wumpus'],
+  'Verb': ['is', 'smell'],
+  'Adjective': ['dead', 'smelly'],
+  'Adverb': ['left', 'back'],
+  'Pronoun': ['me', 'you'],
+  'Name': ['John', 'Mary'],
+  'Article': ['the', 'a'],
+  'Preposition': ['to', 'in'],
+  'Conjunction': ['and', 'or'],
+  'Digit': ['0', '1'],
+  
+  'S': [['NP', 'VP'], ['S', 'Comjunction', 'S']],
+  'NP': ['Pronoun', 'Noun', ['Article', 'Noun'], ['Digit', 'Digit'], 
+         ['NP', 'PP'], ['NP', 'RelClause']],
+  'VP': ['Verb', ['VP', 'NP'], ['VP', 'Adjective'], ['VP', 'PP'], 
+         ['VP', 'Adverb']],
+  'PP': [['Preposition', 'NP']],
+  'RelClause': [['that', 'VP']]
+  }
+  
+
+def parse(forest, grammar):
+    if len(forest) == 1 and category(forest[0]) == 'S':
+        return forest[0]
+    for i in range(len(forest)):
+        for lhs in grammar.keys():
+            for rhs in grammar[lhs]:
+		rhs = mklist(rhs)
+		n = len(rhs)
+		subsequence = forest[i:i+n]
+		if match(subsequence, rhs):
+                    print subsequence, lhs, '=>', rhs
+		    forest2 = forest[:]
+		    forest2[i:i+n] = [(lhs, subsequence)]
+		    result = parse(forest2, grammar)
+		    if result != None:
+			return result
+    return None
+
+def mklist(x):
+    if type(x) == type([]): return x
+    else: return [x]
+
+def match(forest, rhs):
+    for i in range(len(rhs)):
+        if category(forest[i]) != rhs[i] and forest[i] != rhs[i]: return 0
+    return 1
+
+def category(forest):
+    if type(forest) == type(()): return forest[0]
+    else: return 'word'
diff --git a/pytudes/py/py2html.py b/pytudes/py/py2html.py
new file mode 100644
index 0000000..896d0de
--- /dev/null
+++ b/pytudes/py/py2html.py
@@ -0,0 +1,110 @@
+"""Pretty-print Python code to colorized, hyperlinked html.
+
+In python, do:
+    py2html.convert_files(['file1.py', 'file2.py', ...]) 
+From the shell, do:
+    python py2html.py *.py"""
+
+import re, string, time, os
+
+
+id = r'[a-zA-Z_][a-zA-Z_0-9]*' ## RE for a Python identifier
+g1, g2, g3, g4 = r'\1 \2 \3 \4'.split() ## groups for re.matches
+def b(text): return '%s' % text
+def i(text): return '%s' % text
+def color(rgb, text): return '%s' % (rgb, text)
+def link(url, anchor): return '%s' % (url, anchor)
+def hilite(text, bg="ffff00"):
+    return '%s' % (
+        bg, text, text)
+
+def modulelink(module, baseurl=''):
+    """Hyperlink to a module, either locally or on python.org"""
+    if module+'.py' not in local_files:
+        baseurl = 'http://www.python.org/doc/current/lib/module-'
+    return link(baseurl+module+'.html', module)
+
+def importer(m):
+    "Turn text such as 'utils, math, re' into a string of HTML links."
+    modules = [modulelink(mod.strip()) for mod in m.group(2).split(',')]
+    return (m.group(1) + ', '.join(modules) + m.group(3))
+
+def find1(regex, str):
+    return (re.findall(regex, str) or [' '])[0]
+
+def convert_files(filenames, local_filenames=None, tblfile='readme.htm'):
+    "Convert files of python code to colorized HTML."
+    global local_files
+    local_files = local_filenames or filenames
+    summary_table = {}
+    for f in filenames:
+        fulltext = '\n'.join(map(string.rstrip, open(f).readlines()))
+        text = fulltext
+        for (pattern, repl) in replacements:
+            text = re.sub(pattern, repl, text)
+        text = '<>
%s
<

' % name, - '

')
-            self.run_docstring(object)
-            names = object.__dict__.keys()
-            names.sort()
-            for name in names:
-                val = object.__dict__[name]
-                if isinstance(val, types.ClassType):
-                    self.run_class(val)
-                elif isinstance(val, types.ModuleType):
-                    pass
-                elif not self.seen(val):
-                    self.run_docstring(val)
-
-    def run_class(self, object):
-        """Run the docstrings, and then all members of the class."""
-        if not self.seen(object):
-            self.run_docstring(object)
-            names = object.__dict__.keys()
-            names.sort()
-            for name in names:
-                self.run_docstring(object.__dict__[name])
-
-    def run_docstring(self, object, search=re.compile(r'(?m)^\s*Ex: ').search):
-        "Run the __doc__ and _docex attributes, if the object has them."
-        if hasattr(object, '__doc__'):
-            s = object.__doc__
-            if isinstance(s, str):
-                match = search(s)
-                if match: self.run_string(s[match.end():])
-        if hasattr(object, '_docex'):
-                self.run_string(object._docex)
-        
-    def run_string(self, teststr):
-        """Run a test string, printing inputs and results."""
-        if not teststr: return
-        teststr = teststr.strip()
-        if teststr.find('\n') > -1:
-            map(self.run_string, teststr.split('\n'))
-        elif teststr == '' or teststr.startswith('#'):
-            self.writeln(teststr)
-        elif teststr.find('; ') > -1:
-            for substr in teststr.split('; '): self.run_string(substr)
-        elif teststr.find('==>') > -1:
-            teststr, result = teststr.split('==>')
-            self.evaluate(teststr, result)
-        elif teststr.find(' raises ') > -1:
-            teststr, exception = teststr.split(' raises ')
-            self.raises(teststr, exception)
-        else: ## Try to eval, but if it is a statement, exec
-            try:
-                self.evaluate(teststr)
-            except SyntaxError:
-                exec teststr in self.dictionary
-
-    def evaluate(self, teststr, resultstr=None):
-        "Eval teststr and check if resultstr (if given) evals to the same."
-        self.writeln('>>> ' +  teststr.strip())
-        result = eval(teststr, self.dictionary)
-        self.dictionary['_'] = result
-        self.writeln(repr(result))
-        if resultstr == None:
-          return
-        elif result == eval(resultstr, self.dictionary):
-          self.passed += 1
-        else:
-          self.fail(teststr, resultstr)
-    
-    def raises(self, teststr, exceptionstr):
-        teststr = teststr.strip()
-        self.writeln('>>> ' + teststr)
-        except_class = eval(exceptionstr, self.dictionary)
-        try:
-            exec teststr in self.dictionary
-        except except_class:
-            self.writeln('# raises %s as expected' % exceptionstr)
-            self.passed += 1
-            return
-        self.fail(teststr, exceptionstr)
-
-    def fail(self, teststr, resultstr):
-        self.writeln('###### ERROR, TEST FAILED: expected %s for %s' 
-                     % (resultstr, teststr),
-                     '', '')
-        self.failed += 1
-
-    def writeln(self, s, before='', after=''):
-        "Write s, html escaped, and wrapped with html code before and after."
-        s = str(s)
-        if self.html:
-            s = s.replace('&','&').replace('<','<').replace('>','>')
-            print '%s%s%s' % (before, s, after)
-        else:
-            print s
-
-    def seen(self, object):
-        """Return true if this object has been seen before.
-        In any case, record that we have seen it."""
-        result = self.already_seen.has_key(id(object))
-        self.already_seen[id(object)] = 1
-        return result
-
-def main(args):
-    """Run Docex.  args should be a list of python filenames.  
-    If the first arg is a non-python filename, it is taken as the
-    name of a log file to which output is written.  If it ends in
-    ".htm" or ".html", then the output is written as html.  If the
-    first arg is "-", then standard output is used as the log file."""
-    import glob
-    out = None
-    html = 0
-    if args[0] != "-" and not args[0].endswith(".py"):
-        out = open(args[0], 'w')
-        if args[0].endswith(".html") or args[0].endswith(".htm"):
-            html = 1
-    modules = []
-    for arg in args:
-        for file in glob.glob(arg):
-            if file.endswith('.py'):
-                modules.append(__import__(file[:-3]))
-    print Docex(modules, html=html, out=out)
-
-if __name__ == '__main__':
-    main(sys.argv[1:])
-
-
diff --git a/pytudes/py/ibol.py b/pytudes/py/ibol.py
deleted file mode 100644
index d2490a6..0000000
--- a/pytudes/py/ibol.py
+++ /dev/null
@@ -1,193 +0,0 @@
-from collections import defaultdict
-
-def get_genomes(fname="byronbayseqs.fas.txt"):
-    "Return a list of genomes, and a list of their corresponding names."
-    import re
-    names, species, genomes = [], [], []
-    for name, g in re.findall('>(.*?)\r([^\r]*)\r*', file(fname).read()):
-        names.append(name)
-        species.append(name.split('|')[-1])
-        genomes.append(g)
-    return names, species, genomes
-
-def get_neighbors(fname="editdistances.txt"):
-    "Return dict: neighbors[i][j] = neighbors[j][i] = d means i,j are d apart."
-    ## Read the data pre-computed from the Java program
-    neighbors = dict((i, {}) for i in range(n))
-    for line in file(fname):
-        i,j,d = map(int, line.split())
-        neighbors[i][j] = neighbors[j][i] = d
-    return neighbors
-        
-def cluster(neighbors, d, dc):
-    """Return a list of clusters, each cluster element is within d of another
-    and within dc of every other cluster element."""
-    unclustered = set(neighbors) ## set of g's not yet clustered
-    return [closure(g, set(), unclustered, d, dc)
-            for g in neighbors if g in unclustered]
-
-def closure(g, s, unclustered, d, dc):
-    "Accumulate in set s the transitive closure of 'near', starting at g"
-    if g not in s and g in unclustered and near(g, s, d, dc):
-        s.add(g); unclustered.remove(g)
-        for g2 in neighbors[g]:
-            closure(g2, s, unclustered, d, dc)
-    return s
-
-def dist(i, j):
-    "Distance between two genomes."
-    if i == j: return 0
-    return neighbors[min(i, j)].get(max(i, j), max_distance)
-
-def near(g, cluster, d, dc):
-    "Is g within d of some member of c, and within dc of every member of c?"
-    distances = [dist(g, g2) for g2 in cluster] or [0]
-    return min(distances) <= d and max(distances) <= dc
-
-def diameter(cluster):
-    "The largest distance between two elements of the cluster"
-    return max([dist(i, j) for i in cluster for j in cluster] or [0])
-
-def margin(cluster):
-    "The distance from a cluster to the nearest g2 outside this cluster."
-    return min([d for g in cluster for g2,d in neighbors[g].items()
-                if g2 not in cluster] or [max_distance])
-
-################################################################ Analysis
-
-def pct(num, den):
-    "Return a string representing the percentage. "
-    if '__len__' in dir(den): den = len(den)
-    if num==den: return ' 100%'
-    return '%.1f%%' % (num*100.0/den)
-
-def histo(items):
-    "Make a histogram from a sequence of items or (item, count) tuples."
