

from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_UpperCamelCase			       =			{
    '''1''': ['''2''', '''3''', '''4''', '''5'''],
    '''2''': ['''1''', '''3''', '''4''', '''5'''],
    '''3''': ['''1''', '''2''', '''4''', '''5''', '''10'''],
    '''4''': ['''1''', '''2''', '''3''', '''5''', '''6'''],
    '''5''': ['''1''', '''2''', '''3''', '''4''', '''7'''],
    '''6''': ['''7''', '''8''', '''9''', '''10''', '''4'''],
    '''7''': ['''6''', '''8''', '''9''', '''10''', '''5'''],
    '''8''': ['''6''', '''7''', '''9''', '''10'''],
    '''9''': ['''6''', '''7''', '''8''', '''10'''],
    '''10''': ['''6''', '''7''', '''8''', '''9''', '''3'''],
}
def 						UpperCamelCase_(			snake_case__:  dict[str, list[str]]   )       -> set[tuple[str, str]]:
 UpperCAmelCase__							=				{node: {node} for node in graph}

 UpperCAmelCase__							=				{node: graph[node][:] for node in graph}

 while len(snake_case__   ) > 2:
  # Choose a random edge.
  UpperCAmelCase__							=				random.choice(list(graph_copy.keys()   )   )
  UpperCAmelCase__							=				random.choice(graph_copy[u]   )

  # Contract edge (u, v) to new node uv
  UpperCAmelCase__							=				u + v
  UpperCAmelCase__							=				list(set(graph_copy[u] + graph_copy[v]   )   )
  uv_neighbors.remove(snake_case__   )
  uv_neighbors.remove(snake_case__   )
  UpperCAmelCase__							=				uv_neighbors
  for neighbor in uv_neighbors:
   graph_copy[neighbor].append(snake_case__   )

  UpperCAmelCase__							=				set(contracted_nodes[u].union(contracted_nodes[v]   )   )

  # Remove nodes u and v.
  del graph_copy[u]
  del graph_copy[v]
  for neighbor in uv_neighbors:
   if u in graph_copy[neighbor]:
    graph_copy[neighbor].remove(snake_case__   )
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(snake_case__   )

    # Find cutset.
 UpperCAmelCase__							=				[contracted_nodes[node] for node in graph_copy]
 return {
     (node, neighbor)
     for node in groups[0]
     for neighbor in graph[node]
     if neighbor in groups[1]
 }


if __name__ == "__main__":
 print(partition_graph(TEST_GRAPH))











"""simple docstring"""







from collections import OrderedDict
from dataclasses import fields
from typing import Any, Tuple

import numpy as np

from .import_utils import is_torch_available






def 					_lowerCAmelCase				(					lowerCAmelCase						):







       '''simple docstring'''
       if is_torch_available():
              import torch

              if isinstance(lowerCAmelCase		,					torch.Tensor						):
                     return True

       return isinstance(lowerCAmelCase		,					np.ndarray						)





class      UpperCamelCase_       (				a_     ):



  def 						UpperCamelCase_ (					self )	->	Dict:



         """simple docstring"""





         UpperCAmelCase					=	fields(self )

         # Safety and consistency checks
         if not len(snake_case__ ):
                raise ValueError(f'''{self.__class__.__name__} has no fields.''' )

         UpperCAmelCase					=	getattr(self       ,						class_fields[0].name )
         UpperCAmelCase					=	all(getattr(self       ,						field.name ) is None for field in class_fields[1:] )

         if other_fields_are_none and isinstance(snake_case__       ,						snake_case__ ):
                for key, value in first_field.items():
                       UpperCAmelCase					=	value
         else:
                for field in class_fields:
                       UpperCAmelCase					=	getattr(self       ,						field.name )
                       if v is not None:
                              UpperCAmelCase					=	v



  def __delitem__(					self       ,						*snake_case__       ,						**snake_case__ )	->	Optional[int]:



         """simple docstring"""





         raise Exception(f'''You cannot use ``__delitem__`` on a {self.__class__.__name__} instance.''' )



  def 						UpperCamelCase_ (					self       ,						*snake_case__       ,						**snake_case__ )	->	List[str]:



         """simple docstring"""





         raise Exception(f'''You cannot use ``setdefault`` on a {self.__class__.__name__} instance.''' )



  def 						UpperCamelCase_ (					self       ,						*snake_case__       ,						**snake_case__ )	->	Optional[int]:



         """simple docstring"""





         raise Exception(f'''You cannot use ``pop`` on a {self.__class__.__name__} instance.''' )



  def 						UpperCamelCase_ (					self       ,						*snake_case__       ,						**snake_case__ )	->	Optional[int]:



         """simple docstring"""





         raise Exception(f'''You cannot use ``update`` on a {self.__class__.__name__} instance.''' )



  def __getitem__(					self       ,						snake_case__ )	->	List[Any]:



         """simple docstring"""





         if isinstance(snake_case__       ,						snake_case__ ):
                UpperCAmelCase					=	dict(self.items() )
                return inner_dict[k]
         else:
                return self.to_tuple()[k]



  def __setattr__(					self       ,						snake_case__       ,						snake_case__ )	->	Union[str, Any]:



         """simple docstring"""





         if name in self.keys() and value is not None:
                # Don't call self.__setitem__ to avoid recursion errors
                super().__setitem__(snake_case__       ,						snake_case__ )
         super().__setattr__(snake_case__       ,						snake_case__ )



  def __setitem__(					self       ,						snake_case__       ,						snake_case__ )	->	Tuple:



         """simple docstring"""





         super().__setitem__(snake_case__       ,						snake_case__ )
         # Don't call self.__setattr__ to avoid recursion errors
         super().__setattr__(snake_case__       ,						snake_case__ )



  def 						UpperCamelCase_ (					self )	->	Tuple[Any]:



         """simple docstring"""





         return tuple(self[k] for k in self.keys() )
