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A double left rotation at X can be defined to be a right rotation at the right child of X followed by a left rotation at X; similarly, a double right rotation at X can be defined to be a left rotation at the left child of X followed by a right rotation at X. Tree rotations are used in a number of tree data structures such as AVL trees, red ...
Fig. 1: AVL tree with balance factors (green) In computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property.
Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:
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AVL trees and red–black trees are two examples of binary search trees that use the left rotation. A single left rotation is done in O(1) time but is often integrated within the node insertion and deletion of binary search trees. The rotations are done to keep the cost of other methods and tree height at a minimum.
The following other wikis use this file: Usage on ar.wikipedia.org شجرة AVL; Usage on bg.wikipedia.org АВЛ Дърво; Usage on bs.wikipedia.org AVL stabla; Usage on cs.wikipedia.org AVL-strom; List (graf) Usage on es.wikipedia.org Árbol AVL; Usage on fa.wikipedia.org درخت جستجوی دودویی خود-متوازن; Usage on fr ...
In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that can be used to implement dictionaries. The numbers mean a tree where every node with children (internal node) has either two, three, or four child nodes: a 2-node has one data element, and if internal has two child nodes;
A T-tree is implemented on top of an underlying self-balancing binary search tree. Specifically, Lehman and Carey's article describes a T-tree balanced like an AVL tree: it becomes out of balance when a node's child trees differ in height by at least two levels. This can happen after an insertion or deletion of a node.