





"""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
_lowerCamelCase  					=     {
    '''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 		lowerCAmelCase_     (  lowercase_       :							dict[str, list[str]]		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      int 							=	{node: {node} for node in graph}

 __SCREAMING_SNAKE_CASE			:      Tuple 							=	{node: graph[node][:] for node in graph}

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

  # Contract edge (u, v) to new node uv
  __SCREAMING_SNAKE_CASE			:      Union[str, Any] 							=	u + v
  __SCREAMING_SNAKE_CASE			:      List[str] 							=	list(set(graph_copy[u] + graph_copy[v]		)		)
  uv_neighbors.remove(lowercase_		)
  uv_neighbors.remove(lowercase_		)
  __SCREAMING_SNAKE_CASE			:      Any 							=	uv_neighbors
  for neighbor in uv_neighbors:
   graph_copy[neighbor].append(lowercase_		)

  __SCREAMING_SNAKE_CASE			:      str 							=	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(lowercase_		)
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(lowercase_		)

    # Find cutset.
 __SCREAMING_SNAKE_CASE			:      Tuple 							=	[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"""





def 		lowerCAmelCase_     (  lowercase_       :							int = 30		):

 '''simple docstring'''






 __SCREAMING_SNAKE_CASE			:      str 							=	exponent + 2
 __SCREAMING_SNAKE_CASE			:      Optional[Any] 							=	(1 + 5**0.5) / 2
 __SCREAMING_SNAKE_CASE			:      Optional[int] 							=	(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

 return int(lowercase_		)


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

