// Add Binary

// 时间复杂度O(n)，空间复杂度O(1)

class Solution {

public:

string addBinary(string a, string b) {

string result;

int i = a.length() - 1;

int j = b.length() - 1;

int carry = 0;

while(i >= 0 || j >= 0 || carry > 0) {

int valueA = i < 0 ? 0 : a[i--] - '0';

int valueB = j < 0 ? 0 : b[j--] - '0';

int sum = valueA + valueB + carry;

result.insert(result.begin(), (sum % 2) + '0');

carry = sum / 2;

}

return result;

}

};