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Bitmask Subset Enumeration

Enumerates subsets by treating integers as bit masks.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Procedural Generation
Difficulty: Intermediate
Family: Combinatorial generation
Tier: Extended
Status: Reviewed
Review: Ai Reviewed
Sources: 1
Formulas: 0
Relationships: 1
Code example: Not ready
Visualization: Not ready
Aliases: Subset bitmask enumeration, Submask enumeration

Overview

Bitmask Subset Enumeration loops over integer masks and interprets each bit as selecting or excluding an element, producing all subsets or all submasks of a set.

Core Concepts

subset enumerationbitmasksubmask iterationexponential search

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(2^n) for all subsets

Average

O(2^n) for all subsets; O(3^n) for nested mask/submask enumeration

Worst

O(2^n) for all subsets; O(3^n) for all masks with all submasks

Space

O(1) iterator state plus output storage if materialized

When to Use

Use when the set is small enough for 2^n enumeration.

When Not to Use

Avoid when the number of subsets is too large for exhaustive enumeration.

What It Does

Maps each bit position to one input element.
Iterates masks to represent all subsets.
Optionally iterates submasks of a fixed mask.

Use Cases

Subset dynamic programming
Brute-force combinatorics
State compression

Inputs

A set represented by bit positions, or a mask whose submasks should be enumerated.

Outputs

A stream of subset masks or submasks.

Pseudocode

1.For mask from 0 to 2^n - 1.
2.Map set bits to selected elements.
3.Emit the subset.

Canonical Example

Input: A set {A, B, C}.
Output: All eight subsets represented by masks 000 through 111.
Explanation: Each mask bit decides whether the corresponding element is present.

Implementation Notes

Submask iteration commonly uses the recurrence sub = (sub - 1) & mask.

Common Pitfalls

Off-by-one errors in mask bounds and signed shifts are common.

Interactive Mechanism Walkthrough

Spatial Primitive & Sweep-Line Canvas

Show bit positions toggling through subset masks and the descending submask iteration pattern.

Step 1 of 3: For mask from 0 to 2^n - 1.

bitmask-enumeration

Notes

Bitmask Subset Enumeration covers explicit subset and submask iteration using integer masks; a stronger textbook or paper source would improve the active application package.