Yıl: 2021 Cilt: 27 Sayı: 1 Sayfa Aralığı: 52 - 59 Metin Dili: İngilizce DOI: 10.5505/pajes.2020.77906 İndeks Tarihi: 18-06-2021

Finding combinations of four-operations with Type-2 tree structure

Öz:
Combination problems are one of the most important issues ofprobability theory. The four-operations combination problem underliesthe basis of some competition programs broadcasted in many nationalchannels. In these competition programs, the competitors are expectedto reach the target number by using six numbers and four basicarithmetic operators. The numbers are used at most once, the operatorscan be used any desired number to reach the target number. In thisproblem, all four-operations combinations include the operation blocksconsisting of two numbers and an operator. Therefore, the fouroperationscombination problem is solved by developing a "Type-2 TreeStructure" which is a new approach to accurately model the operationblocks. The performance of the proposed method for the four-operationscombination problem is examined by a simulation study. Also, thestatistics from experimental results are given in this study.
Anahtar Kelime:

Tip-2 arama yöntemiyle dört işlem kombinasyonlarının bulunması

Öz:
Kombinasyon problemleri olasılık teorisinin en önemli konularından biridir. Dört işlem kombinasyon problemi, birçok ulusal kanalda yayınlanan bazı yarışma programlarının temelini oluşturmaktadır. Bu yarışma programlarında, yarışmacıların 6 adet sayı ve dört işlem operatörlerini kullanarak, hedef sayıya ulaşması beklenmektedir. Hedeflenen sayıya ulaşmak için sayılar en fazla bir kez kullanılırken, dört işlem operatörleri istenilen sayıda kullanılabilir. Bu problemde, bulunacak olası tüm dört işlem kombinasyonları iki sayı ve bir operatörden oluşan işlem öbeklerini içermektedir. Dolayısıyla işlem öbeklerini tam anlamıyla modelleyebilmek için yeni bir yaklaşım olan “Tip-2 Ağaç” yapısı geliştirilerek dört işlem kombinasyon problemi çözülmüştür. Dört işlem kombinasyon problemi için önerilen yöntemin performansı bir simülasyon çalışması ile incelenmiştir. Ayrıca deneysel sonuçlardan elde edilen istatistikler de bu çalışmada verilmiştir.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Colton S. “Countdown numbers game: solved, analysed, extended”. Proceedings of the AISB Symposium on AI and Games, Canterbury, London, 1 April 2014.
  • [2] Defays D. L'esprit en Friche: les Foisonnements de l'intelligence Artificielle. Liege, Belgium, Pierre Mardaga, 1988.
  • [3] Defays D. Numbo: A Study in Cognition and Recognition. Editor: Hofstadter D. Fluid Concepts and Creative Analogies, 131-154, Basic Books Inc, 1995.
  • [4] Hutton G. “The countdown problem”. Journal of Functional Programming, 12(06), 609-616, 2002.
  • [5] Alliot JM. “The (Final) Countdown”. https://arxiv.org/abs/1502.05450 (03.06.2020).
  • [6] Fischler MA, Bolles RC. “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography”. Communications of the ACM, 24(6), 381-395, 1981.
  • [7] Montgomery DC, Runger GC. Applied Statistics and Probability for Engineers. 5th ed. Jefferson City, USA, John Wiley & Sons, 2011.
  • [8] Hines WW, Montgomery DC, Goldsman DM, Borror CM. Probability and Statistics in Engineering. Danvers, Massachusetts, USA, John Wiley & Sons, 2008.
  • [9] Code D. Probability: Mastering Permutations and Combinations. 2nd ed. California, USA, CreateSpace Independent Publishing Platform, 2017.
  • [10] Crawshaw J, Chambers J. A Concise Course in Advanced Level Statistics: With Worked Examples. 6th ed. London, UK, Oxford University Press, 2015.
  • [11] Tier R. Probability with Permutations and Combinations: A Deeper and More Thorough Look at the Fundamental Equations. California, USA, CreateSpace Independent Publishing Platform, 2017.
  • [12] Nicolaides A. Pure Mathematics Series: 10. Combinations, Permutations, Probabilities. London, UK, PASS Publications, 1994.
  • [13] Puntambekar A. Analysis and design of algorithms. 1st ed. Pune, India, Technical Publications, 2008.
  • [14] Mueller J, Massaron L. Algorithms for Dummies. Hoboken, USA, John Wiley & Sons, 2017.
  • [15] Goodrich MT, Tamassia R, Goldwasser, MH. Data Structures and Algorithms in Java. 6th ed. Hoboken, USA, John Wiley & Sons, 2014.
  • [16] Saha S, Shukla S. Advanced Data Structures: Theory and Applications. Boca Raton, USA, CRC Press: Taylor & Francis, 2019.
APA ÖZKUL E, TİRYAKİ B, TEZEL Ö, AĞAYEV E, KESEMEN O (2021). Finding combinations of four-operations with Type-2 tree structure. , 52 - 59. 10.5505/pajes.2020.77906
Chicago ÖZKUL Eda,TİRYAKİ Buğra Kaan,TEZEL Özge,AĞAYEV Elçin,KESEMEN Orhan Finding combinations of four-operations with Type-2 tree structure. (2021): 52 - 59. 10.5505/pajes.2020.77906
MLA ÖZKUL Eda,TİRYAKİ Buğra Kaan,TEZEL Özge,AĞAYEV Elçin,KESEMEN Orhan Finding combinations of four-operations with Type-2 tree structure. , 2021, ss.52 - 59. 10.5505/pajes.2020.77906
AMA ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O Finding combinations of four-operations with Type-2 tree structure. . 2021; 52 - 59. 10.5505/pajes.2020.77906
Vancouver ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O Finding combinations of four-operations with Type-2 tree structure. . 2021; 52 - 59. 10.5505/pajes.2020.77906
IEEE ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O "Finding combinations of four-operations with Type-2 tree structure." , ss.52 - 59, 2021. 10.5505/pajes.2020.77906
ISNAD ÖZKUL, Eda vd. "Finding combinations of four-operations with Type-2 tree structure". (2021), 52-59. https://doi.org/10.5505/pajes.2020.77906
APA ÖZKUL E, TİRYAKİ B, TEZEL Ö, AĞAYEV E, KESEMEN O (2021). Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 27(1), 52 - 59. 10.5505/pajes.2020.77906
Chicago ÖZKUL Eda,TİRYAKİ Buğra Kaan,TEZEL Özge,AĞAYEV Elçin,KESEMEN Orhan Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 27, no.1 (2021): 52 - 59. 10.5505/pajes.2020.77906
MLA ÖZKUL Eda,TİRYAKİ Buğra Kaan,TEZEL Özge,AĞAYEV Elçin,KESEMEN Orhan Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, vol.27, no.1, 2021, ss.52 - 59. 10.5505/pajes.2020.77906
AMA ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2021; 27(1): 52 - 59. 10.5505/pajes.2020.77906
Vancouver ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2021; 27(1): 52 - 59. 10.5505/pajes.2020.77906
IEEE ÖZKUL E,TİRYAKİ B,TEZEL Ö,AĞAYEV E,KESEMEN O "Finding combinations of four-operations with Type-2 tree structure." Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 27, ss.52 - 59, 2021. 10.5505/pajes.2020.77906
ISNAD ÖZKUL, Eda vd. "Finding combinations of four-operations with Type-2 tree structure". Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 27/1 (2021), 52-59. https://doi.org/10.5505/pajes.2020.77906