Set (abstract data type)

A collection of distinct elements that supports membership tests and operations such as insertion, removal, and union. Its defining property is that duplicate elements are not represented.

Set: A mathematical collection of distinct objects, with membership but no inherent order. The abstract data type takes its central idea—distinct membership—from this mathematical structure.
Hash table: A data structure that uses hash values to locate entries in an array of buckets. Hash tables commonly implement sets with expected constant-time membership and updates.
Database index: An auxiliary data structure that speeds up searches and retrievals in a database. Indexes often enforce uniqueness or quickly test whether a key is present.
Multiset: A collection in which each element has a nonnegative multiplicity, allowing duplicates. A multiset preserves occurrence counts that an ordinary set discards.
Equivalence relation: A relation that is reflexive, symmetric, and transitive. Implementations need a consistent rule for deciding when two candidate elements count as the same.
Binary search tree: A binary tree whose keys are ordered so smaller and larger values occupy opposite subtrees. A balanced search tree can implement an ordered set with logarithmic operations.
Graph traversal: The systematic process of visiting vertices and edges in a graph. A visited set prevents traversal algorithms from processing the same vertex repeatedly.
List (abstract data type): An ordered sequence of elements that supports position-based access and updates. Lists preserve order and repeated elements, properties absent from a basic set.
Hash function: A function that maps values to fixed-size outputs, often for indexing data structures. Hash-based sets use these outputs to find possible matches efficiently.
Bit array: A sequence of bits used to represent many Boolean values compactly. For a small, fixed universe of possible elements, one bit per element gives direct membership tests.

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