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Algorithms for Construction and Enumeration of Closed Knight’s Paths

v.genkov@azbuki.bg от v.genkov@azbuki.bg
29-04-2023
in Uncategorized
A A

Prof. DSc. Stoyan Kapralov1), Assoc. Prof. Dr.Valentin Bakoev2),
Kaloyan Kapralov3)
1)University of Gabrovo (Bulgaria)
2)“St. Cyril and St. Methodius” University of Veliko Tarnovo (Bulgaria)
3)Sofia (Bulgaria)

https://doi.org/10.53656/math2023-2-1-alg

Abstract. Two algorithms for constructing all closed knight’s paths of lengths up to 16 are presented. An approach for classification (up to equivalence) of all such paths is considered. Two closed knight’s paths are called equivalent if one can be obtained from the other by applying one or more of the equivalences: translation, rotation, symmetry, or when the corresponding polygons (whose vertices are the cells visited by the knight), are geometrically congruent. By applying the construction algorithms and classification approach, we enumerate both nonequivalent and non-self-intersecting knight’s paths and show the obtained results. Some pedagogical aspects related to the problems under consideration and the teaching of subjects such as “Programming”, “Algorithms and Data Structures”, “Graph Algorithms” and “Competitive Programming” are also discussed.
Keywords: knight graph; closed knight’s path; nonequivalent path; non-self-intersecting path; equivalence; enumeration

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    • About us
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  • Az-buki Weekly
  • Editions
    • Strategies for Policy in Science and Education
    • Bulgarian Language and Literature
    • Pedagogika-Pedagogy
    • Mathematics and Informatics
    • Natural Science and Advanced Technology Education
    • Vocational Education
    • Istoriya-History journal
    • Chuzhdoezikovo Obuchenie-Foreign Language Teaching
    • Filosofiya-Philosophy
    • Az-buki Weekly
  • Monographs, Proceedings
    • Proceedings of 3-rd International Scientific Conference “Industrial Growth Conference 2024”
    • ННП „Oпазване на околната среда и намаляване на риска от неблагоприятни явления и природни бедствия“
    • Помагало по български език „Приятели“ A2
    • Приятели А1 – А2 част 2
    • Приятели А1 – А2 част 1
    • Fascination: E.T.A. Hoffmann
    • III Национална училищна конференция ,,Споделени педагогически практики в преподаването на природни науки”
    • Да литна високо в небето… / Volare in Alto nel Cielo…
    • ПЛАМЕННИ НАДЕЖДИ
    • АТЛАС „КИРИЛ И МЕТОДИЙ“
    • Demographic Situation and Labour Market in Blagoevgrad and Kyustendil Districts
    • Proceeding of 1st International Conference on Environmental Protection and Disaster RISKs
    • Bulgaria - North Macedonia - Slovenia: Intercultural Dialogues in XXI Century
    • Methodology for strategic planning of national energy
    • Europe’s Core-Periphery Relations and Horizontal Disparities
    • Bulgaria - Macedonia - Slovenia: Intercultural Dialogues in the 21st Century, Part II
    • Local and Regional Aspects of Natural Hazards
    • ADAPTED METHODOLOGY OF HISTORY EDUCATION
    • VASIL LEVSKI. FROM THE CURVES OF LITERARY ICONOGRAPHY
    • Bulgaria - Macedonia - Slovenia: Intercultural Dialogues in the 21st Century
    • Gender World In Different Cultural Models
    • ADAPTED METHODOLOGY OF HISTORY EDUCATION 2
    • THEORETICAL MODEL FOR A CUMULATIVE LEXICOGRAPHING OF WORDS OF FOREIGN ORIGIN IN THE BULGARIAN LANGUAGE
    • БЪЛГАРСКИЯТ ЕЗИК, ЛИТЕРАТУРА И КУЛТУРА: ПЪТИЩА ПРЕЗ МУЛТИКУЛТУРНИЯ СВЯТ
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