
"""simple docstring"""




def     __magic_name__      ( __snake_case							:			dict    )					->							set:
       lowercase       :							str									=				set()
       # edges = list of graph's edges
       lowercase       :							Optional[int]									=				get_edges(__snake_case    )

       # 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:
              lowercase						,       lowercase       :							Dict									=				edges.pop()
              chosen_vertices.add(__snake_case    )
              chosen_vertices.add(__snake_case    )
              for edge in edges.copy():
                     if from_node in edge or to_node in edge:
                            edges.discard(__snake_case    )
       return chosen_vertices


def     __magic_name__      ( __snake_case							:			dict    )					->							set:
       lowercase       :							List[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)}")




"""simple docstring"""




def     __magic_name__      ( __snake_case							:			Any	,					__snake_case							:			Union[str, Any]	,					__snake_case							:			Union[str, Any]=False    )					->							Optional[Any]:

       if isinstance(__snake_case	,					__snake_case    ) and isinstance(__snake_case	,					__snake_case    ):
              lowercase       :							Tuple									=				len(set_a.intersection(__snake_case    )    )

              if alternative_union:
                     lowercase       :							Union[str, Any]									=				len(__snake_case    ) + len(__snake_case    )
              else:
                     lowercase       :							Optional[Any]									=				len(set_a.union(__snake_case    )    )

              return intersection / union

       if isinstance(__snake_case	,					(list, tuple)    ) and isinstance(__snake_case	,					(list, tuple)    ):
              lowercase       :							Tuple									=				[element for element in set_a if element in set_b]

              if alternative_union:
                     lowercase       :							List[str]									=				len(__snake_case    ) + len(__snake_case    )
                     return len(__snake_case    ) / union
              else:
                     lowercase       :							Dict									=				set_a + [element for element in set_b if element not in set_a]
                     return len(__snake_case    ) / len(__snake_case    )

              return len(__snake_case    ) / len(__snake_case    )
       return None


if __name__ == "__main__":
   _A     :			List[str]  						=			{"""a""", """b""", """c""", """d""", """e"""}
   _A     :			Dict  						=			{"""c""", """d""", """e""", """f""", """h""", """i"""}
   print(jaccard_similarity(set_a, set_b))


