def     _a				(      lowercase__  :			Tuple     ,  lowercase__  :			int     ,  lowercase__  :			List[Any]=False ):







					'''simple docstring'''


					if isinstance(lowercase__     ,  lowercase__ ) and isinstance(lowercase__     ,  lowercase__ ):
										SCREAMING_SNAKE_CASE__				:				List[Any]			=		len(set_a.intersection(lowercase__ ) )

										if alternative_union:
															SCREAMING_SNAKE_CASE__				:				int			=		len(lowercase__ ) + len(lowercase__ )
										else:
															SCREAMING_SNAKE_CASE__				:				Tuple			=		len(set_a.union(lowercase__ ) )

										return intersection / union

					if isinstance(lowercase__     ,  (list, tuple) ) and isinstance(lowercase__     ,  (list, tuple) ):
										SCREAMING_SNAKE_CASE__				:				Any			=		[element for element in set_a if element in set_b]

										if alternative_union:
															SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		len(lowercase__ ) + len(lowercase__ )
															return len(lowercase__ ) / union
										else:
															SCREAMING_SNAKE_CASE__				:				Any			=		set_a + [element for element in set_b if element not in set_a]
															return len(lowercase__ ) / len(lowercase__ )

										return len(lowercase__ ) / len(lowercase__ )
					return None


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




import heapq as hq
import math
from collections.abc import Iterator

class       snake_case					:




  def __init__(      self     :	str     , a_     :	str				)->       Any:




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				List[str]			=		str(id_				)
       SCREAMING_SNAKE_CASE__				:				Any			=		None
       SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		None
       SCREAMING_SNAKE_CASE__				:				Any			=		[]
       SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		{}  # {vertex:distance}




  def __lt__(      self     :	int     , a_     :	Tuple				)->       Union[str, Any]:




       """simple docstring"""
       return self.key < other.key




  def __repr__(      self     :	Any				)->       Dict:




       """simple docstring"""
       return self.id




  def 	__lowercase(      self     :	Optional[Any]     , a_     :	int				)->       List[str]:




       """simple docstring"""
       self.neighbors.append(a_				)




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




       """simple docstring"""
       SCREAMING_SNAKE_CASE__				:				Tuple			=		weight







def     _a				(      lowercase__  :			Optional[Any]     ,  lowercase__  :			Union[str, Any]     ,  lowercase__  :			Tuple     ,  lowercase__  :			Dict ):







     '''simple docstring'''


     graph[a - 1].add_neighbor(graph[b - 1] )
     graph[b - 1].add_neighbor(graph[a - 1] )
     # add the edges:
     graph[a - 1].add_edge(graph[b - 1]     ,  lowercase__ )
     graph[b - 1].add_edge(graph[a - 1]     ,  lowercase__ )







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__				:				Any			=		[]
     for u in graph:
          SCREAMING_SNAKE_CASE__				:				Dict			=		math.inf
          SCREAMING_SNAKE_CASE__				:				str			=		None
     SCREAMING_SNAKE_CASE__				:				List[str]			=		0
     SCREAMING_SNAKE_CASE__				:				int			=		graph[:]
     while q:
          SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		min(lowercase__ )
          q.remove(lowercase__ )
          for v in u.neighbors:
               if (v in q) and (u.edges[v.id] < v.key):
                    SCREAMING_SNAKE_CASE__				:				int			=		u
                    SCREAMING_SNAKE_CASE__				:				Any			=		u.edges[v.id]
     for i in range(1     ,  len(lowercase__ ) ):
          a.append((int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1) )
     return a







def     _a				(      lowercase__  :			list     ,  lowercase__  :			Vertex ):







     '''simple docstring'''


     for u in graph:
          SCREAMING_SNAKE_CASE__				:				List[str]			=		math.inf
          SCREAMING_SNAKE_CASE__				:				int			=		None
     SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		0

     SCREAMING_SNAKE_CASE__				:				Tuple			=		list(lowercase__ )
     hq.heapify(lowercase__ )

     while h:
          SCREAMING_SNAKE_CASE__				:				Optional[int]			=		hq.heappop(lowercase__ )
          for v in u.neighbors:
               if (v in h) and (u.edges[v.id] < v.key):
                    SCREAMING_SNAKE_CASE__				:				List[str]			=		u
                    SCREAMING_SNAKE_CASE__				:				Dict			=		u.edges[v.id]
                    hq.heapify(lowercase__ )

     for i in range(1     ,  len(lowercase__ ) ):
          yield (int(graph[i].id ) + 1, int(graph[i].pi.id ) + 1)







def     _a				(      ):







     '''simple docstring'''




if __name__ == "__main__":
      import doctest

      doctest.testmod()



