[每日 LeetCode] 13. Roman to Integer

原文链接 [每日 LeetCode] 13. Roman to Integer

Description:

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.
​

思路：本题要求将罗马数字转化为整数。首先理解罗马数字的拼写规则。罗马数字只用来计数，不用做演算。罗马数字共有 7 个，分别为 I(1),V(5),X(10),L(50),C(100),D(500),M(1000)。且有以下几个规则

规则一 ：重复次数

一个罗马数字重复几次，就表示这个数的几倍。最多只能连续出现三次。
​

规则二：右加左减

在较大的罗马数字的右边记上较小的罗马数字，表示大数字加上小数字。

在较大的罗马数字的左边记上较小的罗马数字，表示大数字减去小数字。

左减的数字必须为一位，比如8写成VIII，而不是IIX。
​

规则三：加线乘千 （本题不考虑）

在罗马数字的上方加一条横线或者加上下标M，表示将这个数乘以1000，加两条横线表示乘以1000的平方。
​

实现转化时只需判断当前数字和下一个数字的大小即可。

C++ 代码

class Solution {
public:
    int intval(char c){
        switch(c){
        case 'I': return 1;
                    break;
        case 'V': return 5;
                 break;
        case 'X': return 10;
                 break;
        case 'L': return 50;
                 break;
        case 'C': return 100;
                   break;
        case 'D': return 500;
                  break;
        case 'M': return 1000;
                break;
        }
        return 0;
    }
    int romanToInt(string s) {
        int sum = 0;
        for(int i = 0;i<s.length(); i++){
            if(intval(s[i]) <intval(s[i+1])){
                sum -= intval(s[i]);
            }
            else
                sum+=intval(s[i]);
        }
        return sum;
    }
};
​

运行时间：4ms

运行内存：8.3M