






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 __A   (				__lowerCAmelCase			,		__lowerCAmelCase     )->  Dict:





						"""simple docstring"""



						return numpy.exp(_A     ) + c_parameter


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase     )->  Tuple:





						"""simple docstring"""



						return z_values * z_values + c_parameter


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase     )->  Union[str, Any]:





						"""simple docstring"""



						_UpperCAmelCase     =      numpy.linspace(-window_size			,		_A			,		_A     )
						_UpperCAmelCase     =      x.reshape((nb_pixels, 1)     )
						_UpperCAmelCase     =      numpy.linspace(-window_size			,		_A			,		_A     )
						_UpperCAmelCase     =      y.reshape((1, nb_pixels)     )
						return x + 1.0j * y


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase = None			,		)->  int:





						"""simple docstring"""



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


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		)->  Dict:





						"""simple docstring"""



						_UpperCAmelCase     =      (abs(_A     )).transpose()
						_UpperCAmelCase     =      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   (				)->  Dict:





						"""simple docstring"""



						warnings.filterwarnings(
						    'ignore'			,		category=_A			,		message='overflow encountered in multiply'     )
						warnings.filterwarnings(
						    'ignore'			,		category=_A			,		message='invalid value encountered in multiply'			,		)
						warnings.filterwarnings(
						    'ignore'			,		category=_A			,		message='overflow encountered in absolute'     )
						warnings.filterwarnings(
						    'ignore'			,		category=_A			,		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				     =  1_00_00.0
	_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)








from __future__ import annotations

_a				     =  [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]





class __lowerCamelCase			:





	"""simple docstring"""






	def __init__(							self	,   UpperCAmelCase   ):
							"""simple docstring"""







							_UpperCAmelCase     =      -1
							_UpperCAmelCase     =      -1
							_UpperCAmelCase     =      [-1] * length
							_UpperCAmelCase     =      None
							_UpperCAmelCase     =      None

	def __repr__(							self   ):
							"""simple docstring"""







							return F"""Node(min_value={self.minn} max_value={self.maxx})"""



def __A   (				__lowerCAmelCase     )->  Node | None:





						"""simple docstring"""



						_UpperCAmelCase     =      Node(len(__lowerCAmelCase     )     )
						_UpperCAmelCase ,			_UpperCAmelCase     =      min(__lowerCAmelCase     ), max(__lowerCAmelCase     )
						# Leaf node case where the node contains only one unique value
						if root.minn == root.maxx:
												return root
						_UpperCAmelCase     =      (root.minn + root.maxx) // 2

						_UpperCAmelCase     =      []
						_UpperCAmelCase     =      []

						for index, num in enumerate(__lowerCAmelCase     ):
												if num <= pivot:
																		left_arr.append(__lowerCAmelCase     )
												else:
																		right_arr.append(__lowerCAmelCase     )
												_UpperCAmelCase     =      len(__lowerCAmelCase     )
						_UpperCAmelCase     =      build_tree(__lowerCAmelCase     )
						_UpperCAmelCase     =      build_tree(__lowerCAmelCase     )
						return root


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase     )->  int:





						"""simple docstring"""



						if index < 0 or node is None:
												return 0
						# Leaf node cases
						if node.minn == node.maxx:
												return index + 1 if node.minn == num else 0
						_UpperCAmelCase     =      (node.minn + node.maxx) // 2
						if num <= pivot:
												# go the left subtree and map index to the left subtree
												return rank_till_index(node.left			,		__lowerCAmelCase			,		node.map_left[index] - 1     )
						else:
												# go to the right subtree and map index to the right subtree
												return rank_till_index(node.right			,		__lowerCAmelCase			,		index - node.map_left[index]     )


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase     )->  int:





						"""simple docstring"""



						if start > end:
												return 0
						_UpperCAmelCase     =      rank_till_index(__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase     )
						_UpperCAmelCase     =      rank_till_index(__lowerCAmelCase			,		__lowerCAmelCase			,		start - 1     )
						return rank_till_end - rank_before_start


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase     )->  int:





						"""simple docstring"""



						if index > (end - start) or start > end or node is None:
												return -1
						# Leaf node case
						if node.minn == node.maxx:
												return node.minn
						# Number of elements in the left subtree in interval [start, end]
						_UpperCAmelCase     =      node.map_left[end] - (
						    node.map_left[start - 1] if start else 0
						)
						if num_elements_in_left_tree > index:
												return quantile(
												    node.left			,		__lowerCAmelCase			,		(node.map_left[start - 1] if start else 0)			,		node.map_left[end] - 1			,		)
						else:
												return quantile(
												    node.right			,		index - num_elements_in_left_tree			,		start - (node.map_left[start - 1] if start else 0)			,		end - node.map_left[end]			,		)


def __A   (				__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase			,		__lowerCAmelCase     )->  int:





						"""simple docstring"""



						if (
						    start > end
						    or node is None
						    or start_num > end_num
						    or node.minn > end_num
						    or node.maxx < start_num
						):
												return 0
						if start_num <= node.minn and node.maxx <= end_num:
												return end - start + 1
						_UpperCAmelCase     =      range_counting(
						    node.left			,		(node.map_left[start - 1] if start else 0)			,		node.map_left[end] - 1			,		__lowerCAmelCase			,		__lowerCAmelCase			,		)
						_UpperCAmelCase     =      range_counting(
						    node.right			,		start - (node.map_left[start - 1] if start else 0)			,		end - node.map_left[end]			,		__lowerCAmelCase			,		__lowerCAmelCase			,		)
						return left + right


if __name__ == "__main__":
		import doctest

		doctest.testmod()
