Roman to Integer && Integer to Roman 解答

Roman Numeral Chart

V:5　　X:10　　L:50　　C:100　　D:500　　M:1000

规则：

1. 重复次数表示该数的倍数
2. 右加左减：
较大的罗马数字右边记上较小的罗马数字，表示大数字加小数字
较小的罗马数字右边记上较大的罗马数字，表示大数字减小数字
左减的数字有限制，仅限于I, X, C
左减时不可跨越一个位数。如，99不可以用IC(100 - 1)表示，而是XCIX(100 - 10 + 10 - 1)
左减数字必需为一位
右加数字不可连续超过三位

Roman to Integer

Given a roman numeral, convert it to an integer.

Input is guaranteed to be within the range from 1 to 3999.

基本思路是每次比较当前字母和它下一个字母，如果是increasing order，说明当前字母的符号是减号，如果是decreasing order，说明当前字母的符号是加号。

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

Integer to Roman

根据规则，可以用递归和非递归的方法解答。

注意到规则，跨越的位数不可超过一位。

 public class Solution {
     public String intToRoman(int num) {
         if (num >= 1000) { return "M" + intToRoman(num - 1000); }
         if (num >= 900) { return "CM" + intToRoman(num - 900); }
         if (num >= 500) { return "D" + intToRoman(num - 500); }
         if (num >= 400) { return "CD" + intToRoman(num - 400); }
         if (num >= 100) { return "C" + intToRoman(num - 100); }
         if (num >= 90) { return "XC" + intToRoman(num - 90); }
         if (num >= 50) { return "L" + intToRoman(num - 50); }
         if (num >= 40) { return "XL" + intToRoman(num - 40); }
         if (num >= 10) { return "X" + intToRoman(num - 10); }
         if (num >= 9) { return "IX" + intToRoman(num - 9); }
         if (num >= 5) { return "V" + intToRoman(num - 5); }
         if (num >= 4) { return "IV" + intToRoman(num - 4); }
         if (num >= 1) { return "I" + intToRoman(num - 1); }
         return "";
     }
 }

循环改为非递归

 public class Solution {
     public String intToRoman(int num) {
         String result = "";
         String [] symbol = {"M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"};
         int [] value = {1000,900,500,400, 100, 90,  50, 40,  10, 9,   5,  4,   1};
         for(int i=0;num!=0;i++){
             while(num >= value[i]){
                 num -= value[i];
                 result += symbol[i];
             }
         }
         return result;
     }
 }