




"""simple docstring"""

import math

class 				lowercase					:







				def __init__(							self      :    List[str]					,   _lowerCamelCase      :    Any=0				):  # a graph with Node 0,1,...,N-1



					"""simple docstring"""

					A_     : Union[str, Any]		      =						n
					A_     : str		      =						[
					    [math.inf for j in range(0					,   A_				)] for i in range(0					,   A_				)
					]  # adjacency matrix for weight
					A_     : Any		      =						[
					    [math.inf for j in range(0					,   A_				)] for i in range(0					,   A_				)
					]  # dp[i][j] stores minimum distance from i to j







				def     a_     (							self      :    str					,   _lowerCamelCase      :    List[Any]					,   _lowerCamelCase      :    Any					,   _lowerCamelCase      :    Dict				):



					"""simple docstring"""

					A_     : Dict		      =						w







				def     a_     (							self      :    Optional[int]				):



					"""simple docstring"""

					for k in range(0					,   self.n				):
						for i in range(0					,   self.n				):
							for j in range(0					,   self.n				):
								A_     : List[str]		      =						min(self.dp[i][j]					,   self.dp[i][k] + self.dp[k][j]				)







				def     a_     (							self      :    Dict					,   _lowerCamelCase      :    Optional[int]					,   _lowerCamelCase      :    Union[str, Any]				):



					"""simple docstring"""

					return self.dp[u][v]


if __name__ == "__main__":
		_lowerCamelCase     :	Tuple         =				Graph(5)
		graph.add_edge(0, 2, 9)
		graph.add_edge(0, 4, 10)
		graph.add_edge(1, 3, 5)
		graph.add_edge(2, 3, 7)
		graph.add_edge(3, 0, 10)
		graph.add_edge(3, 1, 2)
		graph.add_edge(3, 2, 1)
		graph.add_edge(3, 4, 6)
		graph.add_edge(4, 1, 3)
		graph.add_edge(4, 2, 4)
		graph.add_edge(4, 3, 9)
		graph.floyd_warshall()
		graph.show_min(1, 4)
		graph.show_min(0, 3)







from __future__ import annotations

import os
from collections.abc import Mapping

_UpperCAmelCase					: Tuple      =       tuple[int, int]


class 				lowercase					:



		def __init__( self				,      A_				,      A_       )  ->					None:
				"""simple docstring"""
				UpperCamelCase		=     vertices
				UpperCamelCase		=     {
				    (min(A_       ), max(A_       )): weight for edge, weight in edges.items()
				}



		def __UpperCamelCase ( self				,      A_				,      A_       )  ->					None:
				"""simple docstring"""
				self.vertices.add(edge[0]       )
				self.vertices.add(edge[1]       )
				UpperCamelCase		=     weight



		def __UpperCamelCase ( self       )  ->					Graph:
				"""simple docstring"""
				UpperCamelCase		=     Graph({min(self.vertices       )}				,      {}       )
				UpperCamelCase		=     42
				UpperCamelCase		=     42
				UpperCamelCase		=     42
				UpperCamelCase		=     42

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

						subgraph.add_edge(A_				,      A_       )

				return subgraph






def       A       (					lowercase = "p107_network.txt" )   ->  int:
		'''simple docstring'''

		UpperCamelCase		=     os.path.abspath(os.path.dirname(lowercase ) )
		UpperCamelCase		=     os.path.join(lowercase    ,       lowercase )
		UpperCamelCase		=     {}
		UpperCamelCase		=     42
		UpperCamelCase		=     42
		UpperCamelCase		=     42

		with open(lowercase ) as f:
				UpperCamelCase		=     f.read().strip().split('\n' )

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

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

		UpperCamelCase		=     Graph(set(range(len(lowercase ) ) )    ,       lowercase )

		UpperCamelCase		=     graph.prims_algorithm()

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

		return initial_total - optimal_total


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