from __future__ import annotations

import os
from collections.abc import Mapping

lowerCAmelCase_ : int						  =      tuple[int, int]





class 							lowercase						:


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


   def __UpperCAmelCase       (   self				:	Optional[int]   ,		__lowerCAmelCase				:	EdgeT   ,		__lowerCAmelCase				:	int)      ->					None:
         self.vertices.add(edge[0])
         self.vertices.add(edge[1])
         lowercase_     =      weight


   def __UpperCAmelCase       (   self				:	List[Any])      ->					Graph:
         lowercase_     =      Graph({min(self.vertices)}   ,		{})
         lowercase_     =      42
         lowercase_     =      42
         lowercase_     =      42
         lowercase_     =      42

         while len(subgraph.vertices) < len(self.vertices):
               lowercase_     =      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_     =      edge
                                 lowercase_     =      weight

               subgraph.add_edge(__lowerCAmelCase   ,		__lowerCAmelCase)

         return subgraph




def __a (	__lowerCamelCase			:						str = "p107_network.txt"				)	->							int:
      '''simple docstring'''


      lowercase_     =      os.path.abspath(os.path.dirname(__lowerCamelCase				)				)
      lowercase_     =      os.path.join(__lowerCamelCase ,		__lowerCamelCase				)
      lowercase_     =      {}
      lowercase_     =      42
      lowercase_     =      42
      lowercase_     =      42

      with open(__lowerCamelCase				) as f:
            lowercase_     =      f.read().strip().split("\n"				)

      lowercase_     =      [line.split(","				) for line in data]

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

      lowercase_     =      Graph(set(range(len(__lowerCamelCase				)				)				) ,		__lowerCamelCase				)

      lowercase_     =      graph.prims_algorithm()

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

      return initial_total - optimal_total


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







'''simple docstring'''

def __a (	__lowerCamelCase			:						list[int] ,		__lowerCamelCase			:						int				)	->							bool:
      '''simple docstring'''


      lowercase_     =      len(__lowerCamelCase				)
      lowercase_     =      [[False] * (required_sum + 1) for _ in range(arr_len + 1				)]

      # for each arr value, a sum of zero(0) can be formed by not taking any element
      # hence True/1
      for i in range(arr_len + 1				):
            lowercase_     =      True

      # sum is not zero and set is empty then false
      for i in range(1 ,		required_sum + 1				):
            lowercase_     =      False

      for i in range(1 ,		arr_len + 1				):
            for j in range(1 ,		required_sum + 1				):
                  if arr[i - 1] > j:
                        lowercase_     =      subset[i - 1][j]
                  if arr[i - 1] <= j:
                        lowercase_     =      subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

      return subset[arr_len][required_sum]


if __name__ == "__main__":
       import doctest

       doctest.testmod()






