


import heapq
import sys

import numpy as np

snake_case_						:			Union[str, Any]													=							tuple[int, int]

class 						A__							:




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


										"""simple docstring"""





										_SCREAMING_SNAKE_CASE			  =[]
										_SCREAMING_SNAKE_CASE			  =set()




						def 							__UpperCamelCase				(       self					:      List[str]  )							->     List[Any]:


										"""simple docstring"""





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




						def 							__UpperCamelCase				(       self					:      List[str]  )							->     Dict:


										"""simple docstring"""





										return len(self.elements  ) == 0




						def 							__UpperCamelCase				(       self					:      Dict				,    _a					:      List[str]				,    _a					:      Dict  )							->     Tuple:


										"""simple docstring"""





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




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


										"""simple docstring"""





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




						def 							__UpperCamelCase				(       self					:      Dict  )							->     str:


										"""simple docstring"""





										return self.elements[0][1]




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


										"""simple docstring"""





										((_SCREAMING_SNAKE_CASE)  ,				(_SCREAMING_SNAKE_CASE))			  =heapq.heappop(self.elements  )
										self.set.remove(_a  )
										return (priority, item)







def 						lowerCamelCase(   a__	,a__):
				# euclidean distance
				_SCREAMING_SNAKE_CASE			  =np.array(a__)
				_SCREAMING_SNAKE_CASE			  =np.array(a__)
				return np.linalg.norm(a - b)







def 						lowerCamelCase(   a__	,a__):
				# integer division by time variable
				return consistent_heuristic(a__	,a__) // t







def 						lowerCamelCase(   a__	,a__):
				# manhattan distance
				return abs(p[0] - goal[0]) + abs(p[1] - goal[1])







def 						lowerCamelCase(   a__	,a__	,a__	,a__):
				_SCREAMING_SNAKE_CASE			  =g_function[start] + Wa * heuristics[i](a__	,a__)
				return ans







def 						lowerCamelCase(   a__	,a__	,a__):
				_SCREAMING_SNAKE_CASE			  =np.chararray((n, n))
				for i in range(a__):
								for j in range(a__):
												_SCREAMING_SNAKE_CASE			  ='''*'''

				for i in range(a__):
								for j in range(a__):
												if (j, (n - 1) - i) in blocks:
																_SCREAMING_SNAKE_CASE			  ='''#'''

				_SCREAMING_SNAKE_CASE			  ='''-'''
				_SCREAMING_SNAKE_CASE			  =back_pointer[goal]
				while x != start:
								((_SCREAMING_SNAKE_CASE)  ,				(_SCREAMING_SNAKE_CASE))			  =x
								# print(x)
								_SCREAMING_SNAKE_CASE			  ='''-'''
								_SCREAMING_SNAKE_CASE			  =back_pointer[x]
				_SCREAMING_SNAKE_CASE			  ='''-'''

				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:-''')
				_SCREAMING_SNAKE_CASE			  =back_pointer[goal]
				while x != start:
								print(a__	,end=''' ''')
								_SCREAMING_SNAKE_CASE			  =back_pointer[x]
				print(a__)
				sys.exit()







def 						lowerCamelCase(   a__):
				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(   a__	,a__	,a__	,a__	,a__	,a__	,a__	,a__	,):
				for itera in range(a__):
								open_list[itera].remove_element(a__)
				# print("s", s)
				# print("j", j)
				((_SCREAMING_SNAKE_CASE)  ,				(_SCREAMING_SNAKE_CASE))			  =s
				_SCREAMING_SNAKE_CASE			  =(x - 1, y)
				_SCREAMING_SNAKE_CASE			  =(x + 1, y)
				_SCREAMING_SNAKE_CASE			  =(x, y + 1)
				_SCREAMING_SNAKE_CASE			  =(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__)
																_SCREAMING_SNAKE_CASE			  =-1
																_SCREAMING_SNAKE_CASE			  =float('''inf''')

												if valid(a__) and g_function[neighbours] > g_function[s] + 1:
																_SCREAMING_SNAKE_CASE			  =g_function[s] + 1
																_SCREAMING_SNAKE_CASE			  =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 						lowerCamelCase(   ):
				_SCREAMING_SNAKE_CASE			  =[]
				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_						:			Tuple													=							{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

snake_case_						:			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),
]
snake_case_						:			Tuple													=							make_common_ground()


snake_case_						:			str													=							blocks_blk
# hyper parameters
snake_case_						:			List[Any]													=							1
snake_case_						:			Union[str, Any]													=							1
snake_case_						:			str													=							20
snake_case_						:			Any													=							3  # one consistent and two other inconsistent

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

snake_case_						:			Optional[int]													=							1







def 						lowerCamelCase(   a__	,a__	,a__):
				_SCREAMING_SNAKE_CASE			  ={start: 0, goal: float('''inf''')}
				_SCREAMING_SNAKE_CASE			  ={start: -1, goal: -1}
				_SCREAMING_SNAKE_CASE			  =[]
				_SCREAMING_SNAKE_CASE			  =set()

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

				_SCREAMING_SNAKE_CASE			  =[]
				_SCREAMING_SNAKE_CASE			  =[]
				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:
																				_SCREAMING_SNAKE_CASE  ,				_SCREAMING_SNAKE_CASE			  =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:
																				_SCREAMING_SNAKE_CASE			  =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)



from datetime import datetime

import matplotlib.pyplot as plt
import torch







def 						lowerCamelCase(   a__):
				for param in module.parameters():
								_SCREAMING_SNAKE_CASE			  =False







def 						lowerCamelCase(   ):
				_SCREAMING_SNAKE_CASE			  ='''cuda''' if torch.cuda.is_available() else '''cpu'''
				if torch.backends.mps.is_available() and torch.backends.mps.is_built():
								_SCREAMING_SNAKE_CASE			  ='''mps'''
				if device == "mps":
								print(
								    '''WARNING: MPS currently doesn\'t seem to work, and messes up backpropagation without any visible torch'''
								    ''' errors. I recommend using CUDA on a colab notebook or CPU instead if you\'re facing inexplicable issues'''
								    ''' with generations.''')
				return device







def 						lowerCamelCase(   a__):
				_SCREAMING_SNAKE_CASE			  =plt.imshow(a__)
				fig.axes.get_xaxis().set_visible(a__)
				fig.axes.get_yaxis().set_visible(a__)
				plt.show()







def 						lowerCamelCase(   ):
				_SCREAMING_SNAKE_CASE			  =datetime.now()
				_SCREAMING_SNAKE_CASE			  =current_time.strftime('''%H:%M:%S''')
				return timestamp