

"""simple docstring"""


from __future__ import annotations

import time
from math import sqrt

# 1 for manhattan, 0 for euclidean
a					:Optional[Any]    = 0

a					:int    = [
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

a					:int    = [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right

a					:List[str]    = tuple[int, int]

class      __a							:






     '''simple docstring'''

     def __init__(						self	,    _a	,    _a	,    _a	,    _a	,    _a	,    _a	,    )  ->      Optional[Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[str]      		=	pos_x
           SCREAMING_SNAKE_CASE__   :      str      		=	pos_y
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	(pos_y, pos_x)
           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	goal_x
           SCREAMING_SNAKE_CASE__   :      Dict      		=	goal_y
           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	g_cost
           SCREAMING_SNAKE_CASE__   :      Dict      		=	parent
           SCREAMING_SNAKE_CASE__   :      str      		=	self.calculate_heuristic()
           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.g_cost + self.h_cost

     def 					_a			(						self  )  ->      List[str]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.pos_x - self.goal_x
           SCREAMING_SNAKE_CASE__   :      List[str]      		=	self.pos_y - self.goal_y
           if HEURISTIC == 1:
                 return abs(UpperCamelCase_  ) + abs(UpperCamelCase_  )
           else:
                 return sqrt(dy**2 + dx**2  )





     def __lt__(						self	,    _a  )  ->      str:


           """simple docstring"""


           return self.f_cost < other.f_cost





class      __a							:






     '''simple docstring'''

     def __init__(						self	,    _a	,    _a  )  ->      Tuple:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	Node(start[1]	,    start[0]	,    goal[1]	,    goal[0]	,    0	,    UpperCamelCase_  )
           SCREAMING_SNAKE_CASE__   :      int      		=	Node(goal[1]	,    goal[0]	,    goal[1]	,    goal[0]	,    99_999	,    UpperCamelCase_  )

           SCREAMING_SNAKE_CASE__   :      List[str]      		=	[self.start]
           SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	[]

           SCREAMING_SNAKE_CASE__   :      Any      		=	False

     def 					_a			(						self  )  ->      Optional[int]:


           """simple docstring"""


           while self.open_nodes:
                 # Open Nodes are sorted using __lt__
                 self.open_nodes.sort()
                 SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	self.open_nodes.pop(0  )

                 if current_node.pos == self.target.pos:
                       return self.retrace_path(UpperCamelCase_  )

                 self.closed_nodes.append(UpperCamelCase_  )
                 SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.get_successors(UpperCamelCase_  )

                 for child_node in successors:
                       if child_node in self.closed_nodes:
                             continue

                       if child_node not in self.open_nodes:
                             self.open_nodes.append(UpperCamelCase_  )
                       else:
                             # retrieve the best current path
                             SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.open_nodes.pop(self.open_nodes.index(UpperCamelCase_  )  )

                             if child_node.g_cost < better_node.g_cost:
                                   self.open_nodes.append(UpperCamelCase_  )
                             else:
                                   self.open_nodes.append(UpperCamelCase_  )

           return [self.start.pos]

     def 					_a			(						self	,    _a  )  ->      Tuple:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[]
           for action in delta:
                 SCREAMING_SNAKE_CASE__   :      Tuple      		=	parent.pos_x + action[1]
                 SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	parent.pos_y + action[0]
                 if not (0 <= pos_x <= len(grid[0]  ) - 1 and 0 <= pos_y <= len(UpperCamelCase_  ) - 1):
                       continue

                 if grid[pos_y][pos_x] != 0:
                       continue

                 successors.append(
                     Node(
                         UpperCamelCase_	,    UpperCamelCase_	,    self.target.pos_y	,    self.target.pos_x	,    parent.g_cost + 1	,    UpperCamelCase_	,    )  )
           return successors





     def 					_a			(						self	,    _a  )  ->      Union[str, Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	node
           SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[]
           while current_node is not None:
                 path.append((current_node.pos_y, current_node.pos_x)  )
                 SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	current_node.parent
           path.reverse()
           return path





class      __a							:






