

from __future__ import annotations

import os
from collections.abc import Mapping

_SCREAMING_SNAKE_CASE					:  Any             =      tuple[int, int]






class 	UpperCAmelCase__		:






		"""simple docstring"""


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






		def 				lowercase_		(							self						:		Tuple     ,       __lowerCamelCase						:		EdgeT     ,       __lowerCamelCase						:		int )		->							None:
							self.vertices.add(edge[0] )
							self.vertices.add(edge[1] )
							SCREAMING_SNAKE_CASE__   =   weight







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

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

												subgraph.add_edge(__lowerCamelCase     ,       __lowerCamelCase )

							return subgraph



def     UpperCAmelCase_       (						_A = "p107_network.txt"    ):





					'''simple docstring'''




					SCREAMING_SNAKE_CASE__   =   os.path.abspath(os.path.dirname(_A    )    )
					SCREAMING_SNAKE_CASE__   =   os.path.join(_A				,		_A    )
					SCREAMING_SNAKE_CASE__   =   {}
					SCREAMING_SNAKE_CASE__   =   42
					SCREAMING_SNAKE_CASE__   =   42
					SCREAMING_SNAKE_CASE__   =   42

					with open(_A    ) as f:
										SCREAMING_SNAKE_CASE__   =   f.read().strip().split('''\n'''    )

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

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

					SCREAMING_SNAKE_CASE__   =   Graph(set(range(len(_A    )    )    )				,		_A    )

					SCREAMING_SNAKE_CASE__   =   graph.prims_algorithm()

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

					return initial_total - optimal_total


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





def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''multiplicative_persistence() only accepts integral values'''    )
     if num < 0:
          raise ValueError('''multiplicative_persistence() does not accept negative values'''    )

     SCREAMING_SNAKE_CASE__   =   0
     SCREAMING_SNAKE_CASE__   =   str(_A    )

     while len(_A    ) != 1:
          SCREAMING_SNAKE_CASE__   =   [int(_A    ) for i in num_string]

          SCREAMING_SNAKE_CASE__   =   1
          for i in range(0				,		len(_A    )    ):
               total *= numbers[i]

          SCREAMING_SNAKE_CASE__   =   str(_A    )

          steps += 1
     return steps
def     UpperCAmelCase_       (						_A    ):





     '''simple docstring'''




     if not isinstance(_A				,		_A    ):
          raise ValueError('''additive_persistence() only accepts integral values'''    )
     if num < 0:
          raise ValueError('''additive_persistence() does not accept negative values'''    )

     SCREAMING_SNAKE_CASE__   =   0
     SCREAMING_SNAKE_CASE__   =   str(_A    )

     while len(_A    ) != 1:
          SCREAMING_SNAKE_CASE__   =   [int(_A    ) for i in num_string]

          SCREAMING_SNAKE_CASE__   =   0
          for i in range(0				,		len(_A    )    ):
               total += numbers[i]

          SCREAMING_SNAKE_CASE__   =   str(_A    )

          steps += 1
     return steps


if __name__ == "__main__":
       import doctest

       doctest.testmod()


