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December 12, 2019 06:26
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Backtracking sudoku solution
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#!/usr/bin/env python | |
def print_board(board): | |
for row in board: | |
for col in row: | |
print(col, end=" ") | |
print("\n") | |
def find_empty_square(board): | |
""" | |
Return a tuple containing the row and column of the first empty square | |
False if no squares are empty | |
""" | |
for i, row in enumerate(board): | |
for j, square in enumerate(row): | |
if square == 0: | |
return (i, j) | |
return False | |
def num_in_row(board, row, num): | |
"""True if num is already in the row, False otherwise""" | |
return num in board[row] | |
def num_in_col(board, col, num): | |
"""True if num is already in the column, False otherwise""" | |
return num in [row[col] for row in board] | |
def num_in_box(board, row, col, num): | |
""" | |
row and col should be the top-left coordinates of the box | |
True if num is already in the 3x3 box, False otherwise | |
""" | |
return num in [board[row+i][col+j] for i in range(3) for j in range(3)] | |
def safe_position(board, row, col, num): | |
""" | |
A safe position is one in which a number can be placed without being | |
repeated in the same row, column or 3x3 box | |
True if position is safe, False otherwise | |
""" | |
return not num_in_row(board, row, num) \ | |
and not num_in_col(board, col, num) \ | |
and not num_in_box(board, row - row %3, col - col %3, num) | |
def solve_sudoku(board): | |
"""Returns True if a solution exists False otherwise""" | |
next_empty_square = find_empty_square(board) | |
if not next_empty_square: # The board is full/solved | |
return True | |
row, col = next_empty_square | |
for num in range(1, 10): | |
if safe_position(board, row, col, num): | |
board[row][col] = num | |
if solve_sudoku(board): | |
return True | |
board[row][col] = 0 # invalid position, unnasign the number | |
return False # backtrack and try another number | |
def main(): | |
grid = [[0,2,6,0,0,0,8,1,0], | |
[3,0,0,7,0,8,0,0,6], | |
[4,0,0,0,5,0,0,0,7], | |
[0,5,0,1,0,7,0,9,0], | |
[0,0,3,9,0,5,1,0,0], | |
[0,4,0,3,0,2,0,5,0], | |
[1,0,0,0,3,0,0,0,2], | |
[5,0,0,2,0,4,0,0,9], | |
[0,3,8,0,0,0,4,6,0]] | |
if solve_sudoku(grid): | |
print_board(grid) | |
else: | |
print("No solution exists!") | |
if __name__ == '__main__': | |
main() |
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