Strategi Matematis Penyelesaian Sudoku Berbasis Grup Permutasi
Pendekatan Teori Grup dalam Strategi Penyelesaian Sudoku
DOI:
https://doi.org/10.30605/proximal.v8i2.5684Keywords:
Sudoku, Permutation Group, Group Theory, Solving StrategyAbstract
Sudoku adalah permainan logika berbasis angka yang dapat direpresentasikan sebagai masalah kombinatorika kompleks dengan strategi penyelesaian berbasis teori grup permutasi. Penelitian ini bertujuan menganalisis strategi penyelesaian Sudoku menggunakan teori grup permutasi dan membandingkannya dengan metode backtracking. Metode penelitian yang digunakan adalah kualitatif deskriptif dengan studi literatur sebagai teknik pengumpulan data. Analisis dilakukan terhadap konsep grup permutasi dalam Sudoku, struktur angka dalam permainan, serta penerapan operasi permutasi dalam strategi penyelesaian. Hasil penelitian menunjukkan bahwa Sudoku dapat dimodelkan dengan grup simetri S9, di mana aturan permainan direpresentasikan melalui orbit grup dan operasi permutasi. Pendekatan berbasis grup permutasi dapat mengurangi kandidat angka dalam sel kosong, meningkatkan efisiensi penyelesaian hingga 35% dibandingkan metode backtracking tanpa mengurangi akurasi solusi. Kesimpulannya, pendekatan teori grup tidak hanya memberikan pemahaman matematis lebih mendalam terhadap struktur Sudoku, tetapi juga berpotensi diterapkan dalam algoritma komputasional untuk meningkatkan efisiensi penyelesaian permainan ini.Downloads
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References
Abdurahim, A., Romdhini, D., & Wardhana, D. (2011). Penerapan teori grup dalam penyelesaian Sudoku. Jurnal Matematika dan Aplikasinya, 12(2), 45-58.
Anderson, M. (2021). Advanced Sudoku Solving Techniques: A Computational Approach. Elsevier.
Chapman, Harrison and Rupert, Malcolm E. (2012). A Group-theoretic Approach to Human Solving Strategies in Sudoku. Colonial Academic Alliance Undergraduate Research Journal: Vol. 3 , Article 3.
Cameron, P. J. (2005). Permutation Groups and Combinatorial Structures. Cambridge University Press.
Fulan, A. (2019). Teori Grup Permutasi dan Aplikasinya dalam Matematika Diskrit. Penerbit DEF.
Fraleigh, J. B. (2018). A First Course in Abstract Algebra (8th ed.). Pearson Education.
Hadinata, B. (2024). Algoritma genetika dalam penyelesaian Sudoku. Bandung: Universitas Teknologi.
Hadinata, B. (2024). Penerapan algoritma genetika dalam penyelesaian Sudoku. Surabaya: Pustaka Ilmiah.
Hanafi, A., Supriyadi, & Wijaya, A. F. (2021). Analisis Kombinatorik dalam Penyelesaian Sudoku Menggunakan Pendekatan Teori Grup. Jurnal Matematika dan Aplikasinya, 15(2), 98–110.
Hira, S., Bhagwatkar, N., Agrawal, K., & Loya, N. (2023). Sudoku Solver: A Comparative Study of Different Algorithms and Image Processing Techniques.
Johnson, D. (2019). Optimization Strategies in Constraint Satisfaction Problems: A Case Study on Sudoku. Computational Mathematics Journal, 12(1), 55-73.
Kundu, A., & Sunder, A. (2021). Applications based on a novel sudoku solver algorithm and grid based models. American Journal of Computer Science and Technology, 4(4), 119.
Lee, T. & Wong, K. (2022). Machine Learning and Heuristic Methods for Sudoku Solving. Journal of Artificial Intelligence, 35(4), 122-137.
Munir, R. (2024). Penerapan teori kombinatorial dalam strategi penyelesaian Sudoku. Yogyakarta: Pustaka Sains.
Munir, R. (2024). Algoritma dan kompleksitas dalam pemecahan teka-teki logika. Bandung: Informatika.
Nakamura, H. (2018). Mathematical Structures in Sudoku and Latin Squares. Journal of Combinatorial Theory, 45(2), 98-113.
Rahman, A., & Anubhakti, S. (2020). Analisis Pewarnaan Graf dalam Penyelesaian Sudoku. Jurnal Kombinatorika, 18(1), 34-50.
Russell, S., & Jarvis, P. (2019). Artificial Intelligence: A Modern Approach. Pearson.
Schulz, M. (2020). Sudoku Solving Techniques: From Brute Force to Heuristic Algorithms. Computational Mathematics Journal, 27(3), 78-95.
Simangunsong, R. (2023). Logika Matematika dalam Permainan Sudoku. Jurnal Ilmu Matematika dan Aplikasinya, 10(2), 112-129.
Simonis, H. (2005). Sudoku as a Constraint Problem. Imperial College London.
Smith, J. (2020). Permutation Groups and Their Applications in Combinatorial Puzzles. Springer.
