Problem32.py

# Code by @AmirMotefaker

# projecteuler.net
# https://projecteuler.net/problem=32

# Pandigital products
# Problem 32

# We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once;
# for example, the 5-digit number, 15234, is 1 through 5 pandigital.

# The product 7254 is unusual, as the identity, 39 × 186 = 7254,
# containing multiplicand, multiplier, and product is 1 through 9 pandigital.

# Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.

# HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

# Pandigital Product: A Pandigital Number is number which makes the use of all digits 1 to 9 exactly once. 
# Examples: 
# Input : 7254
# Output : Yes
# 39 * 186 = 7254. We can notice that
# the three numbers 39, 186 and 7254
# together have all digits from 1 to 9.

# This solution contains:
# 3 x 1 = 3
# 3 x 2 = 6
# 3 x 3 = 9
# 3 x 4 = 12
# 3 x 5 = 15

# 4 x 1 = 4
# 4 x 2 = 8
# 4 x 3 = 12
# ...

# In the above looping process after I had seen that the number 12 is a two digit number,
# and if I have breaked the loop there itself, then we would have saved one iteration.
# Obviously as we are using python even though you will break from one loop another loop will be working.
# If you break the loop at 12(3 x 4) then we will again start at 4 x 1 = 4 and so on. 
# Now in this we will break at 12(4 x 3) again.


import time
start_time = time.time()   #Time at the start of program execution

products = set()   # store the products in a set to avoid duplicates

checked_later = set('123456789')   # Digits from 1-9 which will be checking later

for i in range(9):   # single digit multiplicand
	for j in range(999,9999):
		s = str(i)+str(j)+str(i*j)
		if len(s) == 9 and set(s) == checked_later:
			products.add(i*j)
		elif len(s) > 9:break

for i in range(9,99):   # double digit multiplicand
	for j in range(99,999):
		s = str(i)+str(j)+str(i*j)
		if len(s) == 9 and set(s) == checked_later:
			products.add(i*j)
		elif len(s)>9: break

print ("Sum of all Products as a 1 through 9 pandigital =", sum(products))

end_time = time.time()   #Time at the end of execution
print ("Time of program execution:", (end_time - start_time))   # Time of program execution



### Answer:  45228