题目

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

解答：模拟

从大到小整理出所有单位和对应的罗马字母表示
然后将数字从大到小依次尝试减去这些单位，得到相应的表示
时间复杂度O(logn)，空间复杂度O(1)

时间复杂度和位数成正比，一个整数的位数是 O(logn) 级别

class Solution {
private:
    int v[13] = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
    string s[13] = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};
public:
    string intToRoman(int num) {
        string res;
        int i = 0;
        while (num) {
            if (num >= v[i]) {
                res += s[i];
                num -= v[i];
            }
            else i++;
        }
        return res;
    }
};