





'''simple docstring'''


from __future__ import annotations

a__			:					List[str]       						=						{
    'A': ['B', 'C', 'E'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F', 'G'],
    'D': ['B'],
    'E': ['A', 'B', 'D'],
    'F': ['C'],
    'G': ['C'],
}






class     lowerCAmelCase__ :

       '''simple docstring'''

       def __init__( self					:				Optional[int]       ,     a__					:				dict[str, list[str]]       ,     a__					:				str						):
              UpperCAmelCase  =						graph
              # mapping node to its parent in resulting breadth first tree
              UpperCAmelCase  =						{}
              UpperCAmelCase  =						source_vertex

       def 			__snake_case      ( self					:				Optional[int]						):
              UpperCAmelCase  =						{self.source_vertex}
              UpperCAmelCase  =						None
              UpperCAmelCase  =						[self.source_vertex]  # first in first out queue

              while queue:
                     UpperCAmelCase  =						queue.pop(0						)
                     for adjacent_vertex in self.graph[vertex]:
                            if adjacent_vertex not in visited:
                                   visited.add(a__						)
                                   UpperCAmelCase  =						vertex
                                   queue.append(a__						)



       def 			__snake_case      ( self					:				Any       ,     a__					:				str						):
              if target_vertex == self.source_vertex:
                     return self.source_vertex

              UpperCAmelCase  =						self.parent.get(a__						)
              if target_vertex_parent is None:
                     UpperCAmelCase  =						(
                         f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}"
                     )
                     raise ValueError(a__						)

              return self.shortest_path(a__						) + f"->{target_vertex}"


if __name__ == "__main__":
    a__			:					Tuple       						=						Graph(graph, 'G')
    g.breath_first_search()
    print(g.shortest_path('D'))
    print(g.shortest_path('G'))
    print(g.shortest_path('Foo'))






def 	_lowerCAmelCase					( UpperCamelCase__:  str				,       UpperCamelCase__:  int				,       UpperCamelCase__:  Any=False    )			-> str:





	"""simple docstring"""







	if isinstance(UpperCamelCase__				,       UpperCamelCase__    ) and isinstance(UpperCamelCase__				,       UpperCamelCase__    ):
		A             =					len(set_a.intersection(UpperCamelCase__    )    )

		if alternative_union:
			A             =					len(UpperCamelCase__    ) + len(UpperCamelCase__    )
		else:
			A             =					len(set_a.union(UpperCamelCase__    )    )

		return intersection / union

	if isinstance(UpperCamelCase__				,       (list, tuple)    ) and isinstance(UpperCamelCase__				,       (list, tuple)    ):
		A             =					[element for element in set_a if element in set_b]

		if alternative_union:
			A             =					len(UpperCamelCase__    ) + len(UpperCamelCase__    )
			return len(UpperCamelCase__    ) / union
		else:
			A             =					set_a + [element for element in set_b if element not in set_a]
			return len(UpperCamelCase__    ) / len(UpperCamelCase__    )

		return len(UpperCamelCase__    ) / len(UpperCamelCase__    )
	return None


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



