"""simple docstring"""


import heapq


def   __UpperCAmelCase     (	_snake_case		:       int,				_snake_case		:       Dict,				_snake_case		:       Any       ):
   _lowercase							     =       [(0, start)]  # cost from start node,end node
   _lowercase							     =       set()
   while heap:
      (_lowercase)							     =       heapq.heappop(_snake_case       )
      if u in visited:
         continue
      visited.add(_snake_case       )
      if u == end:
         return cost
      for v, c in graph[u]:
         if v in visited:
            continue
         _lowercase							     =       cost + c
         heapq.heappush(_snake_case,				(next_item, v)       )
   return -1


__UpperCamelCase       :    Optional[int]         =		{
    '''A''': [['''B''', 2], ['''C''', 5]],
    '''B''': [['''A''', 2], ['''D''', 3], ['''E''', 1], ['''F''', 1]],
    '''C''': [['''A''', 5], ['''F''', 3]],
    '''D''': [['''B''', 3]],
    '''E''': [['''B''', 4], ['''F''', 3]],
    '''F''': [['''C''', 3], ['''E''', 3]],
}
__UpperCamelCase       :    List[str]         =		{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''F''', 3]],
    '''F''': [],
}
__UpperCamelCase       :    List[Any]         =		{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}

__UpperCamelCase       :    List[str]         =		dijkstra(G, "E", "C")
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

__UpperCamelCase       :    Optional[int]         =		dijkstra(Ga, "E", "F")
print(short_distance)  # E -- 3 --> F == 3

__UpperCamelCase       :    List[Any]         =		dijkstra(Ga, "E", "F")
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
  import doctest

  doctest.testmod()






'''simple docstring'''






from .hash_table import HashTable
from .number_theory.prime_numbers import is_prime, next_prime



class  lowerCamelCase__				(						snake_case_						):


	"""simple docstring"""





	def __init__(					self   ,     *UpperCAmelCase__   ,     **UpperCAmelCase__			)       ->				Optional[int]:
					super().__init__(*UpperCAmelCase__   ,     **UpperCAmelCase__			)




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Optional[int]:
					_A :				Union[str, Any]				=  (
					    next_prime(value % self.size_table			)
					    if not is_prime(value % self.size_table			)
					    else value % self.size_table
					)  # gt = bigger than
					return next_prime_gt - (data % next_prime_gt)




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)       ->				Union[str, Any]:
					return (increment * self.__hash_function_a(UpperCAmelCase__   ,     UpperCAmelCase__			)) % self.size_table




	def 				_lowerCamelCase				(					self   ,     UpperCAmelCase__   ,     UpperCAmelCase__=None			)       ->				List[Any]:
					_A :				Optional[int]				=  1
					_A :				Optional[int]				=  self.hash_function(UpperCAmelCase__			)

					while self.values[new_key] is not None and self.values[new_key] != key:
									_A :				int				=  (
									    self.__hash_double_function(UpperCAmelCase__   ,     UpperCAmelCase__   ,     UpperCAmelCase__			)
									    if self.balanced_factor() >= self.lim_charge
									    else None
									)
									if new_key is None:
													break
									else:
													i += 1

					return new_key
