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An analytic approach to the height of binary search trees

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Abstract

By using analytic tools it is shown that the expected value of the heightH n of binary search trees of sizen is asymptotically given by EH n =c logn+\(\mathcal{O}\) (log logn) and its variance by VH n =\(\mathcal{O}\)((log logn)2), wherec=4.31107 …. The same bounds have been obtained by Devroye and Reed [3] by completely different methods.

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Authors and Affiliations

  1. Institute für Geometrie, TU Wien, Wiedner Hauptstrasse 8-10/118, A-1040, Wien, Austria

    M. Drmota

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  1. M. Drmota
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Additional information

Communicated by H. Prodinger and W. Szpankowski.

Dedicated to Philippe Flajolet on the occasion of his 50th birthday

This research was supported by the Austrian Science Foundation FWF, Grant P10187-MAT.

Online publication September 22, 2000.

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Drmota, M. An analytic approach to the height of binary search trees. Algorithmica 29, 89–119 (2001). https://doi.org/10.1007/BF02679615

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  • DOI: https://doi.org/10.1007/BF02679615

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