0012. Integer to Roman

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

Analysis

This question is finding the relationship of Roma Integer to decimal integer.

for 1 to 9 (one digit): 1: I, 2: II, 3: III, 4: IV, 5: V, 6: VI, 7: VII, 8: VIII, 9: IX.

for 10 to 99 (two digits): 10: X, 20: XX, 30: XXX, 40: XL, 50: L, 60: LX, 70: LXX, 80: LXXX, 90: XC.

for 100 to 999 (three digits): 100: C, 200: CC, 300: CCC, 400: CD, 500: D, 600: DC, 700: DCC, 800: DCCC, 900: CM.

for 1000 to 3999 (four digits): 1000: M, 2000: MM, 3000: MMM

It can generate any number from the map: e.g. 1234 1: M 2: CC 3: XXX 4: IV -> 1234 = MCCXXXIV

Code

class Solution {
public:
    string intToRoman(int num) {
        int val[] = {
            1000,
            900, 500, 400, 100,
            90, 50, 40, 10,
            9, 5, 4, 1
        };

        string repr[] = {
            "M",
            "CM", "D", "CD", "C",
            "XC", "L", "XL", "X",
            "IX", "V", "IV", "I"
        };

        string res;
        for (int i = 0; i < 13; ++i) {
            while (num >= val[i]) {
                num -= val[i];
                res += repr[i];
            }
        }
        return res;
    }
};

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Last update: April 1, 2022