67. Add Binary

Solution：digit_sum = prev_carry + a[i] + b[i], calculating backwards

Time Complexity: O(max_length(a, b))
Space Complexity: O(max_length(a, b)) for StringBuilder

Solution Code：

class Solution {
    public String addBinary(String a, String b) {
        StringBuilder result = new StringBuilder();
        int i = a.length() - 1, j = b.length() - 1, carry = 0;
        while(i >= 0 || j >= 0) {
            int sum = carry;
            if(i >= 0) sum += a.charAt(i--) - '0';
            if(j >= 0) sum += b.charAt(j--) - '0';
            result.append(sum % 2);
            carry = sum / 2;
        }
        if(carry != 0) result.append(carry);
        
        return result.reverse().toString();
    }
}