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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.
In computer science, a self-balancing binary search tree (BST) is any node -based binary search tree that automatically keeps its height (maximal number of levels below the root) small in the face of arbitrary item insertions and deletions. [ 1 ] These operations when designed for a self-balancing binary search tree, contain precautionary ...
In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced. [1]
WAVL tree. In computer science, a WAVL tree or weak AVL tree is a self-balancing binary search tree. WAVL trees are named after AVL trees, another type of balanced search tree, and are closely related both to AVL trees and red–black trees, which all fall into a common framework of rank balanced trees. Like other balanced binary search trees ...
Various height-balanced binary search trees were introduced to confine the tree height, such as AVL trees, Treaps, and red–black trees. [5] The AVL tree was invented by Georgy Adelson-Velsky and Evgenii Landis in 1962 for the efficient organization of information. [6] [7] It was the first self-balancing binary search tree to be invented. [8]
Day–Stout–Warren algorithm. The Day–Stout–Warren (DSW) algorithm is a method for efficiently balancing binary search trees – that is, decreasing their height to O (log n) nodes, where n is the total number of nodes. Unlike a self-balancing binary search tree, it does not do this incrementally during each operation, but periodically ...
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields. key, of any ordered type. value (optional, only for mappings) left, right, pointer to node. size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.
Generic tree rotations. In discrete mathematics, tree rotation is an operation on a binary tree that changes the structure without interfering with the order of the elements. A tree rotation moves one node up in the tree and one node down. It is used to change the shape of the tree, and in particular to decrease its height by moving smaller ...