Set data structure

In computer science, a set is an abstract data type that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set.

Some set data structures are designed for static or frozen sets that do not change after they are constructed. Static sets allow only query operations on their elements — such as checking whether a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets, allow also the insertion and deletion of elements from the set.

An abstract data structure is a collection, or aggregate, of data. The data may be booleans, numbers, characters, or other data structures. If one considers the structure yielded by packaging or indexing, there are four basic data structures:

In this view, the contents of a set are a bunch, and isolated data items are elementary bunches (elements). Whereas sets contain elements, bunches consist of elements.

Further structuring may be achieved by considering the multiplicity of elements (sets become multisets, bunches become hyperbunches) or their homogeneity (a record is a set of fields, not necessarily all of the same type).

In type theory, sets are generally identified with their indicator function (characteristic function): accordingly, a set of values of type ${\displaystyle A}$ may be denoted by ${\displaystyle 2^{A}}$ or ${\displaystyle {\mathcal {P}}(A)}$. (Subtypes and subsets may be modeled by refinement types, and quotient sets may be replaced by setoids.) The characteristic function ${\displaystyle F}$ of a set ${\displaystyle S}$ is defined as:

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