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.
难度：easy
题目：罗马数字由七个字母表示 I, V, X, L, C, D 为 M.
符号 值
I 1
V 5
X 10
L 50
C 100
D 500
M 1000
例如，2 写法为 II, 由两个 I 组成。12 写法为 XII, X + II. 数字 27 写法为 XXVII, XX + V + II. 罗马数字经常由大向小由左向右。然而 4 的写法并不是 IIII。而是 IV. 因为 1 在 5 之前就减去 1 得到 4. 同样的原理适用于 9（IX）. 有个 6 个实例用这个种减规则：I 可以放在 V (5) 和 X (10) 之前得到 4 和 9. X 可以放在 L (50) 和 C (100) 之前得到 40 和 90. C 可以放在 D (500) 和 M (1000) 之前得到 400 和 900. 给出一个罗马数字，将其转成一个整数。输入保证在 1 到 3999 之间。
思路：递归，分别取当前位置与其下一位置，主要是因为 IV 的表示方式为 V – I，要将这种减规则的数找出来单独处理。因为 VII 的表示方式自左向右或自右向左都为 V + I + I.
Runtime: 41 ms, faster than 57.06% of Java online submissions for Roman to Integer.
public class Solution {
public int romanToInt(String s) {
// I/1 V/5 X/10 L/50 C/100 D/500 M/1000
Map<Character, Integer> table = new HashMap<>();
table.put(‘I’, 1);
table.put(‘V’, 5);
table.put(‘X’, 10);
table.put(‘L’, 50);
table.put(‘C’, 100);
table.put(‘D’, 500);
table.put(‘M’, 1000);
return romanToInt(s, 0, table);
}
public int romanToInt(String s, int begin, Map<Character, Integer> table) {
// I/1 V/5 X/10 L/50 C/100 D/500 M/1000
// left only can keep one, rigth can keep two for V L D
if (begin + 1 == s.length()) {
return table.get(s.charAt(begin));
}
if (begin == s.length()) {
return 0;
}
int left = table.get(s.charAt(begin));
int right = table.get(s.charAt(begin + 1));
return left >= right ? left + romanToInt(s, begin + 1, table) : right – left + romanToInt(s, begin + 2, table);
}
}