
"""simple docstring"""


import math




class    __lowerCamelCase     :




				def __init__(							self       ,	UpperCAmelCase       ,	UpperCAmelCase       ,	UpperCAmelCase       ,	UpperCAmelCase      ):
							lowerCamelCase_ 		=     x
							lowerCamelCase_ 		=     y
							lowerCamelCase_ 		=     step_size
							lowerCamelCase_ 		=     function_to_optimize




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




				def 					UpperCAmelCase__	(							self      ):
							lowerCamelCase_ 		=     self.step_size
							return [
							    SearchProblem(UpperCAmelCase       ,	UpperCAmelCase       ,	UpperCAmelCase       ,	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      ):
							return hash(str(self      )      )




				def __eq__(							self       ,	UpperCAmelCase      ):
							if isinstance(UpperCAmelCase       ,	UpperCAmelCase      ):
										return hash(str(self      )      ) == hash(str(UpperCAmelCase      )      )
							return False





				def __str__(							self      ):
							return f"x: {self.x} y: {self.y}"






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__ = True  ,lowerCAmelCase__ = math.inf  ,lowerCAmelCase__ = -math.inf  ,lowerCAmelCase__ = math.inf  ,lowerCAmelCase__ = -math.inf  ,lowerCAmelCase__ = False  ,lowerCAmelCase__ = 10_000  ,):
			lowerCamelCase_ 		=     search_prob
			lowerCamelCase_ 		=     []  # list to store the current score at each iteration
			lowerCamelCase_ 		=     0
			lowerCamelCase_ 		=     False
			lowerCamelCase_ 		=     set()
			while not solution_found and iterations < max_iter:
						visited.add(lowerCAmelCase__	)
						iterations += 1
						lowerCamelCase_ 		=     current_state.score()
						scores.append(lowerCAmelCase__	)
						lowerCamelCase_ 		=     current_state.get_neighbors()
						lowerCamelCase_ 		=     -math.inf
						lowerCamelCase_ 		=     math.inf
						lowerCamelCase_ 		=     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
									lowerCamelCase_ 		=     neighbor.score() - current_score
									if find_max:  # finding max
												# going to direction with greatest ascent
												if change > max_change and change > 0:
															lowerCamelCase_ 		=     change
															lowerCamelCase_ 		=     neighbor
									else:  # finding min
												# to direction with greatest descent
												if change < min_change and change < 0:
															lowerCamelCase_ 		=     change
															lowerCamelCase_ 		=     neighbor
						if next_state is not None:
									# we found at least one neighbor which improved the current state
									lowerCamelCase_ 		=     next_state
						else:
									# since we have no neighbor that improves the solution we stop the search
									lowerCamelCase_ 		=     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    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__	):
									return (x**2) + (y**2)

						# starting the problem with initial coordinates (3, 4)
						A_						       =				SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						A_						       =				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)
						A_						       =				SearchProblem(x=12, y=47, step_size=1, function_to_optimize=test_fa)
						A_						       =				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    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__	):
									return (3 * x**2) - (6 * y)

						A_						       =				SearchProblem(x=3, y=4, step_size=1, function_to_optimize=test_fa)
						A_						       =				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()}"
						)





"""simple docstring"""


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

import numpy
from matplotlib import pyplot

A_						       =				0.25 + 0.0J
A_						       =				-0.4 + 0.6J
A_						       =				-0.1 + 0.651J
A_						       =				-2.0
A_						       =				56
A_						       =				2.0
A_						       =				666






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__	):
			return numpy.exp(lowerCAmelCase__	) + c_parameter






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__	):
			return z_values * z_values + c_parameter






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__	):
			lowerCamelCase_ 		=     numpy.linspace(-window_size  ,lowerCAmelCase__  ,lowerCAmelCase__	)
			lowerCamelCase_ 		=     x.reshape((nb_pixels, 1)	)
			lowerCamelCase_ 		=     numpy.linspace(-window_size  ,lowerCAmelCase__  ,lowerCAmelCase__	)
			lowerCamelCase_ 		=     y.reshape((1, nb_pixels)	)
			return x + 1.0J * y






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__ = None  ,):
			lowerCamelCase_ 		=     z_a.astype('''complex64'''	)
			for _ in range(lowerCAmelCase__	):
						lowerCamelCase_ 		=     eval_function(lowerCAmelCase__  ,lowerCAmelCase__	)
						if infinity is not None:
									numpy.nan_to_num(lowerCAmelCase__  ,copy=lowerCAmelCase__  ,nan=lowerCAmelCase__	)
									lowerCamelCase_ 		=     infinity
			return z_n






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,):
			lowerCamelCase_ 		=     (abs(lowerCAmelCase__	)).transpose()
			lowerCamelCase_ 		=     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    lowercase	(  ):
			warnings.filterwarnings(
			    '''ignore'''  ,category=lowerCAmelCase__  ,message='''overflow encountered in multiply'''	)
			warnings.filterwarnings(
			    '''ignore'''  ,category=lowerCAmelCase__  ,message='''invalid value encountered in multiply'''  ,)
			warnings.filterwarnings(
			    '''ignore'''  ,category=lowerCAmelCase__  ,message='''overflow encountered in absolute'''	)
			warnings.filterwarnings(
			    '''ignore'''  ,category=lowerCAmelCase__  ,message='''overflow encountered in exp'''	)


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

						ignore_overflow_warnings()  # See file header for explanations

						A_						       =				24
						A_						       =				2 * abs(c_cauliflower) + 1
						A_						       =				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)

						A_						       =				64
						A_						       =				2 * abs(c_polynomial_a) + 1
						A_						       =				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)

						A_						       =				161
						A_						       =				2 * abs(c_polynomial_a) + 1
						A_						       =				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)

						A_						       =				12
						A_						       =				10000.0
						A_						       =				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)