     '''simple docstring'''

     def __init__(						self	,    _a	,    _a  )  ->      Union[str, Any]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	AStar(UpperCamelCase_	,    UpperCamelCase_  )
           SCREAMING_SNAKE_CASE__   :      Any      		=	AStar(UpperCamelCase_	,    UpperCamelCase_  )
           SCREAMING_SNAKE_CASE__   :      Any      		=	False

     def 					_a			(						self  )  ->      str:


           """simple docstring"""


           while self.fwd_astar.open_nodes or self.bwd_astar.open_nodes:
                 self.fwd_astar.open_nodes.sort()
                 self.bwd_astar.open_nodes.sort()
                 SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	self.fwd_astar.open_nodes.pop(0  )
                 SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	self.bwd_astar.open_nodes.pop(0  )

                 if current_bwd_node.pos == current_fwd_node.pos:
                       return self.retrace_bidirectional_path(
                           UpperCamelCase_	,    UpperCamelCase_  )

                 self.fwd_astar.closed_nodes.append(UpperCamelCase_  )
                 self.bwd_astar.closed_nodes.append(UpperCamelCase_  )

                 SCREAMING_SNAKE_CASE__   :      str      		=	current_bwd_node
                 SCREAMING_SNAKE_CASE__   :      Any      		=	current_fwd_node

                 SCREAMING_SNAKE_CASE__   :      Dict      		=	{
                     self.fwd_astar: self.fwd_astar.get_successors(UpperCamelCase_  ),
                     self.bwd_astar: self.bwd_astar.get_successors(UpperCamelCase_  ),
                 }

                 for astar in [self.fwd_astar, self.bwd_astar]:
                       for child_node in successors[astar]:
                             if child_node in astar.closed_nodes:
                                   continue

                             if child_node not in astar.open_nodes:
                                   astar.open_nodes.append(UpperCamelCase_  )
                             else:
                                   # retrieve the best current path
                                   SCREAMING_SNAKE_CASE__   :      str      		=	astar.open_nodes.pop(
                                       astar.open_nodes.index(UpperCamelCase_  )  )

                                   if child_node.g_cost < better_node.g_cost:
                                         astar.open_nodes.append(UpperCamelCase_  )
                                   else:
                                         astar.open_nodes.append(UpperCamelCase_  )

           return [self.fwd_astar.start.pos]





     def 					_a			(						self	,    _a	,    _a  )  ->      Optional[int]:


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Tuple      		=	self.fwd_astar.retrace_path(UpperCamelCase_  )
           SCREAMING_SNAKE_CASE__   :      List[Any]      		=	self.bwd_astar.retrace_path(UpperCamelCase_  )
           bwd_path.pop()
           bwd_path.reverse()
           SCREAMING_SNAKE_CASE__   :      str      		=	fwd_path + bwd_path
           return path


if __name__ == "__main__":
    # all coordinates are given in format [y,x]
    a					:Any    = (0, 0)
    a					:Optional[int]    = (len(grid) - 1, len(grid[0]) - 1)
    for elem in grid:
        print(elem)

    a					:List[Any]    = time.time()
    a					:Dict    = AStar(init, goal)
    a					:Dict    = a_star.search()
    a					:int    = time.time() - start_time
    print(f'AStar execution time = {end_time:f} seconds')

    a					:str    = time.time()
    a					:Any    = BidirectionalAStar(init, goal)
    a					:Tuple    = time.time() - bd_start_time
    print(f'BidirectionalAStar execution time = {bd_end_time:f} seconds')







"""simple docstring"""


from math import sqrt




def  _lowercase					(    __lowerCAmelCase							)       ->				bool:

      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5  ,					int(sqrt(__lowerCAmelCase							) + 1							)  ,					6							):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True




def  _lowercase					(    __lowerCAmelCase = 1_0001							)       ->				int:
      SCREAMING_SNAKE_CASE__   :      Dict      		=	0
      SCREAMING_SNAKE_CASE__   :      Tuple      		=	1
      while count != nth and number < 3:
            number += 1
            if is_prime(__lowerCAmelCase							):
                  count += 1
      while count != nth:
            number += 2
            if is_prime(__lowerCAmelCase							):
                  count += 1
      return number


if __name__ == "__main__":
  print(f'{solution() = }')