-    D = defaultdict(int)
-    for item in items:
-        if isinstance(item, tuple): D[item[0]] += item[1]
-        else: D[item] += 1
-    return D
-
-def showh(d):
-    "Show a histogram"
-    if not isinstance(d, dict): d = histo(d)
-    return ' '.join('%s:%s' % i for i in sorted(d.items()))
-
-def greport(genomes):
-    print "Number of genomes: %d (%d distinct)" % (len(genomes), len(set(genomes)))
-    G = dict((g, set()) for g in genomes)
-    for i in range(n):
-        G[genomes[i]].add(species[i])
-    print "Multi-named genomes:", (
-        len([s for s in G.values() if len(s) > 1]))
-    lens = map(len, genomes)
-    print "Genome lengths: min=%d, max=%d" % (min(lens), max(lens))
-    print "Character counts: ", showh(c for g in genomes for c in g)
-    
-def nreport(neighbors):
-    NN, NumN = defaultdict(int), defaultdict(int) ## Nearest, Number of neighbors
-    for n in neighbors:
-        nn = min(neighbors[n].values() or ['>25'])
-        NN[nn] += 1
-        for d2 in neighbors[n].values():
-            NumN[d2] += 1 
-    print
-    print "Nearest neighbor counts:", showh(NN)
-    print "Number of neighbors at each distance:", showh(NumN)
-
-def nspecies(c): return len(set(species[g] for g in c))
-
-def showc(c):
-    return "N=%d, D=%d, M=%d: %s %s" % (
-        len(c), diameter(c), margin(c), list(c), showh(species[g] for g in c))
-
-def creport(drange, dcrange):
-    def table(what, fn):
-        print "\n" + what
-        print ' '*8, ' '.join([' '+pct(dc, glen) for dc in dcrange])
-        for d in drange:
-            print '%s (%2d)' % (pct(d, glen), d),
-            for dc in dcrange:
-                print '%5s' % fn(cluster(neighbors, d, dc)),
-            print
-    print '\nNearest neighbor must be closer than this percentage (places). '
-    print 'Each column: all genomes in cluster within this percentage of each other.'
-    table("Number of clusters", len)
-    cluster1 = cluster(neighbors, 8, 15) ## splits Cleora
-    print '\nNumber of clusters of different sizes:', showh(len(c) for c in cluster1)
-    M, T = defaultdict(int), defaultdict(int)
-    for c in cluster1:
-        M[margin(c)] += 1; T[margin(c)] += len(c)
-    for x in M: print '%d\t%d\t%d'% (x,M[x],T[x])
-    print '\nMargins', showh(M)
-    for c in cluster1:
-        if margin(c) <= 16:
-            print showc(c)
-    print '\nScatter plot of cluster diameter vs. margin.'
-    for c in cluster1:
-        if diameter(c) > 0:
-            pass
-            #print '%d\t%d' % (diameter(c), margin(c))
-    print '\nDifference from cluster(neighbors, 11, 14):'
-    #table(lambda cl: pct(len(cluster1)-compare(cluster1, cl),max(len(cluster1),len(cl))))
-    print '\nNumber of clusters witth more than one species name:'
-    #table(lambda cl: sum(nspecies(c) > 1 for c in cl))
-    def pct_near_another(clusters, P=1.25):
-        total = 0
-        for c in clusters:
-            d = diameter(c)
-            for g in c:
-                for g2 in neighbors[g]:
-                    if g2 not in c and dist(g, g2) < P*d:
-                        total += 1
-        return pct(total, n)
-    def f(P):
-        print '\nPercent of individuals within %.2f*diameter of another cluster.'%P
-        table(lambda cl: pct_near_another(cl, P))
-    #map(f, [1.2, 1.33, 1.5])
-
-def sreport(species):
-    SS = defaultdict(int)
-    print
-    for s in set(species):
-        c = [g for g in range(n) if species[g] == s]
-        d = diameter(c)
-        if d > 14:
-            if d==glen: d = '>25'
-            print 'diameter %s for %s (%d elements)' % (d, s, len(c))
-        SS[d] += 1
-    print 'Diameters of %d labeled clusters: %s' % (len(set(species)), showh(SS))
-    
-def compare(cl1, cl2):
-    "Compare two lists of clusters"
-    return sum(c1==c2 or 0.5*(abs(len(c1)-len(c2))==1 and
-                              (c1.issubset(c2) or c2.issubset(c1)))
-               for c1 in cl1 for c2 in cl2)
-
-def unit_tests():
-    assert set(len(g) for g in genomes) == set([glen])
-    clusters = cluster(neighbors, 11, 11)
-    assert sum(len(c) for c in clusters) == len(genomes)
-    assert len(set(g for c in clusters for g in c)) == len(genomes)
-    assert dist(17, 42) == dist(42, 17)
-    assert diameter(set()) == 0
-    assert diameter([17, 42]) == dist(17, 42)
-    assert pct(1, 2) == '50.0%'
-    print '\nAll tests pass.\n'
-
-    
-
-################################################################ Main body
- 
-max_distance = 26
-names, species, genomes = get_genomes() ## genomes = ['ACT...', ...]
-n = len(genomes)
-glen = len(genomes[0])
-neighbors = get_neighbors() ## neighbor[g] = {g2:d2, g3:g3, ...}
-greport(genomes)
-nreport(neighbors)
-creport(range(6, 15), [glen,16,15,14,13, 12, 11])
-#sreport(species)
-
-unit_tests()
diff --git a/pytudes/py/lettercount.py b/pytudes/py/lettercount.py
deleted file mode 100644
index 3c6db88..0000000
--- a/pytudes/py/lettercount.py
+++ /dev/null
@@ -1,443 +0,0 @@
-"""
-Code to support http://norvig.com/mayzner.html
-Read files in the Google Books ngram format, and convert them to a simpler format.
-The original format looks like this:
-
-    word     \t year \t word_count \t book_count
-    word_POS \t year \t word_count \t book_count
-
-for example,
-
-    accreted_VERB	1846	7	4
-    accreted_VERB	1847	1	1
-    accreted_VERB	1848	1	1
-
-The function 'read_year_file' will convert a file of this form into a dict of
-{WORD: count} pairs, where the WORD is uppercased, and the count is the total
-over all years (you have the option to specify a starting year) and all
-capitalizations.  Then 'read_dict' and 'write_dict' convert between a dict and
-an external file format that looks like this:
-
-    ACCRETED	9
-
-"""
-
-from __future__ import division
-from collections import Counter, defaultdict
-
-#### Read files in Books-Ngram format; convert to a dict
-
-def read_year_file(filename, dic=None):
-    """Read a file of 'word year word_count book_count' lines and convert to a dict
-    {WORD: totalcount}. Uppercase all words, and only include all-alphabetic words."""
-    if dic is None: dic = {}
-    for line in file(filename):
-        word, year, c1, c2 = line.split('\t')
-        if '_' in word:
-            word = word[:word.index('_')]
-        if word.isalpha():
-            word = word.upper()
-            dic[word] = dic.get(word, 0) + int(c1)
-    return dic
-
-#### Read and write files of the form 'WORD \t count \n'
-
-def write_dict(dic, filename):
-    "Write a {word:count} dict as 'word \t count' lines in filename."
-    out = file(filename, 'w')
-    for key in sorted(dic):
-        out.write('%s\t%s\n' % (key, dic[key]))
-    return out.close()
-        
-def read_dict(filename, sep='\t'):
-    "Read 'word \t count' lines from file and make them into a dict of {word:count}."
-    pairs = (line.split(sep) for line in file(filename))
-    return {word: int(count) for (word, count) in pairs}
-
-#### Convert a bunch of year files into dict file format.
-
-def convert_files(filenames, mincount=1e5):
-    def report(filename, D, adj):
-        import time
-        N = len(D)
-        W = sum(v for v in D.itervalues())
-        print '%s: %s %s words (%s tokens) at %s' % (
-            filename, adj, format(W, ',d'), format(N, ',d'),
-            time.strftime("%H:%M:%S", time.gmtime()))
-    for f in filenames:
-        report(f, {}, 'starting')
-        D = read_year_file(f)
-        report(f, D, 'total')
-        for key in list(D):
-            if D[key] < mincount:
-                del D[key]
-        write_dict(D, 'WORD-' + f[-1].upper())
-        report(f, D, 'popular')
-
-def load(filename='top-words.txt'):
-    "Load file of 'word \t count' lines into D (a dict), W (length of D) and M (total number of words)."
-    global D, W, M
-    D = read_dict(filename)
-    W = len(D)
-    M = sum(D.values())
-    
-#### Compute letter counts and save as HTML files.
-
-def histogram(items):
-    "Return a Counter of the number of times each key occurs in (key, val) pairs."
-    C = Counter()
-    for (key, val) in items:
-        C[key] += val
-    return C
-
-def end(name): return '/' + name
-
-def tag(name, **kwds): return '<' + name + keywords(kwds) + '>'
-
-def row(cells, **kwds):
-    return '' + ''
-    
-def ngram_tables(dic, N, pos=[0, 1, 2, 3, 4, -5, -4, -3, -2, -1]):
-    """Return three dicts of letter N-grams of length N: counts, counts1, counts2.
-    counts is a dict of {'AB': 123} that counts how often 'AB' occurs.
-    counts1[i] is a dict of {'AB': 123} that counts how often 'AB' occurs at position i.
-    counts2[i][j] is a dict of {'AB': 123} that counts how often 'AB' occurs at position i."""
-    L = len(max(D, key=len))
-    counts = Counter()
-    counts1 = [Counter() for _ in range(L)]
-    counts2 = [[Counter() for i in range(L)]]
-
-def counter(pairs):
-    "Make a Counter from an iterable of (value, count) pairs."
-    c = Counter()
-    for (value, count) in pairs:
-        c[value] += count
-    return c
-
-def ngrams(word, N):
-    return [word[i:i+N] for i in range(len(word)+1-N)]
-
-
-import glob
-#convert_files(glob.glob('book?'))
-              
-#DB = [[letter_counts() for length in range(length)] for length in range(maxlen)]
-      
-
-## Unused ???
-
-def letter_counts(wc):
-    """From word_counts dictionary wc, Create a dictionary of {(s, i, L): count}
-    where s is a letter n-gram, i is the starting position, and L is the length
-    of the word in which it appears."""
-    result = defaultdict(int)
-    for (word, count) in wc.iteritems():
-        for p in pieces(word):
-            result[p] += count
-    return result
-
-def pieces(word):
-    "Yield the 1- and 2-letter grams in (s, i, L) format."
-    L = len(word)
-    for i in range(L):
-        yield (word[i], i, L)
-        if i+1 < L:
-            yield (word[i:i+2], i, L)
-
-def getcount(counts, s, pos, length):
-    """The count for letter sequence s (one or two letters) starting at
-    position i of words of length length.  If any argument is all, sum them up."""
