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For height-balanced binary trees, the height is defined to be logarithmic () in the number of items. This is the case for many binary search trees, such as AVL trees and red–black trees . 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.
A tournament tree can be represented as a balanced binary tree by adding sentinels to the input lists (i.e. adding a member to the end of each list with a value of infinity) and by adding null lists (comprising only a sentinel) until the number of lists is a power of two. The balanced tree can be stored in a single array.
The Day–Stout–Warren (DSW) algorithm is a method for efficiently balancing binary search trees – that is, decreasing their height to O(log n) nodes, where n is the total number of nodes. Unlike a self-balancing binary search tree , it does not do this incrementally during each operation, but periodically, so that its cost can be amortized ...
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height (the number of edges from the top-most node to the farthest node in a subtree) by no more than 1 (or the skew is no greater than 1). [22]
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.
These trees maintained all paths from root to leaf with the same number of nodes, creating perfectly balanced trees. However, they were not binary search trees. Bayer called them a "symmetric binary B-tree" in his paper and later they became popular as 2–3–4 trees or even 2–3 trees. [5] In a 1978 paper, "A Dichromatic Framework for ...
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.
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 ...