12.IntegerToRoman.cpp

/*
 * @lc app=leetcode id=12 lang=cpp
 *
 * [12] Integer to Roman
 *
 * https://leetcode.com/problems/integer-to-roman/description/
 *
 * algorithms
 * Medium (54.91%)
 * Likes:    1218
 * Dislikes: 2746
 * Total Accepted:    384.6K
 * Total Submissions: 694.3K
 * Testcase Example:  '3'
 *
 * 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, two is written as II in Roman numeral, just two one's added
 * together. Twelve is written as, XII, which is simply X + II. The number
 * twenty seven 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. Input is guaranteed to be
 * within the range from 1 to 3999.
 * 
 * Example 1:
 * 
 * 
 * Input: 3
 * Output: "III"
 * 
 * Example 2:
 * 
 * 
 * Input: 4
 * Output: "IV"
 * 
 * Example 3:
 * 
 * 
 * Input: 9
 * Output: "IX"
 * 
 * Example 4:
 * 
 * 
 * Input: 58
 * Output: "LVIII"
 * Explanation: L = 50, V = 5, III = 3.
 * 
 * 
 * Example 5:
 * 
 * 
 * Input: 1994
 * Output: "MCMXCIV"
 * Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.
 * 
 */

// @lc code=start
#include <string>
#include <vector>
#include <algorithm>

class Solution {
public:
    std::string intToRoman(int num) {
        std::string result = "";
        
        // 0 ~ 9
        helper(num, 'I', 'V', 'X', result);
        num /= 10;

        // 10 ~ 90
        helper(num, 'X', 'L', 'C', result);
        num /= 10;

        // 100 ~ 900
        helper(num, 'C', 'D', 'M', result);
        num /= 10;

        // 1000 ~ 3000
        if (num > 0) {
            result += std::string(num, 'M');
        }

        std::reverse(result.begin(), result.end());

        return result;
    }

private:
    void helper(int num, char small, char median, char large, std::string& result) {
        if (num == 0) return;

        int res = num % 10;
        if (res <= 3) {
            result += std::string(res, small);
        } else if (res == 4) {
            result += median;
            result += small;
        } else if (res <= 8) {
            result += std::string(res - 5, small);
            result += median;
        } else {
            result += large;
            result += small;
        }
    }
};
// @lc code=end