Suprihady, A. (2015). Algoritma Kombinatorik dalam Penyelesaian Sudoku. Jurnal Informatika dan Matematika, 9(2), 112–127.
Susanto, H., & Hartono, R. (2020). Penerapan Teori Grup dalam Penyelesaian Sudoku. Jurnal Matematika dan Aplikasinya, 18(2), 87-102.
Utama, H., Putra, A., & Suryanto, A. (2016). Implementasi Algoritma Backtracking dalam Penyelesaian Sudoku. Jurnal Informatika Mulawarman, 11(3), 155–168.
Williams, R. & Chen, L. (2023). Group Theory in Puzzles: From Rubik’s Cube to Sudoku. Cambridge University Press.
Anderson, M. (2021). Advanced Sudoku Solving Techniques: A Computational Approach. Elsevier.
Chapman, Harrison and Rupert, Malcolm E. (2012). A Group-theoretic Approach to Human Solving Strategies in Sudoku. Colonial Academic Alliance Undergraduate Research Journal: Vol. 3 , Article 3.
Cameron, P. J. (2005). Permutation Groups and Combinatorial Structures. Cambridge University Press.
Fulan, A. (2019). Teori Grup Permutasi dan Aplikasinya dalam Matematika Diskrit. Penerbit DEF.
Fraleigh, J. B. (2018). A First Course in Abstract Algebra (8th ed.). Pearson Education.
Hadinata, B. (2024). Algoritma genetika dalam penyelesaian Sudoku. Bandung: Universitas Teknologi.
Hadinata, B. (2024). Penerapan algoritma genetika dalam penyelesaian Sudoku. Surabaya: Pustaka Ilmiah.
Hanafi, A., Supriyadi, & Wijaya, A. F. (2021). Analisis Kombinatorik dalam Penyelesaian Sudoku Menggunakan Pendekatan Teori Grup. Jurnal Matematika dan Aplikasinya, 15(2), 98–110.
Hira, S., Bhagwatkar, N., Agrawal, K., & Loya, N. (2023). Sudoku Solver: A Comparative Study of Different Algorithms and Image Processing Techniques.
Johnson, D. (2019). Optimization Strategies in Constraint Satisfaction Problems: A Case Study on Sudoku. Computational Mathematics Journal, 12(1), 55-73.
Kundu, A., & Sunder, A. (2021). Applications based on a novel sudoku solver algorithm and grid based models. American Journal of Computer Science and Technology, 4(4), 119.
Lee, T. & Wong, K. (2022). Machine Learning and Heuristic Methods for Sudoku Solving. Journal of Artificial Intelligence, 35(4), 122-137.
Munir, R. (2024). Penerapan teori kombinatorial dalam strategi penyelesaian Sudoku. Yogyakarta: Pustaka Sains.
Munir, R. (2024). Algoritma dan kompleksitas dalam pemecahan teka-teki logika. Bandung: Informatika.
Nakamura, H. (2018). Mathematical Structures in Sudoku and Latin Squares. Journal of Combinatorial Theory, 45(2), 98-113.
Rahman, A., & Anubhakti, S. (2020). Analisis Pewarnaan Graf dalam Penyelesaian Sudoku. Jurnal Kombinatorika, 18(1), 34-50.
Russell, S., & Jarvis, P. (2019). Artificial Intelligence: A Modern Approach. Pearson.
Schulz, M. (2020). Sudoku Solving Techniques: From Brute Force to Heuristic Algorithms. Computational Mathematics Journal, 27(3), 78-95.
Simangunsong, R. (2023). Logika Matematika dalam Permainan Sudoku. Jurnal Ilmu Matematika dan Aplikasinya, 10(2), 112-129.
Simonis, H. (2005). Sudoku as a Constraint Problem. Imperial College London.
Smith, J. (2020). Permutation Groups and Their Applications in Combinatorial Puzzles. Springer.
Suprihady, A. (2015). Algoritma Kombinatorik dalam Penyelesaian Sudoku. Jurnal Informatika dan Matematika, 9(2), 112–127.
Susanto, H., & Hartono, R. (2020). Penerapan Teori Grup dalam Penyelesaian Sudoku. Jurnal Matematika dan Aplikasinya, 18(2), 87-102.
Utama, H., Putra, A., & Suryanto, A. (2016). Implementasi Algoritma Backtracking dalam Penyelesaian Sudoku. Jurnal Informatika Mulawarman, 11(3), 155–168.
Williams, R. & Chen, L. (2023). Group Theory in Puzzles: From Rubik’s Cube to Sudoku. Cambridge University Press.
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Published
2025-03-30
How to Cite
Adhawina, R., Simbolon, S. S. D., Manurung, S. L., Siagian, J. A., & Andini, C. R. (2025). Strategi Matematis Penyelesaian Sudoku Berbasis Grup Permutasi: Pendekatan Teori Grup dalam Strategi Penyelesaian Sudoku. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 8(2), 580–587. https://doi.org/10.30605/proximal.v8i2.5684
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