Design and Analysis of a Modified 3D Sudoku Solver

Abstract

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.