

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

import numpy
from matplotlib import pyplot

A_						:     Optional[Any]			  =				0.25 + 0.0J
A_						:     Union[str, Any]			  =				-0.4 + 0.6J
A_						:     List[Any]			  =				-0.1 + 0.651J
A_						:     Optional[Any]			  =				-2.0
A_						:     Tuple			  =				56
A_						:     Union[str, Any]			  =				2.0
A_						:     Optional[Any]			  =				666


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       numpy.ndarray:






    '''simple docstring'''
    return numpy.exp(SCREAMING_SNAKE_CASE ) + c_parameter


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       numpy.ndarray:






    '''simple docstring'''
    return z_values * z_values + c_parameter


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       numpy.ndarray:






    '''simple docstring'''
    __UpperCAmelCase			   =     numpy.linspace(-window_size    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )
    __UpperCAmelCase			   =     x.reshape((nb_pixels, 1) )
    __UpperCAmelCase			   =     numpy.linspace(-window_size    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )
    __UpperCAmelCase			   =     y.reshape((1, nb_pixels) )
    return x + 1.0j * y


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE = None    ,				) ->       numpy.ndarray:






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


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				) ->       None:






    '''simple docstring'''
    __UpperCAmelCase			   =     (abs(SCREAMING_SNAKE_CASE )).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    (				) ->       None:






    '''simple docstring'''
    warnings.filterwarnings(
        '''ignore'''    ,				category=SCREAMING_SNAKE_CASE    ,				message='''overflow encountered in multiply''' )
    warnings.filterwarnings(
        '''ignore'''    ,				category=SCREAMING_SNAKE_CASE    ,				message='''invalid value encountered in multiply'''    ,				)
    warnings.filterwarnings(
        '''ignore'''    ,				category=SCREAMING_SNAKE_CASE    ,				message='''overflow encountered in absolute''' )
    warnings.filterwarnings(
        '''ignore'''    ,				category=SCREAMING_SNAKE_CASE    ,				message='''overflow encountered in exp''' )


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

       ignore_overflow_warnings()  # See file header for explanations

       A_						:     Any			  =				24
       A_						:     Dict			  =				2 * abs(c_cauliflower) + 1
       A_						:     Optional[Any]			  =				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_						:     str			  =				64
       A_						:     Dict			  =				2 * abs(c_polynomial_a) + 1
       A_						:     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)

       A_						:     Any			  =				161
       A_						:     List[str]			  =				2 * abs(c_polynomial_a) + 1
       A_						:     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)

       A_						:     List[str]			  =				12
       A_						:     List[str]			  =				10000.0
       A_						:     Optional[int]			  =				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


def  __a    (				SCREAMING_SNAKE_CASE ) ->       list[int]:






    '''simple docstring'''
    if not list_of_ints:
        return []

    if min(SCREAMING_SNAKE_CASE ) < 0:
        raise ValueError('''All numbers must be positive''' )

    __UpperCAmelCase			   =     max(len(bin(SCREAMING_SNAKE_CASE )[2:] ) for x in list_of_ints )
    return _msd_radix_sort(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       list[int]:






    '''simple docstring'''
    if bit_position == 0 or len(SCREAMING_SNAKE_CASE ) in [0, 1]:
        return list_of_ints

    __UpperCAmelCase			   =     []
    __UpperCAmelCase			   =     []
    # Split numbers based on bit at bit_position from the right
    for number in list_of_ints:
        if (number >> (bit_position - 1)) & 1:
            # number has a one at bit bit_position
            ones.append(SCREAMING_SNAKE_CASE )
        else:
            # number has a zero at bit bit_position
            zeros.append(SCREAMING_SNAKE_CASE )

    # recursively split both lists further
    __UpperCAmelCase			   =     _msd_radix_sort(SCREAMING_SNAKE_CASE    ,				bit_position - 1 )
    __UpperCAmelCase			   =     _msd_radix_sort(SCREAMING_SNAKE_CASE    ,				bit_position - 1 )

    # recombine lists
    __UpperCAmelCase			   =     zeros
    res.extend(SCREAMING_SNAKE_CASE )

    return res


def  __a    (				SCREAMING_SNAKE_CASE ) ->       Optional[int]:






    '''simple docstring'''
    __UpperCAmelCase			   =     len(SCREAMING_SNAKE_CASE )
    if not list_of_ints or length == 1:
        return

    if min(SCREAMING_SNAKE_CASE ) < 0:
        raise ValueError('''All numbers must be positive''' )

    __UpperCAmelCase			   =     max(len(bin(SCREAMING_SNAKE_CASE )[2:] ) for x in list_of_ints )
    _msd_radix_sort_inplace(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				0    ,				SCREAMING_SNAKE_CASE )


def  __a    (				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE ) ->       int:






    '''simple docstring'''
    if bit_position == 0 or end_index - begin_index <= 1:
        return

    bit_position -= 1

    __UpperCAmelCase			   =     begin_index
    __UpperCAmelCase			   =     end_index - 1
    while i <= j:
        __UpperCAmelCase			   =     False
        if not (list_of_ints[i] >> bit_position) & 1:
            # found zero at the beginning
            i += 1
            __UpperCAmelCase			   =     True
        if (list_of_ints[j] >> bit_position) & 1:
            # found one at the end
            j -= 1
            __UpperCAmelCase			   =     True

        if changed:
            continue

        __UpperCAmelCase   ,       __UpperCAmelCase			   =     list_of_ints[j], list_of_ints[i]
        j -= 1
        if j != i:
            i += 1

    _msd_radix_sort_inplace(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )
    _msd_radix_sort_inplace(SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE    ,				SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
       import doctest

       doctest.testmod()




