Bitwise Algorithms

Bitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Sift and Right Shift.

Basics

• Introduction to Bitwise Algorithms
• Bitwise Operators in C/C++
• Bitwise Operators in Java
• Python Bitwise Operators
• JavaScript Bitwise Operators
• All about Bit Manipulation
• Little and Big Endian Mystery

Bit Manipulation Tips and Tricks

• Bits manipulation (Important tactics)
• Bitwise Hacks for Competitive Programming

Easy Problems on Bit Algorithms:

• Binary Representation
• Turn off the rightmost set bit
• Check if K-th Bit Set
• Set the K-th Bit
• Modulus division by 2's Power
• Odd Occurring Number
• Power of two
• The only set bit
• Add Bit Strings
• Check for Integer Overflow
• XOR without using XOR
• Check for Equal
• Check for opposite signs
• Swap Two Numbers
• Russian Peasant

Medium Problems on Bit Algorithms:

• Most Significant Set Bit
• Rightmost Set Bit
• Count Set Bits
• Swap Bits
• Rotate Bits
• Smallest of Three
• Minimum without branching
• Smallest power of 2 greater than or equal to n
• Program to find parity
• Check if binary is palindrome
• Generate n-bit Gray Codes
• Check for Sparse
• Euclid when % and / are costly
• Square without using *, / and pow()
• Cyclic Redundancy Check and Modulo-2 Division
• Set Bits in a Range
• Check for Bleak
• Gray to Binary and Vice Versa

Hard Problems on Bit Algorithms:

• Next higher with same set bits
• Karatsuba Algorithm for fast Multiplication
• Max Subarray XOR
• Longest Sequence of 1’s in Binary with One Flip
• Closest Smaller and greater with same set bits
• Bitmasking and Dynamic Programming
• Compute the Parity
• XOR Encryption by Shifting Plaintext
• Count pairs with at least one digit common
• Floating to Binary
• Booth’s Multiplication Algorithm
• Pairs with Pandigital Concatenation
• n-th number whose binary is a palindrome
• Two non-repeating in an array of repeating

Quick Links :

• DSA Tutorial
• ‘Practice Problems’ on Bit Magic
• ‘Quiz’ on Bit Magic
• ‘Videos’ on Bit Magic

What are Bitwise Algorithms?

Bitwise algorithms are algorithms that operate on individual bits of data rather than on larger data types like integers or floating-point numbers. These algorithms manipulate bits directly, typically using bitwise operators such as AND, OR, XOR, shift left, shift right, and complement.

Common Bitwise Algorithms and Operations:

Here are some common bitwise algorithms and operations:

• Bitwise AND (&): Takes two numbers as input and performs a bitwise AND operation on their corresponding bits. It returns 1 only if both bits are 1; otherwise, it returns 0.
• Bitwise OR (|): Performs a bitwise OR operation on the corresponding bits of two numbers. It returns 1 if at least one of the bits is 1.
• Bitwise XOR (^): Performs a bitwise exclusive OR operation on the corresponding bits of two numbers. It returns 1 if the bits are different and 0 if they are the same.
• Bitwise NOT (~): Performs a bitwise NOT operation, which flips each bit of the input (1 becomes 0 and 0 becomes 1).
• Left Shift (<<) and Right Shift (>>): These operators shift the bits of a number to the left or right by a specified number of positions. Left shifting is equivalent to multiplying the number by 2, while right shifting is equivalent to dividing by 2.

Applications of Bitwise Algorithms:

• Bit manipulation (setting, clearing, toggling bits): Bitwise operators are often used to manipulate individual bits of numbers. This includes tasks such as setting bits (using OR), clearing bits (using AND with the complement), toggling bits (using XOR with 1), and checking the value of a specific bit.
• Efficient storage of data: Bitwise algorithms play a crucial role in data compression techniques like Huffman coding. They can efficiently represent and process compressed data by manipulating bits directly.
• Cryptography: Many cryptographic algorithms, such as AES (Advanced Encryption Standard), DES (Data Encryption Standard), and SHA (Secure Hash Algorithm), utilize bitwise operations for encryption, decryption, and hashing. Bitwise XOR, in particular, is commonly used in encryption algorithms for its simplicity and effectiveness.
• Networking and Protocol Handling: Bitwise algorithms are used in networking protocols for tasks like IP address manipulation, subnet masking, and packet parsing. For example, bitwise AND is used in subnet masking to determine the network address from an IP address and subnet mask.
• Low-Level System Programming: Bitwise operations are essential in low-level system programming for tasks such as device control, memory management, and bit-level I/O operations. They are used to manipulate hardware registers, set/clear flags, and optimize code for performance.
• Error Detection and Correction: Bitwise algorithms are employed in error detection and correction techniques, such as CRC (Cyclic Redundancy Check) and Hamming codes. These algorithms use bitwise XOR and other operations to detect and correct errors in transmitted data.

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