leetcode 12. Integer to Roman

题目内容

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 an integer, convert it to a roman numeral. Input is guaranteed to be within the range from 1 to 3999.

Example:

Input: 3
Output: "III"
Example 2:

Input: 4
Output: "IV"
Example 3:

Input: 9
Output: "IX"
Example 4:

Input: 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.
Example 5:

Input: 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.

分析过程

• 题目归类：
  数组
• 题目分析：
  方法一：本题可以直接使用数组并且使用取余方式来计算。但是效率很低。
  方法二：可以将所有可能的值放在一个数组中，然后一次判断，如果大于可能值就输出一个可能值，然后sum相减。
• 边界分析：
  • 空值分析
  • 循环边界分析
• 方法分析：
  • 数据结构分析
  • 状态机
  • 状态转移方程
  • 最优解
• 测试用例构建

代码实现

class Solution {
    public String intToRoman(int num) {
        String[] I = {"","I","II","III","IV","V","VI","VII","VIII","IX"};
        String[] X = {"","X","XX","XXX","XL","L","LX","LXX","LXXX","XC"};
        String[] C = {"","C","CC","CCC","CD","D","DC","DCC","DCCC","CM"};
        String[] M = {"","M","MM","MMM"};
        return M[(num/1000)]+C[(num/100)%10]+X[(num/10)%10]+I[num%10];
    }
}

效率提高

class Solution {
    public String intToRoman(int num) {
        int []m = {1000,900,500,400,100,90,50,40,10,9,5,4,1};
        String []k = {"M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"};
        StringBuilder SB = new StringBuilder();
        for(int i = 0; i<k.length;i++){
            while(num-m[i]>=0){
                SB.append(k[i]);
                num = num - m[i];
            }
        }
        return SB.toString();
    }
}

拓展问题

13. Roman to Integer