67. Add Binary

Given two binary strings a and b, return their sum as a binary string.

Example 1:

Input: a = "11", b = "1"
Output: "100"

Example 2:

Input: a = "1010", b = "1011"
Output: "10101"

Constraints:

• 1 <= a.length, b.length <= 104
• a and b consist only of '0' or '1' characters.
• Each string does not contain leading zeros except for the zero itself.

class Solution {
    public String addBinary(String a, String b) {
        int n = a.length();
        int m = b.length();
        if (n < m ){
            return addBinary(b, a);
        }

        int L = Math.max(n,m);


        int carry = 0;
        int j = m-1;

        StringBuilder sb = new StringBuilder();
        for (int i = L - 1; i > -1; i--){
            if (a.charAt(i) == '1'){
                carry++;
            }

            if (j > -1 && b.charAt(j--) == '1'){
                carry++;
            }

            if (carry % 2 == 1){
                sb.append('1');
            }else{
                sb.append('0');
            }

            carry = carry/2;
        }

        if (carry == 1){
            sb.append('1');

        }
        sb.reverse();
        return sb.toString();


    }
}