题目

罗马数字包含以下七种字符： I， V， X， L，C，D 和 M。

字符          数值
I             1
V             5
X             10
L             50
C             100
D             500
M             1000

例如，罗马数字 2 写做 II ，即为两个并列的 1。12 写做 XII ，即为 X + II 。 27 写做 XXVII, 即为 XX + V + II 。

通常情况下，罗马数字中小的数字在大的数字的右边。但也存在特例，例如 4 不写做 IIII，而是 IV。数字 1 在数字 5 的左边，所表示的数等于大数 5 减小数 1 得到的数值 4 。同样地，数字 9 表示为 IX。这个特殊的规则只适用于以下六种情况：

I 可以放在 V (5) 和 X (10) 的左边，来表示 4 和 9。
X 可以放在 L (50) 和 C (100) 的左边，来表示 40 和 90。
C 可以放在 D (500) 和 M (1000) 的左边，来表示 400 和 900。

给定一个整数，将其转为罗马数字。输入确保在 1 到 3999 的范围内。

示例 1:

1 2	输入: 3 输出: "III"

示例 2:

1 2	输入: 4 输出: "IV"

示例 3:

1 2	输入: 9 输出: "IX"

示例 4:

1
2
3

输入: 58
输出: "LVIII"
解释: L = 50, V = 5, III = 3.

示例 5:

1
2
3

输入: 1994
输出: "MCMXCIV"
解释: M = 1000, CM = 900, XC = 90, IV = 4.

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:

1 2	Input: 3 Output: "III"

Example 2:

1 2	Input: 4 Output: "IV"

Example 3:

1 2	Input: 9 Output: "IX"

Example 4:

1
2
3

Input: 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.

Example 5:

1
2
3

Input: 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.

解题方法

用两个数组保存罗马数字单位和对应的十进制单位，将num从最大单位逐步递减，每次相减，结果字符串加上对应罗马单位，知道num被减为0。因为会频繁对结果字符串进行修改，所以使用StringBuilder而不是直接使用String。这段代码跑了45ms，超过了98.87%的Java提交。

public Class Solution {
		// Method 1 45ms 98.87%
    public String intToRoman(int num) {
        int[] dimensions = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
        String[] strings = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};
        StringBuilder res = new StringBuilder();    // store result StringBuilder
        for (int i = 0; i < dimensions.length; i++) {
            while (num >= dimensions[i]) {
                num -= dimensions[i];    // subtract decimal dimension
                res.append(strings[i]);    // the result string append Roman dimension
            }
        }
        return res.toString();    // transform into String
    }
}