Add Binary

LeetCode 67 | Difficulty: Easy

Easy

Problem Description

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 <= 10^4`

- `a` and `b` consist only of `'0'` or `'1'` characters.

- Each string does not contain leading zeros except for the zero itself.

Topics: Math, String, Bit Manipulation, Simulation

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Approach

Bit Manipulation

Operate directly on binary representations. Key operations: AND (&), OR (|), XOR (^), NOT (~), shifts (<<, >>). XOR is especially useful: a ^ a = 0, a ^ 0 = a.

When to use

Finding unique elements, power of 2 checks, subset generation, toggling flags.

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 96 ms)

Metric	Value
Runtime	96 ms
Memory	N/A
Date	2018-03-25

Solution

public class Solution {
    public string AddBinary(string a, string b) {
        int m = a.Length-1;
    int n = b.Length-1;
    int carry = 0;
    string result = "";
    while(m>=0 || n>=0)
    {
        int sum = carry;
        if(m>=0)
        {
            sum += a[m]-'0';
            m--;
        }
        if(n>=0)
        {
            sum+=b[n]-'0';
            n--;
        }
        
        result = sum%2 + result;
        carry = sum/2;
        
    }
    if(carry>0) result = carry.ToString() + result;
    return result;
}
}

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Complexity Analysis

Approach	Time	Space
Bit Manipulation	$O(n) or O(1)$	$O(1)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.