

import heapq
import sys

import numpy as np

a__												=						tuple[int, int]

class 							UpperCAmelCase_						:
							"""simple docstring"""







							def __init__(     self			)       ->       Dict:
												_a      :       str   =						[]
												_a      :       int   =						set()


							def 							__lowercase							(     self			)       ->       Union[str, Any]:
												if not self.empty():
																	return self.elements[0][0]
												else:
																	return float('''inf'''			)


							def 							__lowercase							(     self			)       ->       Tuple:
												return len(self.elements			) == 0


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


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


							def 							__lowercase							(     self			)       ->       Tuple:
												return self.elements[0][1]




							def 							__lowercase							(     self			)       ->       int:
												((_a) ,   (_a))      :       List[Any]   =						heapq.heappop(self.elements			)
												self.set.remove(_a			)
												return (priority, item)



def   __UpperCAmelCase					(      __a :     TPos						,__a :     TPos      )     ->	Optional[Any]:

					"""simple docstring"""

					_a      :       int   =						np.array(__a      )
					_a      :       int   =						np.array(__a      )
					return np.linalg.norm(a - b      )



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

					"""simple docstring"""

					return consistent_heuristic(__a						,__a      ) // t



def   __UpperCAmelCase					(      __a :     TPos						,__a :     TPos      )     ->	str:

					"""simple docstring"""

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



def   __UpperCAmelCase					(      __a :     TPos						,__a :     int						,__a :     TPos						,__a :     dict[TPos, float]      )     ->	Optional[int]:

					"""simple docstring"""

					_a      :       Optional[int]   =						g_function[start] + Wa * heuristics[i](__a						,__a      )
					return ans



def   __UpperCAmelCase					(      __a :     Any						,__a :     Any						,__a :     Dict      )     ->	Optional[Any]:

					"""simple docstring"""

					_a      :       Optional[Any]   =						np.chararray((n, n)      )
					for i in range(__a      ):
										for j in range(__a      ):
															_a      :       Any   =						'''*'''

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

					_a      :       Optional[int]   =						'''-'''
					_a      :       List[str]   =						back_pointer[goal]
					while x != start:
										((_a) ,   (_a))      :       int   =						x
										# print(x)
										_a      :       Dict   =						'''-'''
										_a      :       Tuple   =						back_pointer[x]
					_a      :       Optional[int]   =						'''-'''

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



def   __UpperCAmelCase					(      __a :     TPos      )     ->	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   __UpperCAmelCase					(      __a :     Union[str, Any]						,__a :     List[str]						,__a :     List[str]						,__a :     Any						,__a :     Dict						,__a :     Optional[Any]						,__a :     List[Any]						,__a :     Any						,)     ->	Optional[Any]:

					"""simple docstring"""

					for itera in range(__a      ):
										open_list[itera].remove_element(__a      )
					# print("s", s)
					# print("j", j)
					((_a) ,   (_a))      :       Optional[Any]   =						s
					_a      :       Any   =						(x - 1, y)
					_a      :       Dict   =						(x + 1, y)
					_a      :       str   =						(x, y + 1)
					_a      :       str   =						(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      )
																				_a      :       Optional[int]   =						-1
																				_a      :       Union[str, Any]   =						float('''inf'''      )

															if valid(__a      ) and g_function[neighbours] > g_function[s] + 1:
																				_a      :       Dict   =						g_function[s] + 1
																				_a      :       Optional[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   __UpperCAmelCase					(      )     ->	List[str]:

					"""simple docstring"""

					_a      :       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


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   __UpperCAmelCase					(      __a :     TPos						,__a :     TPos						,__a :     int      )     ->	List[Any]:

					"""simple docstring"""

					_a      :       Optional[int]   =						{start: 0, goal: float('''inf'''      )}
					_a      :       int   =						{start: -1, goal: -1}
					_a      :       Union[str, Any]   =						[]
					_a      :       Optional[int]   =						set()

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

					_a      :       list[int]   =						[]
					_a      :       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:
																									_a ,   _a      :       Any   =						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:
																									_a      :       Tuple   =						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 __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
a__												=						numpy.array([0, 0])
a__												=						numpy.array([0.5, 0.8660254])
a__												=						numpy.array([1, 0])
a__												=						[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]



def   __UpperCAmelCase					(      __a :     list[numpy.ndarray]						,__a :     int      )     ->	list[numpy.ndarray]:

					"""simple docstring"""

					_a      :       Tuple   =						initial_vectors
					for _ in range(__a      ):
										_a      :       int   =						iteration_step(__a      )
					return vectors



def   __UpperCAmelCase					(      __a :     list[numpy.ndarray]      )     ->	list[numpy.ndarray]:

					"""simple docstring"""

					_a      :       Tuple   =						[]
					for i, start_vector in enumerate(vectors[:-1]      ):
										_a      :       str   =						vectors[i + 1]
										new_vectors.append(__a      )
										_a      :       Optional[int]   =						end_vector - start_vector
										new_vectors.append(start_vector + difference_vector / 3      )
										new_vectors.append(
										    start_vector + difference_vector / 3 + rotate(difference_vector / 3						,60      )      )
										new_vectors.append(start_vector + difference_vector * 2 / 3      )
					new_vectors.append(vectors[-1]      )
					return new_vectors



def   __UpperCAmelCase					(      __a :     numpy.ndarray						,__a :     float      )     ->	numpy.ndarray:

					"""simple docstring"""

					_a      :       Tuple   =						numpy.radians(__a      )
					_a ,   _a      :       List[Any]   =						numpy.cos(__a      ), numpy.sin(__a      )
					_a      :       Dict   =						numpy.array(((c, -s), (s, c))      )
					return numpy.dot(__a						,__a      )



def   __UpperCAmelCase					(      __a :     list[numpy.ndarray]      )     ->	None:

					"""simple docstring"""

					_a      :       str   =						plt.gca()
					axes.set_aspect('''equal'''      )

					# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
					# y-coordinates as inputs, which are constructed from the vector-list using
					# zip()
					_a ,   _a      :       Optional[int]   =						zip(*__a      )
					plt.plot(__a						,__a      )
					plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			a__												=						iterate(INITIAL_VECTORS, 5)
			plot(processed_vectors)



