Add Binary

Given two binary strings, return their sum (also a binary string).

For example,
a = "11"
b = "1"
Return "100".

Analyse: Using XOR(^) to compute the result of the bit-add and line 22 to reserve the carry bit. Be cautious about the last carry.

class Solution {
public:
    string addBinary(string a, string b) {
        int carry = 0;
        string result;
        for(int i = a.length() - 1, j = b.length() - 1; i >= 0 || j >= 0; i--, j--){
            int sa, sb;
            if(i < 0) {
                sa = 0; 
                sb = b[j] - '0';
            }
            else if(j < 0){
                sb = 0; 
                sa = a[i] - '0';
            }
            else{
                sa = a[i] - '0';
                sb = b[j] - '0';
            }
            char current = sa ^ sb ^ carry + '0';
            result = current + result;
            if((carry + sa + sb) / 2) carry = 1;
            else carry = 0;
        }
        if(carry) result = '1' + result;
        return result;
    }
};