code: 
  
  
  
  
  
  
  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					)   -> set[tuple[str, str]]:
  
       '''simple docstring'''
       UpperCAmelCase__			:     List[str]										= {node: {node} for node in graph}
  
       UpperCAmelCase__			:     str										= {node: graph[node][:] for node in graph}
  
       while len(__lowerCamelCase					) > 2:
            # Choose a random edge.
            UpperCAmelCase__			:     List[Any]										= random.choice(list(graph_copy.keys()					)					)
            UpperCAmelCase__			:     str										= 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__			:     List[str]										= uv_neighbors
            for neighbor in uv_neighbors:
                 graph_copy[neighbor].append(__lowerCamelCase					)
  
            UpperCAmelCase__			:     Tuple										= 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__			:     List[str]										= [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: 
  
  
  
  
  
  
  from .stack import Stack
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase					)   -> bool:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Stack[str]										= Stack()
       UpperCAmelCase__			:     str										= {"""(""": """)""", """[""": """]""", """{""": """}"""}
       for bracket in parentheses:
            if bracket in bracket_pairs:
                 stack.push(__lowerCamelCase					)
            elif bracket in (")", "]", "}"):
                 if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                      return False
       return stack.is_empty()
  
  
  if __name__ == "__main__":
        from doctest import testmod
  
        testmod()
  
        SCREAMING_SNAKE_CASE__		:       Any   							=							["""((()))""", """((())""", """(()))"""]
        print("""Balanced parentheses demonstration:\n""")
        for example in examples:
              SCREAMING_SNAKE_CASE__		:       List[str]   							=							"""""" if balanced_parentheses(example) else """not """
              print(f'''{example} is {not_str}balanced''')
  
  
  
  
  
  
  