


'''simple docstring'''






from __future__ import annotations

__UpperCAmelCase       							=				list[list[int]]

# assigning initial values to the grid
__UpperCAmelCase       							=				[
    [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
__UpperCAmelCase       							=				[
    [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    _snake_case  (	A					,       A					,       A					,       A			)		->       bool:
							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    _snake_case  (	A			)		->       tuple[int, int] | None:
							for i in range(9			):
														for j in range(9			):
																					if grid[i][j] == 0:
																												return i, j
							return None


def    _snake_case  (	A			)		->       Matrix | None:
							if location := find_empty_location(A			):
														lowerCAmelCase__  ,   lowerCAmelCase__			  =      location
							else:
														# If the location is ``None``, then the grid is solved.
														return grid

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

																					if sudoku(A			) is not None:
																												return grid

																					lowerCAmelCase__			  =      0

							return None


def    _snake_case  (	A			)		->       None:
							for row in grid:
														for cell in row:
																					print(A					,       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:''')
				__UpperCAmelCase       							=				sudoku(example_grid)
				if solution is not None:
						print_solution(solution)
				else:
						print('''Cannot find a solution.''')






"""simple docstring"""
from __future__ import annotations

import os
from collections.abc import Mapping

__UpperCamelCase     :						Optional[Any]						       =  tuple[int, int]







class       a							:



 def __init__(     self				,       _snake_case				,       _snake_case     ):







  """simple docstring"""






  lowerCAmelCase    				= vertices
  lowerCAmelCase    				= {
      (min(_snake_case     ), max(_snake_case     )): weight for edge, weight in edges.items()
  }



 def    UpperCamelCase__  (     self				,       _snake_case				,       _snake_case     ):







  """simple docstring"""






  self.vertices.add(edge[0]     )
  self.vertices.add(edge[1]     )
  lowerCAmelCase    				= weight



 def    UpperCamelCase__  (     self     ):







  """simple docstring"""






  lowerCAmelCase    				= Graph({min(self.vertices     )}				,       {}     )
  lowerCAmelCase    				= 42
  lowerCAmelCase    				= 42
  lowerCAmelCase    				= 42
  lowerCAmelCase    				= 42

  while len(subgraph.vertices     ) < len(self.vertices     ):
   lowerCAmelCase    				= max(self.edges.values()     ) + 1
   for edge, weight in self.edges.items():
    if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
     if weight < min_weight:
      lowerCAmelCase    				= edge
      lowerCAmelCase    				= weight

   subgraph.add_edge(_snake_case				,       _snake_case     )

  return subgraph


def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    str = "p107_network.txt"			):
 lowerCAmelCase    				= os.path.abspath(os.path.dirname(_UpperCAmelCase			)			)
 lowerCAmelCase    				= os.path.join(_UpperCAmelCase  ,     _UpperCAmelCase			)
 lowerCAmelCase    				= {}
 lowerCAmelCase    				= 42
 lowerCAmelCase    				= 42
 lowerCAmelCase    				= 42

 with open(_UpperCAmelCase			) as f:
  lowerCAmelCase    				= f.read().strip().split('\n'			)

 lowerCAmelCase    				= [line.split(','			) for line in data]

 for edgea in range(1  ,     len(_UpperCAmelCase			)			):
  for edgea in range(_UpperCAmelCase			):
   if adjaceny_matrix[edgea][edgea] != "-":
    lowerCAmelCase    				= int(adjaceny_matrix[edgea][edgea]			)

 lowerCAmelCase    				= Graph(set(range(len(_UpperCAmelCase			)			)			)  ,     _UpperCAmelCase			)

 lowerCAmelCase    				= graph.prims_algorithm()

 lowerCAmelCase    				= sum(graph.edges.values()			)
 lowerCAmelCase    				= sum(subgraph.edges.values()			)

 return initial_total - optimal_total


if __name__ == "__main__":
       print(f'''{solution() = }''')





