An Efficient Sudoku Solver Application Based on Graph Theory

Year 2021, Volume: 5 Issue: 2, 218 - 224, 31.12.2021

Mustafa Batar

https://doi.org/10.46460/ijiea.982908

Abstract

This article has explained in detail what the puzzle of Sudoku is – the meaning of Sudoku –, where it comes from – the origin of Sudoku – and how it can be solved – the solution way of Sudoku. Especially, this paper has analyzed the solution of the problem – Sudoku can be taken as a problem – based on the graph theory. This theory consists of several algorithms, methods, rules and principles which are about the graph in general. In addition, this study has focused on the Welsh-Powell algorithm – greedy coloring algorithm – and Karger’s algorithm – contraction algorithm – among those graph algorithms by trying to give explanations about them (these two methods). Also, based on the rules and principles of those two algorithms, “Sudoku Solver Application” has been designed and developed in order to solve the puzzle of Sudoku. Moreover, the paper has presented a specific solution way of the puzzle Sudoku, and has showed its efficiency and usability by showing complexity and run time of the application among several available solutions based on the graph theory. So, the study has offered “Sudoku Solver Application” to the game world, science world, and education world as well for its use.

Keywords

Graph theory, Sudoku, Welsh-Powell algorithm, Karger’s algorithm.

Grafik Teorisine Dayalı Etkin Bir Sudoku Çözücü Uygulaması

Abstract

Bu makale, Sudoku bulmacasının ne olduğunu (anlamını), nereden geldiğini (kökenini) ve nasıl çözülebileceğini (çözüm yolunu) açıklamaktadır. Özellikle, problemin çözümünü – Sudoku bulmacası bir problem olarak ele alınabilir – grafik teorisine dayalı olarak analiz etmektedir. Bu teori, genel olarak grafiklerle ilgili çeşitli algoritmalar, yöntemler, kurallar ve ilkelerden oluşmaktadır. Ayrıca, grafik algoritmalarından Welsh-Powell (açgözlü renklendirme algoritması) ve Karger (daraltma algoritması) algoritmaları üzerinde durularak bu iki yöntem hakkında bu çalışmada detaylı bir bilgilendirme yapılmıştır. Bununla birlikte, bu iki algoritmanın kural ve prensipleri dikkate alınarak, bu makalede, “Sudoku Çözücü Uygulaması” tasarlanmış ve geliştirilmiştir. Ayrıca, uygulamanın çalışma süresi hesaplanıp etkinliği ve kullanılabilirliği ortaya konmuştur. Buna ek olarak, bu çalışma, Sudoku bulmacasının belirli bir çözüm yolunu grafik teorisine dayalı algoritmalar yardımıyla bulup, kullanımı için hem oyun dünyasına, hem bilim dünyasına, hem de eğitim dünyasına sunmuştur.

Keywords

Grafik teorisi, Sudoku, Welsh-Powell algoritması, Karger algoritması.

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