

"""simple docstring"""


import heapq
import sys

import numpy as np

a					:str    = tuple[int, int]

class      __a							:






     '''simple docstring'''

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


           """simple docstring"""


           SCREAMING_SNAKE_CASE__   :      Dict      		=	[]
           SCREAMING_SNAKE_CASE__   :      str      		=	set()

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


           """simple docstring"""


           if not self.empty():
                 return self.elements[0][0]
           else:
                 return float("""inf"""  )

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


           """simple docstring"""


           return len(self.elements  ) == 0

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


           """simple docstring"""


           if item not in self.set:
                 heapq.heappush(self.elements	,    (priority, item)  )
                 self.set.add(_UpperCAmelCase  )
           else:
                 # update
                 # print("update", item)
                 SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	[]
                 ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      Optional[Any]      		=	heapq.heappop(self.elements  )
                 while x != item:
                       temp.append((pri, x)  )
                       ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      Optional[Any]      		=	heapq.heappop(self.elements  )
                 temp.append((priority, item)  )
                 for pro, xxx in temp:
                       heapq.heappush(self.elements	,    (pro, xxx)  )

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


           """simple docstring"""


           if item in self.set:
                 self.set.remove(_UpperCAmelCase  )
                 SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[]
                 ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      Tuple      		=	heapq.heappop(self.elements  )
                 while x != item:
                       temp.append((pro, x)  )
                       ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      str      		=	heapq.heappop(self.elements  )
                 for prito, yyy in temp:
                       heapq.heappush(self.elements	,    (prito, yyy)  )

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


           """simple docstring"""


           return self.elements[0][1]





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


           """simple docstring"""


           ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      Tuple      		=	heapq.heappop(self.elements  )
           self.set.remove(_UpperCAmelCase  )
           return (priority, item)





def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase							)       ->				Union[str, Any]:
      # euclidean distance
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	np.array(lowerCAmelCase__							)
      SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	np.array(lowerCAmelCase__							)
      return np.linalg.norm(a - b							)




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase							)       ->				str:
      # integer division by time variable
      return consistent_heuristic(lowerCAmelCase__  ,					lowerCAmelCase__							) // t




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase							)       ->				Optional[int]:
      # manhattan distance
      return abs(p[0] - goal[0]							) + abs(p[1] - goal[1]							)




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				Tuple:
      SCREAMING_SNAKE_CASE__   :      int      		=	g_function[start] + Wa * heuristics[i](lowerCAmelCase__  ,					lowerCAmelCase__							)
      return ans




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				int:
      SCREAMING_SNAKE_CASE__   :      Tuple      		=	np.chararray((n, n)							)
      for i in range(lowerCAmelCase__							):
            for j in range(lowerCAmelCase__							):
                  SCREAMING_SNAKE_CASE__   :      Any      		=	"""*"""

      for i in range(lowerCAmelCase__							):
            for j in range(lowerCAmelCase__							):
                  if (j, (n - 1) - i) in blocks:
                        SCREAMING_SNAKE_CASE__   :      Optional[Any]      		=	"""#"""

      SCREAMING_SNAKE_CASE__   :      Any      		=	"""-"""
      SCREAMING_SNAKE_CASE__   :      int      		=	back_pointer[goal]
      while x != start:
            ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      List[str]      		=	x
            # print(x)
            SCREAMING_SNAKE_CASE__   :      List[Any]      		=	"""-"""
            SCREAMING_SNAKE_CASE__   :      Any      		=	back_pointer[x]
      SCREAMING_SNAKE_CASE__   :      str      		=	"""-"""

      for i in range(lowerCAmelCase__							):
            for j in range(lowerCAmelCase__							):
                  if (i, j) == (0, n - 1):
                        print(grid[i][j]  ,					end=""" """							)
                        print("""<-- End position"""  ,					end=""" """							)
                  else:
                        print(grid[i][j]  ,					end=""" """							)
            print()
      print("""^"""							)
      print("""Start position"""							)
      print()
      print("""# is an obstacle"""							)
      print("""- is the path taken by algorithm"""							)
      print("""PATH TAKEN BY THE ALGORITHM IS:-"""							)
      SCREAMING_SNAKE_CASE__   :      str      		=	back_pointer[goal]
      while x != start:
            print(lowerCAmelCase__  ,					end=""" """							)
            SCREAMING_SNAKE_CASE__   :      int      		=	back_pointer[x]
      print(lowerCAmelCase__							)
      sys.exit()




def  _lowercase					(    __lowerCAmelCase							)       ->				Any:
      if p[0] < 0 or p[0] > n - 1:
            return False
      if p[1] < 0 or p[1] > n - 1:
            return False
      return True




