On the Variance of the Height of Random Binary Search Trees

  • Authors:

  • Luc Devroye;Bruce Reed

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1995

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Abstract

Let $H_n$ be the height of a random binary search tree on $n$ nodes. We show that there exists a constant $\alpha = 4.31107\ldots$ such that ${\rm P} \{ |H_n - \alpha \log n | \beta \log \log n \} \to 0$, where $\beta15 \alpha / \ln 2 = 93.2933\ldots$. The proof uses the second moment method and does not rely on properties of branching processes. We also show that $\Var \{ H_n \} = O( (\log \log n)^2)$.