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The AVL tree is named after its two Soviet inventors, Georgy Adelson-Velsky and Evgenii Landis, who published it in their 1962 paper "An algorithm for the organization of information". [2] It is the oldest self-balancing binary search tree data structure to be invented. [3]
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]
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 ...
In 2016, Blelloch et al. formally proposed the join-based algorithms, and formalized the join algorithm for four different balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps. In the same work they proved that Adams' algorithms on union, intersection and difference are work-optimal on all the four balancing schemes.
Tree traversal. 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.
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.
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.
Using an AVL tree implementation of t, the algorithm has a running time of O(n log k). In order to assess the space requirement, assume that the elements of b can have m possible values, so the storage of a value v i needs O(log m) bits. Since each counter c i may have a value as high as n, its storage needs O(log n) bits.