bit-manipulation

Count set bits efficiently using Kernighan's method, a bit manipulation technique that clears the lowest set bit in each iteration to achieve O(number of set bits) complexity. The skill provides this as a core utility for fast problem solving.

Generate all subsets for bitmask DP by iterating through bitmask combinations and applying binary operations to enumerate set states. The skill provides utilities to generate bitmasks and subsets, enabling efficient state representation in dynamic programming problems.

Set, clear, and toggle bits using binary operations like OR, AND, and XOR with specific bitmask patterns. The skill covers core bit operations including set, clear, toggle, and bit tests, enforcing strict input validation for numeric parameters.

Solve single number and Hamming distance problems using XOR tricks to identify unique elements or count differing bits. The skill includes object-level examples for both tasks, demonstrating practical applications of binary operations.

Configurable retry and logging are supported for bit operations, ensuring deterministic execution and traceability. The skill enforces strict input validation for numeric parameters and documents complexity for key operations.

Use bit manipulation instead of standard arithmetic when optimizing for speed and deterministic performance, as binary operations run in constant time. The skill is designed for high-performance algorithms and competitive programming where runtime reduction is critical.