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In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [ 1 ] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.
O(n)[1] In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them ...
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is ...
Enumerated type. In computer programming, an enumerated type (also called enumeration, enum, or factor in the R programming language, and a categorical variable in statistics) is a data type consisting of a set of named values called elements, members, enumeral, or enumerators of the type. The enumerator names are usually identifiers that ...
Tagged union. In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type, or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field explicitly ...
Set (abstract data type) In computer science, a set is an abstract data type that can store unique values, without any particular order. 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 ...
The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. Given a set of elements {1, 2, …, n} , (henceforth referred to as the universe, specifying all possible elements under consideration) and a collection, referred to as S, of a given m subsets whose union equals the ...
Inclusion–exclusion principle. In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as. where A and B are two finite sets and | S | indicates the cardinality of a ...