Find the missing number in an array containing n distinct numbers taken from 0, 1, 2, ..., n. Read full solution .

Check if a given integer is a power of two. Read full solution .

Reverse the bits of a given 32-bit unsigned integer. Read full solution .

Find the single number that appears once in an array where every other number appears twice. Read full solution .

Bit Manipulation

Master bitwise operations and binary manipulation techniques.

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QUESTION	DIFFICULTY
Missing Number Find the missing number in an array containing n distinct numbers taken from 0, 1, 2, ..., n.	Medium
Power of Two Check if a given integer is a power of two.	Medium
Reverse Bits Reverse the bits of a given 32-bit unsigned integer.	Medium
Single Number Find the single number that appears once in an array where every other number appears twice.	Medium

Overview

Bit manipulation involves direct manipulation of bits in binary representation. This section covers bitwise operators and their clever applications in solving problems efficiently.

Key Concepts

Bitwise operators (AND, OR, XOR, NOT, shifts)
Bit masks and flags
Setting, clearing, and toggling bits
Counting set bits
Power of two checks
XOR properties

Common Problems

Easy

Single Number
Number of 1 Bits
Reverse Bits
Power of Two

Medium

Single Number II
Single Number III
Bitwise AND of Numbers Range
Maximum XOR of Two Numbers

Hard

Maximum XOR with an Element from Array
Minimum XOR Sum of Two Arrays

Practice Tips

Know operators: Master AND, OR, XOR, NOT, left/right shifts
XOR properties: a ^ a = 0, a ^ 0 = a, commutative
Bit tricks: Learn common patterns (isolate rightmost bit, etc.)
Binary representation: Understand two’s complement