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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, [ 1 ] [ 2 ] except for the root node, which has no parent (i.e., the ...
A rooted tree T that is a subgraph of some graph G is a normal tree if the ends of every T-path in G are comparable in this tree-order (Diestel 2005, p. 15). Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure.
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
The level ancestor query LA(v,d) requests the ancestor of node v at depth d, where the depth of a node v in a tree is the number of edges on the shortest path from the root of the tree to node v. It is possible to solve this problem in constant time per query, after a preprocessing algorithm that takes O( n ) and that builds a data structure ...
The Oxford English Dictionary records use of both the terms "tree structure" and "tree-diagram" from 1965 in Noam Chomsky's Aspects of the Theory of Syntax. [2] In a tree structure there is one and only one path from any point to any other point. Computer science uses tree structures extensively (see Tree (data structure) and telecommunications.)
Outside the tree, there is often a reference to the "root" node (the ancestor of all nodes), if it exists. Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left, mid or right child. Ternary trees are used to implement Ternary search trees and Ternary heaps.
A tree is called fully infinite if all its paths are infinite. Given an alphabet Σ, a Σ-labeled tree is a pair (T,V), where T is a tree and V: T → Σ maps each node of T to a symbol in Σ. A labeled tree formally defines a commonly used term tree structure. A set of labeled trees is called a tree language.
Using a simple binary heap data structure, Prim's algorithm can now be shown to ... Since tree Y 1 is a spanning tree of graph P, there is a path in tree Y 1 joining ...