Tree (data structure)

In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.

A tree data structure can be defined recursively (locally) as a collection of nodes (starting at a root node), where each node is a data structure consisting of a value, together with a list of references to nodes (the "children"), with the constraints that no reference is duplicated, and none points to the root.

Alternatively, a tree can be defined abstractly as a whole (globally) as an ordered tree, with a value assigned to each node. Both these perspectives are useful: while a tree can be analyzed mathematically as a whole, when actually represented as a data structure it is usually represented and worked with separately by node (rather than as a list of nodes and an adjacency list of edges between nodes, as one may represent a digraph, for instance). For example, looking at a tree as a whole, one can talk about "the parent node" of a given node, but in general as a data structure a given node only contains the list of its children, but does not contain a reference to its parent (if any).

A tree is a (possibly non-linear) data structure made up of nodes or vertices and edges without having any cycle. The tree with no nodes is called the null or empty tree. A tree that is not empty consists of a root node and potentially many levels of additional nodes that form a hierarchy.

There is a distinction between a tree as an abstract data type and as a concrete data structure, analogous to the distinction between a list and a linked list. As a data type, a tree has a value and children, and the children are themselves trees; the value and children of the tree are interpreted as the value of the root node and the subtrees of the children of the root node. To allow finite trees, one must either allow the list of children to be empty (in which case trees can be required to be non-empty, an "empty tree" instead being represented by a forest of zero trees), or allow trees to be empty, in which case the list of children can be of fixed size (branching factor, especially 2 or "binary"), if desired.

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