12. Integer to Roman

Seven different symbols represent Roman numerals with the following values:

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.

Example 1:

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:

50 = L
 8 = VIII

Example 3:

1000 = M
 900 = CM
  90 = XC
   4 = IV

Constraints:

• 1 <= num <= 3999

Approach 01: Greedy with Symbols

class Solution {
public:
    string intToRoman(int num) {
        vector> syms = {
            {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 res = "";
        for (auto& sym : syms) {
            while (num >= sym.first) {
                res += sym.second;
                num -= sym.first;
            }
        }
        return res;
    }
};

class Solution:
    def intToRoman(self, num: int) -> str:
        syms = [
            (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")
        ]
        res = []
        for val, sym in syms:
            if num == 0: break
            count, num = divmod(num, val)
            res.append(sym * count)
        return "".join(res)

class Solution {
    public String intToRoman(int num) {
        int[] values = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
        String[] symbols = {"M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"};
        StringBuilder res = new StringBuilder();
        for (int i = 0; i < values.length && num > 0; i++) {
            while (num >= values[i]) {
                num -= values[i];
                res.append(symbols[i]);
            }
        }
        return res.toString();
    }
}