AVL_tree

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AVL tree From Wikipedia, the free encyclopedia In computer science, an AVL tree is a self-balancing binary search tree, and it is the first such data structure to be invented. [1] In an AVL tree, the heights of the two child subtrees of any node differ by at most one; therefore, it is also said to be height-balanced. Lookup, insertion, and deletion all take O(log n ) time in both the average and worst cases, where n is the number of nodes in the tree prior to the operation. Insertions and deletions may require the tree to be rebalanced by one or more tree rotations. The AVL tree is named after its two inventors, G.M. Adelson-Velsky and E.M. Landis, who published it in their 1962 paper "An algorithm for the organization of information." The balance factor of a node is the height of its right subtree minus the height of its left subtree and a node with balance factor 1, 0, or -1 is considered balanced. A node with any other balance factor is considered unbalanced and requires rebalancing the tree. The balance factor is either stored directly at each node or computed from the heights of the subtrees. AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O(log n ) time for the basic operations. AVL trees perform better than red-black trees for lookup-intensive applications. [2] The AVL tree balancing algorithm appears in many computer science curricula. Operations The basic operations of an AVL tree generally involve carrying out the same actions as would be carried out on an unbalanced binary search tree, but preceded or followed by one or more operations called tree rotations, which help to restore the height balance of the subtrees. Insertion Insertion into an AVL tree may be carried out by inserting the given value into the tree as if it were an unbalanced binary search tree, and then retracing one's steps toward the root updating the balance factor of the nodes. If the balance factor becomes -1, 0, or 1 then the tree is still in AVL form, and no rotations are necessary.

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AVL_tree - AVL tree Make a donation to Wikipedia and give...

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