-    if length == all:
-        return sum(getcount(counts, s, pos, L) for L in all_lengths)
-    elif pos == all:
-        return sum(getcount(counts, s, i, length) for i in range(length))
-    else:
-        return counts[s, pos, length]
-
-
-print 'start'
-#wc = word_counts('count_100K.txt')
-#counts = letter_counts(wc)
-print 'end'
-
-
-
-def test():
-    D = {'the': 100, 'of': 70, 'and': 60, 'to': 50, 'a': 40}
-
-def num(ch):
-    "Translate 'a' or 'A' to 0, ... 'z' or 'Z' to 25."
-    return 'abcdefghijklmnopqrstuvwxyz'.index(ch.lower())
-    
-
-def stats(D, NS = (1, 2, 3, 4, 5, 6)):
-    counts = {n: Counter() for n in NS}
-    print 'words ' + ' '.join('   %d-grams  ' % n for n in NS)
-    for (i, word) in enumerate(sortedby(D), 1):
-        for n in NS:
-            for ng in ngrams(word, n):
-                counts[n][ng] += 1
-        if i % 5000 == 0 or i == len(D):
-            print "%4dK" % (i/1000),
-            for n in NS:
-                c = len(counts[n])
-                field = "%5d (%d%%)" % (c, int(round(c*100/(26**n))))
-                print '%12s' % field,
-            print
-
-letters = 'ETAOINSRHLDCUMFPGWYBVKXJQZ'
-alphabet = ''.join(sorted(letters))
-
-from itertools import cycle, izip
-
-colors = 'ygobp'
-
-def bar(text, color, count, N, pixels, height=16):
-    width = int(round(pixels * count / N))
-    if width < 2: width = 3
-    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
-    return '%s' % (
-        title, color, height, width, -width+2, text) # -int(width/2+5)
-
-def letter_bar(LC, N=None, factor='', pixels=700):
-    if N is None: N = sum(LC.values())
-    #divisor = {'':1., 'K':1e3, 'M':1e6, 'B':1e9}[factor]
-    return ''.join(
-        bar(L.lower(), color, LC[L], N, pixels)
-        for (L, color) in izip(letters, cycle(colors)))
-        
-
-def singleton(x): return [x]
-
-positions = [0, 1, 2, 3, 4, 5, 6, -7, -6, -5, -4, -3, -2, -1]
-
-def substr(word, pos, length):
-    """Return the substr of word of given length starting/ending at pos; or None."""
-    W = len(word)
-    if pos >= 0 and pos+length <= W:
-        return word[pos:pos+length]
-    elif pos < 0 and abs(pos)+length-1 <= W:
-        return word[W+pos+1-length:W+pos+1]
-    else:
-        return None
-        
-def lettercount(D, pos):
-    LC = histogram((substr(w, pos, 1), D[w]) for w in D)
-    del LC[None]
-    print LC
-    pos_name = (str(pos)+'+' if isinstance(pos, tuple) else
-                pos if pos < 0 else
-                pos+1)
-    return '\n
\n%-3s %s' % (pos_name, letter_bar(LC))
-
-def ngramcount(D, n=2):
-    return histogram((ng, D[w]) for w in D for ng in ngrams(w, n))
-
-def twograms(D2):
-    N = sum(D2.values())
-    header = ''
-    rows = [tr([cell(A+B, D2, N) for A in alphabet]) for B in alphabet]
-    return '\n'.join([header] + rows + ['
'])
-
-def cell(text, D2, N, height=16, maxwidth=25, scale=27):
-    count = D2.get(text, 0)
-    width = int(round(maxwidth * count * scale * 1. / N))
-    if width < 1: width = 1
-    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
-    return '%s' % (
-        title, height, width, -width+2, text)
-
-def cell(text, D2, N, height=16, maxwidth=25, scale=27):
-    count = D2.get(text, 0)
-    width = int(round(maxwidth * count * scale * 1. / N))
-    if width < 1: width = 1
-    title = '{}: {:.3f}%; {:,}'.format(text, count*100./N, count)
-    return '%s' % (
-        title, height, width, text) 
-
-def tr(cells):
-    return '' + ''.join(cells)
-
-def comma(n): return '{:,}'.format(n)
-
-def ngram_stats(D, n, k=5):
-    DN = ngramcount(D, n)
-    topk = ', '.join(sortedby(DN)[:k])
-    return '%d-grams%s%scounts-%d.csvcounts-%d.html%s' % (
-        n, comma(len(DN)), comma(sum(DN.values())), n, n, n, n, topk)
-
-#### Tables
-
-def sortedby(D):
-    return sorted(D, key=lambda x: -D[x])
-
-ANY = '*'
-
-wordlengths = range(1, 10)
-
-def col(*args): return args
-
-def columns(n, wordlengths=wordlengths):
-    lengths = [k for k in wordlengths if k >= n]
-    return ([col(ANY, ANY)]
-            + [col(k, ANY) for k in lengths]
-            + [col(k, start, start+n-1) for k in lengths for start in range(1, 2+k-n)]
-            + [col(ANY, start, start+n-1) for start in wordlengths]
-            + [col(ANY, -k, -k+n-1) for k in reversed(lengths) if -k+n-1 < 0])
-
-def colname(col):
-    fmt = '%s/%s' if (len(col) == 2) else '%s/%d:%d'
-    return  fmt % col
-
-def csvline(first, rest):
-    return '\t'.join([first] + map(str, rest))
-
-def makecsv(n, D=D):
-    out = file('ngrams%d.csv' % n, 'w')
-    cols = columns(n)
-    Dng = defaultdict(lambda: defaultdict(int))
-    for w in D:
-        for (start, ng) in enumerate(ngrams(w, n), 1):
-            entry = Dng[ng]
-            N = D[w]
-            wlen = len(w)
-            entry[ANY, ANY] += N
-            entry[wlen, ANY] += N
-            if start <= 9:
-                entry[wlen, start, start+n-1] += N
-                entry[ANY, start, start+n-1] += N
-            from_end = wlen-start+1
-            if from_end <= 9:
-                entry[ANY, -from_end, -from_end+n-1] += N
-        # enumerate ngrams from word and increment counts for each one
-    print >> out, csvline('%d-gram' % n,  map(colname, cols))
-    for ng in sorted(Dng, key=lambda ng: -Dng[ng][(ANY, ANY)]):
-        print >> out, csvline(ng, [Dng[ng].get(col, 0) for col in cols])
-    out.close()
-    return Dng
-
-### Tests
-
-"""
->>> for w in words:
-    print '%-6s %6.2f B (%4.2f%%) ' % (w.lower(), D[w]/1e9, D[w]*100./N, int(round(D[w]*4000./N)))
-... 
-the     53.10 B (7.14%) 
-of      30.97 B (4.16%) 
-and     22.63 B (3.04%) 
-to      19.35 B (2.60%) 
-in      16.89 B (2.27%) 
-a       15.31 B (2.06%) 
-is       8.38 B (1.13%) 
-that     8.00 B (1.08%) 
-for      6.55 B (0.88%) 
-it       5.74 B (0.77%) 
-as       5.70 B (0.77%) 
-was      5.50 B (0.74%) 
-with     5.18 B (0.70%) 
-be       4.82 B (0.65%) 
-by       4.70 B (0.63%) 
-on       4.59 B (0.62%) 
-not      4.52 B (0.61%) 
-he       4.11 B (0.55%) 
-i        3.88 B (0.52%) 
-this     3.83 B (0.51%) 
-are      3.70 B (0.50%) 
-or       3.67 B (0.49%) 
-his      3.61 B (0.49%) 
-from     3.47 B (0.47%) 
-at       3.41 B (0.46%) 
-which    3.14 B (0.42%) 
-but      2.79 B (0.38%) 
-have     2.78 B (0.37%) 
-an       2.73 B (0.37%) 
-had      2.62 B (0.35%) 
-they     2.46 B (0.33%) 
-you      2.34 B (0.31%) 
-were     2.27 B (0.31%) 
-their    2.15 B (0.29%) 
-one      2.15 B (0.29%) 
-all      2.06 B (0.28%) 
-we       2.06 B (0.28%) 
-can      1.67 B (0.22%) 
-her      1.63 B (0.22%) 
-has      1.63 B (0.22%) 
-there    1.62 B (0.22%) 
-been     1.62 B (0.22%) 
-if       1.56 B (0.21%) 
-more     1.55 B (0.21%) 
-when     1.52 B (0.20%) 
-will     1.49 B (0.20%) 
-would    1.47 B (0.20%) 
-who      1.46 B (0.20%) 
-so       1.45 B (0.19%) 
-no       1.40 B (0.19%) 
-
->>> for n in sorted(H):
-    print '%2d %9.2f M (%6.3f%%)  %d' % (n, H[n]/1e6, H[n]*100./NN, H[n]*3000./NN, n)
-... 
- 1  22301.22 M ( 2.998%)  1
- 2 131293.85 M (17.651%)  2
- 3 152568.38 M (20.511%)  3
- 4 109988.33 M (14.787%)  4
- 5  79589.32 M (10.700%)  5
- 6  62391.21 M ( 8.388%)  6
- 7  59052.66 M ( 7.939%)  7
- 8  44207.29 M ( 5.943%)  8
- 9  33006.93 M ( 4.437%)  9
-10  22883.84 M ( 3.076%)  10
-11  13098.06 M ( 1.761%)  11
-12   7124.15 M ( 0.958%)  12
-13   3850.58 M ( 0.518%)  13
-14   1653.08 M ( 0.222%)  14
-15    565.24 M ( 0.076%)  15
-16    151.22 M ( 0.020%)  16
-17     72.81 M ( 0.010%)  17
-18     28.62 M ( 0.004%)  18
-19      8.51 M ( 0.001%)  19
-20      6.35 M ( 0.001%)  20
-21      0.13 M ( 0.000%)  21
-22      0.81 M ( 0.000%)  22
-23      0.32 M ( 0.000%)  23
-
->>> NL = sum(LC.values())
-
->>> for L in sorted(LC, key=lambda L: -LC[L]):
-    print '%s %8.1f B (%5.2f%%) ' % (L, LC[L]/1e9, LC[L]*100./NL, LC[L]*3000./NL)
-...
