



from __future__ import annotations

import os
from collections.abc import Mapping

_lowercase		:				List[Any]      		=tuple[int, int]

class        snake_case__    :







						"""simple docstring"""




						def __init__(       self ,       __lowercase ,       __lowercase  ) ->				None:
									"""simple docstring"""




									a__       :						set[int]							=  vertices
									a__       :						dict[EdgeT, int]							=  {
									    (min(__lowercase  ), max(__lowercase  )): weight for edge, weight in edges.items()
									}

						def 							SCREAMING_SNAKE_CASE__(       self ,       __lowercase ,       __lowercase  ) ->				None:
									"""simple docstring"""




									self.vertices.add(edge[0]  )
									self.vertices.add(edge[1]  )
									a__       :						Union[str, Any]							=  weight

						def 							SCREAMING_SNAKE_CASE__(       self  ) ->				Graph:
									"""simple docstring"""




									a__       :						Graph							=  Graph({min(self.vertices  )} ,       {}  )
									a__       :						EdgeT
									a__       :						int
									a__       :						EdgeT
									a__       :						int

									while len(subgraph.vertices  ) < len(self.vertices  ):
												a__       :						Union[str, 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__       :						Union[str, Any]							=  edge
																					a__       :						List[Any]							=  weight

												subgraph.add_edge(__lowercase ,       __lowercase  )

									return subgraph




def      lowerCAmelCase_					(  _lowercase    :       str = "p107_network.txt")							->	int:







			"""simple docstring"""
			a__       :						str							=  os.path.abspath(os.path.dirname(_lowercase))
			a__       :						str							=  os.path.join(_lowercase						,       _lowercase)
			a__       :						dict[EdgeT, int]							=  {}
			a__       :						list[str]
			a__       :						int
			a__       :						int

			with open(_lowercase) as f:
						a__       :						Optional[Any]							=  f.read().strip().split("""\n""")

			a__       :						Any							=  [line.split(""",""") for line in data]

			for edgea in range(1						,       len(_lowercase)):
						for edgea in range(_lowercase):
									if adjaceny_matrix[edgea][edgea] != "-":
												a__       :						Optional[int]							=  int(adjaceny_matrix[edgea][edgea])

			a__       :						Graph							=  Graph(set(range(len(_lowercase)))						,       _lowercase)

			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() = }')









from __future__ import annotations

def      lowerCAmelCase_					(  _lowercase    :       float						,       _lowercase    :       float						,       _lowercase    :       float						,       )							->	tuple[str, float]:







			"""simple docstring"""
			if (stress, tangential_force, area).count(0) != 1:
						raise ValueError("""You cannot supply more or less than 2 values""")
			elif stress < 0:
						raise ValueError("""Stress cannot be negative""")
			elif tangential_force < 0:
						raise ValueError("""Tangential Force cannot be negative""")
			elif area < 0:
						raise ValueError("""Area cannot be negative""")
			elif stress == 0:
						return (
						    "stress",
						    tangential_force / area,
						)
			elif tangential_force == 0:
						return (
						    "tangential_force",
						    stress * area,
						)
			else:
						return (
						    "area",
						    tangential_force / stress,
						)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




