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Splay trees and treaps are self-balancing but not height-balanced, as their height is not guaranteed to be logarithmic in the number of items. Self-balancing binary search trees provide efficient implementations for mutable ordered lists, and can be used for other abstract data structures such as associative arrays, priority queues and sets.
The splay tree is a form of binary search tree invented in 1985 by Daniel Sleator and Robert Tarjan on which the standard search tree operations run in ( ()) amortized time. [10] It is conjectured to be dynamically optimal in the required sense. That is, a splay tree is believed to perform any sufficiently long access sequence X in time O ...
A weight-balanced tree is a binary search tree that stores the sizes of subtrees in the nodes. That is, a node has fields key, of any ordered type; value (optional, only for mappings) left, right, pointer to node; size, of type integer. By definition, the size of a leaf (typically represented by a nil pointer) is zero.
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
In computer science, a scapegoat tree is a self-balancing binary search tree, invented by Arne Andersson [2] in 1989 and again by Igal Galperin and Ronald L. Rivest in 1993. [1] It provides worst-case O ( log n ) {\displaystyle {\color {Blue}O(\log n)}} lookup time (with n {\displaystyle n} as the number of entries) and O ( log n ...
In computer science, join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized algorithms for various balanced binary search trees. The algorithmic framework is based on a single operation join. [1]
In computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property.
As with binary search trees more generally, a WAVL tree consists of a collection of nodes, of two types: internal nodes and external nodes.An internal node stores a data item, and is linked to its parent (except for a designated root node that has no parent) and to exactly two children in the tree, the left child and the right child.