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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.
PAM (Parallel Augmented Maps) is an open-source parallel C++ library implementing the interface for sequence, ordered sets, ordered maps, and augmented maps. [1] The library is available on GitHub. It uses the underlying balanced binary tree structure using join-based algorithms . [ 1 ]
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
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 ...
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.
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]
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 ...