



"""simple docstring"""
from queue import PriorityQueue
from typing import Any

import numpy as np





def      __magic_name__				(							lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			):
   for nxt, d in graph[v]:
      if nxt in visited_forward:
         continue
      SCREAMING_SNAKE_CASE_: Optional[Any]     			=cst_fwd.get(lowercase							,			np.inf )
      SCREAMING_SNAKE_CASE_: Optional[Any]     			=cst_fwd[v] + d
      if new_cost_f < old_cost_f:
         queue.put((new_cost_f, nxt) )
         SCREAMING_SNAKE_CASE_: List[str]     			=new_cost_f
         SCREAMING_SNAKE_CASE_: Any     			=v
      if nxt in visited_backward:
         if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
            SCREAMING_SNAKE_CASE_: Union[str, Any]     			=cst_fwd[v] + d + cst_bwd[nxt]
   return shortest_distance





def      __magic_name__				(							lowercase							,			lowercase							,			lowercase							,			lowercase ):
   SCREAMING_SNAKE_CASE_: List[Any]     			=-1

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

   SCREAMING_SNAKE_CASE_: Tuple     			=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():
      SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Tuple     			=queue_forward.get()
      visited_forward.add(lowercase )

      SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Tuple     			=queue_backward.get()
      visited_backward.add(lowercase )

      SCREAMING_SNAKE_CASE_: Dict     			=pass_and_relaxation(
          lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			)

      SCREAMING_SNAKE_CASE_: Tuple     			=pass_and_relaxation(
          lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			lowercase							,			)

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

   if shortest_distance != np.inf:
      SCREAMING_SNAKE_CASE_: List[str]     			=shortest_distance
   return shortest_path_distance


_UpperCAmelCase     =			{
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}
_UpperCAmelCase     =			{
    """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"""
from math import pi





def      __magic_name__				(							lowercase							,			lowercase ):
   return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
   print(arc_length(9_0, 1_0))