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase  ,					)       ->				Dict:
      for itera in range(lowerCAmelCase__							):
            open_list[itera].remove_element(lowerCAmelCase__							)
      # print("s", s)
      # print("j", j)
      ((SCREAMING_SNAKE_CASE__)		,		(SCREAMING_SNAKE_CASE__))   :      Any      		=	s
      SCREAMING_SNAKE_CASE__   :      Union[str, Any]      		=	(x - 1, y)
      SCREAMING_SNAKE_CASE__   :      Any      		=	(x + 1, y)
      SCREAMING_SNAKE_CASE__   :      List[Any]      		=	(x, y + 1)
      SCREAMING_SNAKE_CASE__   :      int      		=	(x, y - 1)

      for neighbours in [left, right, up, down]:
            if neighbours not in blocks:
                  if valid(lowerCAmelCase__							) and neighbours not in visited:
                        # print("neighbour", neighbours)
                        visited.add(lowerCAmelCase__							)
                        SCREAMING_SNAKE_CASE__   :      Dict      		=	-1
                        SCREAMING_SNAKE_CASE__   :      Any      		=	float("""inf"""							)

                  if valid(lowerCAmelCase__							) and g_function[neighbours] > g_function[s] + 1:
                        SCREAMING_SNAKE_CASE__   :      int      		=	g_function[s] + 1
                        SCREAMING_SNAKE_CASE__   :      List[Any]      		=	s
                        if neighbours not in close_list_anchor:
                              open_list[0].put(lowerCAmelCase__  ,					key(lowerCAmelCase__  ,					0  ,					lowerCAmelCase__  ,					lowerCAmelCase__							)							)
                              if neighbours not in close_list_inad:
                                    for var in range(1  ,					lowerCAmelCase__							):
                                          if key(lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__							) <= Wa * key(
                                              lowerCAmelCase__  ,					0  ,					lowerCAmelCase__  ,					lowerCAmelCase__							):
                                                open_list[j].put(
                                                    lowerCAmelCase__  ,					key(lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__							)							)




def  _lowercase					(    )       ->				str:
      SCREAMING_SNAKE_CASE__   :      List[str]      		=	[]
      for x in range(1  ,					5							):
            for y in range(1  ,					6							):
                  some_list.append((x, y)							)

      for x in range(15  ,					20							):
            some_list.append((x, 17)							)

      for x in range(10  ,					19							):
            for y in range(1  ,					15							):
                  some_list.append((x, y)							)

    # L block
      for x in range(1  ,					4							):
            for y in range(12  ,					19							):
                  some_list.append((x, y)							)
      for x in range(3  ,					13							):
            for y in range(16  ,					19							):
                  some_list.append((x, y)							)
      return some_list


a					:str    = {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

a					:Optional[int]    = [
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
a					:int    = make_common_ground()


a					:List[Any]    = blocks_blk
# hyper parameters
a					:str    = 1
a					:List[str]    = 1
a					:Optional[int]    = 20
a					:List[str]    = 3  # one consistent and two other inconsistent

# start and end destination
a					:str    = (0, 0)
a					:Tuple    = (n - 1, n - 1)

a					:Tuple    = 1




def  _lowercase					(    __lowerCAmelCase  ,					__lowerCAmelCase  ,					__lowerCAmelCase							)       ->				List[Any]:
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	{start: 0, goal: float("""inf"""							)}
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	{start: -1, goal: -1}
      SCREAMING_SNAKE_CASE__   :      Optional[int]      		=	[]
      SCREAMING_SNAKE_CASE__   :      str      		=	set()

      for i in range(lowerCAmelCase__							):
            open_list.append(PriorityQueue()							)
            open_list[i].put(lowerCAmelCase__  ,					key(lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__							)							)

      SCREAMING_SNAKE_CASE__   :      int      		=	[]
      SCREAMING_SNAKE_CASE__   :      Any      		=	[]
      while open_list[0].minkey() < float("""inf"""							):
            for i in range(1  ,					lowerCAmelCase__							):
                  # print(open_list[0].minkey(), open_list[i].minkey())
                  if open_list[i].minkey() <= Wa * open_list[0].minkey():
                        global t
                        t += 1
                        if g_function[goal] <= open_list[i].minkey():
                              if g_function[goal] < float("""inf"""							):
                                    do_something(lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__							)
                        else:
                              SCREAMING_SNAKE_CASE__		,		SCREAMING_SNAKE_CASE__   :      Dict      		=	open_list[i].top_show()
                              visited.add(lowerCAmelCase__							)
                              expand_state(
                                  lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					)
                              close_list_inad.append(lowerCAmelCase__							)
                  else:
                        if g_function[goal] <= open_list[0].minkey():
                              if g_function[goal] < float("""inf"""							):
                                    do_something(lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__							)
                        else:
                              SCREAMING_SNAKE_CASE__   :      List[str]      		=	open_list[0].top_show()
                              visited.add(lowerCAmelCase__							)
                              expand_state(
                                  lowerCAmelCase__  ,					0  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					lowerCAmelCase__  ,					)
                              close_list_anchor.append(lowerCAmelCase__							)
      print("""No path found to goal"""							)
      print()
      for i in range(n - 1  ,					-1  ,					-1							):
            for j in range(lowerCAmelCase__							):
                  if (j, i) in blocks:
                        print("""#"""  ,					end=""" """							)
                  elif (j, i) in back_pointer:
                        if (j, i) == (n - 1, n - 1):
                              print("""*"""  ,					end=""" """							)
                        else:
                              print("""-"""  ,					end=""" """							)
                  else:
                        print("""*"""  ,					end=""" """							)
                  if (j, i) == (n - 1, n - 1):
                        print("""<-- End position"""  ,					end=""" """							)
            print()
      print("""^"""							)
      print("""Start position"""							)
      print()
      print("""# is an obstacle"""							)
      print("""- is the path taken by algorithm"""							)


if __name__ == "__main__":
    multi_a_star(start, goal, n_heuristic)







"""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() = }')




