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Author Devroye, Luc
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1986
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Let $\textit{Hn}$ be the height of a binary search tree with $\textit{n}$ nodes constructed by standard insertions from a random permutation of 1, … , $\textit{n}.$ It is shown that $\textit{Hn}/log$ $\textit{n}$ → $\textit{c}$ = 4.31107 … in probability as $\textit{n}$ → ∞, where $\textit{c}$ is the unique solution of $\textit{c}$ $log((2\textit{e})/\textit{c})$ = 1, $\textit{c}$ ≥ 2. Also, for all $\textit{p}$ > 0, $lim\textit{n}→∞\textit{E}(\textit{Hpn})/$ $log\textit{pn}$ = $\textit{cp}.$ Finally, it is proved that $\textit{Sn}/log$ $\textit{n}$ → $\textit{c}*$ = 0.3733 … , in probability, where $\textit{c}*$ is defined by $\textit{c}$ $log((2\textit{e})/\textit{c})$ = 1, $\textit{c}$ ≤ 1, and $\textit{Sn}$ is the saturation level of the same tree, that is, the number of full levels in the tree.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1986-05-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 33
Issue Number 3
Page Count 10
Starting Page 489
Ending Page 498


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Source: ACM Digital Library