
from __future__ import annotations

lowerCamelCase__          =		[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							)				->		tuple[list[list[int]], list[list[int]]]:
			lowerCAmelCase__      :      List[Any]         =		[
			    [0 for col in range(len(grid[0]     )     )] for row in range(len(SCREAMING_SNAKE_CASE_     )     )
			]  # the reference grid
			lowerCAmelCase__      :      Dict         =		1
			lowerCAmelCase__      :      Dict         =		[
			    [0 for col in range(len(grid[0]     )     )] for row in range(len(SCREAMING_SNAKE_CASE_     )     )
			]  # the action grid

			lowerCAmelCase__      :      int         =		init[0]
			lowerCAmelCase__      :      Any         =		init[1]
			lowerCAmelCase__      :      str         =		0
			lowerCAmelCase__      :      Dict         =		g + heuristic[x][y]  # cost from starting cell to destination cell
			lowerCAmelCase__      :      Tuple         =		[[f, g, x, y]]

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

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

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

			lowerCAmelCase__      :      Tuple         =		[]
			for i in range(len(SCREAMING_SNAKE_CASE_     )     ):
						path.append(invpath[len(SCREAMING_SNAKE_CASE_     ) - 1 - i]     )
			return path, action


if __name__ == "__main__":
					lowerCamelCase__          =		[
					    [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],
					]

					lowerCamelCase__          =		[0, 0]
					# all coordinates are given in format [y,x]
					lowerCamelCase__          =		[len(grid) - 1, len(grid[0]) - 1]
					lowerCamelCase__          =		1

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

					lowerCamelCase__      ,					lowerCamelCase__          =		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

import math

lowerCamelCase__          =		"""2020.9.26"""
lowerCamelCase__          =		"""xcodz-dot, cclaus, dhruvmanila"""
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		tuple[float, float]:
			if not all(isinstance(SCREAMING_SNAKE_CASE_       ,							(float, int)     ) for val in locals().values()     ):
						lowerCAmelCase__      :      List[str]         =		F'''Input values must either be float or int: {list(locals().values()     )}'''
						raise TypeError(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      Tuple         =		((x * distance) / (z + distance)) * scale
			lowerCAmelCase__      :      Optional[int]         =		((y * distance) / (z + distance)) * scale
			return projected_x, projected_y
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		tuple[float, float, float]:
			if not isinstance(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ):
						raise TypeError('Axis must be a str'     )
			lowerCAmelCase__      :      Optional[int]         =		locals()
			del input_variables["axis"]
			if not all(isinstance(SCREAMING_SNAKE_CASE_       ,							(float, int)     ) for val in input_variables.values()     ):
						lowerCAmelCase__      :      List[Any]         =		(
						    'Input values except axis must either be float or int: '
						    F'''{list(input_variables.values()     )}'''
						)
						raise TypeError(SCREAMING_SNAKE_CASE_     )
			lowerCAmelCase__      :      int         =		(angle % 360) / 450 * 180 / math.pi
			if axis == "z":
						lowerCAmelCase__      :      Tuple         =		x * math.cos(SCREAMING_SNAKE_CASE_     ) - y * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[str]         =		y * math.cos(SCREAMING_SNAKE_CASE_     ) + x * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Optional[int]         =		z
			elif axis == "x":
						lowerCAmelCase__      :      Dict         =		y * math.cos(SCREAMING_SNAKE_CASE_     ) - z * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[str]         =		z * math.cos(SCREAMING_SNAKE_CASE_     ) + y * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Tuple         =		x
			elif axis == "y":
						lowerCAmelCase__      :      str         =		x * math.cos(SCREAMING_SNAKE_CASE_     ) - z * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      Optional[int]         =		z * math.cos(SCREAMING_SNAKE_CASE_     ) + x * math.sin(SCREAMING_SNAKE_CASE_     )
						lowerCAmelCase__      :      List[Any]         =		y
			else:
						raise ValueError('not a valid axis, choose one of \'x\', \'y\', \'z\''     )

			return new_x, new_y, new_z


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
					print(F"""{rotate(1.0, 2.0, 3.0, "y", 90.0) = }""")