Add Binary Strings.cpp

class Solution {
  public:
    string addBinary(string& s1, string& s2) {
        string result = "";
        int i = s1.size() - 1, j = s2.size() - 1, carry = 0;

        
        while (i >= 0 || j >= 0 || carry > 0) {
            int bit1 = (i >= 0) ? s1[i] - '0' : 0;
            int bit2 = (j >= 0) ? s2[j] - '0' : 0;

            int sum = bit1 + bit2 + carry;
            result.push_back((sum % 2) + '0'); 
            carry = sum / 2; 

            i--;
            j--;
        }

        
        reverse(result.begin(), result.end());

        
        size_t pos = result.find_first_not_of('0');
        return (pos != string::npos) ? result.substr(pos) : "0";
    }
};