In this paper we prove that if the nodes of an arbitrary <mml:math alttext="$n$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi></mml:math>-node binary search tree <mml:math alttext="$T$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> are splayed according to the preorder sequence of <mml:math alttext="$T$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>T</mml:mi></mml:math> then the total time is <mml:math alttext="$O\left( n \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. This is a special case of the splay tree traversal conjecture of Sleator and Tarjan [1].

International Journal of Mathematics and Mathematical Sciences

Splaying a search tree in preorder takes linear time

Abstract

Copyright