



"""simple docstring"""





from __future__ import annotations

lowerCamelCase      =		list[list[int]]

# assigning initial values to the grid
lowerCamelCase      =		[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCamelCase      =		[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__   ):
      for i in range(9   ):
            if grid[row][i] == n or grid[i][column] == n:
                  return False

      for i in range(3   ):
            for j in range(3   ):
                  if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
                        return False

      return True
def      a__			(   lowerCAmelCase__   ):
      for i in range(9   ):
            for j in range(9   ):
                  if grid[i][j] == 0:
                        return i, j
      return None
def      a__			(   lowerCAmelCase__   ):
      if location := find_empty_location(lowerCAmelCase__   ):
            UpperCAmelCase_				,					UpperCAmelCase_    				=							location
      else:
            # If the location is ``None``, then the grid is solved.
            return grid

      for digit in range(1			,    10   ):
            if is_safe(lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__   ):
                  UpperCAmelCase_    				=							digit

                  if sudoku(lowerCAmelCase__   ) is not None:
                        return grid

                  UpperCAmelCase_    				=							0

      return None
def      a__			(   lowerCAmelCase__   ):
      for row in grid:
            for cell in row:
                  print(lowerCAmelCase__			,    end=" "   )
            print()


if __name__ == "__main__":
  # make a copy of grid so that you can compare with the unmodified grid
  for example_grid in (initial_grid, no_solution):
    print("""\nExample grid:\n""" + """=""" * 20)
    print_solution(example_grid)
    print("""\nExample grid solution:""")
    lowerCamelCase      =		sudoku(example_grid)
    if solution is not None:
      print_solution(solution)
    else:
      print("""Cannot find a solution.""")









"""simple docstring"""





from heapq import heappop, heappush

import numpy as np
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    ):
      UpperCAmelCase_				,					UpperCAmelCase_    				=							grid.shape
      UpperCAmelCase_    				=							[-1, 1, 0, 0]
      UpperCAmelCase_    				=							[0, 0, -1, 1]
      if allow_diagonal:
            dx += [-1, -1, 1, 1]
            dy += [-1, 1, -1, 1]

      UpperCAmelCase_				,					UpperCAmelCase_    				=							[(0, source)], set()
      UpperCAmelCase_    				=							np.full((rows, cols)			,    np.inf   )
      UpperCAmelCase_    				=							0
      UpperCAmelCase_    				=							np.empty((rows, cols)			,    dtype=lowerCAmelCase__   )
      UpperCAmelCase_    				=							None

      while queue:
            ((UpperCAmelCase_)				,					(UpperCAmelCase_))    				=							heappop(lowerCAmelCase__   )
            if (x, y) in visited:
                  continue
            visited.add((x, y)   )

            if (x, y) == destination:
                  UpperCAmelCase_    				=							[]
                  while (x, y) != source:
                        path.append((x, y)   )
                        UpperCAmelCase_				,					UpperCAmelCase_    				=							predecessors[x, y]
                  path.append(lowerCAmelCase__   )  # add the source manually
                  path.reverse()
                  return matrix[destination], path

            for i in range(len(lowerCAmelCase__   )   ):
                  UpperCAmelCase_				,					UpperCAmelCase_    				=							x + dx[i], y + dy[i]
                  if 0 <= nx < rows and 0 <= ny < cols:
                        UpperCAmelCase_    				=							grid[nx][ny]
                        if next_node == 1 and matrix[nx, ny] > dist + 1:
                              heappush(lowerCAmelCase__			,    (dist + 1, (nx, ny))   )
                              UpperCAmelCase_    				=							dist + 1
                              UpperCAmelCase_    				=							(x, y)

      return np.inf, []


if __name__ == "__main__":
  import doctest

  doctest.testmod()




