code: 
  
  
  
  
  
  
  '''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
  SCREAMING_SNAKE_CASE__		:       Dict   							=							{
      """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	(	__lowerCamelCase					)   -> Optional[int]:
  
       '''simple docstring'''
       UpperCAmelCase__			:     List[Any]										= {node: {node} for node in graph}
  
       UpperCAmelCase__			:     List[str]										= {node: graph[node][:] for node in graph}
  
       while len(__lowerCamelCase					) > 2:
            # Choose a random edge.
            UpperCAmelCase__			:     Any										= random.choice(list(graph_copy.keys()					)					)
            UpperCAmelCase__			:     int										= random.choice(graph_copy[u]					)
  
            # Contract edge (u, v) to new node uv
            UpperCAmelCase__			:     Optional[int]										= u + v
            UpperCAmelCase__			:     Union[str, Any]										= list(set(graph_copy[u] + graph_copy[v]					)					)
            uv_neighbors.remove(__lowerCamelCase					)
            uv_neighbors.remove(__lowerCamelCase					)
            UpperCAmelCase__			:     Optional[int]										= uv_neighbors
            for neighbor in uv_neighbors:
                 graph_copy[neighbor].append(__lowerCamelCase					)
  
            UpperCAmelCase__			:     List[Any]										= 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(__lowerCamelCase					)
                 if v in graph_copy[neighbor]:
                      graph_copy[neighbor].remove(__lowerCamelCase					)
  
      # Find cutset.
       UpperCAmelCase__			:     int										= [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))
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  import random
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
  
  
  
  
       def __init__(							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     Union[str, Any]										= x
            UpperCAmelCase__			:     Union[str, Any]										= y
  
  
  
  
       def      __UpperCAmelCase     (							self		):
            return (self.x**2 + self.y**2) <= 1
  
  
  
  
       @classmethod
       def      __UpperCAmelCase     (							cls		):
            return cls(x=random.random()  ,	y=random.random()		)
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase					)   -> float:
  
       '''simple docstring'''
       if number_of_simulations < 1:
            raise ValueError("""At least one simulation is necessary to estimate PI."""					)
  
       UpperCAmelCase__			:     Dict										= 0
       for _ in range(__lowerCamelCase					):
            UpperCAmelCase__			:     Union[str, Any]										= Point.random_unit_square()
  
            if random_point.is_in_unit_circle():
                 number_in_unit_circle += 1
  
       return 4 * number_in_unit_circle / number_of_simulations
  
  
  if __name__ == "__main__":
        # import doctest
  
        # doctest.testmod()
        from math import pi
  
        SCREAMING_SNAKE_CASE__		:       List[str]   							=							"""Please enter the desired number of Monte Carlo simulations: """
        SCREAMING_SNAKE_CASE__		:       int   							=							estimate_pi(int(input(prompt).strip()))
        print(f'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')
  
  
  
  
  
  
  