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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 ...
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 ...
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.
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 ] Under this framework, the join operation captures all balancing criteria of different balancing schemes, and all other functions join have generic implementation across ...
A Binary Search Tree is a node-based data structure where each node contains a key and two subtrees, the left and right. For all nodes, the left subtree's key must be less than the node's key, and the right subtree's key must be greater than the node's key.
Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...