



import math

class 						lowerCamelCase_     :






						'''simple docstring'''







						def __init__(						self   :      List[str]						,						__lowerCamelCase   :      int						,						__lowerCamelCase   :      int						,						__lowerCamelCase   :      int						,						__lowerCamelCase   :      List[Any]			)   ->					Optional[int]:
									A				:       str														=    x
									A				:       Dict														=    y
									A				:       Any														=    step_size
									A				:       str														=    function_to_optimize







						def       SCREAMING_SNAKE_CASE__		(						self   :      Dict			)   ->					int:
									return self.function(self.x						,						self.y			)







						def       SCREAMING_SNAKE_CASE__		(						self   :      int			)   ->					Union[str, Any]:
									A				:       Dict														=    self.step_size
									return [
									    SearchProblem(__lowerCamelCase						,						__lowerCamelCase						,						__lowerCamelCase						,						self.function			)
									    for x, y in (
									        (self.x - step_size, self.y - step_size),
									        (self.x - step_size, self.y),
									        (self.x - step_size, self.y + step_size),
									        (self.x, self.y - step_size),
									        (self.x, self.y + step_size),
									        (self.x + step_size, self.y - step_size),
									        (self.x + step_size, self.y),
									        (self.x + step_size, self.y + step_size),
									    )
									]







						def __hash__(						self   :      Tuple			)   ->					List[str]:
									return hash(str(self			)			)







						def __eq__(						self   :      Optional[Any]						,						__lowerCamelCase   :      Tuple			)   ->					Tuple:
									if isinstance(__lowerCamelCase						,						__lowerCamelCase			):
												return hash(str(self			)			) == hash(str(__lowerCamelCase			)			)
									return False







						def __str__(						self   :      Tuple			)   ->					List[str]:
									return F"""x: {self.x} y: {self.y}"""







def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase = True			,     _lowerCamelCase = math.inf			,     _lowerCamelCase = -math.inf			,     _lowerCamelCase = math.inf			,     _lowerCamelCase = -math.inf			,     _lowerCamelCase = False			,     _lowerCamelCase = 1_0000			,     ):
			A				:       Union[str, Any]														=    search_prob
			A				:       Union[str, Any]														=    []  # list to store the current score at each iteration
			A				:       List[str]														=    0
			A				:       int														=    False
			A				:       List[Any]														=    set()
			while not solution_found and iterations < max_iter:
						visited.add(_lowerCamelCase     )
						iterations += 1
						A				:       Dict														=    current_state.score()
						scores.append(_lowerCamelCase     )
						A				:       str														=    current_state.get_neighbors()
						A				:       Optional[Any]														=    -math.inf
						A				:       str														=    math.inf
						A				:       Optional[Any]														=    None  # to hold the next best neighbor
						for neighbor in neighbors:
									if neighbor in visited:
												continue  # do not want to visit the same state again
									if (
									    neighbor.x > max_x
									    or neighbor.x < min_x
									    or neighbor.y > max_y
									    or neighbor.y < min_y
									):
												continue  # neighbor outside our bounds
									A				:       Tuple														=    neighbor.score() - current_score
									if find_max:  # finding max
												# going to direction with greatest ascent
												if change > max_change and change > 0:
															A				:       List[Any]														=    change
															A				:       int														=    neighbor
									else:  # finding min
												# to direction with greatest descent
												if change < min_change and change < 0:
															A				:       List[str]														=    change
															A				:       List[Any]														=    neighbor
						if next_state is not None:
									# we found at least one neighbor which improved the current state
									A				:       str														=    next_state
						else:
									# since we have no neighbor that improves the solution we stop the search
									A				:       Union[str, Any]														=    True

			if visualization:
						from matplotlib import pyplot as plt

						plt.plot(range(_lowerCamelCase     )			,     _lowerCamelCase     )
						plt.xlabel("Iterations"     )
						plt.ylabel("Function values"     )
						plt.show()

			return current_state


if __name__ == "__main__":
							import doctest

							doctest.testmod()




							def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase     ):
										return (x**2) + (y**2)

							# starting the problem with initial coordinates (3, 4)
							__SCREAMING_SNAKE_CASE     =	SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							__SCREAMING_SNAKE_CASE     =	hill_climbing(prob, find_max=False)
							print(
							    """The minimum score for f(x, y) = x^2 + y^2 found via hill climbing: """
							    F"""{local_min.score()}"""
							)

							# starting the problem with initial coordinates (12, 47)
							__SCREAMING_SNAKE_CASE     =	SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
							__SCREAMING_SNAKE_CASE     =	hill_climbing(
							    prob, find_max=False, max_x=100, min_x=5, max_y=50, min_y=-5, visualization=True
							)
							print(
							    """The minimum score for f(x, y) = x^2 + y^2 with the domain 100 > x > 5 """
							    F"""and 50 > y > - 5 found via hill climbing: {local_min.score()}"""
							)




							def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase     ):
										return (3 * x**2) - (6 * y)

							__SCREAMING_SNAKE_CASE     =	SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
							__SCREAMING_SNAKE_CASE     =	hill_climbing(prob, find_max=True)






							print(
							    """The maximum score for f(x, y) = x^2 + y^2 found via hill climbing: """
							    F"""{local_min.score()}"""
							)




from collections.abc import Callable

__SCREAMING_SNAKE_CASE     =	Callable[[float], float]  # type alias for a real -> real function




def 						UpperCAmelCase (    _lowerCamelCase			,     _lowerCamelCase			,     _lowerCamelCase			,     ):
			A				:       int														=    float(_lowerCamelCase     )
			while True:
						try:
									A				:       Optional[int]														=    prev_guess - function(_lowerCamelCase     ) / derivative(_lowerCamelCase     )
						except ZeroDivisionError:
									raise ZeroDivisionError("Could not find root"     ) from None
						if abs(prev_guess - next_guess     ) < 10**-5:
									return next_guess
						A				:       Any														=    next_guess




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return (x**3) - (2 * x) - 5




def 						UpperCAmelCase (    _lowerCamelCase     ):
			return 3 * (x**2) - 2


if __name__ == "__main__":
							print(newton(f, fa, 3))