





'''simple docstring'''






from __future__ import annotations







def 					_a						(       _lowerCamelCase ) ->				None:



			"""simple docstring"""


			create_state_space_tree(_lowerCamelCase    ,	[]    ,	0    ,	[0 for i in range(len(_lowerCamelCase ) )] )







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	) ->				None:



			"""simple docstring"""


			if index == len(_lowerCamelCase ):
						print(_lowerCamelCase )
						return

			for i in range(len(_lowerCamelCase ) ):
						if not index_used[i]:
									current_sequence.append(sequence[i] )
									__snake_case					:      Tuple							      =     True
									create_state_space_tree(_lowerCamelCase    ,	_lowerCamelCase    ,	index + 1    ,	_lowerCamelCase )
									current_sequence.pop()
									__snake_case					:      str							      =     False
__UpperCamelCase					    =	[3, 1, 2, 4]
generate_all_permutations(sequence)

__UpperCamelCase					    =	["A", "B", "C"]

generate_all_permutations(sequence_a)









'''simple docstring'''






from __future__ import annotations

__UpperCamelCase					    =	[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	) ->				tuple[list[list[int]], list[list[int]]]:



			"""simple docstring"""


			__snake_case					:      List[str]							      =     [
			    [0 for col in range(len(grid[0] ) )] for row in range(len(_lowerCamelCase ) )
			]  # the reference grid
			__snake_case					:      Tuple							      =     1
			__snake_case					:      List[str]							      =     [
			    [0 for col in range(len(grid[0] ) )] for row in range(len(_lowerCamelCase ) )
			]  # the action grid

			__snake_case					:      List[str]							      =     init[0]
			__snake_case					:      str							      =     init[1]
			__snake_case					:      int							      =     0
			__snake_case					:      int							      =     g + heuristic[x][y]  # cost from starting cell to destination cell
			__snake_case					:      List[str]							      =     [[f, g, x, y]]

			__snake_case					:      Any							      =     False  # flag that is set when search is complete
			__snake_case					:      int							      =     False  # flag set if we can't find expand

			while not found and not resign:
						if len(_lowerCamelCase ) == 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()
									__snake_case					:      Tuple							      =     cell.pop()
									__snake_case					:      Optional[int]							      =     next_cell[2]
									__snake_case					:      List[Any]							      =     next_cell[3]
									__snake_case					:      int							      =     next_cell[1]

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

			__snake_case					:      Optional[int]							      =     []
			for i in range(len(_lowerCamelCase ) ):
						path.append(invpath[len(_lowerCamelCase ) - 1 - i] )
			return path, action


if __name__ == "__main__":
	__UpperCamelCase					    =	[
	    [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					    =	[0, 0]
	# all coordinates are given in format [y,x]
	__UpperCamelCase					    =	[len(grid) - 1, len(grid[0]) - 1]
	__UpperCamelCase					    =	1

	# the cost map which pushes the path closer to the goal
	__UpperCamelCase					    =	[[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					    =	abs(i - goal[0]) + abs(j - goal[1])
			if grid[i][j] == 1:
				# added extra penalty in the heuristic map
				__UpperCamelCase					    =	99

	__UpperCamelCase    ,		__UpperCamelCase					    =	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])


