Solving Every Sudoku Puzzle (2006)
18 days ago
- #Python
- #Algorithm
- #Sudoku
- The essay discusses solving Sudoku puzzles using constraint propagation and search.
- A Sudoku puzzle is solved when each unit (row, column, or 3x3 box) contains a permutation of digits 1 to 9 without repetition.
- The solution involves two main strategies: eliminating impossible values (constraint propagation) and searching through possibilities when stuck.
- The Python implementation includes functions for parsing the puzzle grid, assigning values, and eliminating possibilities.
- The search algorithm uses depth-first search with backtracking, prioritizing squares with the fewest remaining possibilities (minimum remaining values heuristic).
- The solver can handle both easy and hard puzzles, with most puzzles solved in under a second, though some hard puzzles take significantly longer.
- Random puzzles were generated to test the solver, with checks to ensure at least 17 squares filled and 8 different digits to avoid trivial or unsolvable puzzles.
- The solver's performance was analyzed, showing that most puzzles are solved quickly, but a few take much longer due to specific value choices leading to deep searches.
- The essay concludes with the solver successfully solving a variety of puzzles, including those labeled as the hardest, demonstrating the effectiveness of the approach.