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 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.

阿拉伯数字到古罗马数字的转化，最关键的是确定数字的范围，但是这里有一个小技巧，如果是100，那么M的值为0个，应该怎么在代码中优雅的表述尼？

public static String intToRoman(int num) {  

        //1000-3000
        String M[] = {"", "M", "MM", "MMM"};
        //100-900
        String C[] = {"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"};
        //10-90
        String X[] = {"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"};
        //0-9
        String I[] = {"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"};
        // is so beautiful
        return M[num/1000] + C[(num%1000)/100] + X[(num%100)/10] + I[num%10];
    }

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.

古罗马数字到的阿拉伯数字转化

public int romanToInt(String s) {

  if(s == null || s.length() == 0) return 0;
	int len = s.length();
	HashMap<Character,Integer> map = new HashMap<Character,Integer>();
	 map.put('I',1);
	 map.put('V',5);
	 map.put('X',10);
	 map.put('L',50);
	 map.put('C',100);
	 map.put('D',500);
	 map.put('M',1000);

	 int result = map.get(s.charAt(len -1));
	 int pivot = result;
	 for(int i = len -2; i>= 0;i--){
			 int curr = map.get(s.charAt(i));
			 if(curr >=  pivot){
			      result += curr;
			 }else{
			       result -= curr;
			 }
	 		 pivot = curr;
	 }
	return result;
}