Integer to Roman

Q:
Given an integer, convert it to a roman numeral.
Input is guaranteed to be within the range from 1 to 3999.
A:
--------------2 nd pass-------------------------
思路：
就是把  单位放到数组里，一个个 单位 来对比。

public class Solution {
    public String intToRoman(int num) {
        HashMap<Integer,Character> map = new HashMap();
        StringBuffer buf = new StringBuffer();
        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');
        int [] A = {1000,500,100,50,10,5,1};
        int i =0;
        while(num>0 && i<A.length){
            if(num/A[i] == 0){
                i++;
            }else if((i == 1 || i == 3 | i == 5 ) && num/A[i+ 1]== 9 ){
                buf.append(""+map.get(A[i+1])+map.get(A[i-1]));
                num -= 9*A[i+1];
            }else if(num/A[i]==4 ){
                buf.append(""+map.get(A[i])+map.get(A[i-1]));
                num -= 4*A[i];
            }else{
                buf.append(""+map.get(A[i]));
                num -= A[i];
            }
        }
        return buf.toString();
    }
}

Mistakes:
1：    45  不能写成 VL的形式。 只有10的单位的，可以写成减法的形式。
       只有  I  X  C 才能被放到前面 做减法。

-----------1st pass--------------------

public class Solution {
    public String intToRoman(int num) {
        // Symbol    I    V    X    L    C    D    M
        // Value    1    5    10    50    100    500    1,000
        Map<Integer,String> map = new HashMap<>();
        map.put(1000,"M");
        map.put(900,"CM");
        map.put(500,"D");
        map.put(400,"CD");
        map.put(100,"C");
        map.put(90,"XC");
        map.put(50,"L");
        map.put(40,"XL");
        map.put(10,"X");
        map.put(9,"IX");
        map.put(5,"V");
        map.put(4,"IV");
        map.put(1,"I");
        int[]A = {1000,900,500,400,100,90,50,40,10,9,5,4,1};
        String res = "";
        int i =0;
        while(num > 0){
            if(num >= A[i]){
                num-= A[i];
                res += map.get(A[i]);
            }else{
                i++;
            }
        }
        return res;
    }
}

Mistakes:
1:  开始的时候， buffer.replace(start ,end, String)的时候， 要 replace掉4个长度的string，  那么 end = start+4即可。  而不是 end = start+5;


Learned:
1:   罗马数字的基本单位：
Symbol     Value
I     1
V     5
X     10
L     50
C     100
D     500
M     1,000

Numbers are formed by combining symbols together and adding the values. So II is two ones, i.e. 2, and XIII is a ten and three ones, i.e. 13. There is no zero in this system, so 207, for example, is CCVII, using the symbols for two hundreds, a five and two ones. 1066 is MLXVI, one thousand, fifty and ten, a five and a one.


Symbols are placed from left to right in order of value, starting with the largest. However, in a few specific cases,[2] to avoid four characters being repeated in succession (such as IIII or XXXX) these can be reduced using subtractive notation as follows:[3][4]

    the numeral I can be placed before V and X to make 4 units (IV) and 9 units (IX) respectively
    X can be placed before L and C to make 40 (XL) and 90 (XC) respectively
    C can be placed before D and M to make 400 (CD) and 900 (CM) according to the same pattern[5]
n example using the above rules would be 1904: this is composed of 1 (one thousand), 9 (nine hundreds), 0 (zero tens), and 4 (four units). To write the Roman numeral, each of the non-zero digits should be treated separately. Thus 1,000 = M, 900 = CM, and 4 = IV. Therefore, 1904 is MCMIV.