




import numpy as np




class 						__lowercase		:




      """simple docstring"""





      def __init__(				self     )		->    Union[str, Any]:
         snake_case				:    str           =	(0, 0)
         snake_case				:    int           =	None
         snake_case				:    Tuple           =	0
         snake_case				:    int           =	0
         snake_case				:    Union[str, Any]           =	0

      def __eq__(				self    ,				A     )		->    Dict:
         return self.position == cell.position

      def      UpperCAmelCase				(				self     )		->    Dict:
         print(self.position     )




class 						__lowercase		:




      """simple docstring"""





      def __init__(				self    ,				A=(5, 5)     )		->    Dict:
         snake_case				:    Union[str, Any]           =	np.zeros(A     )
         snake_case				:    int           =	world_size[0]
         snake_case				:    Any           =	world_size[1]

      def      UpperCAmelCase				(				self     )		->    Any:
         print(self.w     )

      def      UpperCAmelCase				(				self    ,				A     )		->    Tuple:
         snake_case				:    Any           =	[
             (-1, -1),
             (-1, 0),
             (-1, 1),
             (0, -1),
             (0, 1),
             (1, -1),
             (1, 0),
             (1, 1),
         ]
         snake_case				:    Dict           =	cell.position[0]
         snake_case				:    Optional[Any]           =	cell.position[1]
         snake_case				:    Union[str, Any]           =	[]
         for n in neughbour_cord:
            snake_case				:    List[Any]           =	current_x + n[0]
            snake_case				:    Optional[int]           =	current_y + n[1]
            if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
               snake_case				:    Optional[Any]           =	Cell()
               snake_case				:    Dict           =	(x, y)
               snake_case				:    List[Any]           =	cell
               neighbours.append(A     )
         return neighbours




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase						,lowercase					)  ->       List[str]:
   snake_case				:    Any           =	[]
   snake_case				:    Optional[Any]           =	[]
   _open.append(lowercase					)

   while _open:
      snake_case				:    Optional[Any]           =	np.argmin([n.f for n in _open]					)
      snake_case				:    Union[str, Any]           =	_open[min_f]
      _closed.append(_open.pop(lowercase					)					)
      if current == goal:
         break
      for n in world.get_neigbours(lowercase					):
         for c in _closed:
            if c == n:
               continue
         snake_case				:    str           =	current.g + 1
         snake_case     , snake_case				:    Any           =	n.position
         snake_case     , snake_case				:    Tuple           =	goal.position
         snake_case				:    int           =	(ya - ya) ** 2 + (xa - xa) ** 2
         snake_case				:    Optional[int]           =	n.h + n.g

         for c in _open:
            if c == n and c.f < n.f:
               continue
         _open.append(lowercase					)
   snake_case				:    Any           =	[]
   while current.parent is not None:
      path.append(current.position					)
      snake_case				:    Tuple           =	current.parent
   path.append(current.position					)
   return path[::-1]


if __name__ == "__main__":
       lowerCamelCase	:	List[Any]				=   Gridworld()
       # Start position and goal
       lowerCamelCase	:	Optional[Any]				=   Cell()
       lowerCamelCase	:	List[Any]				=   (0, 0)
       lowerCamelCase	:	Optional[Any]				=   Cell()
       lowerCamelCase	:	Optional[Any]				=   (4, 4)
       print(f"""path from {start.position} to {goal.position}""")
       lowerCamelCase	:	Union[str, Any]				=   astar(world, start, goal)
       #   Just for visual reasons.
       for i in s:
              lowerCamelCase	:	Optional[Any]				=   1
       print(world.w)











from math import pow




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase						,lowercase						,lowercase						,lowercase						,)  ->       tuple[int, int]:
   if current_sum == needed_sum:
      # If the sum of the powers is equal to needed_sum, then we have a solution.
      solutions_count += 1
      return current_sum, solutions_count

   snake_case				:    Union[str, Any]           =	int(pow(lowercase						,lowercase					)					)
   if current_sum + i_to_n <= needed_sum:
      # If the sum of the powers is less than needed_sum, then continue adding powers.
      current_sum += i_to_n
      snake_case     , snake_case				:    List[Any]           =	backtrack(
          lowercase						,lowercase						,current_number + 1						,lowercase						,lowercase					)
      current_sum -= i_to_n
   if i_to_n < needed_sum:
      # If the power of i is less than needed_sum, then try with the next power.
      snake_case     , snake_case				:    str           =	backtrack(
          lowercase						,lowercase						,current_number + 1						,lowercase						,lowercase					)
   return current_sum, solutions_count




def 						SCREAMING_SNAKE_CASE__ (   lowercase						,lowercase					)  ->       int:
   if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
      raise ValueError(
          """Invalid input\n"""
          """needed_sum must be between 1 and 1000, power between 2 and 10."""					)

   return backtrack(lowercase						,lowercase						,1						,0						,0					)[1]  # Return the solutions_count


if __name__ == "__main__":
       import doctest

       doctest.testmod()





