Abstract data types

In computer science, a list or sequence is a collection of items that are finite in number and in a particular order. An instance of a list is a computer representation of the mathematical concept of a tuple or finite sequence.

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes).

In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. It supports 'lookup', 'remove', and 'insert' operations.

In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This mathematical model contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user. For example, a stack has push/pop operations that follow a Last-In-First-Out rule, and can be concretely implemented using either a list or an array. Another example is a set which stores values, without any particular order, and no repeated values. Values themselves are not retrieved from sets; rather, one tests a value for membership to obtain a Boolean "in" or "not in".

In computer science, a priority queue is an abstract data type similar to a regular queue or stack abstract data type.

An ordinal tree, by analogy with an ordinal number, is a rooted tree of arbitrary degree in which the children of each node are ordered, so that one refers to the ith child in the sequence of children of a node.

In computer science, a linked data structure is a data structure which consists of a set of data records (nodes) linked together and organized by references (links or pointers). The link between data can also be called a connector.

In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain. It supports 'lookup', 'remove', and 'insert' operations.

A cardinal tree (or trie) of degree k, by analogy with cardinal numbers and by opposition with ordinal trees, is a rooted tree in which each node has k positions for an edge to a child. Each node has up to k children and each child of a given node is labeled by a unique integer from the set {1, 2, . . ., k}. For instance, a binary tree is a cardinal tree of degree 2.

A monoque is a linear data structure which provides dynamic array semantics. A monoque is similar in structure to a deque but is limited to operations on one end. Hence the name, mono-que. A monoque offers O(1) random access and O(1) push_back/pop_back. Unlike a C++ vector, the push_back/pop_back functions are not amortized and are strictly O(1) in time complexity. Because the block list is never reallocated or resized, it maintains strictly O(1) non-amortized worst case performance. Unlike C++'s deque, the O(1) performance guarantee includes the time complexity of working with the block list, whereas the C++ standard only guarantees the deque to be O(1) in terms of operations on the underlying value type.