On the maximum path length of AVL trees

  • Rolf Klein
  • Derick Wood
Tree Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 299)


We prove that the internal path length of an AVL tree of size N is bounded from above by
$$1.4404N(\log _2 N - \log _2 \log _2 N) + O(N)$$
and show that this bound is achieved by an infinite family of AVL trees. But AVL trees of maximal height do not have maximal path length. These results carry over to the comparison cost of brother trees.

Key words

AVL trees brother trees path length comparison cost node visit cost 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Rolf Klein
    • 1
  • Derick Wood
    • 2
  1. 1.Institut für InformatikUniversität FreiburgFreiburgFed. Rep. of Germany
  2. 2.Data Structuring Group, Department of Computer ScienceUniversity of WaterlooWATERLOOCanada

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