12. Integer to Roman

1. Description

Seven different symbols represent Roman numerals with the following values:

Symbol Value
I 1
V 5
X 10
L 50
C 100
D 500
M 1000

Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules:

• If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral.
• If the value starts with 4 or 9 use the subtractive form representing one symbol subtracted from the following symbol, for example, 4 is 1 (I) less than 5 (V): IV and 9 is 1 (I) less than 10 (X): IX. Only the following subtractive forms are used: 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD) and 900 (CM).
• Only powers of 10 (I, X, C, M) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (V), 50 (L), or 500 (D) multiple times. If you need to append a symbol 4 times use the subtractive form.

Given an integer, convert it to a Roman numeral.

2. Example

Example 1

Input: num = 3749
Output: “MMMDCCXLIX”
Explanation:
3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M)
700 = DCC as 500 (D) + 100 (C) + 100 (C)
40 = XL as 10 (X) less of 50 (L)
9 = IX as 1 (I) less of 10 (X)
Note: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places

Example 2

Input: num = 58
Output: “LVIII”
Explanation:
50 = L
8 = VIII

Example 3

Input: num = 1994
Output: “MCMXCIV”
Explanation:
1000 = M
900 = CM
90 = XC
4 = IV

3. Constraints

• 1 <= num <= 3999

4. Solutions

Greedy

n = num
Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    string intToRoman(int num) {
        array<pair<int, string>, 13> expressions{
            {{1000, "M"},
             {900, "CM"},
             {500, "D"},
             {400, "CD"},
             {100, "C"},
             {90, "XC"},
             {50, "L"},
             {40, "XL"},
             {10, "X"},
             {9, "IX"},
             {5, "V"},
             {4, "IV"},
             {1, "I"}}};

        string roman;
        int i = 0;
        for (const auto &[value, symbol] : expressions) {
            while (num >= value) {
                num -= value;
                roman += symbol;
            }
        }

        return roman;
    }
};