


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
__SCREAMING_SNAKE_CASE					=						{
    """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 						__a      (  a					):





       """simple docstring"""







       _a          =				{node: {node} for node in graph}

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

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

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

              _a          =				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(a					)
                     if v in graph_copy[neighbor]:
                            graph_copy[neighbor].remove(a					)

    # Find cutset.
       _a          =				[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 __future__ import annotations

from collections.abc import Iterator
from typing import Any





class __snake_case		:







   """simple docstring"""




   def __init__(		self							:List[Any]				,  UpperCamelCase__							:Any       ):
          _a          =				data
          _a          =				None




   def __str__(		self							:Any       ):
          return f'{self.data}'






class __snake_case		:







   """simple docstring"""




   def __init__(		self							:Any       ):
          _a          =				None
          _a          =				None




   def __iter__(		self							:List[str]       ):
          _a          =				self.front
          while node:
                 yield node.data
                 _a          =				node.next




   def __len__(		self							:List[str]       ):
          return len(tuple(iter(self       )       )       )




   def __str__(		self							:Union[str, Any]       ):
          return " <- ".join(str(UpperCamelCase__       ) for item in self       )




   def SCREAMING_SNAKE_CASE_      (		self							:Any       ):
          return len(self       ) == 0




   def SCREAMING_SNAKE_CASE_      (		self							:List[str]				,  UpperCamelCase__							:Any       ):
          _a          =				Node(UpperCamelCase__       )
          if self.is_empty():
                 _a          =				_a          =				node
          else:
                 assert isinstance(self.rear				,  UpperCamelCase__       )
                 _a          =				node
                 _a          =				node




   def SCREAMING_SNAKE_CASE_      (		self							:Tuple       ):
          if self.is_empty():
                 raise IndexError("dequeue from empty queue"       )
          assert isinstance(self.front				,  UpperCamelCase__       )
          _a          =				self.front
          _a          =				self.front.next
          if self.front is None:
                 _a          =				None
          return node.data




   def SCREAMING_SNAKE_CASE_      (		self							:int       ):
          _a          =				_a          =				None


if __name__ == "__main__":
   from doctest import testmod

   testmod()
