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  2. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    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.

  3. Interval tree - Wikipedia

    en.wikipedia.org/wiki/Interval_tree

    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

  4. List of data structures - Wikipedia

    en.wikipedia.org/wiki/List_of_data_structures

    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 ...

  5. Join-based tree algorithms - Wikipedia

    en.wikipedia.org/wiki/Join-based_tree_algorithms

    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.

  6. Red–black tree - Wikipedia

    en.wikipedia.org/wiki/Red–black_tree

    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.

  7. Binary search tree - Wikipedia

    en.wikipedia.org/wiki/Binary_search_tree

    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]

  8. Self-balancing binary search tree - Wikipedia

    en.wikipedia.org/wiki/Self-balancing_binary...

    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:

  9. Data structure - Wikipedia

    en.wikipedia.org/wiki/Data_structure

    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 ...