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A Comparison of Warnsdorff’s Rule and Backtracking for Knight’s Tour on Square Boards

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Emerging Research in Electronics, Computer Science and Technology

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 545))

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Abstract

Knight’s tour has been an intriguing chess puzzle for many computer scientists and mathematicians. In this paper, we describe and analyze two of the most commonly used algorithms to solve the Knight’s tour puzzle in computer science—Warnsdorff’s rule and backtracking. Various case studies are performed to showcase the differences in time complexity of each algorithm. We also point out that the starting position and dimensions of a board play a key role in determining whether a tour is possible. By doing this, we prove that a tour does not exist when the knight starts from odd squares on boards of odd dimensions.

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References

  1. McGown K, Leininger A (2002) Knight’s tours. Cull, Paul (advisor). Oregon State Univesity, MIT and Oregon State University, 15 Aug 2002

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  2. Bi B, Butler S, DeGraaf S, Doebel E (2015) Knight’s tours on boards with odd dimensions. Involv J Math 8(4):615–616

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  3. Squirrel D, Cull P (1996) A warnsdorff-rule algorithm for knight’s tours on square boards

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  4. Stack Overflow (2018) https://stackoverflow.com/questions/19214109/how-to-optimize-knights-tour-algorithm. Accessed 09 June 2018

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, New Horizon College of Engineering, Bangalore, India

    M. Pranav & S. Nithin

  2. Department of Information Science and Engineering, New Horizon College of Engineering, Bangalore, India

    N. Guruprasad

Authors
  1. M. Pranav
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  2. S. Nithin
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  3. N. Guruprasad
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Corresponding author

Correspondence to M. Pranav .

Editor information

Editors and Affiliations

  1. Department of Electronics and Communication Engineering, PES College of Engineering, Mandya, Karnataka, India

    V. Sridhar

  2. Department of Computer Science and Engineering, PES College of Engineering, Mandya, Karnataka, India

    M.C. Padma

  3. Department of Electronics and Communication Engineering, PES College of Engineering, Mandya, Karnataka, India

    K.A. Radhakrishna Rao

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© 2019 Springer Nature Singapore Pte Ltd.

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Cite this paper

Pranav, M., Nithin, S., Guruprasad, N. (2019). A Comparison of Warnsdorff’s Rule and Backtracking for Knight’s Tour on Square Boards. In: Sridhar, V., Padma, M., Rao, K. (eds) Emerging Research in Electronics, Computer Science and Technology. Lecture Notes in Electrical Engineering, vol 545. Springer, Singapore. https://doi.org/10.1007/978-981-13-5802-9_16

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  • DOI: https://doi.org/10.1007/978-981-13-5802-9_16

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-5801-2

  • Online ISBN: 978-981-13-5802-9

  • eBook Packages: EngineeringEngineering (R0)

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