-E    445.2 B (12.49%) 
-T    330.5 B ( 9.28%) 
-A    286.5 B ( 8.04%) 
-O    272.3 B ( 7.64%) 
-I    269.7 B ( 7.57%) 
-N    257.8 B ( 7.23%) 
-S    232.1 B ( 6.51%) 
-R    223.8 B ( 6.28%) 
-H    180.1 B ( 5.05%) 
-L    145.0 B ( 4.07%) 
-D    136.0 B ( 3.82%) 
-C    119.2 B ( 3.34%) 
-U     97.3 B ( 2.73%) 
-M     89.5 B ( 2.51%) 
-F     85.6 B ( 2.40%) 
-P     76.1 B ( 2.14%) 
-G     66.6 B ( 1.87%) 
-W     59.7 B ( 1.68%) 
-Y     59.3 B ( 1.66%) 
-B     52.9 B ( 1.48%) 
-V     37.5 B ( 1.05%) 
-K     19.3 B ( 0.54%) 
-X      8.4 B ( 0.23%) 
-J      5.7 B ( 0.16%) 
-Q      4.3 B ( 0.12%) 
-Z      3.2 B ( 0.09%) 
-
->>> D2 = ngramcount(D, 2)
-
->>> for ng in sorted(D2, key=lambda L: -D2[L])[:50]: print '%s %8.1f B (%5.2f%%) ' % (ng, D2[ng]/1e9, D2[ng]*100./N2, D2[ng]*15000./N2)
-
-def doit(k=25):
-    counts = [sortedby(ngramcount(D, n))[:k] for n in range(2, 10)]
-    for i in range(k):
-        print ('     '.join(count[i] for count in counts)).lower()
-"""
diff --git a/pytudes/py/lis.py b/pytudes/py/lis.py
deleted file mode 100644
index 2d031ad..0000000
--- a/pytudes/py/lis.py
+++ /dev/null
@@ -1,145 +0,0 @@
-################ Lispy: Scheme Interpreter in Python
-
-## (c) Peter Norvig, 2010-16; See http://norvig.com/lispy.html
-
-from __future__ import division
-import math
-import operator as op
-
-################ Types
-
-Symbol = str          # A Lisp Symbol is implemented as a Python str
-List   = list         # A Lisp List is implemented as a Python list
-Number = (int, float) # A Lisp Number is implemented as a Python int or float
-
-################ Parsing: parse, tokenize, and read_from_tokens
-
-def parse(program):
-    "Read a Scheme expression from a string."
-    return read_from_tokens(tokenize(program))
-
-def tokenize(s):
-    "Convert a string into a list of tokens."
-    return s.replace('(',' ( ').replace(')',' ) ').split()
-
-def read_from_tokens(tokens):
-    "Read an expression from a sequence of tokens."
-    if len(tokens) == 0:
-        raise SyntaxError('unexpected EOF while reading')
-    token = tokens.pop(0)
-    if '(' == token:
-        L = []
-        while tokens[0] != ')':
-            L.append(read_from_tokens(tokens))
-        tokens.pop(0) # pop off ')'
-        return L
-    elif ')' == token:
-        raise SyntaxError('unexpected )')
-    else:
-        return atom(token)
-
-def atom(token):
-    "Numbers become numbers; every other token is a symbol."
-    try: return int(token)
-    except ValueError:
-        try: return float(token)
-        except ValueError:
-            return Symbol(token)
-
-################ Environments
-
-def standard_env():
-    "An environment with some Scheme standard procedures."
-    env = Env()
-    env.update(vars(math)) # sin, cos, sqrt, pi, ...
-    env.update({
-        '+':op.add, '-':op.sub, '*':op.mul, '/':op.truediv, 
-        '>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq, 
-        'abs':     abs,
-        'append':  op.add,  
-        'apply':   apply,
-        'begin':   lambda *x: x[-1],
-        'car':     lambda x: x[0],
-        'cdr':     lambda x: x[1:], 
-        'cons':    lambda x,y: [x] + y,
-        'eq?':     op.is_, 
-        'equal?':  op.eq, 
-        'length':  len, 
-        'list':    lambda *x: list(x), 
-        'list?':   lambda x: isinstance(x,list), 
-        'map':     map,
-        'max':     max,
-        'min':     min,
-        'not':     op.not_,
-        'null?':   lambda x: x == [], 
-        'number?': lambda x: isinstance(x, Number),   
-        'procedure?': callable,
-        'round':   round,
-        'symbol?': lambda x: isinstance(x, Symbol),
-    })
-    return env
-
-class Env(dict):
-    "An environment: a dict of {'var':val} pairs, with an outer Env."
-    def __init__(self, parms=(), args=(), outer=None):
-        self.update(zip(parms, args))
-        self.outer = outer
-    def find(self, var):
-        "Find the innermost Env where var appears."
-        return self if (var in self) else self.outer.find(var)
-
-global_env = standard_env()
-
-################ Interaction: A REPL
-
-def repl(prompt='lis.py> '):
-    "A prompt-read-eval-print loop."
-    while True:
-        val = eval(parse(raw_input(prompt)))
-        if val is not None: 
-            print(lispstr(val))
-
-def lispstr(exp):
-    "Convert a Python object back into a Lisp-readable string."
-    if isinstance(exp, List):
-        return '(' + ' '.join(map(lispstr, exp)) + ')' 
-    else:
-        return str(exp)
-
-################ Procedures
-
-class Procedure(object):
-    "A user-defined Scheme procedure."
-    def __init__(self, parms, body, env):
-        self.parms, self.body, self.env = parms, body, env
-    def __call__(self, *args): 
-        return eval(self.body, Env(self.parms, args, self.env))
-
-################ eval
-
-def eval(x, env=global_env):
-    "Evaluate an expression in an environment."
-    if isinstance(x, Symbol):      # variable reference
-        return env.find(x)[x]
-    elif not isinstance(x, List):  # constant literal
-        return x                
-    elif x[0] == 'quote':          # (quote exp)
-        (_, exp) = x
-        return exp
-    elif x[0] == 'if':             # (if test conseq alt)
-        (_, test, conseq, alt) = x
-        exp = (conseq if eval(test, env) else alt)
-        return eval(exp, env)
-    elif x[0] == 'define':         # (define var exp)
-        (_, var, exp) = x
-        env[var] = eval(exp, env)
-    elif x[0] == 'set!':           # (set! var exp)
-        (_, var, exp) = x
-        env.find(var)[var] = eval(exp, env)
-    elif x[0] == 'lambda':         # (lambda (var...) body)
-        (_, parms, body) = x
-        return Procedure(parms, body, env)
-    else:                          # (proc arg...)
-        proc = eval(x[0], env)
-        args = [eval(exp, env) for exp in x[1:]]
-        return proc(*args)
\ No newline at end of file
diff --git a/pytudes/py/lispy.py b/pytudes/py/lispy.py
deleted file mode 100644
index 08923c1..0000000
--- a/pytudes/py/lispy.py
+++ /dev/null
@@ -1,318 +0,0 @@
-################ Scheme Interpreter in Python
-
-## (c) Peter Norvig, 2010; See http://norvig.com/lispy2.html
-
-################ Symbol, Procedure, classes
-
-from __future__ import division
-import re, sys, StringIO
-
-class Symbol(str): pass
-
-def Sym(s, symbol_table={}):
-    "Find or create unique Symbol entry for str s in symbol table."
-    if s not in symbol_table: symbol_table[s] = Symbol(s)
-    return symbol_table[s]
-
-_quote, _if, _set, _define, _lambda, _begin, _definemacro, = map(Sym, 
-"quote   if   set!  define   lambda   begin   define-macro".split())
-
-_quasiquote, _unquote, _unquotesplicing = map(Sym,
-"quasiquote   unquote   unquote-splicing".split())
-
-class Procedure(object):
-    "A user-defined Scheme procedure."
-    def __init__(self, parms, exp, env):
-        self.parms, self.exp, self.env = parms, exp, env
-    def __call__(self, *args): 
-        return eval(self.exp, Env(self.parms, args, self.env))
-
-################ parse, read, and user interaction
-
-def parse(inport):
-    "Parse a program: read and expand/error-check it."
-    # Backwards compatibility: given a str, convert it to an InPort
-    if isinstance(inport, str): inport = InPort(StringIO.StringIO(inport))
-    return expand(read(inport), toplevel=True)
-
-eof_object = Symbol('#') # Note: uninterned; can't be read
-
-class InPort(object):
-    "An input port. Retains a line of chars."
-    tokenizer = r"""\s*(,@|[('`,)]|"(?:[\\].|[^\\"])*"|;.*|[^\s('"`,;)]*)(.*)"""
-    def __init__(self, file):
-        self.file = file; self.line = ''
-    def next_token(self):
-        "Return the next token, reading new text into line buffer if needed."
-        while True:
-            if self.line == '': self.line = self.file.readline()
-            if self.line == '': return eof_object
-            token, self.line = re.match(InPort.tokenizer, self.line).groups()
-            if token != '' and not token.startswith(';'):
-                return token
-
-def readchar(inport):
-    "Read the next character from an input port."
-    if inport.line != '':
-        ch, inport.line = inport.line[0], inport.line[1:]
-        return ch
-    else:
-        return inport.file.read(1) or eof_object
-
-def read(inport):
-    "Read a Scheme expression from an input port."
-    def read_ahead(token):
-        if '(' == token: 
-            L = []
-            while True:
-                token = inport.next_token()
-                if token == ')': return L
-                else: L.append(read_ahead(token))
-        elif ')' == token: raise SyntaxError('unexpected )')
-        elif token in quotes: return [quotes[token], read(inport)]
-        elif token is eof_object: raise SyntaxError('unexpected EOF in list')
-        else: return atom(token)
-    # body of read:
-    token1 = inport.next_token()
-    return eof_object if token1 is eof_object else read_ahead(token1)
-
-quotes = {"'":_quote, "`":_quasiquote, ",":_unquote, ",@":_unquotesplicing}
-
-def atom(token):
-    'Numbers become numbers; #t and #f are booleans; "..." string; otherwise Symbol.'
-    if token == '#t': return True
-    elif token == '#f': return False
-    elif token[0] == '"': return token[1:-1].decode('string_escape')
-    try: return int(token)
-    except ValueError:
-        try: return float(token)
-        except ValueError:
-            try: return complex(token.replace('i', 'j', 1))
-            except ValueError:
-                return Sym(token)
-
-def to_string(x):
-    "Convert a Python object back into a Lisp-readable string."
-    if x is True: return "#t"
-    elif x is False: return "#f"
-    elif isa(x, Symbol): return x
-    elif isa(x, str): return '"%s"' % x.encode('string_escape').replace('"',r'\"')
-    elif isa(x, list): return '('+' '.join(map(to_string, x))+')'
-    elif isa(x, complex): return str(x).replace('j', 'i')
-    else: return str(x)
-
-def load(filename):
-    "Eval every expression from a file."
-    repl(None, InPort(open(filename)), None)
-
-def repl(prompt='lispy> ', inport=InPort(sys.stdin), out=sys.stdout):
-    "A prompt-read-eval-print loop."
-    sys.stderr.write("Lispy version 2.0\n")
-    while True:
-        try:
-            if prompt: sys.stderr.write(prompt)
-            x = parse(inport)
-            if x is eof_object: return
-            val = eval(x)
-            if val is not None and out: print >> out, to_string(val)
-        except Exception as e:
-            print '%s: %s' % (type(e).__name__, e)
-
-################ Environment class
-
-class Env(dict):
-    "An environment: a dict of {'var':val} pairs, with an outer Env."
