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With the new operations, the implementation of AVL trees can be more efficient and highly-parallelizable. [13] The function Join on two AVL trees t 1 and t 2 and a key k will return a tree containing all elements in t 1, t 2 as well as k. It requires k to be greater than all keys in t 1 and smaller than all keys in t 2.
For comparison, an AVL tree is guaranteed to be within a factor of 1.44 of the optimal height while requiring only two additional bits of storage in a naive implementation. [1] Therefore, most self-balancing BST algorithms keep the height within a constant factor of this lower bound.
Under this framework, the join operation captures all balancing criteria of different balancing schemes, and all other functions join have generic implementation across different balancing schemes. The join-based algorithms can be applied to at least four balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps.
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 ...
The library is available on GitHub. It uses the underlying balanced binary tree structure using join-based algorithms. [1] PAM supports four balancing schemes, including AVL trees, red-black trees, treaps and weight-balanced trees. PAM is a parallel library and is also safe for concurrency.
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]
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.
CGAL : Computational Geometry Algorithms Library in C++ contains a robust implementation of Range Trees; Boost.Icl offers C++ implementations of interval sets and maps. IntervalTree (Python) - a centered interval tree with AVL balancing, compatible with tagged intervals; Interval Tree (C#) - an augmented interval tree, with AVL balancing