


'''simple docstring'''
import heapq
import sys

import numpy as np

__snake_case				 =	tuple[int, int]
class   lowercase      :

		"""simple docstring"""

		def __init__(						self				):

							'''simple docstring'''


							UpperCamelCase__  :Optional[Any]				   =					[]
							UpperCamelCase__  :Any				   =					set()




		def        lowerCAmelCase__							(						self				):

							'''simple docstring'''


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




		def        lowerCAmelCase__							(						self				):

							'''simple docstring'''


							return len(self.elements				) == 0




		def        lowerCAmelCase__							(						self       ,  UpperCamelCase_       ,  UpperCamelCase_				):

							'''simple docstring'''


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




		def        lowerCAmelCase__							(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							if item in self.set:
												self.set.remove(UpperCamelCase_				)
												UpperCamelCase__  :Any				   =					[]
												((UpperCamelCase__)   ,							(UpperCamelCase__))  :Any				   =					heapq.heappop(self.elements				)
												while x != item:
																	temp.append((pro, x)				)
																	((UpperCamelCase__)   ,							(UpperCamelCase__))  :int				   =					heapq.heappop(self.elements				)
												for prito, yyy in temp:
																	heapq.heappush(self.elements       ,  (prito, yyy)				)




		def        lowerCAmelCase__							(						self				):

							'''simple docstring'''


							return self.elements[0][1]




		def        lowerCAmelCase__							(						self				):

							'''simple docstring'''


							((UpperCamelCase__)   ,							(UpperCamelCase__))  :List[str]				   =					heapq.heappop(self.elements				)
							self.set.remove(UpperCamelCase_				)
							return (priority, item)



def      a (     __a					,   __a  )    ->      List[Any]:



					'''simple docstring'''






					UpperCamelCase__  :Tuple				   =					np.array(__a  )
					UpperCamelCase__  :Tuple				   =					np.array(__a  )
					return np.linalg.norm(a - b  )


def      a (     __a					,   __a  )    ->      List[Any]:



					'''simple docstring'''






					return consistent_heuristic(__a					,   __a  ) // t


def      a (     __a					,   __a  )    ->      int:



					'''simple docstring'''






					return abs(p[0] - goal[0]  ) + abs(p[1] - goal[1]  )


def      a (     __a					,   __a					,   __a					,   __a  )    ->      Any:



					'''simple docstring'''






					UpperCamelCase__  :Tuple				   =					g_function[start] + Wa * heuristics[i](__a					,   __a  )
					return ans


def      a (     __a					,   __a					,   __a  )    ->      Optional[int]:



					'''simple docstring'''






					UpperCamelCase__  :Dict				   =					np.chararray((n, n)  )
					for i in range(__a  ):
										for j in range(__a  ):
															UpperCamelCase__  :str				   =					'''*'''

					for i in range(__a  ):
										for j in range(__a  ):
															if (j, (n - 1) - i) in blocks:
																				UpperCamelCase__  :Tuple				   =					'''#'''

					UpperCamelCase__  :List[Any]				   =					'''-'''
					UpperCamelCase__  :str				   =					back_pointer[goal]
					while x != start:
										((UpperCamelCase__)   ,							(UpperCamelCase__))  :List[str]				   =					x
										# print(x)
										UpperCamelCase__  :Optional[Any]				   =					'''-'''
										UpperCamelCase__  :Any				   =					back_pointer[x]
					UpperCamelCase__  :Optional[Any]				   =					'''-'''

					for i in range(__a  ):
										for j in range(__a  ):
															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:-'''  )
					UpperCamelCase__  :Any				   =					back_pointer[goal]
					while x != start:
										print(__a					,   end=''' '''  )
										UpperCamelCase__  :Union[str, Any]				   =					back_pointer[x]
					print(__a  )
					sys.exit()


def      a (     __a  )    ->      List[str]:



					'''simple docstring'''






					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      a (     __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   )    ->      Union[str, Any]:



