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A visual proof for an average case of list searching

Published: 01 June 2008 Publication History

Abstract

This paper describes how the more mathematical topics in the data structures curriculum can be illustrated with visual proofs. This frees students from difficult algebraic manipulation. Visual proofs are provided for the average case of searching for a unique item in a list and for searching for an item which occurs independently (and not necessarily uniquely) in the list with a known probability.

References

[1]
Joint Task Force on Computing Curricula, Computing Curricula 2001, IEEE-CS and ACM, Appendix B, Dec. 15, 2001, pg. 165.
[2]
Roger B. Nelsen, Proofs without Words ---Exercises in Visual Thinking, Mathematical Association of America, Washington D.C., 1993, ISBN: 0-88385-700-6 pg 69.
[3]
Goodrich, M. T. and Tamassia, R. 1998. Teaching the analysis of algorithms with visual proofs. In Proceedings of the Twenty-Ninth SIGCSE Technical Symposium on Computer Science Education (Atlanta, Georgia, United States, February 26 - March 01, 1998). D. Joyce and J. Impagliazzo, Eds. SIGCSE '98. ACM Press, New York, NY, 207--211. DOI= http://doi.acm.org/10.1145/273133.274298
[4]
Tall, D, The Cognitive Development of Proof: Is Mathematical Proof For All or For Some?, Z. Usiskin (Ed.), Developments in School Mathematics Education Around the World, vol, 4, 117--136. Reston, Virginia: NCTM.
[5]
Borwein, P. and Jörgenson, L., 2001, Visible Structures in Number Theory, The American Mathematical Monthly, vol 108(10) 897--910, MAA.

Cited By

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  • (2017)Evaluating the Effectiveness of Algorithm Analysis VisualizationsProceedings of the 2017 ACM SIGCSE Technical Symposium on Computer Science Education10.1145/3017680.3017698(201-206)Online publication date: 8-Mar-2017
  • (2011)An alternative visual analysis of the build heap algorithmACM Inroads10.1145/2003616.20036302:3(31-32)Online publication date: 31-Aug-2011

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Published In

cover image ACM SIGCSE Bulletin
ACM SIGCSE Bulletin  Volume 40, Issue 2
June 2008
146 pages
ISSN:0097-8418
DOI:10.1145/1383602
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 June 2008
Published in SIGCSE Volume 40, Issue 2

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Author Tags

  1. analysis of algorithms
  2. computer science education
  3. data structures

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Cited By

View all
  • (2017)Evaluating the Effectiveness of Algorithm Analysis VisualizationsProceedings of the 2017 ACM SIGCSE Technical Symposium on Computer Science Education10.1145/3017680.3017698(201-206)Online publication date: 8-Mar-2017
  • (2011)An alternative visual analysis of the build heap algorithmACM Inroads10.1145/2003616.20036302:3(31-32)Online publication date: 31-Aug-2011

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