Acta Informatica

, Volume 28, Issue 7, pp 703–712 | Cite as

Postorder trees and Eulerian numbers

  • Thomas P. Whaley
Article

Abstract

Binary search trees built from the postorder traversal sequence of other binary search trees are characterized in terms of their binary tree structure. A connection is established between this structure and the Eulerian numbers. This yields considerable information concerning the “average” binary search tree with a given number of nodes. Periodicity is established for the process of repeatedly taking postorder sequences and building binary search trees. Finally, the average depth of a node in a postorder tree withn nodes is determined.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data structures and algorithms. Reading, MA: Addison Wesley 1983Google Scholar
  2. 2.
    Gassner, B.J.: Sorting by replacement selecting. Commun. ACM10, 89–93 (1967)Google Scholar
  3. 3.
    Knuth, D.E.: The art of computer programming, vol. 3, Reading, MA: Addison Wesley 1973Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Thomas P. Whaley
    • 1
  1. 1.Department of Computer ScienceWashington and Lee UniversityLexingtonUSA

Personalised recommendations