from __future__ import annotations

import os
from collections.abc import Mapping

SCREAMING_SNAKE_CASE__		:					Dict						=					tuple[int, int]

class       snake_case					:




  def __init__(      self     :	Optional[int]     , a_     :	set[int]     , a_     :	Mapping[EdgeT, int]				)->       Union[str, Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				set[int]			=		vertices
       SCREAMING_SNAKE_CASE__				:				dict[EdgeT, int]			=		{
           (min(UpperCAmelCase__				), max(UpperCAmelCase__				)): weight for edge, weight in edges.items()
       }




  def 	__lowercase(      self     :	Any     , a_     :	EdgeT     , a_     :	int				)->       Any:




       """simple docstring"""
       self.vertices.add(edge[0]				)
       self.vertices.add(edge[1]				)
       SCREAMING_SNAKE_CASE__				:				str			=		weight




  def 	__lowercase(      self     :	List[Any]				)->       List[Any]:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Graph			=		Graph({min(self.vertices				)}     , {}				)
       SCREAMING_SNAKE_CASE__				:				EdgeT
       SCREAMING_SNAKE_CASE__				:				int
       SCREAMING_SNAKE_CASE__				:				EdgeT
       SCREAMING_SNAKE_CASE__				:				int

       while len(subgraph.vertices				) < len(self.vertices				):
            SCREAMING_SNAKE_CASE__				:				List[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:
                           SCREAMING_SNAKE_CASE__				:				List[Any]			=		edge
                           SCREAMING_SNAKE_CASE__				:				int			=		weight

            subgraph.add_edge(UpperCAmelCase__     , UpperCAmelCase__				)

       return subgraph







def     _a				(      lowercase__  :			str = "p107_network.txt" ):







     '''simple docstring'''


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

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

     SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		[line.split(',' ) for line in data]

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

     SCREAMING_SNAKE_CASE__				:				Graph			=		Graph(set(range(len(lowercase__ ) ) )     ,  lowercase__ )

     SCREAMING_SNAKE_CASE__				:				Graph			=		graph.prims_algorithm()

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

     return initial_total - optimal_total


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




# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import torch

from accelerate import PartialState
from accelerate.utils.operations import broadcast, gather, gather_object, pad_across_processes, reduce







def     _a				(      lowercase__  :			Any ):







     '''simple docstring'''


     return (torch.arange(state.num_processes ) + 1.0 + (state.num_processes * state.process_index)).to(state.device )







def     _a				(      lowercase__  :			Tuple ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				int			=		create_tensor(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		gather(lowercase__ )
     assert gathered_tensor.tolist() == list(range(1     ,  state.num_processes**2 + 1 ) )







def     _a				(      lowercase__  :			List[Any] ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				str			=		[state.process_index]
     SCREAMING_SNAKE_CASE__				:				Any			=		gather_object(lowercase__ )
     assert len(lowercase__ ) == state.num_processes, f'''{gathered_obj}, {len(lowercase__ )} != {state.num_processes}'''
     assert gathered_obj == list(range(state.num_processes ) ), f'''{gathered_obj} != {list(range(state.num_processes ) )}'''







def     _a				(      lowercase__  :			str ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		create_tensor(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		broadcast(lowercase__ )
     assert broadcasted_tensor.shape == torch.Size([state.num_processes] )
     assert broadcasted_tensor.tolist() == list(range(1     ,  state.num_processes + 1 ) )







def     _a				(      lowercase__  :			int ):







     '''simple docstring'''


     if state.is_main_process:
          SCREAMING_SNAKE_CASE__				:				Optional[int]			=		torch.arange(state.num_processes + 1 ).to(state.device )
     else:
          SCREAMING_SNAKE_CASE__				:				List[Any]			=		torch.arange(state.num_processes ).to(state.device )
     SCREAMING_SNAKE_CASE__				:				Any			=		pad_across_processes(lowercase__ )
     assert padded_tensor.shape == torch.Size([state.num_processes + 1] )
     if not state.is_main_process:
          assert padded_tensor.tolist() == list(range(0     ,  state.num_processes ) ) + [0]







def     _a				(      lowercase__  :			Optional[Any] ):







     '''simple docstring'''


     if state.num_processes != 2:
          return
     SCREAMING_SNAKE_CASE__				:				List[Any]			=		create_tensor(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				str			=		reduce(lowercase__     ,  'sum' )
     SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		torch.tensor([4.0, 6] ).to(state.device )
     assert torch.allclose(lowercase__     ,  lowercase__ ), f'''{reduced_tensor} != {truth_tensor}'''







def     _a				(      lowercase__  :			int ):







     '''simple docstring'''


     if state.num_processes != 2:
          return
     SCREAMING_SNAKE_CASE__				:				Any			=		create_tensor(lowercase__ )
     SCREAMING_SNAKE_CASE__				:				List[Any]			=		reduce(lowercase__     ,  'mean' )
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		torch.tensor([2.0, 3] ).to(state.device )
     assert torch.allclose(lowercase__     ,  lowercase__ ), f'''{reduced_tensor} != {truth_tensor}'''







def     _a				(      lowercase__  :			int ):







     '''simple docstring'''


     main()







def     _a				(      ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				int			=		PartialState()
     state.print(f'''State: {state}''' )
     state.print('testing gather' )
     test_gather(lowercase__ )
     state.print('testing gather_object' )
     test_gather_object(lowercase__ )
     state.print('testing broadcast' )
     test_broadcast(lowercase__ )
     state.print('testing pad_across_processes' )
     test_pad_across_processes(lowercase__ )
     state.print('testing reduce_sum' )
     test_reduce_sum(lowercase__ )
     state.print('testing reduce_mean' )
     test_reduce_mean(lowercase__ )


if __name__ == "__main__":
      main()



