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An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a 1, a 2,... a n}. [5] [6] [7]
add a new (,) pair to the collection, mapping the key to its new value. Any existing mapping is overwritten. The arguments to this operation are the key and the value. Remove or delete remove a (,) pair from the collection, unmapping a given key from its value. The argument to this operation is the key.
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 in a set.
It continues doing this for each pair of adjacent elements to the end of the data set. It then starts again with the first two elements, repeating until no swaps have occurred on the last pass. [35] This algorithm's average time and worst-case performance is O(n 2), so it is rarely used to sort large, unordered data sets. Bubble sort can be ...
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
A name–value pair, also called an attribute–value pair, key–value pair, or field–value pair, is a fundamental data representation in computing systems and applications. Designers often desire an open-ended data structure that allows for future extension without modifying existing code or data.
r : E → {{x,y} : x, y ∈ V}, assigning to each edge an unordered pair of endpoint nodes. Some authors allow multigraphs to have loops , that is, an edge that connects a vertex to itself, [ 2 ] while others call these pseudographs , reserving the term multigraph for the case with no loops.
In computer programming, a collection is an abstract data type that is a grouping of items that can be used in a polymorphic way. Often, the items are of the same data type such as int or string. Sometimes the items derive from a common type; even deriving from the most general type of a programming language such as object or variant.