• 分类：Math

• 考察知识点：Math

• 最优解时间复杂度：**O(n) **

13. 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.

代码：

大佬的方法:

class Solution:
    def romanToInt(self, s):
        """
        :type s: str
        :rtype: int
        """
        if s=="":
            return 0
        
        num_dict={"M":1000,"D":500,"C":100,"L":50,"X":10,"V":5,"I":1}
        res=0
        for i in range(len(s)):
            if i>0 and num_dict[s[i]]>num_dict[s[i-1]]:
                res+=(num_dict[s[i]]-(num_dict[s[i-1]]*2))
            else:
                res+=num_dict[s[i]]
        return res

讨论：

1.这个题主要考对罗马数字的理解，有哪些特殊情况，比如900，400这些，然后需要一一考虑进去
2.罗马数字的规律：如果左边的数字小于右边的数字，那么这时应该num[右]-num[左]*2
3.这个题应该熟练掌握，因为面试中还是会经常考到

优秀！