On Generating All Binary Trees

  • Authors:
  • Władysław Skarbek

  • Affiliations:
  • Faculty of Electronics and Information Technology, Warsaw University of Technology, Nowowiejska 16/19, 02-665 Warszawa, Poland. E-mail: W.Skarbek@ire.pw.edu.pl

  • Venue:
  • Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
  • Year:
  • 2007

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Abstract

In context of Pawlak's machine a general iterative meta scheme for generating of combinatorial objects is introduced and applied to proof the correctness of ASR (Arm Switching and Rotation) algorithm generating all binary trees on k nodes. The average time complexity of the ASR algorithm and B* are analyzed and compared to the B algorithm discussed by Knuth. The analyzed algorithms are all obtained by various natural correspondences from author's DCP (Degrade and Compress Path) algorithm for generating all ordered trees on k+1 nodes.