-    def __init__(self, parms=(), args=(), outer=None):
-        # Bind parm list to corresponding args, or single parm to list of args
-        self.outer = outer
-        if isa(parms, Symbol): 
-            self.update({parms:list(args)})
-        else: 
-            if len(args) != len(parms):
-                raise TypeError('expected %s, given %s, ' 
-                                % (to_string(parms), to_string(args)))
-            self.update(zip(parms,args))
-    def find(self, var):
-        "Find the innermost Env where var appears."
-        if var in self: return self
-        elif self.outer is None: raise LookupError(var)
-        else: return self.outer.find(var)
-
-def is_pair(x): return x != [] and isa(x, list)
-def cons(x, y): return [x]+y
-
-def callcc(proc):
-    "Call proc with current continuation; escape only"
-    ball = RuntimeWarning("Sorry, can't continue this continuation any longer.")
-    def throw(retval): ball.retval = retval; raise ball
-    try:
-        return proc(throw)
-    except RuntimeWarning as w:
-        if w is ball: return ball.retval
-        else: raise w
-
-def add_globals(self):
-    "Add some Scheme standard procedures."
-    import math, cmath, operator as op
-    self.update(vars(math))
-    self.update(vars(cmath))
-    self.update({
-     '+':op.add, '-':op.sub, '*':op.mul, '/':op.div, 'not':op.not_, 
-     '>':op.gt, '<':op.lt, '>=':op.ge, '<=':op.le, '=':op.eq, 
-     'equal?':op.eq, 'eq?':op.is_, 'length':len, 'cons':cons,
-     'car':lambda x:x[0], 'cdr':lambda x:x[1:], 'append':op.add,  
-     'list':lambda *x:list(x), 'list?': lambda x:isa(x,list),
-     'null?':lambda x:x==[], 'symbol?':lambda x: isa(x, Symbol),
-     'boolean?':lambda x: isa(x, bool), 'pair?':is_pair, 
-     'port?': lambda x:isa(x,file), 'apply':lambda proc,l: proc(*l), 
-     'eval':lambda x: eval(expand(x)), 'load':lambda fn: load(fn), 'call/cc':callcc,
-     'open-input-file':open,'close-input-port':lambda p: p.file.close(), 
-     'open-output-file':lambda f:open(f,'w'), 'close-output-port':lambda p: p.close(),
-     'eof-object?':lambda x:x is eof_object, 'read-char':readchar,
-     'read':read, 'write':lambda x,port=sys.stdout:port.write(to_string(x)),
-     'display':lambda x,port=sys.stdout:port.write(x if isa(x,str) else to_string(x))})
-    return self
-
-isa = isinstance
-
-global_env = add_globals(Env())
-
-################ eval (tail recursive)
-
-def eval(x, env=global_env):
-    "Evaluate an expression in an environment."
-    while True:
-        if isa(x, Symbol):       # variable reference
-            return env.find(x)[x]
-        elif not isa(x, list):   # constant literal
-            return x                
-        elif x[0] is _quote:     # (quote exp)
-            (_, exp) = x
-            return exp
-        elif x[0] is _if:        # (if test conseq alt)
-            (_, test, conseq, alt) = x
-            x = (conseq if eval(test, env) else alt)
-        elif x[0] is _set:       # (set! var exp)
-            (_, var, exp) = x
-            env.find(var)[var] = eval(exp, env)
-            return None
-        elif x[0] is _define:    # (define var exp)
-            (_, var, exp) = x
-            env[var] = eval(exp, env)
-            return None
-        elif x[0] is _lambda:    # (lambda (var*) exp)
-            (_, vars, exp) = x
-            return Procedure(vars, exp, env)
-        elif x[0] is _begin:     # (begin exp+)
-            for exp in x[1:-1]:
-                eval(exp, env)
-            x = x[-1]
-        else:                    # (proc exp*)
-            exps = [eval(exp, env) for exp in x]
-            proc = exps.pop(0)
-            if isa(proc, Procedure):
-                x = proc.exp
-                env = Env(proc.parms, exps, proc.env)
-            else:
-                return proc(*exps)
-
-################ expand
-
-def expand(x, toplevel=False):
-    "Walk tree of x, making optimizations/fixes, and signaling SyntaxError."
-    require(x, x!=[])                    # () => Error
-    if not isa(x, list):                 # constant => unchanged
-        return x
-    elif x[0] is _quote:                 # (quote exp)
-        require(x, len(x)==2)
-        return x
-    elif x[0] is _if:                    
-        if len(x)==3: x = x + [None]     # (if t c) => (if t c None)
-        require(x, len(x)==4)
-        return map(expand, x)
-    elif x[0] is _set:                   
-        require(x, len(x)==3); 
-        var = x[1]                       # (set! non-var exp) => Error
-        require(x, isa(var, Symbol), "can set! only a symbol")
-        return [_set, var, expand(x[2])]
-    elif x[0] is _define or x[0] is _definemacro: 
-        require(x, len(x)>=3)            
-        _def, v, body = x[0], x[1], x[2:]
-        if isa(v, list) and v:           # (define (f args) body)
-            f, args = v[0], v[1:]        #  => (define f (lambda (args) body))
-            return expand([_def, f, [_lambda, args]+body])
-        else:
-            require(x, len(x)==3)        # (define non-var/list exp) => Error
-            require(x, isa(v, Symbol), "can define only a symbol")
-            exp = expand(x[2])
-            if _def is _definemacro:     
-                require(x, toplevel, "define-macro only allowed at top level")
-                proc = eval(exp)       
-                require(x, callable(proc), "macro must be a procedure")
-                macro_table[v] = proc    # (define-macro v proc)
-                return None              #  => None; add v:proc to macro_table
-            return [_define, v, exp]
-    elif x[0] is _begin:
-        if len(x)==1: return None        # (begin) => None
-        else: return [expand(xi, toplevel) for xi in x]
-    elif x[0] is _lambda:                # (lambda (x) e1 e2) 
-        require(x, len(x)>=3)            #  => (lambda (x) (begin e1 e2))
-        vars, body = x[1], x[2:]
-        require(x, (isa(vars, list) and all(isa(v, Symbol) for v in vars))
-                or isa(vars, Symbol), "illegal lambda argument list")
-        exp = body[0] if len(body) == 1 else [_begin] + body
-        return [_lambda, vars, expand(exp)]   
-    elif x[0] is _quasiquote:            # `x => expand_quasiquote(x)
-        require(x, len(x)==2)
-        return expand_quasiquote(x[1])
-    elif isa(x[0], Symbol) and x[0] in macro_table:
-        return expand(macro_table[x[0]](*x[1:]), toplevel) # (m arg...) 
-    else:                                #        => macroexpand if m isa macro
-        return map(expand, x)            # (f arg...) => expand each
-
-def require(x, predicate, msg="wrong length"):
-    "Signal a syntax error if predicate is false."
-    if not predicate: raise SyntaxError(to_string(x)+': '+msg)
-
-_append, _cons, _let = map(Sym, "append cons let".split())
-
-def expand_quasiquote(x):
-    """Expand `x => 'x; `,x => x; `(,@x y) => (append x y) """
-    if not is_pair(x):
-        return [_quote, x]
-    require(x, x[0] is not _unquotesplicing, "can't splice here")
-    if x[0] is _unquote:
-        require(x, len(x)==2)
-        return x[1]
-    elif is_pair(x[0]) and x[0][0] is _unquotesplicing:
-        require(x[0], len(x[0])==2)
-        return [_append, x[0][1], expand_quasiquote(x[1:])]
-    else:
-        return [_cons, expand_quasiquote(x[0]), expand_quasiquote(x[1:])]
-
-def let(*args):
-    args = list(args)
-    x = cons(_let, args)
-    require(x, len(args)>1)
-    bindings, body = args[0], args[1:]
-    require(x, all(isa(b, list) and len(b)==2 and isa(b[0], Symbol)
-                   for b in bindings), "illegal binding list")
-    vars, vals = zip(*bindings)
-    return [[_lambda, list(vars)]+map(expand, body)] + map(expand, vals)
-
-macro_table = {_let:let} ## More macros can go here
-
-eval(parse("""(begin
-
-(define-macro and (lambda args 
-   (if (null? args) #t
-       (if (= (length args) 1) (car args)
-           `(if ,(car args) (and ,@(cdr args)) #f)))))
-
-;; More macros can also go here
-
-)"""))
-
-if __name__ == '__main__':
-    repl()
-
diff --git a/pytudes/py/lispytest.py b/pytudes/py/lispytest.py
deleted file mode 100644
index bed5307..0000000
--- a/pytudes/py/lispytest.py
+++ /dev/null
@@ -1,121 +0,0 @@
-
-################ Tests for lis.py and lispy.py
-
-lis_tests = [
-    ("(quote (testing 1 (2.0) -3.14e159))", ['testing', 1, [2.0], -3.14e159]),
-    ("(+ 2 2)", 4),
-    ("(+ (* 2 100) (* 1 10))", 210),
-    ("(if (> 6 5) (+ 1 1) (+ 2 2))", 2),
-    ("(if (< 6 5) (+ 1 1) (+ 2 2))", 4),
-    ("(define x 3)", None), ("x", 3), ("(+ x x)", 6),
-    ("(begin (define x 1) (set! x (+ x 1)) (+ x 1))", 3),
-    ("((lambda (x) (+ x x)) 5)", 10),
-    ("(define twice (lambda (x) (* 2 x)))", None), ("(twice 5)", 10),
-    ("(define compose (lambda (f g) (lambda (x) (f (g x)))))", None),
-    ("((compose list twice) 5)", [10]),
-    ("(define repeat (lambda (f) (compose f f)))", None),
-    ("((repeat twice) 5)", 20), ("((repeat (repeat twice)) 5)", 80),
-    ("(define fact (lambda (n) (if (<= n 1) 1 (* n (fact (- n 1))))))", None),
-    ("(fact 3)", 6),
-    ("(fact 50)", 30414093201713378043612608166064768844377641568960512000000000000),
-    ("(define abs (lambda (n) ((if (> n 0) + -) 0 n)))", None),
-    ("(list (abs -3) (abs 0) (abs 3))", [3, 0, 3]),
-    ("""(define combine (lambda (f)
-    (lambda (x y)
-      (if (null? x) (quote ())
-          (f (list (car x) (car y))
-             ((combine f) (cdr x) (cdr y)))))))""", None),
-    ("(define zip (combine cons))", None),
-    ("(zip (list 1 2 3 4) (list 5 6 7 8))", [[1, 5], [2, 6], [3, 7], [4, 8]]),
-    ("""(define riff-shuffle (lambda (deck) (begin
-    (define take (lambda (n seq) (if (<= n 0) (quote ()) (cons (car seq) (take (- n 1) (cdr seq))))))
-    (define drop (lambda (n seq) (if (<= n 0) seq (drop (- n 1) (cdr seq)))))
-    (define mid (lambda (seq) (/ (length seq) 2)))
-    ((combine append) (take (mid deck) deck) (drop (mid deck) deck)))))""", None),
