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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 ...
An AA tree in computer science is a form of balanced tree used for storing and retrieving ordered data efficiently. 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 ...
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.
Instead of the small incremental rebalancing operations used by most balanced tree algorithms, scapegoat trees rarely but expensively choose a "scapegoat" and completely rebuilds the subtree rooted at the scapegoat into a complete binary tree. Thus, scapegoat trees have () worst-case update performance.
Binary trees labelled this way are used to implement binary search trees and binary heaps, and are used for efficient searching and sorting. The designation of non-root nodes as left or right child even when there is only one child present matters in some of these applications, in particular, it is significant in binary search trees. [10]
The B-tree generalizes the binary search tree, allowing for nodes with more than two children. [2] Unlike other self-balancing binary search trees, the B-tree is well suited for storage systems that read and write relatively large blocks of data, such as databases and file systems.
Searching for a specific key in an AVL tree can be done the same way as that of any balanced or unbalanced binary search tree. [8]: ch. 8 In order for search to work effectively it has to employ a comparison function which establishes a total order (or at least a total preorder) on the set of keys.
Then based on this generic tree, we can further come up with some special cases: (1) balanced binary tree; (2) linked list. [7] A balanced binary tree has exactly two branches for each vertex except for leaves. This gives a O(log n) bound on the depth of the tree. [8] A linked list is also a tree where every vertex has only one child.