



'''simple docstring'''




import heapq
import sys

import numpy as np

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

class 			UpperCamelCase_ :





	def __init__(  self    )			->			Union[str, Any]:
								UpperCAmelCase     :		Tuple							     =		[]
								UpperCAmelCase     :		str							     =		set()





	def  _lowercase(  self    )			->			Dict:
								if not self.empty():
															return self.elements[0][0]
								else:
															return float("""inf"""    )





	def  _lowercase(  self    )			->			List[str]:
								return len(self.elements    ) == 0





	def  _lowercase(  self		,		A		,		A    )			->			int:
								if item not in self.set:
															heapq.heappush(self.elements		,		(priority, item)    )
															self.set.add(A    )
								else:
															# update
															# print("update", item)
															UpperCAmelCase     :		List[str]							     =		[]
															((UpperCAmelCase)     ,     (UpperCAmelCase))     :		List[Any]							     =		heapq.heappop(self.elements    )
															while x != item:
																						temp.append((pri, x)    )
																						((UpperCAmelCase)     ,     (UpperCAmelCase))     :		List[Any]							     =		heapq.heappop(self.elements    )
															temp.append((priority, item)    )
															for pro, xxx in temp:
																						heapq.heappush(self.elements		,		(pro, xxx)    )





	def  _lowercase(  self		,		A    )			->			Any:
								if item in self.set:
															self.set.remove(A    )
															UpperCAmelCase     :		Optional[int]							     =		[]
															((UpperCAmelCase)     ,     (UpperCAmelCase))     :		int							     =		heapq.heappop(self.elements    )
															while x != item:
																						temp.append((pro, x)    )
																						((UpperCAmelCase)     ,     (UpperCAmelCase))     :		List[str]							     =		heapq.heappop(self.elements    )
															for prito, yyy in temp:
																						heapq.heappush(self.elements		,		(prito, yyy)    )





	def  _lowercase(  self    )			->			Dict:
								return self.elements[0][1]






	def  _lowercase(  self    )			->			Any:
								((UpperCAmelCase)     ,     (UpperCAmelCase))     :		Any							     =		heapq.heappop(self.elements    )
								self.set.remove(A    )
								return (priority, item)




def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			str:
							# euclidean distance
							UpperCAmelCase     :		Optional[Any]							     =		np.array(_lowercase		)
							UpperCAmelCase     :		Dict							     =		np.array(_lowercase		)
							return np.linalg.norm(a - b		)



def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			Any:
							# integer division by time variable
							return consistent_heuristic(_lowercase	,				_lowercase		) // t



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



def       __lowerCamelCase  (					_lowercase	,				_lowercase	,				_lowercase	,				_lowercase		)      ->			Tuple:
							UpperCAmelCase     :		Optional[int]							     =		g_function[start] + Wa * heuristics[i](_lowercase	,				_lowercase		)
							return ans



def       __lowerCamelCase  (					_lowercase	,				_lowercase	,				_lowercase		)      ->			Any:
							UpperCAmelCase     :		Tuple							     =		np.chararray((n, n)		)
							for i in range(_lowercase		):
														for j in range(_lowercase		):
																					UpperCAmelCase     :		Optional[Any]							     =		"""*"""

							for i in range(_lowercase		):
														for j in range(_lowercase		):
																					if (j, (n - 1) - i) in blocks:
																												UpperCAmelCase     :		int							     =		"""#"""

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

							for i in range(_lowercase		):
														for j in range(_lowercase		):
																					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     :		List[Any]							     =		back_pointer[goal]
							while x != start:
														print(_lowercase	,				end=""" """		)
														UpperCAmelCase     :		Optional[Any]							     =		back_pointer[x]
							print(_lowercase		)
							sys.exit()



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

							for neighbours in [left, right, up, down]:
														if neighbours not in blocks:
																					if valid(_lowercase		) and neighbours not in visited:
																												# print("neighbour", neighbours)
																												visited.add(_lowercase		)
																												UpperCAmelCase     :		Optional[int]							     =		-1
																												UpperCAmelCase     :		List[Any]							     =		float("""inf"""		)

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



def       __lowerCamelCase  (					)      ->			Optional[Any]:
							UpperCAmelCase     :		str							     =		[]
							for x in range(1	,				5		):
														for y in range(1	,				6		):
																					some_list.append((x, y)		)

							for x in range(1_5	,				2_0		):
														some_list.append((x, 1_7)		)

							for x in range(1_0	,				1_9		):
														for y in range(1	,				1_5		):
																					some_list.append((x, y)		)

    # L block
							for x in range(1	,				4		):
														for y in range(1_2	,				1_9		):
																					some_list.append((x, y)		)
							for x in range(3	,				1_3		):
														for y in range(1_6	,				1_9		):
																					some_list.append((x, y)		)
							return some_list


a   :			Optional[int]					  =    {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),
    (1_0, 1),
    (1_1, 1),
    (1_2, 1),
    (1_3, 1),
    (1_4, 1),
    (1_5, 1),
    (1_6, 1),
    (1_7, 1),
    (1_8, 1),
    (1_9, 1),
]
a   :			Any					  =    make_common_ground()


a   :			Union[str, Any]					  =    blocks_blk
# hyper parameters
a   :			List[str]					  =    1
a   :			Tuple					  =    1
a   :			int					  =    2_0
a   :			List[str]					  =    3  # one consistent and two other inconsistent

# start and end destination
a   :			Tuple					  =    (0, 0)
a   :			Optional[Any]					  =    (n - 1, n - 1)

a   :			str					  =    1



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

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

							UpperCAmelCase     :		list[int]							     =		[]
							UpperCAmelCase     :		list[int]							     =		[]
							while open_list[0].minkey() < float("""inf"""		):
														for i in range(1	,				_lowercase		):
																					# 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(_lowercase	,				_lowercase	,				_lowercase		)
																												else:
																																			UpperCAmelCase     ,     UpperCAmelCase     :		str							     =		open_list[i].top_show()
																																			visited.add(_lowercase		)
																																			expand_state(
																																			    _lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				)
																																			close_list_inad.append(_lowercase		)
																					else:
																												if g_function[goal] <= open_list[0].minkey():
																																			if g_function[goal] < float("""inf"""		):
																																										do_something(_lowercase	,				_lowercase	,				_lowercase		)
																												else:
																																			UpperCAmelCase     :		Optional[Any]							     =		open_list[0].top_show()
																																			visited.add(_lowercase		)
																																			expand_state(
																																			    _lowercase	,				0	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				_lowercase	,				)
																																			close_list_anchor.append(_lowercase		)
							print("""No path found to goal"""		)
							print()
							for i in range(n - 1	,				-1	,				-1		):
														for j in range(_lowercase		):
																					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'''




def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			int:
							if b == 0:
														return 1
							if (b % 2) == 0:
														return actual_power(_lowercase	,				int(b / 2		)		) * actual_power(_lowercase	,				int(b / 2		)		)
							else:
														return a * actual_power(_lowercase	,				int(b / 2		)		) * actual_power(_lowercase	,				int(b / 2		)		)



def       __lowerCamelCase  (					_lowercase	,				_lowercase		)      ->			float:
							if b < 0:
														return 1 / actual_power(_lowercase	,				_lowercase		)
							return actual_power(_lowercase	,				_lowercase		)


if __name__ == "__main__":
							print(power(-2, -3))

