





def 					lowerCAmelCase_			(	__a		)					->		set:







  """simple docstring"""





  lowerCamelCase__:				Optional[Any]        =set()
  # edges = list of graph's edges
  lowerCamelCase__:				Tuple        =get_edges(__a		)

  # While there are still elements in edges list, take an arbitrary edge
  # (from_node, to_node) and add his extremity to chosen_vertices and then
  # remove all arcs adjacent to the from_node and to_node
  while edges:
    lowerCamelCase__  , lowerCamelCase__:				Union[str, Any]        =edges.pop()
    chosen_vertices.add(__a		)
    chosen_vertices.add(__a		)
    for edge in edges.copy():
      if from_node in edge or to_node in edge:
        edges.discard(__a		)
  return chosen_vertices





def 					lowerCAmelCase_			(	__a		)					->		set:







  """simple docstring"""





  lowerCamelCase__:				str        =set()
  for from_node, to_nodes in graph.items():
    for to_node in to_nodes:
      edges.add((from_node, to_node)		)
  return edges


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
     # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")








from ..utils import DummyObject, requires_backends



class        _SCREAMING_SNAKE_CASE						(     metaclass=__SCREAMING_SNAKE_CASE   ):







 '''simple docstring'''
 lowercase_		=      ["torch", "torchsde"]

 def __init__(self    :       Union[str, Any]	,			*UpperCAmelCase_    :       Dict	,			**UpperCAmelCase_    :       Tuple)	->Any:



   '''simple docstring'''



   requires_backends(self	,			["torch", "torchsde"])

 @classmethod
 def 							SCREAMING_SNAKE_CASE_ (cls    :       Dict	,			*UpperCAmelCase_    :       Optional[int]	,			**UpperCAmelCase_    :       Optional[int])	->List[Any]:



   '''simple docstring'''



   requires_backends(cls	,			["torch", "torchsde"])







 @classmethod
 def 							SCREAMING_SNAKE_CASE_ (cls    :       Tuple	,			*UpperCAmelCase_    :       Tuple	,			**UpperCAmelCase_    :       Any)	->Any:



   '''simple docstring'''



   requires_backends(cls	,			["torch", "torchsde"])

