A simple bound for sequential access in splay trees
نویسنده
چکیده
It is known that to traverse a binary tree in inorder, by repeated splay-to-root, uses O(n) rotations. Estimates vary from 15n to 4.5n in proofs of varying length and difficulty. We present a fairly easy estimate of 6n rotations. (1) The process under consideration is inorder traversal of a binary tree using repeated splay-to-root: n is the number of nodes in the tree. Call the operation of seeking the next node in inorder a ‘fetch’: the first fetch seeks the leftmost node in the tree, then brings it to the root by splaying; subsequently, each fetch operation seeks the leftmost child of the root’s right child and brings it to the root by splaying. In the illustration, first x0 is fetched, then y:
منابع مشابه
On the sequential access theorem and deque conjecture for splay trees
We give a new, simple proof for the sequential access theorem for splay trees. For an n-node splay tree, our bound on the number of rotations is 4:5n, with a smaller constant than the bound of 10:8n concluded by Tarjan. We extend our proof to prove the deque conjecture for output-restricted deques. Our proofs provide additional insights into the workings of splay trees. c © 2004 Elsevier B.V. A...
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