Add binary

通过 String模拟实现二进制的加法。和其他很多事情一样，计算加法看起来简单。至少对于人脑来说，可以说是最基本的逻辑操作。要通过编程实现，对于小白的我来说，仍然需要一番努力。

Given two binary strings, return their sum (also a binary string).
Example
a = 11
b = 1
Return 100

下面这个方法的精妙之处在于，确保 a 是长度最短的 String。这样一来，后面的算法只需要针对一种情况来处理即可，条例清晰，也更concise( 简洁 )。

public class Solution {
    /**
     * @param a a number
     * @param b a number
     * @return the result
     */
    public String addBinary(String a, String b) {
        // Write your code here
        String result = "";
        
        // make sure a is always the shortest
        if (a.length() > b.length()) {
            String temp = b;
            b = a;
            a = temp;
        }    
        int lenA = a.length() - 1;
        int lenB = b.length() - 1;
        
        String rst = "";
        
        int carries = 0;
        
        while(lenA >= 0) {
            int sum = (int)(a.charAt(lenA) - '0') + (int) (b.charAt(lenB) - '0') + carries;
            rst = String.valueOf(sum % 2) + rst;
            carries = sum / 2;
            
            lenA--;
            lenB--;
        }
        
        while (lenB >= 0) {
            int sum = (int) (b.charAt(lenB) - '0') + carries;
            rst = String.valueOf(sum % 2) + rst;
            carries = sum / 2;
            
            lenB--;
        }
        
        if (carries == 1)  rst = "1" + rst;
            
        return rst;
    }
        
}