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This is a list of well-known data structures. For a wider list of terms, see list of terms relating to algorithms and data structures. For a comparison of running times for a subset of this list see comparison of data structures.
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.
In 2016, Blelloch et al. formally proposed the join-based algorithms, and formalized the join algorithm for four different balancing schemes: AVL trees, red–black trees, weight-balanced trees and treaps. In the same work they proved that Adams' algorithms on union, intersection and difference are work-optimal on all the four balancing schemes.
The weak AVL tree is defined by the weak AVL rule: Weak AVL rule: all rank differences are 1 or 2, and all leaf nodes have rank 0. Note that weak AVL tree generalizes the AVL tree by allowing for 2,2 type node. A simple proof shows that a weak AVL tree can be colored in a way that represents a red-black tree.
AVL Trees and also Red Black Trees both perform in O(lg n). However, for AVL trees it is < 1.44 lg n, whereas for Red Black Trees it is < 2 lg n, hence AVL trees are faster. However, AVL trees are much more complicated to implemenent. Gulliveig 04:47, 11 June 2006 (UTC) I strongly disagree.
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Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild. In other words, no red node can be a left sub-child. This results in the simulation of a 2–3 tree instead of a 2–3–4 tree, which greatly simplifies the maintenance operations. The maintenance algorithms for a red–black tree need to consider seven ...
English: A table showing the 4 cases of AVL tree rebalancing using rotations. Note added regarding double rotations on 2016-05-27 Note added regarding double rotations on 2016-05-27 Date