Abstract

In this paper we prove that if the nodes of an arbitrary no-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.

Highlights

  • A binary search tree in which we splay after each access to the node containing the accessed item is called a splay tree

  • < (a) splay depth (SD)(left(x)) d/2 + 3/2 and (b) SD(right(x))< + IA(z,x)l where z is the preorder predecessor of right(x) and IA(z,x)l denotes the cardinality of the set A(z,x)

  • The total time to splay an n-node binary search tree T according to its own preorder sequence is at most 8n

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Summary

Introduction

A binary search tree in which we splay after each access to the node containing the accessed item is called a splay tree.

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