A Novel Search Tree-Based 3D Sudoku Solver

Jana, Sunanda; Mallik, Manjarini; Maji, Arnab Kumar; Pal, Rajat Kumar

doi:10.1007/978-981-33-4084-8_68

Cited by 2 publications

(21 citation statements)

References 7 publications

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“…The 2D Sudoku structure can be extended to 16×16, 25×25, etc. Additionally, a 2D Sudoku can be extended by another dimension, resulting in a 3D Sudoku [2]. Adding an extra dimension will lead to a solid cubic structure of n × n × n elements, where n itself is a perfect square integer.…”

Section: A Two-dimensional Sudokumentioning

confidence: 99%

“…Each cell [i, j] of each grid has a different value. This is because by combining each [i, j] cell of each grid, a column of another 2D Sudoku is obtained for the third dimension; e.g., cell [2,3] of grids 1 through 9 contains the values 5, 7, 6, 4, 2, 8, 3, 1, 9, respectively (see Fig. 2).…”

Section: B Three-dimensional Sudokumentioning

confidence: 99%

“…(i) Grid FIGURE 2: 2D layers of a 3D Sudoku solution each lying in the xz-plane one above another. Grid 1 is the topmost layer and Grid 9 is the layer at the bottom [2]. guess free Sudoku solver algorithm was designed in 2014 [6], which guaranteed all possible solutions for a valid 2D Sudoku instance.…”

Section: B Three-dimensional Sudokumentioning

confidence: 99%

“…Different metaheuristic [10] techniques are there to solve sudoku. In 2009, a new approach in solving Sudoku x y z FIGURE 3: Alignment of the x-, y-, and z-planes [2].…”

Section: Literature Surveymentioning

confidence: 99%

“…• 4×4 • 9×9, also called standard Sudoku • 16×16, also known as Super Sudoku • 25×25, also known as Giant Sudoku Apart from these, there are also several other types of Sudoku [2], which are not so familiar, namely three-dimensional Sudoku invented by Dion Church was first published in The Daily Telegraph in May 2005 and Wordoku, also known as Godoku, where alphabetical placement is required instead of numerical placement.…”

Section: Introductionmentioning

confidence: 99%

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Design and Analysis of a Modified 3D Sudoku Solver

Jana

Mallik

Khan³

et al. 2023

IEEE Access

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Sudoku is a complicated multidimensional mathematical structure with several applications in various computer science domains. 3D Sudoku, compared to 2D, has one more dimension that can potentially provide an extra edge to the different applications of this puzzle game. Various researchers have developed various types of 2D Sudoku solver using different methodologies. But there is very limited research in the area of developing 3D Sudoku solver. We have proposed two different solvers for solving 3D Sudoku puzzles of size 9×9×9. Both the solvers providing all possible solutions for a 3D Sudoku instance. 2D Sudoku puzzles are applied in different research domains with different purposes. Recently 3D structure of Sudoku is also applying in several areas to achieve more effectiveness compared to 2D Sudoku. As well as it can also be used to solve problem in 3D space. Again, solving an NP-complete puzzle by considering its 3D structure is a challenging job. Thus, we have endeavoured to achieve all possible solutions for a 3D Sudoku instance in this work. In the first version of our proposed algorithm all probable values for each blank cell have been computed and stored. Subsequently, few elimination-based methods have been used to reduce the number of probable values (if possible) for each blank cell. Finally, the solutions have been computed using the backtracking method. In the second version of our proposed algorithm, the nine 2D Sudoku puzzles lying in the xz-plane one above the other, which form the 3D puzzle, have been fed as the input. All possible solutions have been obtained for each of the nine puzzles. Then, the obtained solutions have been mapped to achieve one or more solutions for the 3D Sudoku instance. Thus, our proposed techniques provide a new approach for solving 3D Sudoku. In addition, applying the obtained solutions provides us with an advantage over 2D Sudoku, in solving problem of 3D space and where more data is required.

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Section: A Two-dimensional Sudokumentioning

confidence: 99%

Section: B Three-dimensional Sudokumentioning

confidence: 99%

Section: B Three-dimensional Sudokumentioning

confidence: 99%

“…Different metaheuristic [10] techniques are there to solve sudoku. In 2009, a new approach in solving Sudoku x y z FIGURE 3: Alignment of the x-, y-, and z-planes [2].…”

Section: Literature Surveymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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