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Animation showing the insertion of several elements into an AVL tree. It includes left, right, left-right and right-left rotations. 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.
An augmented tree can be built from a simple ordered tree, for example a binary search tree or self-balancing binary search tree, ordered by the 'low' values of the intervals. An extra annotation is then added to every node, recording the maximum upper value among all the intervals from this node down.
For example, if binary tree sort is implemented with a self-balancing BST, we have a very simple-to-describe yet asymptotically optimal () sorting algorithm. Similarly, many algorithms in computational geometry exploit variations on self-balancing BSTs to solve problems such as the line segment intersection problem and the point location ...
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.
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;
Trees are used throughout computer science and many different types of trees – binary search trees, AVL trees, red–black trees, and 2–3 trees to name just a small few – have been developed to properly store, access, and manipulate data while maintaining their structure. Trees are a principal data structure for dictionary implementation.
The worst-case height of AVL is 0.720 times the worst-case height of red-black trees, so AVL trees are more rigidly balanced. The performance measurements of Ben Pfaff with realistic test cases in 79 runs find AVL to RB ratios between 0.677 and 1.077, median at 0.947, and geometric mean 0.910. [22] The performance of WAVL trees lie in between ...
The depth of a tree is the maximum depth of any vertex. Depth is commonly needed in the manipulation of the various self-balancing trees, AVL trees in particular. The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and leaf) has depth and height zero.