


import heapq
import sys

import numpy as np

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

class        a	:




							"""simple docstring"""


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

							def 					__snake_case      (							self :						int       )			->					str:

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

							def 					__snake_case      (							self :						str       )			->					str:
														return len(self.elements       ) == 0

							def 					__snake_case      (							self :						Dict					,			lowerCamelCase :						Tuple					,			lowerCamelCase :						Any       )			->					List[Any]:

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

							def 					__snake_case      (							self :						List[Any]					,			lowerCamelCase :						int       )			->					int:

														if item in self.set:
																					self.set.remove(__SCREAMING_SNAKE_CASE       )
																					__snake_case	:    List[str]											=     []
																					((__snake_case)				,    (__snake_case))	:    Optional[Any]											=     heapq.heappop(self.elements       )
																					while x != item:
																												temp.append((pro, x)       )
																												((__snake_case)				,    (__snake_case))	:    List[Any]											=     heapq.heappop(self.elements       )
																					for prito, yyy in temp:
																												heapq.heappush(self.elements					,			(prito, yyy)       )

							def 					__snake_case      (							self :						str       )			->					Union[str, Any]:
														return self.elements[0][1]






							def 					__snake_case      (							self :						Tuple       )			->					Optional[Any]:
														((__snake_case)				,    (__snake_case))	:    Dict											=     heapq.heappop(self.elements       )
														self.set.remove(__SCREAMING_SNAKE_CASE       )
														return (priority, item)







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							# euclidean distance
							__snake_case	:    int											=     np.array(_UpperCAmelCase			)
							__snake_case	:    str											=     np.array(_UpperCAmelCase			)
							return np.linalg.norm(a - b			)







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):
							# integer division by time variable
							return consistent_heuristic(_UpperCAmelCase							,			_UpperCAmelCase			) // t







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







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase			):
							__snake_case	:    Union[str, Any]											=     g_function[start] + Wa * heuristics[i](_UpperCAmelCase							,			_UpperCAmelCase			)
							return ans







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase			):
							__snake_case	:    Optional[int]											=     np.chararray((n, n)			)
							for i in range(_UpperCAmelCase			):
														for j in range(_UpperCAmelCase			):
																					__snake_case	:    List[Any]											=     "*"

							for i in range(_UpperCAmelCase			):
														for j in range(_UpperCAmelCase			):
																					if (j, (n - 1) - i) in blocks:
																												__snake_case	:    List[Any]											=     "#"

							__snake_case	:    Any											=     "-"
							__snake_case	:    Dict											=     back_pointer[goal]
							while x != start:
														((__snake_case)				,    (__snake_case))	:    List[str]											=     x
														# print(x)
														__snake_case	:    Union[str, Any]											=     "-"
														__snake_case	:    Optional[Any]											=     back_pointer[x]
							__snake_case	:    List[Any]											=     "-"

							for i in range(_UpperCAmelCase			):
														for j in range(_UpperCAmelCase			):
																					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:-"			)
							__snake_case	:    Tuple											=     back_pointer[goal]
							while x != start:
														print(_UpperCAmelCase							,			end=" "			)
														__snake_case	:    List[Any]											=     back_pointer[x]
							print(_UpperCAmelCase			)
							sys.exit()







def        lowerCAmelCase_  (      __lowerCamelCase			):
							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_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			):
							for itera in range(_UpperCAmelCase			):
														open_list[itera].remove_element(_UpperCAmelCase			)
							# print("s", s)
							# print("j", j)
							((__snake_case)				,    (__snake_case))	:    str											=     s
							__snake_case	:    Optional[int]											=     (x - 1, y)
							__snake_case	:    Any											=     (x + 1, y)
							__snake_case	:    List[str]											=     (x, y + 1)
							__snake_case	:    Dict											=     (x, y - 1)

