

import heapq
import sys

import numpy as np

a		=tuple[int, int]






class        A_		:
							def __init__(		self		:			Optional[int]):
								__lowerCamelCase				:				Optional[int]					       = []
								__lowerCamelCase				:				Union[str, Any]					       = set()
							def     lowerCAmelCase     (		self		:			Any):


								if not self.empty():
									return self.elements[0][0]
								else:
									return float('inf')
							def     lowerCAmelCase     (		self		:			List[str]):
								return len(self.elements) == 0
							def     lowerCAmelCase     (		self		:			Any   ,SCREAMING_SNAKE_CASE__		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			List[str]):


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


								if item in self.set:
									self.set.remove(lowerCAmelCase__)
									__lowerCamelCase				:				List[str]					       = []
									((__lowerCamelCase)       , (__lowerCamelCase))				:				Optional[int]					       = heapq.heappop(self.elements)
									while x != item:
										temp.append((pro, x))
										((__lowerCamelCase)       , (__lowerCamelCase))				:				Union[str, Any]					       = heapq.heappop(self.elements)
									for prito, yyy in temp:
										heapq.heappush(self.elements   ,(prito, yyy))
							def     lowerCAmelCase     (		self		:			Any):
								return self.elements[0][1]


							def     lowerCAmelCase     (		self		:			Union[str, Any]):
								((__lowerCamelCase)       , (__lowerCamelCase))				:				Optional[int]					       = heapq.heappop(self.elements)
								self.set.remove(lowerCAmelCase__)
								return (priority, item)






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     int:
	__lowerCamelCase				:				str					       = np.array(lowerCamelCase__			)
	__lowerCamelCase				:				int					       = np.array(lowerCamelCase__			)
	return np.linalg.norm(a - b			)






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     Optional[Any]:
	return consistent_heuristic(lowerCamelCase__	, lowerCamelCase__			) // t






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__			)  ->     List[str]:
	return abs(p[0] - goal[0]			) + abs(p[1] - goal[1]			)






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__			)  ->     Tuple:
	__lowerCamelCase				:				List[str]					       = g_function[start] + Wa * heuristics[i](lowerCamelCase__	, lowerCamelCase__			)
	return ans






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__			)  ->     str:
	__lowerCamelCase				:				Any					       = np.chararray((n, n)			)
	for i in range(lowerCamelCase__			):
		for j in range(lowerCamelCase__			):
			__lowerCamelCase				:				Dict					       = '*'

	for i in range(lowerCamelCase__			):
		for j in range(lowerCamelCase__			):
			if (j, (n - 1) - i) in blocks:
				__lowerCamelCase				:				Any					       = '#'

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

	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:-'			)
	__lowerCamelCase				:				List[Any]					       = back_pointer[goal]
	while x != start:
		print(lowerCamelCase__	, end=' '			)
		__lowerCamelCase				:				Optional[int]					       = back_pointer[x]
	print(lowerCamelCase__			)
	sys.exit()






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__			)  ->     Dict:



	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    SCREAMING_SNAKE_CASE__       (  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)
	((__lowerCamelCase)       , (__lowerCamelCase))				:				List[str]					       = s
	__lowerCamelCase				:				Any					       = (x - 1, y)
	__lowerCamelCase				:				Union[str, Any]					       = (x + 1, y)
	__lowerCamelCase				:				List[Any]					       = (x, y + 1)
	__lowerCamelCase				:				Dict					       = (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__			)
				__lowerCamelCase				:				int					       = -1
				__lowerCamelCase				:				Dict					       = float('inf'			)

			if valid(lowerCamelCase__			) and g_function[neighbours] > g_function[s] + 1:
				__lowerCamelCase				:				Dict					       = g_function[s] + 1
				__lowerCamelCase				:				Dict					       = 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    SCREAMING_SNAKE_CASE__       (  )  ->     Dict:
	__lowerCamelCase				:				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		={0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

a		=[
    (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		=make_common_ground()


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

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

a		=1






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__	, lowerCamelCase__			)  ->     Optional[Any]:
	__lowerCamelCase				:				Union[str, Any]					       = {start: 0, goal: float('inf'			)}
	__lowerCamelCase				:				Tuple					       = {start: -1, goal: -1}
	__lowerCamelCase				:				Optional[int]					       = []
	__lowerCamelCase				:				int					       = set()

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

	__lowerCamelCase				:				Any					       = []
	__lowerCamelCase				:				Tuple					       = []
	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:
					__lowerCamelCase       , __lowerCamelCase				:				Tuple					       = 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:
					__lowerCamelCase				:				Optional[Any]					       = 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)





import gc
import threading
import time

import psutil
import torch




class    _UpperCamelCase      :


			"""simple docstring"""






			def __init__(   self						)     ->					str:

							'''simple docstring'''


							__lowercase 			=							psutil.Process()
							__lowercase 			=							False





			def        _SCREAMING_SNAKE_CASE			(   self						)     ->					str:

							'''simple docstring'''


							__lowercase 			=							-1

							while True:
											__lowercase 			=							max(self.process.memory_info().rss      ,   self.cpu_memory_peak						)

											# can't sleep or will not catch the peak right (this comment is here on purpose)
											if not self.peak_monitoring:
															break





			def        _SCREAMING_SNAKE_CASE			(   self						)     ->					int:

							'''simple docstring'''


							__lowercase 			=							True
							__lowercase 			=							threading.Thread(target=self.peak_monitor						)
							__lowercase 			=							True
							self.thread.start()





			def        _SCREAMING_SNAKE_CASE			(   self						)     ->					str:

							'''simple docstring'''


							__lowercase 			=							False
							self.thread.join()
							return self.cpu_memory_peak


__a  :     List[str]       =  PeakCPUMemory()





def 				UpperCAmelCase						(    ):







				"""simple docstring"""



				__lowercase 			=							{'''time''': time.time()}

				gc.collect()
				torch.cuda.empty_cache()

				# CPU mem
				__lowercase 			=							psutil.Process().memory_info().rss
				cpu_peak_tracker.start()

				# GPU mem
				for i in range(torch.cuda.device_count()							):
								__lowercase 			=							torch.cuda.memory_allocated(lowercase							)
				torch.cuda.reset_peak_memory_stats()

				return measures





def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



				__lowercase 			=							{'''time''': time.time() - start_measures['''time''']}

				gc.collect()
				torch.cuda.empty_cache()

				# CPU mem
				__lowercase 			=							(psutil.Process().memory_info().rss - start_measures['''cpu''']) / 2**20
				__lowercase 			=							(cpu_peak_tracker.stop() - start_measures['''cpu''']) / 2**20

				# GPU mem
				for i in range(torch.cuda.device_count()							):
								__lowercase 			=							(torch.cuda.memory_allocated(lowercase							) - start_measures[str(lowercase							)]) / 2**20
								__lowercase 			=							(torch.cuda.max_memory_allocated(lowercase							) - start_measures[str(lowercase							)]) / 2**20

				return measures





def 				UpperCAmelCase						(    lowercase							,			lowercase							):







				"""simple docstring"""



				print(F"{description}:"							)
				print(F"- Time: {measures['time']:.2f}s"							)
				for i in range(torch.cuda.device_count()							):
								print(F"- GPU {i} allocated: {measures[str(lowercase							)]:.2f}MiB"							)
								__lowercase 			=							measures[F"{i}-peak"]
								print(F"- GPU {i} peak: {peak:.2f}MiB"							)
				print(F"- CPU RAM allocated: {measures['cpu']:.2f}MiB"							)
				print(F"- CPU RAM peak: {measures['cpu-peak']:.2f}MiB"							)