
import heapq
import sys

import numpy as np

_UpperCAmelCase :			str              =	tuple[int, int]


class     lowercase :



		def __init__(			self	)  -> Tuple:
				"""simple docstring"""
				UpperCamelCase          =					[]
				UpperCamelCase          =					set()



		def __UpperCamelCase			(			self	)  -> Tuple:
				"""simple docstring"""
				if not self.empty():
						return self.elements[0][0]
				else:
						return float('inf'	)



		def __UpperCamelCase			(			self	)  -> Tuple:
				"""simple docstring"""
				return len(self.elements	) == 0



		def __UpperCamelCase			(			self    ,				A_    ,				A_	)  -> Optional[int]:
				"""simple docstring"""
				if item not in self.set:
						heapq.heappush(self.elements    ,				(priority, item)	)
						self.set.add(A_	)
				else:
						# update
						# print("update", item)
						UpperCamelCase          =					[]
						((UpperCamelCase)     ,  (UpperCamelCase))          =					heapq.heappop(self.elements	)
						while x != item:
								temp.append((pri, x)	)
								((UpperCamelCase)     ,  (UpperCamelCase))          =					heapq.heappop(self.elements	)
						temp.append((priority, item)	)
						for pro, xxx in temp:
								heapq.heappush(self.elements    ,				(pro, xxx)	)



		def __UpperCamelCase			(			self    ,				A_	)  -> Dict:
				"""simple docstring"""
				if item in self.set:
						self.set.remove(A_	)
						UpperCamelCase          =					[]
						((UpperCamelCase)     ,  (UpperCamelCase))          =					heapq.heappop(self.elements	)
						while x != item:
								temp.append((pro, x)	)
								((UpperCamelCase)     ,  (UpperCamelCase))          =					heapq.heappop(self.elements	)
						for prito, yyy in temp:
								heapq.heappush(self.elements    ,				(prito, yyy)	)



		def __UpperCamelCase			(			self	)  -> int:
				"""simple docstring"""
				return self.elements[0][1]



		def __UpperCamelCase			(			self	)  -> Any:
				"""simple docstring"""
				((UpperCamelCase)     ,  (UpperCamelCase))          =					heapq.heappop(self.elements	)
				self.set.remove(A_	)
				return (priority, item)






def 				A	( lowercase   ,	lowercase			)       ->  Any:
		'''simple docstring'''

		UpperCamelCase          =					np.array(lowercase			)
		UpperCamelCase          =					np.array(lowercase			)
		return np.linalg.norm(a - b			)


def 				A	( lowercase   ,	lowercase			)       ->  List[Any]:
		'''simple docstring'''

		return consistent_heuristic(lowercase   ,	lowercase			) // t


def 				A	( lowercase   ,	lowercase			)       ->  str:
		'''simple docstring'''

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


def 				A	( lowercase   ,	lowercase   ,	lowercase   ,	lowercase			)       ->  List[str]:
		'''simple docstring'''

		UpperCamelCase          =					g_function[start] + Wa * heuristics[i](lowercase   ,	lowercase			)
		return ans


def 				A	( lowercase   ,	lowercase   ,	lowercase			)       ->  Dict:
		'''simple docstring'''

		UpperCamelCase          =					np.chararray((n, n)			)
		for i in range(lowercase			):
				for j in range(lowercase			):
						UpperCamelCase          =					'*'

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

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

		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          =					back_pointer[goal]
		while x != start:
				print(lowercase   ,	end=' '			)
				UpperCamelCase          =					back_pointer[x]
		print(lowercase			)
		sys.exit()


def 				A	( lowercase			)       ->  int:
		'''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 				A	( lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	)       ->  List[Any]:
		'''simple docstring'''

		for itera in range(lowercase			):
				open_list[itera].remove_element(lowercase			)
		# print("s", s)
		# print("j", j)
		((UpperCamelCase)     ,  (UpperCamelCase))          =					s
		UpperCamelCase          =					(x - 1, y)
		UpperCamelCase          =					(x + 1, y)
		UpperCamelCase          =					(x, y + 1)
		UpperCamelCase          =					(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          =					-1
								UpperCamelCase          =					float('inf'			)

						if valid(lowercase			) and g_function[neighbours] > g_function[s] + 1:
								UpperCamelCase          =					g_function[s] + 1
								UpperCamelCase          =					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 				A	( )       ->  Tuple:
		'''simple docstring'''

		UpperCamelCase          =					[]
		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


_UpperCAmelCase :			Optional[int]              =	{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

_UpperCAmelCase :			Optional[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),
]
_UpperCAmelCase :			Optional[Any]              =	make_common_ground()


_UpperCAmelCase :			Optional[int]              =	blocks_blk
# hyper parameters
_UpperCAmelCase :			Dict              =	1
_UpperCAmelCase :			Tuple              =	1
_UpperCAmelCase :			List[Any]              =	20
_UpperCAmelCase :			Optional[Any]              =	3  # one consistent and two other inconsistent

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

_UpperCAmelCase :			List[Any]              =	1


def 				A	( lowercase   ,	lowercase   ,	lowercase			)       ->  Optional[Any]:
		'''simple docstring'''

		UpperCamelCase          =					{start: 0, goal: float('inf'			)}
		UpperCamelCase          =					{start: -1, goal: -1}
		UpperCamelCase          =					[]
		UpperCamelCase          =					set()

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

		UpperCamelCase          =					[]
		UpperCamelCase          =					[]
		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          =					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          =					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)


from __future__ import annotations


def 				A	( lowercase   ,	lowercase			)       ->  tuple[int, int]:
		'''simple docstring'''

		if b == 0:
				return (1, 0)
		((UpperCamelCase)     ,  (UpperCamelCase))          =					extended_euclid(lowercase   ,	a % b			)
		UpperCamelCase          =					a // b
		return (y, x - k * y)


def 				A	( lowercase   ,	lowercase   ,	lowercase   ,	lowercase			)       ->  int:
		'''simple docstring'''

		((UpperCamelCase)     ,  (UpperCamelCase))          =					extended_euclid(lowercase   ,	lowercase			)
		UpperCamelCase          =					na * na
		UpperCamelCase          =					ra * x * na + ra * y * na
		return (n % m + m) % m


def 				A	( lowercase   ,	lowercase			)       ->  int:
		'''simple docstring'''

		((UpperCamelCase)     ,  (UpperCamelCase))          =					extended_euclid(lowercase   ,	lowercase			)
		if b < 0:
				UpperCamelCase          =					(b % n + n) % n
		return b


def 				A	( lowercase   ,	lowercase   ,	lowercase   ,	lowercase			)       ->  int:
		'''simple docstring'''

		UpperCamelCase     ,  UpperCamelCase          =					invert_modulo(lowercase   ,	lowercase			), invert_modulo(lowercase   ,	lowercase			)
		UpperCamelCase          =					na * na
		UpperCamelCase          =					ra * x * na + ra * y * na
		return (n % m + m) % m


if __name__ == "__main__":
					from doctest import testmod

					testmod(name="chinese_remainder_theorem", verbose=True)
					testmod(name="chinese_remainder_theorem2", verbose=True)
					testmod(name="invert_modulo", verbose=True)
					testmod(name="extended_euclid", verbose=True)
