
from __future__ import annotations

import os
from collections.abc import Mapping

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




class   __lowercase						:






	def __init__(self				: int      ,	snake_case				: set[int]      ,	snake_case				: Mapping[EdgeT, int]    ) ->			None:
							_lowercase       :	set[int]           =   vertices
							_lowercase       :	dict[EdgeT, int]           =   {
							    (min(snake_case    ), max(snake_case    )): weight for edge, weight in edges.items()
							}






	def       _a(self				: Optional[int]      ,	snake_case				: EdgeT      ,	snake_case				: int    ) ->			None:
							self.vertices.add(edge[0]    )
							self.vertices.add(edge[1]    )
							_lowercase       :	Any           =   weight






	def       _a(self				: List[str]    ) ->			Graph:
							_lowercase       :	Graph           =   Graph({min(self.vertices    )}      ,	{}    )
							_lowercase       :	EdgeT
							_lowercase       :	int
							_lowercase       :	EdgeT
							_lowercase       :	int

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

													subgraph.add_edge(snake_case      ,	snake_case    )

							return subgraph



def 		UpperCamelCase     (       _UpperCAmelCase  :   str = "p107_network.txt"  )   ->			int:






						'''simple docstring'''

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

						with open(_UpperCAmelCase  ) as f:
												_lowercase       :	Any           =   f.read().strip().split("\n"  )

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

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

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

						_lowercase       :	Graph           =   graph.prims_algorithm()

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

						return initial_total - optimal_total


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






def 		UpperCamelCase     (       _UpperCAmelCase  :   list[int] ,			_UpperCAmelCase  :   list[int]  )   ->			tuple[float, float]:






						'''simple docstring'''

						if not len(_UpperCAmelCase  ) == len(_UpperCAmelCase  ) == 3:
												raise ValueError("Please enter a valid equation."  )
						if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
												raise ValueError("Both a & b of two equations can't be zero."  )

						# Extract the coefficients
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa

						# Calculate the determinants of the matrices
						_lowercase       :	List[Any]           =   aa * ba - aa * ba
						_lowercase       :	Tuple           =   ca * ba - ca * ba
						_lowercase       :	Union[str, Any]           =   aa * ca - aa * ca

						# Check if the system of linear equations has a solution (using Cramer's rule)
						if determinant == 0:
												if determinant_x == determinant_y == 0:
																		raise ValueError("Infinite solutions. (Consistent system)"  )
												else:
																		raise ValueError("No solution. (Inconsistent system)"  )
						else:
												if determinant_x == determinant_y == 0:
																		# Trivial solution (Inconsistent system)
																		return (0.0, 0.0)
												else:
																		_lowercase       :	str           =   determinant_x / determinant
																		_lowercase       :	Union[str, Any]           =   determinant_y / determinant
																		# Non-Trivial Solution (Consistent system)
																		return (x, y)




