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integer-to-roman

README.md

Integer to Roman

Difficulty

Medium

Problem

Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.

Symbol       Value
I             1
V             5
X             10
L             50
C             100
D             500
M             1000
For example, 2 is written as II in Roman numeral, just two one's added together. 12 is written as XII, which is simply X + II. The number 27 is written as XXVII, which is XX + V + II.

Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX. There are six instances where subtraction is used:

I can be placed before V (5) and X (10) to make 4 and 9. X can be placed before L (50) and C (100) to make 40 and 90. C can be placed before D (500) and M (1000) to make 400 and 900. Given an integer, convert it to a roman numeral.

Example 1

Input: num = 3
Output: "III"

Example 2

Input: num = 4
Output: "IV"

Example 3

Input: num = 9
Output: "IX"

Example 4

Input: num = 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.

Example 5

Input: num = 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.

Constraints

1 <= num <= 3999

Solutions (Click to expand)

Explanation

Divide Number into Roman Numerals

To make it easier to decode numbers into roman numerals, we will use to arrays of the same length, values and roman, where values[i] is the value of roman numeral roman[i]. Arrays are used here since we will we need to order the roman numerals from biggest to smallest. An ordered map or a LinkedHashMap would would here as well.

To write a number in roman numerals we first have to use the greatest numberals we can without exceeding the number's value, subtract that value from the number and repeat scaling down roman numerals until we reach a number of 0. We can be more efficient by diving our number into roman numerals instead of subtracting.

Using a roman numeral that does not exceed the value of the number, we will add num / value, where num is the current number and value is the value of the current roman numeral, of value roman numerals to our roman number. Taking the remaninder, we will scaled down to smaller roman numerals until our number reaches 0

num = 1994

string = ""

1994 / 1000 = 1 // add 1 "M" to our string

994 / 900 = 1 // add 1 "CM" to our string

94 / 90 = 1 // add 1 "XC" to our string

4 / 4 = 1 // add 1 "IV" to our string

0

"MCMXCIV"