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Counting nodes in binary trees

Published: 01 February 1986 Publication History

Abstract

This paper describes an original method for introducing linear recurrence relations. Boolean expressions are represented by binary trees and the counting of the internal nodes of these trees yield linear recurrence relations. The method allows the students to create their own family of Boolean expressions, to draw the corresponding binary trees, to deduce the recurrence relation representing the number of nodes in the trees, and finally, to solve and check the solutions of these relations.

References

[1]
C. L. Liu, Elements of Discrete Mathematics. New York: McGraw-Hill Computer Science Series, 1977.
[2]
P. W. Purdon, and C. A. Brown, The Analysis of Algorithms. Holt, Rinehart and Winston, 1985.
[3]
A. S. Tanenbaum, Computer Networks. New Jersey: Prentice-Hall, Inc., 1981.

Cited By

View all
  • (1994)Understanding the bottom-up SLR parserACM SIGCSE Bulletin10.1145/191033.19116326:1(339-343)Online publication date: 12-Mar-1994
  • (1994)Understanding the bottom-up SLR parserProceedings of the twenty-fifth SIGCSE symposium on Computer science education10.1145/191029.191163(339-343)Online publication date: 12-Mar-1994

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  1. Counting nodes in binary trees

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                          Douglas M. Campbell

                          Khuri uses binary trees to introduce elementary linear first order recurrence relations to students in a beginning data structure course. The equations are solved by tricks, rather than by the formal theory. Students are encouraged to discover and solve similar recurrence relations for other structures.

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                          Published In

                          cover image ACM SIGCSE Bulletin
                          ACM SIGCSE Bulletin  Volume 18, Issue 1
                          Proceedings of the 17th SIGCSE symposium on Computer science education
                          February 1986
                          304 pages
                          ISSN:0097-8418
                          DOI:10.1145/953055
                          Issue’s Table of Contents
                          • cover image ACM Conferences
                            SIGCSE '86: Proceedings of the seventeenth SIGCSE technical symposium on Computer science education
                            February 1986
                            336 pages
                            ISBN:0897911784
                            DOI:10.1145/5600
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                          Association for Computing Machinery

                          New York, NY, United States

                          Publication History

                          Published: 01 February 1986
                          Published in SIGCSE Volume 18, Issue 1

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                          Cited By

                          View all
                          • (1994)Understanding the bottom-up SLR parserACM SIGCSE Bulletin10.1145/191033.19116326:1(339-343)Online publication date: 12-Mar-1994
                          • (1994)Understanding the bottom-up SLR parserProceedings of the twenty-fifth SIGCSE symposium on Computer science education10.1145/191029.191163(339-343)Online publication date: 12-Mar-1994

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