


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

import numpy
from matplotlib import pyplot

__lowerCAmelCase     :			int      =0.2_5 + 0.0j
__lowerCAmelCase     :			List[Any]      =-0.4 + 0.6j
__lowerCAmelCase     :			Any      =-0.1 + 0.651j
__lowerCAmelCase     :			Any      =-2.0
__lowerCAmelCase     :			Union[str, Any]      =5_6
__lowerCAmelCase     :			List[str]      =2.0
__lowerCAmelCase     :			Optional[Any]      =6_6_6


def 	_UpperCamelCase							(				lowercase__   ,	lowercase__				):
						return numpy.exp(__UpperCamelCase				) + c_parameter


def 	_UpperCamelCase							(				lowercase__   ,	lowercase__				):
						return z_values * z_values + c_parameter


def 	_UpperCamelCase							(				lowercase__   ,	lowercase__				):
						__SCREAMING_SNAKE_CASE						:					Union[str, Any]		      =		numpy.linspace(-window_size   ,	__UpperCamelCase   ,	__UpperCamelCase				)
						__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		x.reshape((nb_pixels, 1)				)
						__SCREAMING_SNAKE_CASE						:					Any		      =		numpy.linspace(-window_size   ,	__UpperCamelCase   ,	__UpperCamelCase				)
						__SCREAMING_SNAKE_CASE						:					Dict		      =		y.reshape((1, nb_pixels)				)
						return x + 1.0J * y


def 	_UpperCamelCase							(				lowercase__   ,	lowercase__   ,	lowercase__   ,	lowercase__   ,	lowercase__ = None   ,	):
						__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		z_a.astype('''complex64'''				)
						for _ in range(__UpperCamelCase				):
												__SCREAMING_SNAKE_CASE						:					int		      =		eval_function(__UpperCamelCase   ,	__UpperCamelCase				)
												if infinity is not None:
																		numpy.nan_to_num(__UpperCamelCase   ,	copy=__UpperCamelCase   ,	nan=__UpperCamelCase				)
																		__SCREAMING_SNAKE_CASE						:					Any		      =		infinity
						return z_n


def 	_UpperCamelCase							(				lowercase__   ,	lowercase__   ,	lowercase__   ,	lowercase__   ,	):
						__SCREAMING_SNAKE_CASE						:					Dict		      =		(abs(__UpperCamelCase				)).transpose()
						__SCREAMING_SNAKE_CASE						:					Optional[Any]		      =		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 	_UpperCamelCase							(				):
						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__":
						__lowerCAmelCase     :			Tuple      =prepare_grid(window_size, nb_pixels)

						ignore_overflow_warnings()  # See file header for explanations

						__lowerCAmelCase     :			Tuple      =2_4
						__lowerCAmelCase     :			Union[str, Any]      =2 * abs(c_cauliflower) + 1
						__lowerCAmelCase     :			Optional[int]      =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)

						__lowerCAmelCase     :			Dict      =6_4
						__lowerCAmelCase     :			Optional[Any]      =2 * abs(c_polynomial_a) + 1
						__lowerCAmelCase     :			Dict      =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)

						__lowerCAmelCase     :			Tuple      =1_6_1
						__lowerCAmelCase     :			Union[str, Any]      =2 * abs(c_polynomial_a) + 1
						__lowerCAmelCase     :			List[Any]      =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)

						__lowerCAmelCase     :			Optional[Any]      =1_2
						__lowerCAmelCase     :			Any      =1_0_0_0_0.0
						__lowerCAmelCase     :			Dict      =iterate_function(
						    eval_exponential,
						    c_exponential,
						    nb_iterations,
						    z_a + 2,
						    infinity=1.0e1_0,
						)
						show_results('e^z+c', c_exponential, escape_radius, z_final)




from .number_theory.prime_numbers import next_prime
class 	_lowercase				:






