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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 3, Pages 545-551

Splaying a search tree in preorder takes linear time

Department of Computer Science, Eastern Michigan University, Ypsilanti 48197, Michigan, USA

Received 31 May 1990; Revised 1 November 1990

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we prove that if the nodes of an arbitrary n-node binary search tree T are splayed in the preorder sequence of T then the total time is O(n). This is a special case of the splay tree traversal conjecture of Sleator and Tarjan.