






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))














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''')






