Roman to Integer

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:

Input: “III”
Output: 3
Example 2:

Input: “IV”
Output: 4
Example 3:

Input: “IX”
Output: 9
Example 4:

Input: “LVIII”
Output: 58
Explanation: L = 50, V= 5, III = 3.
Example 5:

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

解题思路

我们发现罗马数字有一个特点，就是4：IV，9：IX，也就是说每到各个位数上出现4或者9时，左边的罗马数字一定要比右边的小，比如1994 = MCMXCIV (百位出现9，CM = 900，C<M，XC=90，X<C，IV=4，I<V)。
所以面对这种情况，我们可以进行一个判断，如果当前的罗马数字要小于下一个罗马数字，那么我们就遇到了4或者9，所以我们可以减去这个罗马数字对应的阿拉伯数字，然后加上下一个罗马数字即可。

代码

class Solution:
    def romanToInt(self, s):
        """
        :type s: str
        :rtype: int
        """
        a = {'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}        
        ans=0        
        for i in range(len(s)):            
            if i<len(s)-1 and a[s[i]]<a[s[i+1]]:                
                ans-=a[s[i]]
            else:
                ans+=a[s[i]]
        return ans

结果