-    ("(riff-shuffle (list 1 2 3 4 5 6 7 8))", [1, 5, 2, 6, 3, 7, 4, 8]),
-    ("((repeat riff-shuffle) (list 1 2 3 4 5 6 7 8))",  [1, 3, 5, 7, 2, 4, 6, 8]),
-    ("(riff-shuffle (riff-shuffle (riff-shuffle (list 1 2 3 4 5 6 7 8))))", [1,2,3,4,5,6,7,8]),
-    ]
-
-lispy_tests = [
-    ("()", SyntaxError), ("(set! x)", SyntaxError), 
-    ("(define 3 4)", SyntaxError),
-    ("(quote 1 2)", SyntaxError), ("(if 1 2 3 4)", SyntaxError), 
-    ("(lambda 3 3)", SyntaxError), ("(lambda (x))", SyntaxError),
-    ("""(if (= 1 2) (define-macro a 'a) 
-     (define-macro a 'b))""", SyntaxError),
-    ("(define (twice x) (* 2 x))", None), ("(twice 2)", 4),
-    ("(twice 2 2)", TypeError),
-    ("(define lyst (lambda items items))", None),
-    ("(lyst 1 2 3 (+ 2 2))", [1,2,3,4]),
-    ("(if 1 2)", 2),
-    ("(if (= 3 4) 2)", None),
-    ("(define ((account bal) amt) (set! bal (+ bal amt)) bal)", None),
-    ("(define a1 (account 100))", None),
-    ("(a1 0)", 100), ("(a1 10)", 110), ("(a1 10)", 120),
-    ("""(define (newton guess function derivative epsilon)
-    (define guess2 (- guess (/ (function guess) (derivative guess))))
-    (if (< (abs (- guess guess2)) epsilon) guess2
-        (newton guess2 function derivative epsilon)))""", None),
-    ("""(define (square-root a)
-    (newton 1 (lambda (x) (- (* x x) a)) (lambda (x) (* 2 x)) 1e-8))""", None),
-    ("(> (square-root 200.) 14.14213)", True),
-    ("(< (square-root 200.) 14.14215)", True),
-    ("(= (square-root 200.) (sqrt 200.))", True),
-    ("""(define (sum-squares-range start end)
-         (define (sumsq-acc start end acc)
-            (if (> start end) acc (sumsq-acc (+ start 1) end (+ (* start start) acc))))
-         (sumsq-acc start end 0))""", None),
-    ("(sum-squares-range 1 3000)", 9004500500), ## Tests tail recursion
-    ("(call/cc (lambda (throw) (+ 5 (* 10 (throw 1))))) ;; throw", 1),
-    ("(call/cc (lambda (throw) (+ 5 (* 10 1)))) ;; do not throw", 15),
-    ("""(call/cc (lambda (throw) 
-         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 (escape 3)))))))) ; 1 level""", 35),
-    ("""(call/cc (lambda (throw) 
-         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 (throw 3)))))))) ; 2 levels""", 3),
-    ("""(call/cc (lambda (throw) 
-         (+ 5 (* 10 (call/cc (lambda (escape) (* 100 1))))))) ; 0 levels""", 1005),
-    ("(* 1i 1i)", -1), ("(sqrt -1)", 1j),
-    ("(let ((a 1) (b 2)) (+ a b))", 3),
-    ("(let ((a 1) (b 2 3)) (+ a b))", SyntaxError),
-    ("(and 1 2 3)", 3), ("(and (> 2 1) 2 3)", 3), ("(and)", True),
-    ("(and (> 2 1) (> 2 3))", False),
-    ("(define-macro unless (lambda args `(if (not ,(car args)) (begin ,@(cdr args))))) ; test `", None),
-    ("(unless (= 2 (+ 1 1)) (display 2) 3 4)", None),
-    (r'(unless (= 4 (+ 1 1)) (display 2) (display "\n") 3 4)', 4),
-    ("(quote x)", 'x'), 
-    ("(quote (1 2 three))", [1, 2, 'three']), 
-    ("'x", 'x'),
-    ("'(one 2 3)", ['one', 2, 3]),
-    ("(define L (list 1 2 3))", None),
-    ("`(testing ,@L testing)", ['testing',1,2,3,'testing']),
-    ("`(testing ,L testing)", ['testing',[1,2,3],'testing']),
-    ("`,@L", SyntaxError),
-    ("""'(1 ;test comments '
-     ;skip this line
-     2 ; more ; comments ; ) )
-     3) ; final comment""", [1,2,3]),
-    ]
-
-def test(tests, name=''):
-    "For each (exp, expected) test case, see if eval(parse(exp)) == expected."
-    fails = 0
-    for (x, expected) in tests:
-        try:
-            result = eval(parse(x))
-            print x, '=>', to_string(result)
-            ok = (result == expected)
-        except Exception as e:
-            print x, '=raises=>', type(e).__name__, e
-            ok = issubclass(expected, Exception) and isinstance(e, expected)
-        if not ok:
-            fails += 1
-            print 'FAIL!!!  Expected', expected
-    print '%s %s: %d out of %d tests fail.' % ('*'*45, name, fails, len(tests))
-
-if __name__ == '__main__':
-    from lis import *
-    test(lis_tests, 'lis.py')
-    from lispy import *
-    test(lis_tests+lispy_tests, 'lispy.py')
-
diff --git a/pytudes/py/pal.py b/pytudes/py/pal.py
deleted file mode 100644
index db8f509..0000000
--- a/pytudes/py/pal.py
+++ /dev/null
@@ -1,154 +0,0 @@
-import string, random, os, re, bisect
-
-"""Produce Panama-ish Palindromes. Copyright (C) 2002, Peter Norvig.
-See http://www.norvig.com/license.html and http://www.norvig.com/pal-alg.html"""
-
-def is_panama(p):
-    "Test if p is a Panama-ish palindrome."
-    def is_unique(seq): return len(seq) == len(dict(zip(seq, seq)))
-    return (p.endswith('Panama') and is_palindrome(p)
-	    and is_unique([s.strip() for s in p.split(',')]))
-
-def is_palindrome(phrase):
-    "Test if a phrase is a palindrome."
-    cphrase = canonical(phrase)
-    return cphrase == reverse(cphrase)
-
-def canonical(word, sub=re.compile('[^A-Za-z0-9]').sub):
-    "The canonical form for comparing: lowercase alphanumerics."
-    return sub('', word).lower()
-
-def read_dict(filename='npdict.txt'):
-    "Read the file into global variables _fw and _bw and _truename."
-    global _fw, _bw, _truename
-    _fw, _bw, _truename = [], [], {'': ''}
-    for word in open(filename).read().splitlines():
-        w = canonical(word)
-        _fw.append(w)
-        _bw.append(reverse(w))
-        _truename[w] = word
-    _fw.sort(); _bw.sort()
-    return len(_fw), len(_bw), len(_truename)
-
-def update(obj, **entries): obj.__dict__.update(entries); return obj
-
-class PalDict:
-    """A dictionary from which you can find canonical words that start or end
-    with a given canonical substring, and find the true name of a
-    canonical word."""
-    def __init__(self, fw=None, bw=None, truename=None):
-        update(self, fw=fw or _fw, bw=bw or _bw, truename=truename or _truename)
-
-    def startswith(self, prefix, k=100):
-        """Return up to k canonical words that start with prefix.
-        If there are more than k, choose from them at random."""
-        return k_startingwith(k, self.fw, prefix)
-
-    def endswith(self, suffix, k=100):
-        """Return up to k canonical words that end with suffix.
-        If there are more than k, choose from them at random.
-        Both the suffix and the word returned are reversed."""
-        return k_startingwith(k, self.bw, suffix)
-
-def k_startingwith(k, words, prefix):
-    """Choose up to k words that match the prefix (choose randomly if > k)."""
-    start = bisect.bisect(words, prefix)
-    end = bisect.bisect(words, prefix + 'zzzz')
-    n = end - start
-    if k >= n:
-        results = words[start:end]
-        random.shuffle(results)
-    else: # Should really try to avoid duplicates
-        results = [words[random.randrange(start, end)] for i in range(k)]
-    return results
-
-class Panama:
-    def __init__(self, L='A man, a plan', R='a canal, Panama', dict=None):
-        left = [canonical(w) for w in L.split(', ')]
-        right = [canonical(reverse(w)) for w in reverse(R.split(', '))]
-        update(self, left=left, right=right, dict=dict or PalDict(), best=0, 
-               seen={}, diff=len(''.join(left)) - len(''.join(right)))
-        for word in left + map(reverse, right):
-            self.seen[word] = 1
-
-    def missing(self, k=20):
-        """Return the substring that is missing, and candidate words."""
-        if self.diff >= 0: # Left is longer, missing on right
-            substr =  self.left[-1][-self.diff:]
-            return substr, self.dict.endswith(substr, k)
-        else: # Right is longer, missing on left
-            substr =  self.right[-1][self.diff:]
-            return substr, self.dict.startswith(substr, k)
-
-    def search(self, k=200):
-        "Search for palindromes; consider at most k words at each level."
-        self.stack = [self.missing(k)]
-        while self.stack:
-            substr, words = self.stack[-1]
-            if is_palindrome(substr):
-                self.report()
-            if words:
-                self.extend(words.pop(), k)
-            elif not self.backtrack():
-                return
-
-    def extend(self, word, k):
-        "Add a new word (unless we've already seen it)."
-        if self.diff >= 0: # Left is longer, add to right
-            fword = reverse(word)
-            if fword in self.seen: return
-            self.diff -= len(fword)
-            self.seen[fword] = 1
-            self.right.append(word)
-            self.stack.append(self.missing(k))
-        else: # Right is longer, add to left
-            if word in self.seen: return
-            self.diff += len(word)
-            self.seen[word] = 1
-            self.left.append(word)
-            self.stack.append(self.missing(k))
-
-    def backtrack(self):
-        "Remove the last word added; return 0 if can't backtrack"
-        if self.diff >= 0: # Left is longer, pop from left
-            if not self.left: return 0
-            word = self.left.pop()
-            self.diff -= len(word)
-            del self.seen[word]
-        else: # Right is longer, pop from right
-            if not self.right: return 0
-            word = self.right.pop()
-            self.diff += len(word)
-            del self.seen[reverse(word)]
-        self.stack.pop()
-        return 1
-
-    def report(self):
-        "Write current state to log file."
-        if len(self) > self.best + 200:
-            self.best = len(self)
-            print self.best
-            self.bestphrase = str(self)
-            assert is_panama(self.bestphrase)
-            f = open('pallog%d.txt' % os.getpid(), 'w')
-            f.write(self.bestphrase + '\n')
-            f.close()
-
-    def __len__(self):
-        return len(self.left) + len(self.right)
-
-    def __str__(self):
-        truename = self.dict.truename
-        lefts = [truename[w] for w in self.left]
-        rights = [truename[reverse(w)] for w in reverse(self.right[:])]
-        return ', '.join(lefts + ['*****'] + rights)
-
-def reverse(x):
-    "Reverse a list or string."
