Bit Manipulation

XOR of Numbers in a Given Range

Efficiently compute XOR of numbers in a range [L, R] using optimized bit manipulation. Learn patterns in XOR from 1 to n with C++ code, examples, and O(1) time complexity explanation.

Generate All Possible Subsets of the Array

Divide Two Numbers Without Multiplication and Division

Efficiently divide two integers without using multiplication, division, or modulo operators. Learn optimal C++ approaches using bit manipulation, with edge case handling and O(log²N) time.

Single Number - 3

Find two non-repeating elements in an array where every other number appears twice. Solve it using brute-force, hashmap, or optimal XOR-based bit manipulation in C++ with O(N) time.

Dividing or Multiplying any Number by Two Using Bit Operations

Printing the Binary Representation of a Decimal Number

Find the Element that Appears Once in an Array Where Every Other Element Appears Thrice

Find the unique number in an array where every other element appears thrice. Learn efficient C++ approaches using hash maps, bit counting, and sorting with optimal time and space.

Find the Single Number in an Array Where All Others Appear Twice

Find the single non-repeating element in an array where every other element appears twice. Solve it using hashmap or optimal XOR-based bit manipulation in C++ with O(n) time.

Removing the Last Set Bit

Learn how to remove the last set bit (rightmost 1) in an integer's binary form using efficient bitwise operations in C++. Includes examples, dry run, code, and O(1) complexity.

Understanding Bit Manipulation

Binary numbers use base-2, representing data with 0s and 1s. Learn binary-decimal conversions, bitwise operators, and how computers use 1's and 2's complement to handle signed integers.

Counting Set Bits in an Integer

Count the number of set bits (1s) in a binary representation of a number using C++. Includes 3 methods: bitwise shift, Brian Kernighan’s algorithm, and GCC built-in function with code and analysis.