


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

import numpy
from matplotlib import pyplot

UpperCAmelCase      :						Tuple    =		0.2_5 + 0.0J
UpperCAmelCase      :						List[str]    =		-0.4 + 0.6J
UpperCAmelCase      :						Dict    =		-0.1 + 0.6_51J
UpperCAmelCase      :						Dict    =		-2.0
UpperCAmelCase      :						Union[str, Any]    =		56
UpperCAmelCase      :						Union[str, Any]    =		2.0
UpperCAmelCase      :						List[Any]    =		6_66






def   __lowerCamelCase	(       lowerCamelCase__		:	complex     ,       lowerCamelCase__		:	numpy.ndarray			):





			'''simple docstring'''




			return numpy.exp(lowerCamelCase__			) + c_parameter






def   __lowerCamelCase	(       lowerCamelCase__		:	complex     ,       lowerCamelCase__		:	numpy.ndarray			):





			'''simple docstring'''




			return z_values * z_values + c_parameter






def   __lowerCamelCase	(       lowerCamelCase__		:	float     ,       lowerCamelCase__		:	int			):





			'''simple docstring'''




			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   __lowerCamelCase	(       lowerCamelCase__		:	Callable[[Any, numpy.ndarray], numpy.ndarray]     ,       lowerCamelCase__		:	Any     ,       lowerCamelCase__		:	int     ,       lowerCamelCase__		:	numpy.ndarray     ,       lowerCamelCase__		:	float | None = None     ,       ):





			'''simple docstring'''




			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   __lowerCamelCase	(       lowerCamelCase__		:	str     ,       lowerCamelCase__		:	Any     ,       lowerCamelCase__		:	float     ,       lowerCamelCase__		:	numpy.ndarray     ,       ):





			'''simple docstring'''




			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   __lowerCamelCase	(       ):





			'''simple docstring'''




			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__":
		UpperCAmelCase      :						List[str]    =		prepare_grid(window_size, nb_pixels)

		ignore_overflow_warnings()  # See file header for explanations

		UpperCAmelCase      :						Dict    =		24
		UpperCAmelCase      :						Dict    =		2 * abs(c_cauliflower) + 1
		UpperCAmelCase      :						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)

		UpperCAmelCase      :						Tuple    =		64
		UpperCAmelCase      :						str    =		2 * abs(c_polynomial_a) + 1
		UpperCAmelCase      :						List[str]    =		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)

		UpperCAmelCase      :						List[Any]    =		1_61
		UpperCAmelCase      :						Dict    =		2 * abs(c_polynomial_a) + 1
		UpperCAmelCase      :						Optional[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)

		UpperCAmelCase      :						Union[str, Any]    =		12
		UpperCAmelCase      :						Optional[int]    =		1_0_0_0_0.0
		UpperCAmelCase      :						Tuple    =		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)





from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

UpperCAmelCase      :						List[str]    =		TypeVar("T")
UpperCAmelCase      :						Dict    =		TypeVar("U")







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		def __init__(   self		,			A		,			A  )     ->   Any:







					'''simple docstring'''







					lowerCamelCase								=     key
					lowerCamelCase								=     val
					lowerCamelCase								=     0
					lowerCamelCase								=     None
					lowerCamelCase								=     None







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					return "Node: key: {}, val: {}, freq: {}, has next: {}, has prev: {}".format(
					    self.key		,			self.val		,			self.freq		,			self.next is not None		,			self.prev is not None  )







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		def __init__(   self  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
					lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
					lowerCamelCase		,		lowerCamelCase								=     self.rear, self.head







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					lowerCamelCase								=     ["""DoubleLinkedList"""]
					lowerCamelCase								=     self.head
					while node.next is not None:
								rep.append(str(A  )  )
								lowerCamelCase								=     node.next
					rep.append(str(self.rear  )  )
					return ",\n    ".join(A  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					lowerCamelCase								=     self.rear.prev