-    if type(x) == type(''):
-        return ''.join(reverse(list(x)))
-    else:
-        x.reverse()
-        return x
-
-if __name__ == '__main__': read_dict(); p = Panama(); p.search()
diff --git a/pytudes/py/pal2.py b/pytudes/py/pal2.py
deleted file mode 100644
index 9436ead..0000000
--- a/pytudes/py/pal2.py
+++ /dev/null
@@ -1,262 +0,0 @@
-import random, re, bisect, time
-
-"""Produce Panama-ish Palindromes. Copyright (C) 2002-2008, Peter Norvig."""
-
-################ Checking for Palindromes
-
-def is_panama(s):
-    "Test if string s is a Panama-ish palindrome."
-    return is_palindrome(s) and is_unique(phrases(s))
-
-def is_palindrome(s):
-    "Test if a string is a palindrome."
-    s1 = canonical(s)
-    return s1 == reversestr(s1)
-
-def phrases(s):
-    "Break a string s into comma-separated phrases."
-    return [phrase.strip() for phrase in s.split(',')]
-
-def canonical(word, sub=re.compile('''[-* \t\n\r.,;!?:()`"']''').sub):
-    "The canonical form for comparing: lowercase, no blanks or punctuation."
-    return sub('', word).lower()
-
-################ Utilities
-
-def reversestr(x):
-    "Reverse a string."
-    return x[::-1]
-
-def is_unique(seq):
-    "Return true if seq has no duplicate elements."
-    return len(seq) == len(set(seq))
-
-def update(obj, **entries):
-    "Change attributes of obj, according to the keyword args."
-    obj.__dict__.update(entries)
-    return obj
-
-################ Reading in a dictionary
-
-class PalDict:
-    """A dictionary from which you can find canonical words that start or end
-    with a given canonical substring, and find the true name of a
-    canonical word with d.truename[canonicalword]."""
-    
-    def __init__(self, k=1000, filename='npdict.txt'):
-        words, rwords, truename = [], [], {'': '', 'panama': 'Panama!'}
-        for tword in open(filename).read().splitlines():
-            word = canonical(tword)
-            words.append(word)
-            rwords.append(reversestr(word))
-            truename[word] = tword
-        words.sort()
-        rwords.sort()
-        update(self, k=k, words=words, rwords=rwords, truename=truename,
-               reversibles={}, rangek=range(k), tryharder=False)
-
-    def startswith(self, prefix):
-        """Return up to k canonical words that start with prefix.
-        If there are more than k, choose from them at random."""
-        return self._k_startingwith(self.words, prefix)
-
-    def endswith(self, rsuffix):
-        """Return up to k canonical words that end with the reversed suffix.
-        If you want words ending in 'ing', ask for d.endswith('gni').
-        If there are more than k, choose from them at random."""
-        return map(reversestr, self._k_startingwith(self.rwords, rsuffix))
-
-    def __contains__(self, word):
-        return word in self.truename
-
-    def reversible_words(self):
-        "Find words that have a reverse in the dict, like {'Camus': 'Sumac'}"
-        if not self.reversibles:
-            reversibles = self.reversibles
-            for rw in self.rwords:
-                if rw in self:
-                    w = reversestr(rw)
-                    if w != rw and w not in reversibles:
-                        reversibles[w] = rw
-            self.reversibles = reversibles
-        return self.reversibles
-
-    def _k_startingwith(self, words, prefix):
-        start = bisect.bisect_left(words, prefix)
-        end = bisect.bisect(words, prefix + 'zzzz')
-        n = end - start
-        if self.k >= n: # get all the words that start with prefix
-            results = words[start:end]
-        else: # sample from words starting with prefix 
-            indexes = random.sample(xrange(start, end), self.k)
-            results = [words[i] for i in indexes]
-        random.shuffle(results)
-        ## Consider words that are prefixes of the prefix.
-        ## This is very slow, so don't use it until late in the game.
-        if self.tryharder:
-            for i in range(3, len(prefix)):
-                w = prefix[0:i]
-                if ((words == self.words and w in self.truename) or
-                    (words == self.rwords and reversestr(w) in self.truename)):
-                    results.append(w)
-        return results
-
-paldict = PalDict() 
-
-def anpdictshort():
-    "Find the words that are valid when every phrase must start with 'a'"
-    def segment(word):  return [s for s in word.split('a') if s]
-    def valid(word): return all(reversestr(s) in segments for s in segment(word))
-    words = map(canonical, file('anpdict.txt'))
-    segments = set(s for w in words for s in segment(canonical(w)))
-    valid_words = [paldict.truename[w] for w in words if valid(w)]
-    file('anpdict-short.txt', 'w').write('\n'.join(valid_words))
-
-################ Search for a palindrome
-
-class Panama:
-    def __init__(self, L='A man, a plan', R='a canal, Panama', dict=paldict):
-        ## .left and .right hold lists of canonical words
-        ## .diff holds the number of characters that are not matched,
-        ##  positive for words on left, negative for right.
-        ## .stack holds (action, side, arg) tuples
-        update(self, left=[], right=[], best=0, seen={}, diff=0, stack=[],
-               used_reversibles=False, starttime=time.clock(), dict=dict)
-        for word in L.split(','):
-            self.add('left', canonical(word))
-        for rword in reversestr(R).split(','):
-            self.add('right', canonical(reversestr(rword)))
-        self.consider_candidates()
-        
-    def search(self, steps=50000000):
-        "Search for palindromes."
-        for _ in xrange(steps):
-            if not self.stack:
-                return 'done'
-            action, dir, substr, arg = self.stack[-1]
-            if action == 'added': # undo the last word added
-                self.remove(dir, arg)
-            elif action == 'trying' and arg: # try the next word if there is one
-                self.add(dir, arg.pop()) and self.consider_candidates()
-            elif action == 'trying' and not arg: # otherwise backtrack
-                self.stack.pop()
-            else:
-                raise ValueError(action)
-
-    def add(self, dir, word):
-        "add a word"
-        if word in self.seen:
-            return False
-        else:
-            getattr(self, dir).append(word)
-            self.diff += factor[dir] * len(word)
-            self.seen[word] = True
-            self.stack.append(('added', dir, '?', word))
-            return True
-
-    def remove(self, dir, word):
-        "remove a word"
-        oldword = getattr(self, dir).pop()
-        assert word == oldword
-        self.diff -= factor[dir] * len(word)
-        del self.seen[word]
-        self.stack.pop()
-        
-    def consider_candidates(self):
-        """Push a new state with a set of candidate words onto stack."""
-        if self.diff > 0: # Left is longer, consider adding on right
-            dir = 'right'
-            substr =  self.left[-1][-self.diff:]
-            candidates = self.dict.endswith(substr)
-        elif self.diff < 0: # Right is longer, consider adding on left
-            dir = 'left'
-            substr =  reversestr(self.right[-1][0:-self.diff])
-            candidates = self.dict.startswith(substr)
-        else: # Both sides are same size
-            dir = 'left'
-            if not self.used_reversibles:
-                self.report()
-                self.add_reversibles()
-            substr = ''
-            candidates = self.dict.startswith('')
-        if substr == reversestr(substr):
-            self.report()
-        self.stack.append(('trying', dir, substr, candidates))
-
-    def add_reversibles(self):
-        "Add in reversible words."
-        print 'using reversibles ...'
-        for (word, rword) in self.dict.reversible_words().items():
-            if word not in self.seen and rword not in self.seen:
-                self.add('left', word)
-                self.add('right', rword)
-        self.used_reversibles = True
-        self.stack = []
-        print '...done'
-                
-    def report(self):
-        "Report a new palindrome to log file (if it is sufficiently big)."
-        N = len(self)
-        if N > 13333:
-            self.dict.tryharder = True
-        if N > self.best and (N > 12500 or N > self.best+500):
-            self.best = len(self)
-            self.bestphrase = str(self)
-            print '%5d phrases (%5d words) in %3d seconds' % (
-                self.best, self.bestphrase.count(' ')+1, time.clock() - self.starttime)
-            assert is_panama(self.bestphrase)
-            f = open('pallog%d.txt' % (id(self) % 10000), 'w')
-            f.write(self.bestphrase + '\n')
-            f.close()
-
-    def __len__(self):
-        return len(self.left) + len(self.right)
-
-    def __str__(self):
-        truename = self.dict.truename
-        lefts = [truename[w] for w in self.left]
-        rights =[truename[w] for w in self.right]
-        return ', '.join(lefts + rights[::-1])
-
-factor = {'left': +1, 'right': -1}
-
-# Note that we only allow one truename per canonical name.  Occasionally
-# this means we miss a good word (as in "a node" vs. "an ode"), but there
-# are only 665 of these truename collisions, and most of them are of the
-# form "a mark-up" vs. "a markup" so it seemed better to disallow them.
-
-################ Unit Tests
- 
-def tests(p=Panama()):
-    assert is_panama('A man, a plan, a canal, Panama.')
-    assert is_panama('''A (man),     a   plan,,;, a ```canal?'' -- Panama!''')
-    assert not is_panama('A man, a plan, a radar, a canal, Panama.')
-    assert is_palindrome('A man, a plan, a canal, Panama.')
-    assert is_palindrome('radar, radar? radar!')
-    assert not is_palindrome('radars')
-    assert phrases('A man, a plan, Panama') == ['A man', 'a plan', 'Panama']
-    assert canonical('A man, a plan, a canal, Panama') == 'amanaplanacanalpanama'
-    assert reversestr('foo') == 'oof'
-    assert is_unique([1, 2, 3])
-    assert not is_unique([1, 2, 2])
-    d = p.dict
-    def sameset(a, b): return set(a) == set(b)
-    assert 'panama' in d
-    assert d.words[0] in d
-    assert d.words[-1] in d
-    assert sameset(d.startswith('aword'), ['awording', 'awordbreak',
-        'awordiness', 'awordage', 'awordplay', 'awordlore', 'awordbook',
-        'awordlessness', 'aword', 'awordsmith'])
-    assert sameset(d.endswith('ytisob'), ['aglobosity', 'averbosity',
-        'asubglobosity', 'anonverbosity', 'agibbosity'])
-    d.tryharder = True
-    assert sameset(d.startswith('oklahoma'), ['oklahoma', 'okla'])
-    d.tryharder = False
-    assert d.startswith('oklahoma') == ['oklahoma']
-    assert d.startswith('fsfdsfdsfds') == []
-    print 'all tests pass'
-
-if __name__ == '__main__': 
-    p = Panama();
-    tests(p)
-    p.search()
diff --git a/pytudes/py/pal3.py b/pytudes/py/pal3.py
deleted file mode 100644
index 89e8571..0000000
--- a/pytudes/py/pal3.py
+++ /dev/null
@@ -1,170 +0,0 @@
-from collections import Counter, deque
-import re
-
-class PhraseDict(dict):
-    """A dictionary of {letters: phrase}, such as {'donaldeknuth': 'Donald E. Knuth'}, with:
-    .prefixes: Counter of {'pre': n} where n is the number of keys that start with 'pre'
-    .suffixes: Counter of {'xes': n} where n is the number of keys that end with 'xes'"""
-    def __init__(self, phrases):
-        for phrase in phrases:
-            phrase = phrase.strip()
-            self[letters(phrase)] = phrase
-        self.prefixes = Counter(x for p in self for x in prefixes(p))
-        self.suffixes = Counter(x for p in self for x in suffixes(p))
-        
-def prefixes(phrase): return [phrase[:i] for i in range(1, len(phrase) + 1)]
-
-def suffixes(phrase): return [phrase[-i:] for i in range(1, len(phrase) + 1)]
-
-def letters(phrase, sub=re.compile(r'[\W]+').sub):
-    "Remove all the non-letters from phrase; return lowercase version."
