leetcode Integer to Roman题解

题目描述：

Roman numerals are represented by seven different symbols: I, V, X, L, C, Dand 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 1:

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.

中文理解：

将数字转换为Roman表示，其中Roman具有1,4,5,9,10,40,50,90,100,400,500，900,1000这几种数值表示。

解题思路：

使用贪心的思路，从大数开始不断将数字转换为Roman表示，比如5500，首先5500/1000，得到整数部分为5，放入五个''M"，然后num=5500-5*1000=500，再依次除以900,500，得到还有一个500，放入''D''，得到最终的结果。

代码（java）：

class Solution {
    public String intToRoman(int num) {
        HashMap<Integer,String> map=new HashMap<Integer,String>();
        map.put(1,"I");
        map.put(5,"V");
        map.put(10,"X");
        map.put(50,"L");
        map.put(100,"C");
        map.put(500,"D");
        map.put(1000,"M");
        map.put(4,"IV");
        map.put(9,"IX");
        map.put(40,"XL");
        map.put(90,"XC");
        map.put(400,"CD");
        map.put(900,"CM");
        StringBuffer res=new StringBuffer();
        int element[]={1000,900,500,400,100,90,50,40,10,9,5,4,1};
        for(int val:element){
            if(num>0){
                for(int i=0;i<num/val;i++){
                    res.append(map.get(val));
                }
            }
            num=num-num/val*val;
        }
        return res.toString();
    }
}