






"""simple docstring"""



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
a  :						Union[str, Any]					       =							{
    '''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       snake_case__		(   _SCREAMING_SNAKE_CASE			)    ->set[tuple[str, str]]:
 UpperCAmelCase__ 						=				{node: {node} for node in graph}

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

 while len(a_			) > 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(a_			)
  uv_neighbors.remove(a_			)
  UpperCAmelCase__ 						=				uv_neighbors
  for neighbor in uv_neighbors:
   graph_copy[neighbor].append(a_			)

  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(a_			)
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(a_			)

    # 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))






from __future__ import annotations

from collections.abc import Iterator
from typing import Any

class 					__UpperCamelCase					:







	def __init__( self:			Optional[Any]	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     data
						__magic_name__				=     None







	def __str__( self:			Optional[int]   ):

						'''simple docstring'''





						return F'{self.data}'




class 					__UpperCamelCase					:







	def __init__( self:			List[Any]   ):

						'''simple docstring'''





						__magic_name__				=     None
						__magic_name__				=     None







	def __iter__( self:			str   ):

						'''simple docstring'''





						__magic_name__				=     self.front
						while node:
											yield node.data
											__magic_name__				=     node.next







	def __len__( self:			Any   ):

						'''simple docstring'''





						return len(tuple(iter(self   )   )   )







	def __str__( self:			List[str]   ):

						'''simple docstring'''





						return " <- ".join(str(__UpperCamelCase   ) for item in self   )







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						return len(self   ) == 0







	def 						_SCREAMING_SNAKE_CASE				( self:			Any	,			__UpperCamelCase:			Any   ):

						'''simple docstring'''





						__magic_name__				=     Node(__UpperCamelCase   )
						if self.is_empty():
											__magic_name__				=     __magic_name__				=     node
						else:
											assert isinstance(self.rear	,			__UpperCamelCase   )
											__magic_name__				=     node
											__magic_name__				=     node







	def 						_SCREAMING_SNAKE_CASE				( self:			Any   ):

						'''simple docstring'''





						if self.is_empty():
											raise IndexError('dequeue from empty queue'   )
						assert isinstance(self.front	,			__UpperCamelCase   )
						__magic_name__				=     self.front
						__magic_name__				=     self.front.next
						if self.front is None:
											__magic_name__				=     None
						return node.data







	def 						_SCREAMING_SNAKE_CASE				( self:			Tuple   ):

						'''simple docstring'''





						__magic_name__				=     __magic_name__				=     None


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

						testmod()