					# All nodes other than self.head are guaranteed to have non-None previous
					assert previous is not None

					lowerCamelCase								=     node
					lowerCamelCase								=     previous
					lowerCamelCase								=     node
					lowerCamelCase								=     self.rear
					node.freq += 1
					self._position_node(A  )







		def 				__A      (   self		,			A  )     ->   None:







					'''simple docstring'''







					while node.prev is not None and node.prev.freq > node.freq:
								# swap node with previous node
								lowerCamelCase								=     node.prev

								lowerCamelCase								=     previous_node.prev
								lowerCamelCase								=     node.prev
								lowerCamelCase								=     previous_node
								lowerCamelCase								=     node







		def 				__A      (   self		,			A  )     ->   DoubleLinkedListNode[T, U] | None:







					'''simple docstring'''







					if node.prev is None or node.next is None:
								return None

					lowerCamelCase								=     node.next
					lowerCamelCase								=     node.prev
					lowerCamelCase								=     None
					lowerCamelCase								=     None
					return node







class 					__lowercase					(       Generic[T, U]     ):



		"""simple docstring"""

		UpperCamelCase    :				dict[Callable[[T], U], LFUCache[T, U]] 					=		{}







		def __init__(   self		,			A  )     ->   Union[str, Any]:







					'''simple docstring'''







					lowerCamelCase								=     DoubleLinkedList()
					lowerCamelCase								=     capacity
					lowerCamelCase								=     0
					lowerCamelCase								=     0
					lowerCamelCase								=     0
					lowerCamelCase								=     {}







		def __repr__(   self  )     ->   str:







					'''simple docstring'''







					return (
					    F'CacheInfo(hits={self.hits}, misses={self.miss}, '
					    F'capacity={self.capacity}, current_size={self.num_keys})'
					)







		def __contains__(   self		,			A  )     ->   bool:







					'''simple docstring'''







					return key in self.cache







		def 				__A      (   self		,			A  )     ->   U | None:







					'''simple docstring'''







					if key in self.cache:
								self.hits += 1
								lowerCamelCase								=     self.cache[key]
								lowerCamelCase								=     self.list.remove(self.cache[key]  )
								assert node == value_node

								# node is guaranteed not None because it is in self.cache
								assert node is not None
								self.list.add(A  )
								return node.val
					self.miss += 1
					return None







		def 				__A      (   self		,			A		,			A  )     ->   None:







					'''simple docstring'''







					if key not in self.cache:
								if self.num_keys >= self.capacity:
											# delete first node when over capacity
											lowerCamelCase								=     self.list.head.next

											# guaranteed to have a non-None first node when num_keys > 0
											# explain to type checker via assertions
											assert first_node is not None
											assert first_node.key is not None
											assert self.list.remove(A  ) is not None
											# first_node guaranteed to be in list

											del self.cache[first_node.key]
											self.num_keys -= 1
								lowerCamelCase								=     DoubleLinkedListNode(A		,			A  )
								self.list.add(self.cache[key]  )
								self.num_keys += 1

					else:
								lowerCamelCase								=     self.list.remove(self.cache[key]  )
								assert node is not None  # node guaranteed to be in list
								lowerCamelCase								=     value
								self.list.add(A  )







		@classmethod
		def 				__A      (   cls		,			A = 1_28  )     ->   Callable[[Callable[[T], U]], Callable[..., U]]:







					'''simple docstring'''







					def cache_decorator_inner(A  ) -> Callable[..., U]:
								def cache_decorator_wrapper(*A  ) -> U:
											if func not in cls.decorator_function_to_instance_map:
														lowerCamelCase								=     LFUCache(A  )

											lowerCamelCase								=     cls.decorator_function_to_instance_map[func].get(args[0]  )
											if result is None:
														lowerCamelCase								=     func(*A  )
														cls.decorator_function_to_instance_map[func].put(args[0]		,			A  )
											return result

								def cache_info() -> LFUCache[T, U]:
											return cls.decorator_function_to_instance_map[func]

								setattr(A		,			"""cache_info"""		,			A  )  # noqa: B010

								return cache_decorator_wrapper

					return cache_decorator_inner


if __name__ == "__main__":
		import doctest

		doctest.testmod()

