





"""simple docstring"""






def     __A      (			a_						:int   ,       a_						:int   ,       a_						:list[list[int]])		->		int:

				def update_area_of_max_square(a_						:int   ,       a_						:int) -> int:
								# BASE CASE
								if row >= rows or col >= cols:
												return 0

								__a :						Optional[Any]			       =  update_area_of_max_square(a_   ,       col + 1)
								__a :						Tuple			       =  update_area_of_max_square(row + 1   ,       col + 1)
								__a :						Optional[Any]			       =  update_area_of_max_square(row + 1   ,       a_)

								if mat[row][col]:
												__a :						Union[str, Any]			       =  1 + min([right, diagonal, down])
												__a :						List[Any]			       =  max(largest_square_area[0]   ,       a_)
												return sub_problem_sol
								else:
												return 0

				__a :						List[str]			       =  [0]
				update_area_of_max_square(0   ,       0)
				return largest_square_area[0]

def     __A      (			a_						:int   ,       a_						:int   ,       a_						:list[list[int]])		->		int:

				def update_area_of_max_square_using_dp_array(
				    a_						:int   ,       a_						:int   ,       a_						:list[list[int]]) -> int:
								if row >= rows or col >= cols:
												return 0
								if dp_array[row][col] != -1:
												return dp_array[row][col]

								__a :						List[str]			       =  update_area_of_max_square_using_dp_array(a_   ,       col + 1   ,       a_)
								__a :						List[str]			       =  update_area_of_max_square_using_dp_array(row + 1   ,       col + 1   ,       a_)
								__a :						int			       =  update_area_of_max_square_using_dp_array(row + 1   ,       a_   ,       a_)

								if mat[row][col]:
												__a :						List[Any]			       =  1 + min([right, diagonal, down])
												__a :						Dict			       =  max(largest_square_area[0]   ,       a_)
												__a :						Dict			       =  sub_problem_sol
												return sub_problem_sol
								else:
												return 0

				__a :						int			       =  [0]
				__a :						int			       =  [[-1] * cols for _ in range(a_)]
				update_area_of_max_square_using_dp_array(0   ,       0   ,       a_)

				return largest_square_area[0]

def     __A      (			a_						:int   ,       a_						:int   ,       a_						:list[list[int]])		->		int:
				__a :						Tuple			       =  [[0] * (cols + 1) for _ in range(rows + 1)]
				__a :						List[Any]			       =  0
				for row in range(rows - 1   ,       -1   ,       -1):
								for col in range(cols - 1   ,       -1   ,       -1):
												__a :						Optional[int]			       =  dp_array[row][col + 1]
												__a :						List[str]			       =  dp_array[row + 1][col + 1]
												__a :						List[Any]			       =  dp_array[row + 1][col]

												if mat[row][col] == 1:
																__a :						Optional[int]			       =  1 + min(a_   ,       a_   ,       a_)
																__a :						List[str]			       =  max(dp_array[row][col]   ,       a_)
												else:
																__a :						Dict			       =  0

				return largest_square_area

def     __A      (			a_						:int   ,       a_						:int   ,       a_						:list[list[int]])		->		int:
				__a :						List[str]			       =  [0] * (cols + 1)
				__a :						List[str]			       =  [0] * (cols + 1)
				__a :						List[Any]			       =  0
				for row in range(rows - 1   ,       -1   ,       -1):
								for col in range(cols - 1   ,       -1   ,       -1):
												__a :						Union[str, Any]			       =  current_row[col + 1]
												__a :						Tuple			       =  next_row[col + 1]
												__a :						Any			       =  next_row[col]

												if mat[row][col] == 1:
																__a :						Optional[Any]			       =  1 + min(a_   ,       a_   ,       a_)
																__a :						Union[str, Any]			       =  max(current_row[col]   ,       a_)
												else:
																__a :						Optional[Any]			       =  0
								__a :						int			       =  current_row

				return largest_square_area


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))






"""simple docstring"""






from __future__ import annotations

import os
from collections.abc import Mapping

A 			=  tuple[int, int]




class 				__lowercase			:







					'''simple docstring'''




					def __init__(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									__a :						set[int]			       =  vertices
									__a :						dict[EdgeT, int]			       =  {
									    (min(_UpperCAmelCase     ), max(_UpperCAmelCase     )): weight for edge, weight in edges.items()
									}







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									self.vertices.add(edge[0]     )
									self.vertices.add(edge[1]     )
									__a :						Any			       =  weight







					def  _lowerCamelCase		(						self     ):
									__a :						Graph			       =  Graph({min(self.vertices     )}	,			{}     )
									__a :						EdgeT
									__a :						int
									__a :						EdgeT
									__a :						int

									while len(subgraph.vertices     ) < len(self.vertices     ):
													__a :						List[Any]			       =  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:
																									__a :						str			       =  edge
																									__a :						int			       =  weight

													subgraph.add_edge(_UpperCAmelCase	,			_UpperCAmelCase     )

									return subgraph






def     __A      (			a_						:str = "p107_network.txt")		->		int:
				__a :						str			       =  os.path.abspath(os.path.dirname(a_))
				__a :						str			       =  os.path.join(a_   ,       a_)
				__a :						dict[EdgeT, int]			       =  {}
				__a :						list[str]
				__a :						int
				__a :						int

				with open(a_) as f:
								__a :						Any			       =  f.read().strip().split('''\n''')

				__a :						Union[str, Any]			       =  [line.split(''',''') for line in data]

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

				__a :						Graph			       =  Graph(set(range(len(a_)))   ,       a_)

				__a :						Graph			       =  graph.prims_algorithm()

				__a :						int			       =  sum(graph.edges.values())
				__a :						int			       =  sum(subgraph.edges.values())

				return initial_total - optimal_total


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