13.Roman to Integer¶
Tags: Easy
String
Math
Links: https://leetcode.com/problems/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 beforeV
(5) andX
(10) to make 4 and 9.X
can be placed beforeL
(50) andC
(100) to make 40 and 90.C
can be placed beforeD
(500) andM
(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.
class Solution {
public:
int romanToInt(string s) {
std::ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
unordered_map<char, int> m{{'I', 1}, {'V', 5}, {'X', 10}, {'L', 50}, {'C', 100}, {'D', 500}, {'M', 1000}};
int res = 0;
for (int i = 0; i < s.size(); ++i) {
int val = m[s[i]];
if (i == s.size() - 1 || m[s[i+1]] <= m[s[i]]) res += val;
else res -= val;
}
return res;
}
};
有几条须注意掌握:
1、基本数字Ⅰ、X 、C 中的任何一个,自身连用构成数目,或者放在大数的右边连用构成数目,都不能超过三个;放在大数的左边只能用一个。
2、不能把基本数字V 、L 、D 中的任何一个作为小数放在大数的左边采用相减的方法构成数目;放在大数的右边采用相加的方式构成数目,只能使用一个。
3、V 和X 左边的小数字只能用Ⅰ。
4、L 和C 左边的小数字只能用X。
5、D 和M 左边的小数字只能用C。
而这道题好就好在没有让我们来验证输入字符串是不是罗马数字,这样省掉不少功夫。
考虑两种情况即可:
第一,如果当前数字是最后一个数字,或者之后的数字比它小的话,则加上当前数字。
第二,其他情况则减去这个数字。