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。

给定一个罗马数字，将其转换成整数。输入确保在 1 到 3999 的范围内。

示例 1:

1 2	输入: "III" 输出: 3

示例 2:

1 2	输入: "IV" 输出: 4

示例 3:

1 2	输入: "IX" 输出: 9

示例 4:

1
2
3

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

示例 5:

1
2
3

输入: "MCMXCIV"
输出: 1994
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 a roman numeral, convert it to an integer. Input is guaranteed to be within the range from 1 to 3999.

Example 1:

1 2	Input: "III" Output: 3

Example 2:

1 2	Input: "IV" Output: 4

Example 3:

1 2	Input: "IX" Output: 9

Example 4:

1
2
3

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

Example 5:

1
2
3

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

解题方法

与上一题leetcode——[012]Integer to Roman整数转罗马数字解法基本一样，罗马数字格式是按罗马单位从大到小进行排列的，我们用一个HashMap来保存罗马字符对应的十进制数值，只需要遍历一次字符串，加各个罗马单位对一个的十进制单位相加就可以得到十进制结果。

但一些特殊单位，比如400，会先出现100 C，再出现500 D，我们可以从后往前遍历，可以遇到D先加500，遇到C再减100，这个时候就需要一个char来保存前一个字符，如果当前单位比前一个单位小，则相减；否则相加。

这段代码跑了28ms，超过了100%的Java提交。

public class Solution {
    // Method 1 28ms 100%
    public int romanToInt(String s) {
        if (s.equals("")) {
            return 0;
        }
        // store dimensions
        HashMap<Character, Integer> dimentions = new HashMap<Character, Integer>(){{
            put('M', 1000);
            put('D', 500);
            put('C', 100);
            put('L', 50);
            put('X', 10);
            put('V', 5);
            put('I', 1);
        }};
        char[] chars = s.toCharArray();
        // initiate the pre as 1 because it's the smallest one and the result as 0
        int pre = 1, res = 0;
        for (int i = chars.length - 1; i >= 0 ; i--) {
            int value = dimentions.get(chars[i]);
            // if the previous dimension is bigger than subtract the current dimension
            if (value < pre) {
                res -= value;
            }
            // add the current dimension
            else {
                res += value;
            }
            // update the previous char
            pre = value;
        }
        return res;
    }
}