The Variance of the height of binary search trees

The Variance of the height of binary search trees

Profile and Height of Random Binary Search Trees

The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.

The Height of Binary Search Trees

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The Height of q-Binary Search Trees

The paper [8] introduces for the first time a meaningful q–model of binary search trees: instead of binary search trees, one considers tournament trees, which differ only marginally from binary search trees; if one starts from a permutation ( 1 2 ··· n π1 π2 ··· πn ) , then one inserts the number i instead of the number πi. Thus, traversing the tree in inorder, we might think of the associated ...

On the Variance of the Height of Random Binary Search Trees

Let Hn be the height of a random binary search tree on n nodes. We show that there exists a constant a = 4.31107. .. such that P { I Hn-a log n i > f log log n }-+ 0, where > 15a/ In 2 = 93 .2933. .. . The proof uses the second moment method and does not rely on properties of branching processes. We also show that Var{Hn } = O ((lag log n) 2). 1. Introduction. The height Hn of a random binary s...