(bitmask = 0, bitmask ^= 1 << 1 (1st bit)) Here’s how you can identify bitmasking-friendly problems:
Subset Problems: Problems that involve considering all subsets or combinations of a set or array. Bitmasks can represent subsets in a compact binary form.
Example: "Generate all subsets of a set" or "Find subsets whose sum is divisible by a given number." Set or Subset Management: If a problem involves efficiently managing a set of items where the items can be in one of two states (e.g., selected/not selected, on/off, present/absent).
Example: "Given a set of integers, how many subsets can form a sum divisible by a number?" Even/Odd Parity Tracking: Problems that require tracking even and odd counts or toggling between two states (such as tracking even occurrences of items). Bitmasking is efficient for toggling between even/odd states or switching between binary conditions.
Example: "Find how many subsets of a set have an even sum of elements." Permutations/Combinations with Constraints: Problems that ask you to generate permutations or combinations of elements, possibly with some constraints, like ensuring that certain elements appear an even or odd number of times.
Example: "Find the number of valid combinations of elements where the number of selected elements is even." Dynamic Programming (DP) with Subsets or States: In dynamic programming problems that involve tracking multiple states or subsets, bitmasking is often used to efficiently represent the possible states.
Example: "Find the number of ways to partition an array into two subsets with an equal sum."