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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 of subsets of a given set (its power set) ordered by inclusion (see Fig. 1). Similarly, the set of sequences ordered by subsequence, and the set of strings ordered by substring. The set of natural numbers equipped with the relation of divisibility. (see Fig. 3 and Fig. 6) The vertex set of a directed acyclic graph ordered by reachability.
A set equipped with a total order is a totally ordered set; [5] the terms simply ordered set, [2] linearly ordered set, [3] [5] and loset [6] [7] are also used. The term chain is sometimes defined as a synonym of totally ordered set , [ 5 ] but generally refers to a totally ordered subset of a given partially ordered set.
The set {1, 2, ..., n} with the usual ≤ relation is the most frequently used set in these applications. A number of properties of a permutation are directly related to the total ordering of S, considering the permutation written in one-line notation as a sequence σ = σ ( 1 ) σ ( 2 ) ⋯ σ ( n ) {\displaystyle \sigma =\sigma (1)\sigma (2 ...
Space. Θ (n) [ 1 ] O (n) A small phone book as a hash table. In computing, a hash table is a data structure that implements an associative array, also called a dictionary or simply map; an associative array is an abstract data type that maps keys to values. [ 2 ] A hash table uses a hash function to compute an index, also called a hash code ...
similar to a set, multiset, map, or multimap, respectively, but implemented using a hash table; keys are not ordered, but a hash function must exist for the key type. These types were left out of the C++ standard; similar containers were standardized in C++11, but with different names (unordered_set and unordered_map). Other types of containers ...
A linked list is a sequence of nodes that contain two fields: data (an integer value here as an example) and a link to the next node. The last node is linked to a terminator used to signify the end of the list. In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory.
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 ...