



import numpy as np

class 	lowerCamelCase_    :






						'''simple docstring'''







						def __init__(	self      :			Dict )      ->				Optional[Any]:
									A							:					str              =						(0, 0)
									A							:					List[Any]              =						None
									A							:					Dict              =						0
									A							:					List[str]              =						0
									A							:					Dict              =						0







						def __eq__(	self      :			Tuple	,	__lowerCamelCase      :			int )      ->				List[str]:
									return self.position == cell.position







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Dict )      ->				Optional[Any]:
									print(self.position )







class 	lowerCamelCase_    :






						'''simple docstring'''







						def __init__(	self      :			List[Any]	,	__lowerCamelCase      :			List[Any]=(5, 5) )      ->				int:
									A							:					Tuple              =						np.zeros(__lowerCamelCase )
									A							:					str              =						world_size[0]
									A							:					Dict              =						world_size[1]







						def 			SCREAMING_SNAKE_CASE__		(	self      :			Dict )      ->				Tuple:
									print(self.w )







						def 			SCREAMING_SNAKE_CASE__		(	self      :			str	,	__lowerCamelCase      :			Tuple )      ->				List[str]:
									A							:					Any              =						[
									    (-1, -1),
									    (-1, 0),
									    (-1, 1),
									    (0, -1),
									    (0, 1),
									    (1, -1),
									    (1, 0),
									    (1, 1),
									]
									A							:					Optional[Any]              =						cell.position[0]
									A							:					Optional[Any]              =						cell.position[1]
									A							:					Tuple              =						[]
									for n in neughbour_cord:
												A							:					Any              =						current_x + n[0]
												A							:					Union[str, Any]              =						current_y + n[1]
												if 0 <= x < self.world_x_limit and 0 <= y < self.world_y_limit:
															A							:					Optional[Any]              =						Cell()
															A							:					Union[str, Any]              =						(x, y)
															A							:					List[Any]              =						cell
															neighbours.append(__lowerCamelCase )
									return neighbours







def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase    ):
			A							:					Union[str, Any]              =						[]
			A							:					List[str]              =						[]
			_open.append(_lowerCamelCase    )

			while _open:
						A							:					List[str]              =						np.argmin([n.f for n in _open]    )
						A							:					Dict              =						_open[min_f]
						_closed.append(_open.pop(_lowerCamelCase    )    )
						if current == goal:
									break
						for n in world.get_neigbours(_lowerCamelCase    ):
									for c in _closed:
												if c == n:
															continue
									A							:					Optional[int]              =						current.g + 1
									A       , A							:					List[str]              =						n.position
									A       , A							:					Dict              =						goal.position
									A							:					List[str]              =						(ya - ya) ** 2 + (xa - xa) ** 2
									A							:					List[str]              =						n.h + n.g

									for c in _open:
												if c == n and c.f < n.f:
															continue
									_open.append(_lowerCamelCase    )
			A							:					int              =						[]
			while current.parent is not None:
						path.append(current.position    )
						A							:					List[Any]              =						current.parent
			path.append(current.position    )
			return path[::-1]


if __name__ == "__main__":
							__SCREAMING_SNAKE_CASE           =  Gridworld()
							# Start position and goal
							__SCREAMING_SNAKE_CASE           =  Cell()
							__SCREAMING_SNAKE_CASE           =  (0, 0)
							__SCREAMING_SNAKE_CASE           =  Cell()
							__SCREAMING_SNAKE_CASE           =  (4, 4)
							print(F"""path from {start.position} to {goal.position}""")
							__SCREAMING_SNAKE_CASE           =  astar(world, start, goal)
							#   Just for visual reasons.
							for i in s:
														__SCREAMING_SNAKE_CASE           =  1
							print(world.w)




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase ,    _lowerCamelCase = "x" ,    _lowerCamelCase = 10**-10 ,    _lowerCamelCase = 1 ,    ):
			A							:					str              =						symbols(_lowerCamelCase    )
			A							:					int              =						lambdify(_lowerCamelCase ,    _lowerCamelCase    )
			A							:					List[str]              =						lambdify(_lowerCamelCase ,    diff(_lowerCamelCase ,    _lowerCamelCase    )    )

			A							:					Optional[int]              =						starting_point

			while True:
						if diff_function(_lowerCamelCase    ) != 0:
									A							:					Optional[Any]              =						prev_guess - multiplicity * func(_lowerCamelCase    ) / diff_function(
									    _lowerCamelCase    )
						else:
									raise ZeroDivisionError("Could not find root"    ) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess    ) < precision:
									return next_guess

						A							:					int              =						next_guess


# Let's Execute
if __name__ == "__main__":
							# Find root of trigonometric function
							# Find value of pi
							print(F"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

							# Find root of polynomial
							# Find fourth Root of 5
							print(F"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}""")

							# Find value of e
							print(
							    """The root of log(y) - 1 = 0 is """,
							    F"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
							)

							# Exponential Roots
							print(
							    """The root of exp(x) - 1 = 0 is""",
							    F"""{newton_raphson('exp(x) - 1', 10, precision=0.005)}""",
							)

							# Find root of cos(x)
							print(F"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")