					'''simple docstring'''






					for itera in range(__a  ):
										open_list[itera].remove_element(__a  )
					# print("s", s)
					# print("j", j)
					((UpperCamelCase__)   ,							(UpperCamelCase__))  :int				   =					s
					UpperCamelCase__  :Tuple				   =					(x - 1, y)
					UpperCamelCase__  :List[str]				   =					(x + 1, y)
					UpperCamelCase__  :str				   =					(x, y + 1)
					UpperCamelCase__  :List[Any]				   =					(x, y - 1)

					for neighbours in [left, right, up, down]:
										if neighbours not in blocks:
															if valid(__a  ) and neighbours not in visited:
																				# print("neighbour", neighbours)
																				visited.add(__a  )
																				UpperCamelCase__  :Tuple				   =					-1
																				UpperCamelCase__  :int				   =					float('''inf'''  )

															if valid(__a  ) and g_function[neighbours] > g_function[s] + 1:
																				UpperCamelCase__  :Tuple				   =					g_function[s] + 1
																				UpperCamelCase__  :Union[str, Any]				   =					s
																				if neighbours not in close_list_anchor:
																									open_list[0].put(__a					,   key(__a					,   0					,   __a					,   __a  )  )
																									if neighbours not in close_list_inad:
																														for var in range(1					,   __a  ):
																																			if key(__a					,   __a					,   __a					,   __a  ) <= Wa * key(
																																			    __a					,   0					,   __a					,   __a  ):
																																								open_list[j].put(
																																								    __a					,   key(__a					,   __a					,   __a					,   __a  )  )


def      a (     )    ->      Dict:



					'''simple docstring'''






					UpperCamelCase__  :Optional[Any]				   =					[]
					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


__snake_case				 =	{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

__snake_case				 =	[
    (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),
]
__snake_case				 =	make_common_ground()


__snake_case				 =	blocks_blk
# hyper parameters
__snake_case				 =	1
__snake_case				 =	1
__snake_case				 =	20
__snake_case				 =	3  # one consistent and two other inconsistent

# start and end destination
__snake_case				 =	(0, 0)
__snake_case				 =	(n - 1, n - 1)

__snake_case				 =	1


def      a (     __a					,   __a					,   __a  )    ->      List[Any]:



					'''simple docstring'''






					UpperCamelCase__  :Any				   =					{start: 0, goal: float('''inf'''  )}
					UpperCamelCase__  :str				   =					{start: -1, goal: -1}
					UpperCamelCase__  :List[Any]				   =					[]
					UpperCamelCase__  :Any				   =					set()

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

					UpperCamelCase__  :list[int]				   =					[]
					UpperCamelCase__  :list[int]				   =					[]
					while open_list[0].minkey() < float('''inf'''  ):
										for i in range(1					,   __a  ):
															# 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(__a					,   __a					,   __a  )
																				else:
																									UpperCamelCase__   ,							UpperCamelCase__  :Dict				   =					open_list[i].top_show()
																									visited.add(__a  )
																									expand_state(
																									    __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   )
																									close_list_inad.append(__a  )
															else:
																				if g_function[goal] <= open_list[0].minkey():
																									if g_function[goal] < float('''inf'''  ):
																														do_something(__a					,   __a					,   __a  )
																				else:
																									UpperCamelCase__  :List[str]				   =					open_list[0].top_show()
																									visited.add(__a  )
																									expand_state(
																									    __a					,   0					,   __a					,   __a					,   __a					,   __a					,   __a					,   __a					,   )
																									close_list_anchor.append(__a  )
					print('''No path found to goal'''  )
					print()
					for i in range(n - 1					,   -1					,   -1  ):
										for j in range(__a  ):
															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 __future__ import annotations

import math


def      a (     __a					,   __a					,   __a					,   __a					,   __a  )    ->      int:



					'''simple docstring'''






					if depth < 0:
										raise ValueError('''Depth cannot be less than 0'''  )

					if len(__a  ) == 0:
										raise ValueError('''Scores cannot be empty'''  )

					if depth == height:
										return scores[node_index]

					if is_max:
										return max(
										    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )

					return min(
					    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )


def      a (     )    ->      None:



					'''simple docstring'''






					UpperCamelCase__  :str				   =					[90, 23, 6, 33, 21, 65, 123, 34423]
					UpperCamelCase__  :List[Any]				   =					math.log(len(__a  )					,   2  )
					print('''Optimal value : '''					,   end=''''''  )
					print(minimax(0					,   0					,   __a					,   __a					,   __a  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()