				'''simple docstring'''



				def __init__(	self      :Tuple      ,      lowerCAmelCase__      :int      ,      lowerCAmelCase__      :int | None = None      ,      lowerCAmelCase__      :float | None = None      ,      )		->      None:
										__SCREAMING_SNAKE_CASE						:					Tuple		      =		size_table
										__SCREAMING_SNAKE_CASE						:					Dict		      =		[None] * self.size_table
										__SCREAMING_SNAKE_CASE						:					List[Any]		      =		0.75 if lim_charge is None else lim_charge
										__SCREAMING_SNAKE_CASE						:					Tuple		      =		1 if charge_factor is None else charge_factor
										__SCREAMING_SNAKE_CASE						:					list		      =		[]
										__SCREAMING_SNAKE_CASE						:					dict		      =		{}


				def 		__magic_name__(	self      :List[Any]     )		->      Tuple:
										return self._keys


				def 		__magic_name__(	self      :Any     )		->      Dict:
										return sum(1 for slot in self.values if slot is not None     ) / (
										    self.size_table * self.charge_factor
										)


				def 		__magic_name__(	self      :Optional[Any]      ,      lowerCAmelCase__      :Union[str, Any]     )		->      Optional[Any]:
										return key % self.size_table


				def 		__magic_name__(	self      :int      ,      lowerCAmelCase__      :Union[str, Any]     )		->      List[Any]:
										print(f'''step {step_ord}'''     )
										print(list(range(len(self.values     )     )     )     )
										print(self.values     )


				def 		__magic_name__(	self      :List[str]      ,      lowerCAmelCase__      :Optional[Any]     )		->      Dict:
										__SCREAMING_SNAKE_CASE						:					List[Any]		      =		1
										__SCREAMING_SNAKE_CASE						:					Optional[Any]		      =		values
										for value in values:
																self.insert_data(lowerCAmelCase__     )
																self._step_by_step(lowerCAmelCase__     )
																i += 1


				def 		__magic_name__(	self      :Tuple      ,      lowerCAmelCase__      :List[Any]      ,      lowerCAmelCase__      :Union[str, Any]     )		->      str:
										__SCREAMING_SNAKE_CASE						:					Tuple		      =		data
										__SCREAMING_SNAKE_CASE						:					Any		      =		data


				def 		__magic_name__(	self      :Optional[int]      ,      lowerCAmelCase__      :Any      ,      lowerCAmelCase__      :List[str]=None     )		->      int:
										__SCREAMING_SNAKE_CASE						:					Tuple		      =		self.hash_function(key + 1     )

										while self.values[new_key] is not None and self.values[new_key] != key:
																if self.values.count(lowerCAmelCase__     ) > 0:
																						__SCREAMING_SNAKE_CASE						:					Optional[Any]		      =		self.hash_function(new_key + 1     )
																else:
																						__SCREAMING_SNAKE_CASE						:					int		      =		None
																						break

										return new_key


				def 		__magic_name__(	self      :Optional[int]     )		->      Union[str, Any]:
										__SCREAMING_SNAKE_CASE						:					str		      =		[value for value in self.values if value is not None]
										__SCREAMING_SNAKE_CASE						:					Optional[int]		      =		next_prime(self.size_table      ,      factor=2     )
										self._keys.clear()
										__SCREAMING_SNAKE_CASE						:					Optional[Any]		      =		[None] * self.size_table  # hell's pointers D: don't DRY ;/
										for value in survivor_values:
																self.insert_data(lowerCAmelCase__     )



				def 		__magic_name__(	self      :Tuple      ,      lowerCAmelCase__      :str     )		->      Dict:
										__SCREAMING_SNAKE_CASE						:					Union[str, Any]		      =		self.hash_function(lowerCAmelCase__     )

										if self.values[key] is None:
																self._set_value(lowerCAmelCase__      ,      lowerCAmelCase__     )

										elif self.values[key] == data:
																pass

										else:
																__SCREAMING_SNAKE_CASE						:					Tuple		      =		self._collision_resolution(lowerCAmelCase__      ,      lowerCAmelCase__     )
																if collision_resolution is not None:
																						self._set_value(lowerCAmelCase__      ,      lowerCAmelCase__     )
																else:
																						self.rehashing()
																						self.insert_data(lowerCAmelCase__     )