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

																					if valid(_UpperCAmelCase			) and g_function[neighbours] > g_function[s] + 1:
																												__snake_case	:    List[str]											=     g_function[s] + 1
																												__snake_case	:    Optional[int]											=     s
																												if neighbours not in close_list_anchor:
																																			open_list[0].put(_UpperCAmelCase							,			key(_UpperCAmelCase							,			0							,			_UpperCAmelCase							,			_UpperCAmelCase			)			)
																																			if neighbours not in close_list_inad:
																																										for var in range(1							,			_UpperCAmelCase			):
																																																	if key(_UpperCAmelCase							,			_UpperCAmelCase							,			_UpperCAmelCase							,			_UpperCAmelCase			) <= Wa * key(
																																																	    _UpperCAmelCase							,			0							,			_UpperCAmelCase							,			_UpperCAmelCase			):
																																																								open_list[j].put(
																																																								    _UpperCAmelCase							,			key(_UpperCAmelCase							,			_UpperCAmelCase							,			_UpperCAmelCase							,			_UpperCAmelCase			)			)







def        lowerCAmelCase_  (      ):
							__snake_case	:    Optional[int]											=     []
							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


_snake_case  :	List[Any]			      =       {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_snake_case  :	str			      =       [
    (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  :	Union[str, Any]			      =       make_common_ground()


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

# start and end destination
_snake_case  :	Union[str, Any]			      =       (0, 0)
_snake_case  :	Tuple			      =       (n - 1, n - 1)

_snake_case  :	Optional[int]			      =       1







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase			):
							__snake_case	:    Optional[int]											=     {start: 0, goal: float("inf"			)}
							__snake_case	:    str											=     {start: -1, goal: -1}
							__snake_case	:    str											=     []
							__snake_case	:    Union[str, Any]											=     set()

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

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

import numpy as np







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase							,			__lowerCamelCase = None							,			):
							__snake_case	:    List[str]											=     np.shape(__lowerCamelCase			)
							__snake_case	:    Optional[Any]											=     np.shape(__lowerCamelCase			)
							__snake_case	:    List[str]											=     np.shape(__lowerCamelCase			)

							if shape_a[0] != shape_b[0]:
														__snake_case	:    Any											=     (
														    "Expected the same number of rows for A and B. "
														    F'Instead found A of size {shape_a} and B of size {shape_b}'
														)
														raise ValueError(__lowerCamelCase			)

							if shape_b[1] != shape_c[1]:
														__snake_case	:    int											=     (
														    "Expected the same number of columns for B and C. "
														    F'Instead found B of size {shape_b} and C of size {shape_c}'
														)
														raise ValueError(__lowerCamelCase			)

							__snake_case	:    str											=     pseudo_inv
							if a_inv is None:
														try:
																					__snake_case	:    Optional[Any]											=     np.linalg.inv(__lowerCamelCase			)
														except np.linalg.LinAlgError:
																					raise ValueError(
																					    "Input matrix A is not invertible. Cannot compute Schur complement."			)

							return mat_c - mat_b.T @ a_inv @ mat_b

class        a	(unittest.TestCase   ):




							"""simple docstring"""


							def 					__snake_case      (							self :						Tuple       )			->					None:
														__snake_case	:    str											=     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
														__snake_case	:    str											=     np.array([[0, 3], [3, 0], [2, 3]]       )
														__snake_case	:    Dict											=     np.array([[2, 1], [6, 3]]       )

														__snake_case	:    Dict											=     schur_complement(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )

														__snake_case	:    int											=     np.block([[a, b], [b.T, c]]       )

														__snake_case	:    Optional[int]											=     np.linalg.det(lowerCamelCase       )
														__snake_case	:    Any											=     np.linalg.det(lowerCamelCase       )
														__snake_case	:    Tuple											=     np.linalg.det(lowerCamelCase       )

														self.assertAlmostEqual(lowerCamelCase					,			det_a * det_s       )

							def 					__snake_case      (							self :						int       )			->					None:
														__snake_case	:    str											=     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
														__snake_case	:    Dict											=     np.array([[0, 3], [3, 0], [2, 3]]       )
														__snake_case	:    Tuple											=     np.array([[2, 1], [6, 3]]       )

														with self.assertRaises(lowerCamelCase       ):
																					schur_complement(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )






							def 					__snake_case      (							self :						List[Any]       )			->					None:
														__snake_case	:    List[Any]											=     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]       )
														__snake_case	:    Tuple											=     np.array([[0, 3], [3, 0], [2, 3]]       )
														__snake_case	:    List[Any]											=     np.array([[2, 1, 3], [6, 3, 5]]       )

														with self.assertRaises(lowerCamelCase       ):
																					schur_complement(lowerCamelCase					,			lowerCamelCase					,			lowerCamelCase       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			unittest.main()

