





from __future__ import annotations

__UpperCamelCase	: Union[str, Any]    		=  [
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def    A			(					_lowercase	,						_lowercase	,						_lowercase	,						_lowercase	,						_lowercase	,						):
						SCREAMING_SNAKE_CASE							:					Any           =							[
						    [0 for col in range(len(grid[0]		)		)] for row in range(len(_lowercase		)		)
						]  # the reference grid
						SCREAMING_SNAKE_CASE							:					int           =							1
						SCREAMING_SNAKE_CASE							:					int           =							[
						    [0 for col in range(len(grid[0]		)		)] for row in range(len(_lowercase		)		)
						]  # the action grid

						SCREAMING_SNAKE_CASE							:					Any           =							init[0]
						SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							init[1]
						SCREAMING_SNAKE_CASE							:					List[Any]           =							0
						SCREAMING_SNAKE_CASE							:					Optional[Any]           =							g + heuristic[x][y]  # cost from starting cell to destination cell
						SCREAMING_SNAKE_CASE							:					Any           =							[[f, g, x, y]]

						SCREAMING_SNAKE_CASE							:					List[Any]           =							False  # flag that is set when search is complete
						SCREAMING_SNAKE_CASE							:					Tuple           =							False  # flag set if we can't find expand

						while not found and not resign:
												if len(_lowercase		) == 0:
																		raise ValueError('''Algorithm is unable to find solution'''		)
												else:  # to choose the least costliest action so as to move closer to the goal
																		cell.sort()
																		cell.reverse()
																		SCREAMING_SNAKE_CASE							:					List[str]           =							cell.pop()
																		SCREAMING_SNAKE_CASE							:					Tuple           =							next_cell[2]
																		SCREAMING_SNAKE_CASE							:					Dict           =							next_cell[3]
																		SCREAMING_SNAKE_CASE							:					List[Any]           =							next_cell[1]

																		if x == goal[0] and y == goal[1]:
																								SCREAMING_SNAKE_CASE							:					Tuple           =							True
																		else:
																								for i in range(len(_lowercase		)		):  # to try out different valid actions
																														SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							x + DIRECTIONS[i][0]
																														SCREAMING_SNAKE_CASE							:					Tuple           =							y + DIRECTIONS[i][1]
																														if xa >= 0 and xa < len(_lowercase		) and ya >= 0 and ya < len(grid[0]		):
																																				if closed[xa][ya] == 0 and grid[xa][ya] == 0:
																																										SCREAMING_SNAKE_CASE							:					Union[str, Any]           =							g + cost
																																										SCREAMING_SNAKE_CASE							:					Any           =							ga + heuristic[xa][ya]
																																										cell.append([fa, ga, xa, ya]		)
																																										SCREAMING_SNAKE_CASE							:					Any           =							1
																																										SCREAMING_SNAKE_CASE							:					Optional[int]           =							i
						SCREAMING_SNAKE_CASE							:					str           =							[]
						SCREAMING_SNAKE_CASE							:					List[str]           =							goal[0]
						SCREAMING_SNAKE_CASE							:					Optional[int]           =							goal[1]
						invpath.append([x, y]		)  # we get the reverse path from here
						while x != init[0] or y != init[1]:
												SCREAMING_SNAKE_CASE							:					Dict           =							x - DIRECTIONS[action[x][y]][0]
												SCREAMING_SNAKE_CASE							:					List[str]           =							y - DIRECTIONS[action[x][y]][1]
												SCREAMING_SNAKE_CASE							:					Optional[Any]           =							xa
												SCREAMING_SNAKE_CASE							:					Dict           =							ya
												invpath.append([x, y]		)

						SCREAMING_SNAKE_CASE							:					List[str]           =							[]
						for i in range(len(_lowercase		)		):
												path.append(invpath[len(_lowercase		) - 1 - i]		)
						return path, action


if __name__ == "__main__":
					__UpperCamelCase	: List[str]    		=  [
					    [0, 1, 0, 0, 0, 0],
					    [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
					    [0, 1, 0, 0, 0, 0],
					    [0, 1, 0, 0, 1, 0],
					    [0, 0, 0, 0, 1, 0],
					]

					__UpperCamelCase	: Union[str, Any]    		=  [0, 0]
					# all coordinates are given in format [y,x]
					__UpperCamelCase	: Optional[Any]    		=  [len(grid) - 1, len(grid[0]) - 1]
					__UpperCamelCase	: Union[str, Any]    		=  1

					# the cost map which pushes the path closer to the goal
					__UpperCamelCase	: List[Any]    		=  [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
					for i in range(len(grid)):
										for j in range(len(grid[0])):
															__UpperCamelCase	: Union[str, Any]    		=  abs(i - goal[0]) + abs(j - goal[1])
															if grid[i][j] == 1:
																				# added extra penalty in the heuristic map
																				__UpperCamelCase	: str    		=  99

					__UpperCamelCase	: List[Any]    		=  search(grid, init, goal, cost, heuristic)

					print('ACTION MAP')
					for i in range(len(action)):
										print(action[i])

					for i in range(len(path)):
										print(path[i])






from __future__ import annotations

from typing import Any





class       lowercase__		(     UpperCamelCase_):
						pass






class       lowercase__		:


						def __init__( self			:       Union[str, Any]					,	UpperCamelCase__			:       Any		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE							:					Any           =							data
												SCREAMING_SNAKE_CASE							:					Node | None           =							None


						def __iter__( self			:       Any		):





												'''simple docstring'''





												SCREAMING_SNAKE_CASE							:					List[str]           =							self
												SCREAMING_SNAKE_CASE							:					Tuple           =							[]
												while node:
																		if node in visited:
																								raise ContainsLoopError
																		visited.append(UpperCamelCase__		)
																		yield node.data
																		SCREAMING_SNAKE_CASE							:					Dict           =							node.next_node



						@property
						def  __A ( self			:       Optional[int]		):





												'''simple docstring'''





												try:
																		list(self		)
																		return False
												except ContainsLoopError:
																		return True


if __name__ == "__main__":
					__UpperCamelCase	: List[Any]    		=  Node(1)
					__UpperCamelCase	: str    		=  Node(2)
					__UpperCamelCase	: Dict    		=  Node(3)
					__UpperCamelCase	: List[Any]    		=  Node(4)
					print(root_node.has_loop)  # False
					__UpperCamelCase	: int    		=  root_node.next_node
					print(root_node.has_loop)  # True

					__UpperCamelCase	: Union[str, Any]    		=  Node(5)
					__UpperCamelCase	: Union[str, Any]    		=  Node(6)
					__UpperCamelCase	: List[Any]    		=  Node(5)
					__UpperCamelCase	: List[str]    		=  Node(6)
					print(root_node.has_loop)  # False

					__UpperCamelCase	: List[Any]    		=  Node(1)
					print(root_node.has_loop)  # False





