





from __future__ import annotations

from typing import Generic, TypeVar

lowercase :			Union[str, Any]     		=    TypeVar("""T""")





class 					A__       (				Generic[T]      ):




   """simple docstring"""



   def __init__(   self   ,    lowercase)     ->		Tuple:







          '''simple docstring'''

          a__		:      int					=							data
          a__		:      Optional[int]					=							self
          a__		:      Any					=							0





class 					A__       (				Generic[T]      ):




   """simple docstring"""



   def __init__(   self)     ->		List[str]:







          '''simple docstring'''

          a__		:      dict[T, DisjointSetTreeNode[T]]					=							{}

   def 				__lowercase						(   self   ,    lowercase)     ->		Optional[int]:







          '''simple docstring'''

          a__		:      Optional[Any]					=							DisjointSetTreeNode(_a)

   def 				__lowercase						(   self   ,    lowercase)     ->		Optional[int]:







          '''simple docstring'''

          a__		:      str					=							self.map[data]
          if elem_ref != elem_ref.parent:
                 a__		:      Optional[int]					=							self.find_set(elem_ref.parent.data)
          return elem_ref.parent

   def 				__lowercase						(   self   ,    lowercase   ,    lowercase)     ->		Optional[int]:







          '''simple docstring'''

          if nodea.rank > nodea.rank:
                 a__		:      int					=							nodea
          else:
                 a__		:      List[Any]					=							nodea
                 if nodea.rank == nodea.rank:
                        nodea.rank += 1

   def 				__lowercase						(   self   ,    lowercase   ,    lowercase)     ->		int:







          '''simple docstring'''

          self.link(self.find_set(_a)   ,    self.find_set(_a))





class 					A__       (				Generic[T]      ):




   """simple docstring"""



   def __init__(   self)     ->		Union[str, Any]:







          '''simple docstring'''

          a__		:      dict[T, dict[T, int]]					=							{}

   def 				__lowercase						(   self   ,    lowercase)     ->		Any:







          '''simple docstring'''

          if node not in self.connections:
                 a__		:      int					=							{}

   def 				__lowercase						(   self   ,    lowercase   ,    lowercase   ,    lowercase)     ->		List[str]:







          '''simple docstring'''

          self.add_node(_a)
          self.add_node(_a)
          a__		:      Any					=							weight
          a__		:      Any					=							weight

   def 				__lowercase						(   self)     ->		Dict:







          '''simple docstring'''

          a__		:      Optional[int]					=							[]
          a__		:      Any					=							set()
          for start in self.connections:
                 for end in self.connections[start]:
                        if (start, end) not in seen:
                               seen.add((end, start))
                               edges.append((start, end, self.connections[start][end]))
          edges.sort(key=lambda lowercase: x[2])

          # creating the disjoint set
          a__		:      List[Any]					=							DisjointSetTree[T]()
          for node in self.connections:
                 disjoint_set.make_set(_a)

          # MST generation
          a__		:      Union[str, Any]					=							0
          a__		:      List[Any]					=							0
          a__		:      Dict					=							GraphUndirectedWeighted[T]()
          while num_edges < len(self.connections) - 1:
                 a__		:      Optional[int]					=							edges[index]
                 index += 1
                 a__		:      Optional[int]					=							disjoint_set.find_set(_a)
                 a__		:      List[str]					=							disjoint_set.find_set(_a)
                 if parent_u != parent_v:
                        num_edges += 1
                        graph.add_edge(_a   ,    _a   ,    _a)
                        disjoint_set.union(_a   ,    _a)
          return 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))


