


"""simple docstring"""






import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

lowercase  		=			0.2_5 + 0.0J
lowercase  		=			-0.4 + 0.6J
lowercase  		=			-0.1 + 0.651J
lowercase  		=			-2.0
lowercase  		=			56
lowercase  		=			2.0
lowercase  		=			666



def 			A__		(					_UpperCAmelCase    :      complex				,    _UpperCAmelCase    :      numpy.ndarray	)							->	numpy.ndarray:

	'''simple docstring'''


	return numpy.exp(_UpperCAmelCase	) + c_parameter



def 			A__		(					_UpperCAmelCase    :      complex				,    _UpperCAmelCase    :      numpy.ndarray	)							->	numpy.ndarray:

	'''simple docstring'''


	return z_values * z_values + c_parameter



def 			A__		(					_UpperCAmelCase    :      float				,    _UpperCAmelCase    :      int	)							->	numpy.ndarray:

	'''simple docstring'''


	snake_case__  :						Tuple		=      numpy.linspace(-window_size				,    _UpperCAmelCase				,    _UpperCAmelCase	)
	snake_case__  :						int		=      x.reshape((nb_pixels, 1)	)
	snake_case__  :						Union[str, Any]		=      numpy.linspace(-window_size				,    _UpperCAmelCase				,    _UpperCAmelCase	)
	snake_case__  :						Optional[int]		=      y.reshape((1, nb_pixels)	)
	return x + 1.0J * y



def 			A__		(					_UpperCAmelCase    :      Callable[[Any, numpy.ndarray], numpy.ndarray]				,    _UpperCAmelCase    :      Any				,    _UpperCAmelCase    :      int				,    _UpperCAmelCase    :      numpy.ndarray				,    _UpperCAmelCase    :      float | None = None				,    )							->	numpy.ndarray:

	'''simple docstring'''


	snake_case__  :						Optional[int]		=      z_a.astype("complex64"	)
	for _ in range(_UpperCAmelCase	):
		snake_case__  :						List[Any]		=      eval_function(_UpperCAmelCase				,    _UpperCAmelCase	)
		if infinity is not None:
			numpy.nan_to_num(_UpperCAmelCase				,    copy=_UpperCAmelCase				,    nan=_UpperCAmelCase	)
			snake_case__  :						Any		=      infinity
	return z_n



def 			A__		(					_UpperCAmelCase    :      str				,    _UpperCAmelCase    :      Any				,    _UpperCAmelCase    :      float				,    _UpperCAmelCase    :      numpy.ndarray				,    )							->	None:

	'''simple docstring'''


	snake_case__  :						int		=      (abs(_UpperCAmelCase	)).transpose()
	snake_case__  :						Tuple		=      abs_z_final[::-1, :]
	pyplot.matshow(abs_z_final < escape_radius	)
	pyplot.title(F"""Julia set of ${function_label}$, $c={function_params}$"""	)
	pyplot.show()



def 			A__		(					)							->	None:

	'''simple docstring'''


	warnings.filterwarnings(
	    "ignore"				,    category=_UpperCAmelCase				,    message="overflow encountered in multiply"	)
	warnings.filterwarnings(
	    "ignore"				,    category=_UpperCAmelCase				,    message="invalid value encountered in multiply"				,    )
	warnings.filterwarnings(
	    "ignore"				,    category=_UpperCAmelCase				,    message="overflow encountered in absolute"	)
	warnings.filterwarnings(
	    "ignore"				,    category=_UpperCAmelCase				,    message="overflow encountered in exp"	)


if __name__ == "__main__":
					lowercase  		=			prepare_grid(window_size, nb_pixels)

					ignore_overflow_warnings()  # See file header for explanations

					lowercase  		=			24
					lowercase  		=			2 * abs(c_cauliflower) + 1
					lowercase  		=			iterate_function(
					    eval_quadratic_polynomial,
					    c_cauliflower,
					    nb_iterations,
					    z_a,
					    infinity=1.1 * escape_radius,
					)
					show_results("""z^2+c""", c_cauliflower, escape_radius, z_final)

					lowercase  		=			64
					lowercase  		=			2 * abs(c_polynomial_a) + 1
					lowercase  		=			iterate_function(
					    eval_quadratic_polynomial,
					    c_polynomial_a,
					    nb_iterations,
					    z_a,
					    infinity=1.1 * escape_radius,
					)
					show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

