Add Binary

Problem

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

Constraints

• 1 ≤ a.length, b.length ≤ 10⁴

Approach — Core Patterns

This is a Core Patterns problem. The idea: pick the data structure best matched to the constraints and solve it in one clean pass. Work through the reference code below line by line, then re-derive it yourself in the editor — that's how the pattern sticks.

Complexity: see the walkthrough below.

Solution code

Python

class Solution:
    def addBinary(self, a, b):
        return bin(int(a, 2) + int(b, 2))[2:]

Java

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

Practice it

Reading a solution isn't the same as being able to write it under pressure. Open this problem in the in-browser editor, hide the solution, and solve it from scratch — your code runs against real test cases instantly.