'''simple docstring'''




def 	UpperCamelCase_							(					_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      str    )    ->    float:


       """simple docstring"""







       def get_matched_characters(_UpperCAmelCase  :      str			,	_UpperCAmelCase  :      str    ) -> str:
              _UpperCAmelCase     :  Tuple							      =    []
              _UpperCAmelCase     :  Dict							      =    min(len(_stra    )			,	len(_stra    )    ) // 2
              for i, l in enumerate(_stra    ):
                     _UpperCAmelCase     :  int							      =    int(max(0			,	i - limit    )    )
                     _UpperCAmelCase     :  Any							      =    int(min(i + limit + 1			,	len(_stra    )    )    )
                     if l in _stra[left:right]:
                            matched.append(_UpperCAmelCase    )
                            _UpperCAmelCase     :  List[Any]							      =    F"""{_stra[0:_stra.index(_UpperCAmelCase    )]} {_stra[_stra.index(_UpperCAmelCase    ) + 1:]}"""

              return "".join(_UpperCAmelCase    )

       # matching characters
       _UpperCAmelCase     :  Union[str, Any]							      =    get_matched_characters(_UpperCAmelCase			,	_UpperCAmelCase    )
       _UpperCAmelCase     :  Tuple							      =    get_matched_characters(_UpperCAmelCase			,	_UpperCAmelCase    )
       _UpperCAmelCase     :  Tuple							      =    len(_UpperCAmelCase    )

       # transposition
       _UpperCAmelCase     :  Optional[Any]							      =    (
           len([(ca, ca) for ca, ca in zip(_UpperCAmelCase			,	_UpperCAmelCase    ) if ca != ca]    ) // 2
       )

       if not match_count:
              _UpperCAmelCase     :  Dict							      =    0.0
       else:
              _UpperCAmelCase     :  Optional[int]							      =    (
                  1
                  / 3
                  * (
                      match_count / len(_UpperCAmelCase    )
                      + match_count / len(_UpperCAmelCase    )
                      + (match_count - transpositions) / match_count
                  )
              )

       # common prefix up to 4 characters
       _UpperCAmelCase     :  str							      =    0
       for ca, ca in zip(stra[:4]			,	stra[:4]    ):
              if ca == ca:
                     prefix_len += 1
              else:
                     break

       return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(jaro_winkler("""hello""", """world"""))





from __future__ import annotations

A      :    Union[str, Any]		=					{
    "A": ["B", "C", "E"],
    "B": ["A", "D", "E"],
    "C": ["A", "F", "G"],
    "D": ["B"],
    "E": ["A", "B", "D"],
    "F": ["C"],
    "G": ["C"],
}







class 			_lowercase :


       """simple docstring"""




       def __init__(   self							:			Tuple					,      __lowerCamelCase							:			dict[str, list[str]]					,      __lowerCamelCase							:			str       ):


             '''simple docstring'''



             lowerCamelCase__		:				Union[str, Any]    =  graph
             # mapping node to its parent in resulting breadth first tree
             lowerCamelCase__		:				dict[str, str | None]    =  {}
             lowerCamelCase__		:				Dict    =  source_vertex





       def 						lowerCAmelCase     (   self							:			Any       ):


             '''simple docstring'''



             lowerCamelCase__		:				int    =  {self.source_vertex}
             lowerCamelCase__		:				Optional[int]    =  None
             lowerCamelCase__		:				Dict    =  [self.source_vertex]  # first in first out queue

             while queue:
                   lowerCamelCase__		:				Optional[int]    =  queue.pop(0       )
                   for adjacent_vertex in self.graph[vertex]:
                         if adjacent_vertex not in visited:
                               visited.add(__lowerCamelCase       )
                               lowerCamelCase__		:				List[str]    =  vertex
                               queue.append(__lowerCamelCase       )





       def 						lowerCAmelCase     (   self							:			Optional[Any]					,      __lowerCamelCase							:			str       ):


             '''simple docstring'''



             if target_vertex == self.source_vertex:
                   return self.source_vertex

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

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


if __name__ == "__main__":
    A      :    List[str]		=					Graph(graph, "G")
    g.breath_first_search()
    print(g.shortest_path("D"))
    print(g.shortest_path("G"))
    print(g.shortest_path("Foo"))


