12. 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, 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.

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题目大意：

  把阿拉伯数字转化为罗马数字。罗马数字能够用I, V, X, L, C, D 和M这七个数字来表示。注意：数字介于1到3999之间。

解题思路：

  emmmmmmmmmmmmmmmmmmm~~~~~~~~~~~~~~~~，思路很简单（手动滑稽

  采用工业化的解法（doge.jpg

  直接每一位穷举，1-3999每位出现的数字一共有34种情况，直接存到一个表里就行，有点像实际应用中的质数查找，直接遍历一个范围内的质数，然后存到容器里直接查找

解题代码：

class Solution {
public:
    string intToRoman(int num) {
        string res, table[4][10] = {
        {"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"},
        {"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"},
        {"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"},
        {"", "M", "MM", "MMM"}
        };
        int carry = 0, temp = 0;
        while (num) {
            temp = num % 10;
            num /= 10;
            res = table[carry][temp] + res;
            ++carry;
        }
        return res;
    }
};