Affiliation:
1. McGill Univ., Montreal, Canada
Abstract
Let
H
n
be the height of a binary search tree with
n
nodes constructed by standard insertions from a random permutation of 1, … ,
n
. It is shown that
H
n
/log
n
→
c
= 4.31107 … in probability as
n
→ ∞, where
c
is the unique solution of
c
log((2
e
)/
c
) = 1,
c
≥ 2. Also, for all
p
> 0, lim
n
→∞
E
(
H
p
n
)/ log
p
n
=
c
p
. Finally, it is proved that
S
n
/log
n
→
c
*
= 0.3733 … , in probability, where
c
*
is defined by
c
log((2
e
)/
c
) = 1,
c
≤ 1, and
S
n
is the saturation level of the same tree, that is, the number of full levels in the tree.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
161 articles.
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