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* Pyupgrade to Python 3.9
* updating DIRECTORY.md
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133 lines
3.9 KiB
Python
133 lines
3.9 KiB
Python
"""
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Given a partially filled 9×9 2D array, the objective is to fill a 9×9
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square grid with digits numbered 1 to 9, so that every row, column, and
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and each of the nine 3×3 sub-grids contains all of the digits.
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This can be solved using Backtracking and is similar to n-queens.
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We check to see if a cell is safe or not and recursively call the
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function on the next column to see if it returns True. if yes, we
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have solved the puzzle. else, we backtrack and place another number
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in that cell and repeat this process.
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"""
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from __future__ import annotations
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Matrix = list[list[int]]
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# assigning initial values to the grid
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initial_grid: Matrix = [
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[3, 0, 6, 5, 0, 8, 4, 0, 0],
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[5, 2, 0, 0, 0, 0, 0, 0, 0],
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[0, 8, 7, 0, 0, 0, 0, 3, 1],
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[0, 0, 3, 0, 1, 0, 0, 8, 0],
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[9, 0, 0, 8, 6, 3, 0, 0, 5],
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[0, 5, 0, 0, 9, 0, 6, 0, 0],
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[1, 3, 0, 0, 0, 0, 2, 5, 0],
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[0, 0, 0, 0, 0, 0, 0, 7, 4],
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[0, 0, 5, 2, 0, 6, 3, 0, 0],
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]
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# a grid with no solution
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no_solution: Matrix = [
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[5, 0, 6, 5, 0, 8, 4, 0, 3],
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[5, 2, 0, 0, 0, 0, 0, 0, 2],
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[1, 8, 7, 0, 0, 0, 0, 3, 1],
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[0, 0, 3, 0, 1, 0, 0, 8, 0],
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[9, 0, 0, 8, 6, 3, 0, 0, 5],
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[0, 5, 0, 0, 9, 0, 6, 0, 0],
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[1, 3, 0, 0, 0, 0, 2, 5, 0],
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[0, 0, 0, 0, 0, 0, 0, 7, 4],
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[0, 0, 5, 2, 0, 6, 3, 0, 0],
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]
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def is_safe(grid: Matrix, row: int, column: int, n: int) -> bool:
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"""
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This function checks the grid to see if each row,
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column, and the 3x3 subgrids contain the digit 'n'.
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It returns False if it is not 'safe' (a duplicate digit
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is found) else returns True if it is 'safe'
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"""
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for i in range(9):
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if grid[row][i] == n or grid[i][column] == n:
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return False
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for i in range(3):
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for j in range(3):
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if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
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return False
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return True
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def find_empty_location(grid: Matrix) -> tuple[int, int] | None:
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"""
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This function finds an empty location so that we can assign a number
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for that particular row and column.
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"""
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for i in range(9):
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for j in range(9):
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if grid[i][j] == 0:
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return i, j
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return None
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def sudoku(grid: Matrix) -> Matrix | None:
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"""
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Takes a partially filled-in grid and attempts to assign values to
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all unassigned locations in such a way to meet the requirements
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for Sudoku solution (non-duplication across rows, columns, and boxes)
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>>> sudoku(initial_grid) # doctest: +NORMALIZE_WHITESPACE
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[[3, 1, 6, 5, 7, 8, 4, 9, 2],
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[5, 2, 9, 1, 3, 4, 7, 6, 8],
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[4, 8, 7, 6, 2, 9, 5, 3, 1],
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[2, 6, 3, 4, 1, 5, 9, 8, 7],
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[9, 7, 4, 8, 6, 3, 1, 2, 5],
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[8, 5, 1, 7, 9, 2, 6, 4, 3],
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[1, 3, 8, 9, 4, 7, 2, 5, 6],
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[6, 9, 2, 3, 5, 1, 8, 7, 4],
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[7, 4, 5, 2, 8, 6, 3, 1, 9]]
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>>> sudoku(no_solution) is None
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True
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"""
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if location := find_empty_location(grid):
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row, column = location
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else:
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# If the location is ``None``, then the grid is solved.
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return grid
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for digit in range(1, 10):
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if is_safe(grid, row, column, digit):
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grid[row][column] = digit
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if sudoku(grid) is not None:
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return grid
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grid[row][column] = 0
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return None
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def print_solution(grid: Matrix) -> None:
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"""
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A function to print the solution in the form
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of a 9x9 grid
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"""
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for row in grid:
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for cell in row:
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print(cell, end=" ")
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print()
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if __name__ == "__main__":
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# make a copy of grid so that you can compare with the unmodified grid
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for example_grid in (initial_grid, no_solution):
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print("\nExample grid:\n" + "=" * 20)
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print_solution(example_grid)
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print("\nExample grid solution:")
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solution = sudoku(example_grid)
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if solution is not None:
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print_solution(solution)
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else:
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print("Cannot find a solution.")
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