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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 .
A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n, but the cost of search, insert, and delete operations grows with the depth of the tree. As with any balanced tree, the cost grows much more slowly than the number of elements.
WAVL trees are named after AVL trees, another type of balanced search tree, and are closely related both to AVL trees and red–black trees, which all fall into a common framework of rank balanced trees. Like other balanced binary search trees, WAVL trees can handle insertion, deletion, and search operations in time O(log n) per operation. [1] [2]
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
Lookup is not modified from a standard binary search tree, and has a worst-case time of ().This is in contrast to splay trees which have a worst-case time of ().The reduced node memory overhead compared to other self-balancing binary search trees can further improve locality of reference and caching.
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. These subtrees must all qualify as binary search trees.
Any change in structure does not affect performance due to balanced tree properties. [7] The data is stored in the leaf nodes and more branching of internal nodes helps to reduce the tree's height, thus, reduce search time. As a result, it works well in secondary storage devices. [8]
Below there is an implementation of splay trees in C++, which uses pointers to represent each node on the tree. This implementation is based on bottom-up splaying version and uses the second method of deletion on a splay tree. Also, unlike the above definition, this C++ version does not splay the tree on finds – it only splays on insertions ...