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In computer science, a red–black tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree hold an extra "color" bit, often drawn as red and black, which help ensure that the tree is always approximately balanced.
AA trees are named after their originator, Swedish computer scientist Arne Andersson. [1] AA trees are a variation of the red–black tree, a form of binary search tree which supports efficient addition and deletion of entries. Unlike red–black trees, red nodes on an AA tree can only be added as a right subchild.
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WAVL trees, like red–black trees, use only a constant number of tree rotations, and the constant is even better than for red–black trees. [1] [2] WAVL trees were introduced by Haeupler, Sen & Tarjan (2015). The same authors also provided a common view of AVL trees, WAVL trees, and red–black trees as all being a type of rank-balanced tree. [2]
All of the red-black tree algorithms that have been proposed are characterized by a worst-case search time bounded by a small constant multiple of log N in a tree of N keys, and the behavior observed in practice is typically that same multiple faster than the worst-case bound, close to the optimal log N nodes examined that would be observed in a perfectly balanced tree.
2–3–4 trees are B-trees of order 4; [1] like B-trees in general, they can search, insert and delete in O(log n) time.One property of a 2–3–4 tree is that all external nodes are at the same depth.
The only thing about NIL nodes that is special for red-black trees is that it is useful to consider them to be black. 99.11.197.75 00:04, 5 May 2011 (UTC) NIL nodes seem to be an unneeded complexity while treating red-black trees, just the set of properties should be somewhat adjusted: Properties 2 and 3 deleted
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