
"""simple docstring"""


from queue import PriorityQueue
from typing import Any

import numpy as np






def    _snake_case					(		snake_case__ :  dict						,   snake_case__ :  str						,   snake_case__ :  set						,   snake_case__ :  set						,   snake_case__ :  dict						,   snake_case__ :  dict						,   snake_case__ :  PriorityQueue						,   snake_case__ :  dict						,   snake_case__ :  float | int						,   ):
	for nxt, d in graph[v]:
		if nxt in visited_forward:
			continue
		A     = cst_fwd.get(snake_case__						,   np.inf  )
		A     = cst_fwd[v] + d
		if new_cost_f < old_cost_f:
			queue.put((new_cost_f, nxt)  )
			A     = new_cost_f
			A     = v
		if nxt in visited_backward:
			if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
				A     = cst_fwd[v] + d + cst_bwd[nxt]
	return shortest_distance






def    _snake_case					(		snake_case__ :  str						,   snake_case__ :  str						,   snake_case__ :  dict						,   snake_case__ :  dict  ):
	A     = -1

	A     = set()
	A     = set()
	A     = {source: 0}
	A     = {destination: 0}
	A     = {source: None}
	A     = {destination: None}
	A     = PriorityQueue()
	A     = PriorityQueue()

	A     = 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     = queue_forward.get()
		visited_forward.add(snake_case__  )

		A ,   A     = queue_backward.get()
		visited_backward.add(snake_case__  )

		A     = pass_and_relaxation(
		    snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   )

		A     = pass_and_relaxation(
		    snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   snake_case__						,   )

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

	if shortest_distance != np.inf:
		A     = shortest_distance
	return shortest_path_distance


_lowercase				 =					{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}
_lowercase				 =					{
    '''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 			_lowerCAmelCase     (    __snake_case    :					int					,				__snake_case    :					int					,				__snake_case    :					int     )	->	float:
     __A		:					Dict						=			(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
     # formula for sum of series
     return total






def 			_lowerCAmelCase     (    )	->	Union[str, Any]:
     print(sum_of_series(1					,				1					,				10     )     )


if __name__ == "__main__":
  import doctest

  doctest.testmod()