12. Integer to Roman

Description of the 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"
Explanation: 3 is represented as 3 ones.

Example 2:

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

Example 3:

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

Constraints:

• 1 <= num <= 3999

Solution

Explanation

Subtraction occurs in only six instances (i.e. CM, CD, XC, XL, IX, IV).

To convert an integer to a roman number, we shall consider larger numbers first (see the code below).

Code (Rust)

impl Solution {
    pub fn int_to_roman(num: i32) -> String {
        let mut num = num;
        let mut s = String::from("");
        
        while num > 0 {
            if 1000 <= num && num <= 3999 {
                s.push_str("M");
                num -= 1000;
            } else if 900 <= num && num < 1000 {
                s.push_str("CM");
                num -= 900;
            } else if 500 <= num && num < 900 {
                s.push_str("D");
                num -= 500;
            } else if 400 <= num && num < 500 {
                s.push_str("CD");
                num -= 400;
            } else if 100 <= num && num < 400 {
                s.push_str("C");
                num -= 100;
            } else if 90 <= num && num < 100 {
                s.push_str("XC");
                num -= 90;
            } else if 50 <= num && num < 90 {
                s.push_str("L");
                num -= 50;
            } else if 40 <= num && num < 50 {
                s.push_str("XL");
                num -= 40;
            } else if 10 <= num && num < 40 {
                s.push_str("X");
                num -= 10;
            } else if 9 <= num && num < 10 {
                s.push_str("IX");
                num -= 9;
            } else if 5 <= num && num < 9 {
                s.push_str("V");
                num -= 5;
            } else if 4 <= num && num < 5 {
                s.push_str("IV");
                num -= 4;
            } else {
                s.push_str("I");
                num -= 1;
            }
        }
        
        return s;
    }
}

Code (Java)

class Solution {
    public String intToRoman(int num) {
        StringBuilder sb = new StringBuilder();
        
        while (num > 0) {
            if (1000 <= num && num <= 3999) {
                sb.append("M");
                num -= 1000;
            } else if (900 <= num && num < 1000) {
                sb.append("CM");
                num -= 900;
            } else if (500 <= num && num < 900) {
                sb.append("D");
                num -= 500;
            } else if (400 <= num && num < 500) {
                sb.append("CD");
                num -= 400;
            } else if (100 <= num && num < 400) {
                sb.append("C");
                num -= 100;
            } else if (90 <= num && num < 100) {
                sb.append("XC");
                num -= 90;
            } else if (50 <= num && num < 90) {
                sb.append("L");
                num -= 50;
            } else if (40 <= num && num < 50) {
                sb.append("XL");
                num -= 40;
            } else if (10 <= num && num < 40) {
                sb.append("X");
                num -= 10;
            } else if (9 <= num && num < 10) {
                sb.append("IX");
                num -= 9;
            } else if (5 <= num && num < 9) {
                sb.append("V");
                num -= 5;
            } else if (4 <= num && num < 5) {
                sb.append("IV");
                num -= 4;
            } else {
                sb.append("I");
                num -= 1;
            }
        }

        return sb.toString();
    }
}