-    return sub('', phrase).lower()
-
-DICT = PhraseDict(open('npdict.txt'))
-
-class Panama:
-    """Panama represents a palindrome, or a state in searching for one.
-    It has .left and .right to hold the phrases that are chosen,
-    and .L and .R to hold the current partial phrases in the middle (still working on these).
-    Also, a .set of all complete phrases, and the .dict of allowable phrases to choose from."""
-    
-    def __init__(self, left=['aman', 'aplan'], L='aca', R='', right=['acanal', 'panama'], dict=DICT):
-        assert cat(left + [L]) == cat([R] + right)[::-1]
-        self.left   = list(left)        # list of complete phrases on left
-        self.L      = L                 # an incomplete phrase on left
-        self.R      = R                 # an incomplete phrase on right
-        self.right  = deque(right)      # deque of complete phrases on right
-        self.dict   = dict              # a {letters: actual_phrase} mapping
-        self.set    = set(left + right) # a set of all complete phrases in palindrome
-        self.best   = []                # list of phrases in longest palindrome found
-        self.Nshown = 0                 # the number of phrases shown in the previous printout
-        self.i      = 0                 # the number of steps taken in the search
-        self.check()
-
-    def __str__(self): return self.original_phrases(self.best)
-    
-    def original_phrases(self, phrases): return ', '.join(self.dict[phrase] for phrase in phrases)
-
-    def search(self, steps=10**5):
-        """Depth-first search for palindromes. From the current state, find all applicable actions.
-        Do the first one, and put on the stack reminders to undo it and try the others,
-        but first search deeper from the result of the first action."""
-        stack = [self.applicable_actions()]
-        for self.i in range(steps):
-            if not stack: 
-                return
-            command = stack.pop()
-            if isinstance(command, UndoCommand):
-                self.undo(command)
-            elif command:
-                act = command.pop()
-                self.do(act)
-                self.check()
-                stack.extend([command, UndoCommand(act), self.applicable_actions()])
-                
-    def do(self, act):
-        "Modify the current state by adding a letter, or finishing a phrase."
-        if act == ',': # finish phrase on left
-            self.set.add(self.L)
-            self.left.append(self.L)
-            self.L = ''
-        elif act == ';': # finish phrase on right
-            self.set.add(self.R)
-            self.right.appendleft(self.R)
-            self.R = ''
-        else: # add a letter
-            self.L = self.L + act 
-            self.R = act + self.R
-    
-    def undo(self, act):
-        "Modify the current state by undoing an action that was previously done."
-        if act == ',': # unfinish phrase on left
-            assert self.L == ''
-            self.L = self.left.pop()
-            self.set.remove(self.L)
-        elif act == ';': # unfinish phrase on right
-            assert self.R == ''
-            self.R = self.right.popleft()
-            self.set.remove(self.R)
-        else: # remove a letter
-            self.L = self.L[:-1]
-            self.R = self.R[1:]
-            
-    def check(self):
-        "Check to see if current state is a palindrome, and if so, record it and maybe print."
-        if not self.is_palindrome(): return
-        N = len(self.left) + len(self.right) 
-        if N > len(self.best):
-            self.best = self.left + list(self.right)
-            if N - self.Nshown > 1000 or (N > 14000 and N - self.Nshown > 100) or N > 14500:
-                self.Nshown = N
-                print(self.report())
-            
-    def report(self):
-        N = len(self.best)
-        nwords = N + sum(self.dict[p].count(' ') for p in self.best)
-        nletters = sum(len(p) for p in self.best)
-        return ('Pal: {:6,d} phrases, {:6,d} words, {:6,d} letters (at step {:,d})'
-                .format(N, nwords, nletters, self.i+1))
-        
-    def applicable_actions(self):
-        L, R, D = self.L, self.R, self.dict
-        actions = []
-
-        def score(A): return D.prefixes[L+A] * D.suffixes[A+R]
-        if self.is_allowed(L):
-            actions.append(',')
-        if self.is_allowed(R):
-            actions.append(';')
-        for A in sorted(alphabet, key=score):
-            if score(A) > 0:
-                actions.append(A)    
-
-        return actions
- 
-    def is_allowed(self, phrase): return phrase in self.dict and phrase not in self.set
-        
-    def is_palindrome(self): 
-        "Is this a palindrome? (Does any extra .L or .R match the other side?)"
-        return ((self.L == '' and self.left[-1].endswith(self.R)) or 
-                (self.R == '' and self.right[0].startswith(self.L)))
-
-alphabet    = 'abcdefghijklmnopqrstuvwxyz'
-cat         = ''.join
-UndoCommand = str
-DoCommand   = list
-                      
-################ Unit Tests
-
-def test1():
-    assert prefixes('hello') == ['h', 'he', 'hel', 'hell', 'hello']
-    assert suffixes('hello') == ['o', 'lo', 'llo', 'ello', 'hello']
-    assert letters('a man') == 'aman'
-    assert letters('an elk') == 'anelk'
-    assert letters('Mr. T') == 'mrt'
-    assert letters('Donald E. Knuth') == 'donaldeknuth'
-    assert len(DICT) == 125512
-    assert 'panama' in DICT
-    assert 'aman' in DICT
-    assert 'threemen' not in DICT
-    assert DICT['acanal'] == 'a canal'
-    return 'ok'
-
-def test2():
-    p1 = Panama()
-    assert p1.is_palindrome()
-    assert str(p1) == 'a man, a plan, a canal, Panama'
-    p2 = Panama(['aman','aplan'], 'acadd','dd', ['acanal', 'panama'])
-    assert not p2.is_palindrome()
-    p3 = Panama(['maya'], '', '', ['ayam'])
-    assert p3.is_palindrome()
-    assert str(p3) == 'Maya, a yam'
-    return 'ok'
-
-if __name__ == '__main__': 
-    p = Panama();
-    test1()
-    test2()
-    p.search(10**6)
-    print(p.report())
-    print(str(p))
diff --git a/pytudes/py/parse.py b/pytudes/py/parse.py
deleted file mode 100644
index 8c7e4ea..0000000
--- a/pytudes/py/parse.py
+++ /dev/null
@@ -1,52 +0,0 @@
-grammar = {
-  'Noun': ['stench', 'wumpus'],
-  'Verb': ['is', 'smell'],
-  'Adjective': ['dead', 'smelly'],
-  'Adverb': ['left', 'back'],
-  'Pronoun': ['me', 'you'],
-  'Name': ['John', 'Mary'],
-  'Article': ['the', 'a'],
-  'Preposition': ['to', 'in'],
-  'Conjunction': ['and', 'or'],
-  'Digit': ['0', '1'],
-  
-  'S': [['NP', 'VP'], ['S', 'Comjunction', 'S']],
-  'NP': ['Pronoun', 'Noun', ['Article', 'Noun'], ['Digit', 'Digit'], 
-         ['NP', 'PP'], ['NP', 'RelClause']],
-  'VP': ['Verb', ['VP', 'NP'], ['VP', 'Adjective'], ['VP', 'PP'], 
-         ['VP', 'Adverb']],
-  'PP': [['Preposition', 'NP']],
-  'RelClause': [['that', 'VP']]
-  }
-  
-
-def parse(forest, grammar):
-    if len(forest) == 1 and category(forest[0]) == 'S':
-        return forest[0]
-    for i in range(len(forest)):
-        for lhs in grammar.keys():
-            for rhs in grammar[lhs]:
-		rhs = mklist(rhs)
-		n = len(rhs)
-		subsequence = forest[i:i+n]
-		if match(subsequence, rhs):
-                    print subsequence, lhs, '=>', rhs
-		    forest2 = forest[:]
-		    forest2[i:i+n] = [(lhs, subsequence)]
-		    result = parse(forest2, grammar)
-		    if result != None:
-			return result
-    return None
-
-def mklist(x):
-    if type(x) == type([]): return x
-    else: return [x]
-
-def match(forest, rhs):
-    for i in range(len(rhs)):
-        if category(forest[i]) != rhs[i] and forest[i] != rhs[i]: return 0
-    return 1
-
-def category(forest):
-    if type(forest) == type(()): return forest[0]
-    else: return 'word'
diff --git a/pytudes/py/py2html.py b/pytudes/py/py2html.py
deleted file mode 100644
index 896d0de..0000000
--- a/pytudes/py/py2html.py
+++ /dev/null
@@ -1,110 +0,0 @@
-"""Pretty-print Python code to colorized, hyperlinked html.
-
-In python, do:
-    py2html.convert_files(['file1.py', 'file2.py', ...]) 
-From the shell, do:
-    python py2html.py *.py"""
-
-import re, string, time, os
-
-
-id = r'[a-zA-Z_][a-zA-Z_0-9]*' ## RE for a Python identifier
-g1, g2, g3, g4 = r'\1 \2 \3 \4'.split() ## groups for re.matches
-def b(text): return '%s' % text
-def i(text): return '%s' % text
-def color(rgb, text): return '%s' % (rgb, text)
-def link(url, anchor): return '%s' % (url, anchor)
-def hilite(text, bg="ffff00"):
-    return '%s' % (
-        bg, text, text)
-
-def modulelink(module, baseurl=''):
-    """Hyperlink to a module, either locally or on python.org"""
-    if module+'.py' not in local_files:
-        baseurl = 'http://www.python.org/doc/current/lib/module-'
-    return link(baseurl+module+'.html', module)
-
-def importer(m):
-    "Turn text such as 'utils, math, re' into a string of HTML links."
-    modules = [modulelink(mod.strip()) for mod in m.group(2).split(',')]
-    return (m.group(1) + ', '.join(modules) + m.group(3))
-
-def find1(regex, str):
-    return (re.findall(regex, str) or [' '])[0]
-
-def convert_files(filenames, local_filenames=None, tblfile='readme.htm'):
-    "Convert files of python code to colorized HTML."
-    global local_files
-    local_files = local_filenames or filenames
-    summary_table = {}
-    for f in filenames:
-        fulltext = '\n'.join(map(string.rstrip, open(f).readlines()))
-        text = fulltext
-        for (pattern, repl) in replacements:
-            text = re.sub(pattern, repl, text)
-        text = '<>
%s
<