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To traverse arbitrary trees (not necessarily binary trees) with depth-first search, perform the following operations at each node: If the current node is empty then return. Visit the current node for pre-order traversal. For each i from 1 to the current node's number of subtrees − 1, or from the latter to the former for reverse traversal, do:
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
Search trees store data in a way that makes an efficient search algorithm possible via tree traversal. A binary search tree is a type of binary tree; Representing sorted lists of data; Computer-generated imagery: Space partitioning, including binary space partitioning; Digital compositing; Storing Barnes–Hut trees used to simulate galaxies ...
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
6-ary tree represented as a binary tree. Every multi-way or k-ary tree structure studied in computer science admits a representation as a binary tree, which goes by various names including child-sibling representation, [1] left-child, right-sibling binary tree, [2] doubly chained tree or filial-heir chain.
First, the tree is turned into a linked list by means of an in-order traversal, reusing the pointers in the tree's nodes. A series of left-rotations forms the second phase. [3] The Stout–Warren modification generates a complete binary tree, namely one in which the bottom-most level is filled strictly from left to right.
In computer science, a B-tree is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree generalizes the binary search tree, allowing for nodes with more than two children. [2]
A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full binary tree.