






'''simple docstring'''







from queue import PriorityQueue
from typing import Any

import numpy as np





def 		_UpperCAmelCase   (							__A							:   dict						,		__A							:   str						,		__A							:   set						,		__A							:   set						,		__A							:   dict						,		__A							:   dict						,		__A							:   PriorityQueue						,		__A							:   dict						,		__A							:   float | int						,		):
				for nxt, d in graph[v]:
								if nxt in visited_forward:
												continue
								a_		:  str											=      cst_fwd.get(__A						,		np.inf      )
								a_		:  List[str]											=      cst_fwd[v] + d
								if new_cost_f < old_cost_f:
												queue.put((new_cost_f, nxt)      )
												a_		:  Dict											=      new_cost_f
												a_		:  int											=      v
								if nxt in visited_backward:
												if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
																a_		:  Optional[Any]											=      cst_fwd[v] + d + cst_bwd[nxt]
				return shortest_distance





def 		_UpperCAmelCase   (							__A							:   str						,		__A							:   str						,		__A							:   dict						,		__A							:   dict      ):
				a_		:  int											=      -1

				a_		:  Optional[Any]											=      set()
				a_		:  Optional[Any]											=      set()
				a_		:  Any											=      {source: 0}
				a_		:  Dict											=      {destination: 0}
				a_		:  str											=      {source: None}
				a_		:  List[Any]											=      {destination: None}
				a_		:  PriorityQueue[Any]											=      PriorityQueue()
				a_		:  PriorityQueue[Any]											=      PriorityQueue()

				a_		:  Optional[Any]											=      np.inf

				queue_forward.put((0, source)      )
				queue_backward.put((0, destination)      )

				if source == destination:
								return 0

				while not queue_forward.empty() and not queue_backward.empty():
								a_				,			a_		:  int											=      queue_forward.get()
								visited_forward.add(__A      )

								a_				,			a_		:  Optional[int]											=      queue_backward.get()
								visited_backward.add(__A      )

								a_		:  Tuple											=      pass_and_relaxation(
								    __A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		)

								a_		:  Any											=      pass_and_relaxation(
								    __A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		__A						,		)

								if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
												break

				if shortest_distance != np.inf:
								a_		:  Union[str, Any]											=      shortest_distance
				return shortest_path_distance


__lowerCAmelCase       		=      {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
__lowerCAmelCase       		=      {
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()












'''simple docstring'''







def 		_UpperCAmelCase   (							__A							:   str						,		__A							:   str      ):

				def get_matched_characters(__A							:   str						,		__A							:   str      ) -> str:
								a_		:  Union[str, Any]											=      []
								a_		:  int											=      min(len(_stra      )						,		len(_stra      )      ) // 2
								for i, l in enumerate(_stra      ):
												a_		:  Any											=      int(max(0						,		i - limit      )      )
												a_		:  Union[str, Any]											=      int(min(i + limit + 1						,		len(_stra      )      )      )
												if l in _stra[left:right]:
																matched.append(__A      )
																a_		:  Any											=      f'{_stra[0:_stra.index(__A      )]} {_stra[_stra.index(__A      ) + 1:]}'

								return "".join(__A      )

				# matching characters
				a_		:  Optional[Any]											=      get_matched_characters(__A						,		__A      )
				a_		:  int											=      get_matched_characters(__A						,		__A      )
				a_		:  Any											=      len(__A      )

				# transposition
				a_		:  List[Any]											=      (
				    len([(ca, ca) for ca, ca in zip(__A						,		__A      ) if ca != ca]      ) // 2
				)

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

				# common prefix up to 4 characters
				a_		:  List[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'))




