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

Key Findings & Data:Therefore, the four-operations combination problem is solved by developing a "Type-2 Tree Structure" which is a new approach to accurately model the operation blocks.

💡

Conclusion & Impact:Also, the statistics from experimental results are given in this study.

🔬Design:Modeling & Simulation

📍Scope:Comprehensive Sample

⚙️Variables:Combination · Four-Operations · Type-2 tree

Abstract

Combination problems are one of the most important issues of probability theory. The four-operations combination problem underlies the basis of some competition programs broadcasted in many national channels. In these competition programs, the competitors are expected to reach the target number by using six numbers and four basic arithmetic operators. The numbers are used at most once, the operators can be used any desired number to reach the target number. In this problem, all four-operations combinations include the operation blocks consisting of two numbers and an operator. Therefore, the four-operations combination problem is solved by developing a "Type-2 Tree Structure" which is a new approach to accurately model the operation blocks. The performance of the proposed method for the four-operations combination problem is examined by a simulation study. Also, the statistics from experimental results are given in this study.

Keywords

Combination Four-Operations Type-2 tree Operation block

🔖

Cite This Article

ÖZKUL, E., TİRYAKİ, B. K., TEZEL, Ö., AĞAYEV, E., KESEMEN, O. (2021). Finding combinations of four-operations with Type-2 tree structure. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, Cilt: 27 - Sayı: 1, 52–59. https://ajindex.com/articles/83319

📄 Full Text PDF Viewer

Open in New Tab ↗

↗New Tab

📄

PDF görüntüleyici hazırlanıyor...

References (16)

Colton S. “Countdown numbers game: solved, analysed, extended”. Proceedings of the AISB Symposium on AI and Games, Canterbury, London, 1 April 2014
Defays D. L'esprit en Friche: les Foisonnements de l'intelligence Artificielle. Liege, Belgium, Pierre Mardaga, 1988
Defays D. Numbo: A Study in Cognition and Recognition. Editor: Hofstadter D. Fluid Concepts and Creative Analogies, 131-154, Basic Books Inc, 1995
Hutton G. “The countdown problem”. Journal of Functional Programming, 12(06), 609-616, 2002
Alliot JM. “The (Final) Countdown”. https://arxiv.org/abs/1502.05450 (03.06.2020)
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
Montgomery DC, Runger GC. Applied Statistics and Probability for Engineers. 5th ed. Jefferson City, USA, John Wiley & Sons, 2011
Hines WW, Montgomery DC, Goldsman DM, Borror CM. Probability and Statistics in Engineering. Danvers, Massachusetts, USA, John Wiley & Sons, 2008
Code D. Probability: Mastering Permutations and Combinations. 2nd ed. California, USA, CreateSpace Independent Publishing Platform, 2017
Crawshaw J, Chambers J. A Concise Course in Advanced Level Statistics: With Worked Examples. 6th ed. London, UK, Oxford University Press, 2015
Tier R. Probability with Permutations and Combinations: A Deeper and More Thorough Look at the Fundamental Equations. California, USA, CreateSpace Independent Publishing Platform, 2017
Nicolaides A. Pure Mathematics Series: 10. Combinations, Permutations, Probabilities. London, UK, PASS Publications, 1994
Puntambekar A. Analysis and design of algorithms. 1st ed. Pune, India, Technical Publications, 2008
Mueller J, Massaron L. Algorithms for Dummies. Hoboken, USA, John Wiley & Sons, 2017
Goodrich MT, Tamassia R, Goldwasser, MH. Data Structures and Algorithms in Java. 6th ed. Hoboken, USA, John Wiley & Sons, 2014
Saha S, Shukla S. Advanced Data Structures: Theory and Applications. Boca Raton, USA, CRC Press: Taylor & Francis, 2019.