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Both AVL trees and red–black (RB) trees are self-balancing binary search trees and they are related mathematically. Indeed, every AVL tree can be colored red–black, [14] but there are RB trees which are not AVL balanced. For maintaining the AVL (or RB) tree's invariants, rotations play an important role.
Interval Tree (C#) - an augmented interval tree, with AVL balancing; Interval Tree (Ruby) - a centered interval tree, immutable, compatible with tagged intervals; IntervalTree (Java) - an augmented interval tree, with AVL balancing, supporting overlap, find, Collection interface, id-associated intervals
AA tree; AVL tree; Binary search tree; Binary tree; Cartesian tree; Conc-tree list; Left-child right-sibling binary tree; Order statistic tree; Pagoda; Randomized binary search tree; Red–black tree; Rope; Scapegoat tree; Self-balancing binary search tree; Splay tree; T-tree; Tango tree; Threaded binary tree; Top tree; Treap; WAVL tree; Weight ...
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.
The performance of WAVL trees lie in between AVL trees and red-black trees. [citation needed] Red–black trees are also particularly valuable in functional programming, where they are one of the most common persistent data structures, used to construct associative arrays and sets that can retain previous versions after mutations.
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]
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:
Trees are widely used in various algorithms and data storage scenarios. Binary trees (particularly heaps), AVL trees, and B-trees are some popular types of trees. They enable efficient and optimal searching, sorting, and hierarchical representation of data. A trie, or prefix tree, is a special type of tree used to efficiently retrieve strings ...