					lowercase  		=			161
					lowercase  		=			2 * abs(c_polynomial_a) + 1
					lowercase  		=			iterate_function(
					    eval_quadratic_polynomial,
					    c_polynomial_a,
					    nb_iterations,
					    z_a,
					    infinity=1.1 * escape_radius,
					)
					show_results("""z^2+c""", c_polynomial_a, escape_radius, z_final)

					lowercase  		=			12
					lowercase  		=			1_0_0_0_0.0
					lowercase  		=			iterate_function(
					    eval_exponential,
					    c_exponential,
					    nb_iterations,
					    z_a + 2,
					    infinity=1.0e10,
					)
					show_results("""e^z+c""", c_exponential, escape_radius, z_final)











import math


class  lowerCamelCase     :






			'''simple docstring'''





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

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

			def 				UpperCAmelCase__							(			self      : Dict	)    -> Any:
								__magic_name__				:						Optional[int]     				=				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      : Dict	)    -> Tuple:
								return hash(str(self	)	)

			def __eq__(			self      : List[str]							,    lowerCamelCase_      : Dict	)    -> Union[str, Any]:
								if isinstance(lowerCamelCase_							,    lowerCamelCase_	):
													return hash(str(self	)	) == hash(str(lowerCamelCase_	)	)
								return False


			def __str__(			self      : Tuple	)    -> Tuple:
								return F'''x: {self.x} y: {self.y}'''







def 		lowercase__ (		__A:						int				,__A:						bool = True				,__A:						float = math.inf				,__A:						float = -math.inf				,__A:						float = math.inf				,__A:						float = -math.inf				,__A:						bool = False				,__A:						int = 1_0_0_0_0				,):





					'''simple docstring'''






					__magic_name__				:						Union[str, Any]     				=				search_prob
					__magic_name__				:						int     				=				[]  # list to store the current score at each iteration
					__magic_name__				:						Any     				=				0
					__magic_name__				:						Optional[Any]     				=				False
					__magic_name__				:						Dict     				=				set()
					while not solution_found and iterations < max_iter:
										visited.add(__A					)
										iterations += 1
										__magic_name__				:						int     				=				current_state.score()
										scores.append(__A					)
										__magic_name__				:						Union[str, Any]     				=				current_state.get_neighbors()
										__magic_name__				:						str     				=				-math.inf
										__magic_name__				:						Optional[Any]     				=				math.inf
										__magic_name__				:						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
															__magic_name__				:						Tuple     				=				neighbor.score() - current_score
															if find_max:  # finding max
																				# going to direction with greatest ascent
																				if change > max_change and change > 0:
																									__magic_name__				:						List[str]     				=				change
																									__magic_name__				:						List[str]     				=				neighbor
															else:  # finding min
																				# to direction with greatest descent
																				if change < min_change and change < 0:
																									__magic_name__				:						List[Any]     				=				change
																									__magic_name__				:						Optional[int]     				=				neighbor
										if next_state is not None:
															# we found at least one neighbor which improved the current state
															__magic_name__				:						Any     				=				next_state
										else:
															# since we have no neighbor that improves the solution we stop the search
															__magic_name__				:						List[str]     				=				True

					if visualization:
										from matplotlib import pyplot as plt

										plt.plot(range(__A					)				,__A					)
										plt.xlabel('''Iterations'''					)
										plt.ylabel('''Function values'''					)
										plt.show()

					return current_state


if __name__ == "__main__":
	import doctest

	doctest.testmod()







	def 		lowercase__ (		__A:						Optional[Any]				,__A:						str					):





						'''simple docstring'''






						return (x**2) + (y**2)

	# starting the problem with initial coordinates (3, 4)
	__lowerCamelCase :    Any      						=      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Any      						=      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)
	__lowerCamelCase :    Optional[int]      						=      SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Union[str, Any]      						=      hill_climbing(
	    prob, find_max=False, max_x=1_00, 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 		lowercase__ (		__A:						List[Any]				,__A:						int					):





						'''simple docstring'''






						return (3 * x**2) - (6 * y)

	__lowerCamelCase :    List[str]      						=      SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
	__lowerCamelCase :    Optional[int]      						=      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()}"""
	)



