

import colorsys

from PIL import Image  # type: ignore
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     int   ,      SCREAMING_SNAKE_CASE__      :     Optional[int]   ,      SCREAMING_SNAKE_CASE__      :     Any				)							->				float:





				'''simple docstring'''






				A__   				=       x
				A__   				=       y
				for step in range(_lowerCamelCase				):  # noqa: B007
								A__   				=       a * a - b * b + x
								A__   				=       2 * a * b + y
								A__   				=       a_new

								# divergence happens for all complex number with an absolute value
								# greater than 4
								if a * a + b * b > 4:
												break
				return step / (max_step - 1)
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Optional[Any]				)							->				tuple:





				'''simple docstring'''






				if distance == 1:
								return (0, 0, 0)
				else:
								return (255, 255, 255)
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     Union[str, Any]				)							->				tuple:





				'''simple docstring'''






				if distance == 1:
								return (0, 0, 0)
				else:
								return tuple(round(i * 255				) for i in colorsys.hsv_to_rgb(_lowerCamelCase   ,      1   ,      1				)				)
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     int = 800   ,      SCREAMING_SNAKE_CASE__      :     Dict = 600   ,      SCREAMING_SNAKE_CASE__      :     Optional[int] = -0.6   ,      SCREAMING_SNAKE_CASE__      :     Optional[Any] = 0   ,      SCREAMING_SNAKE_CASE__      :     Optional[int] = 3.2   ,      SCREAMING_SNAKE_CASE__      :     int = 50   ,      SCREAMING_SNAKE_CASE__      :     List[str] = True   ,      )							->				Image.Image:





				'''simple docstring'''






				A__   				=       Image.new('RGB'   ,      (image_width, image_height)				)
				A__   				=       img.load()

				# loop through the image-coordinates
				for image_x in range(_lowerCamelCase				):
								for image_y in range(_lowerCamelCase				):
												# determine the figure-coordinates based on the image-coordinates
												A__   				=       figure_width / image_width * image_height
												A__   				=       figure_center_x + (image_x / image_width - 0.5) * figure_width
												A__   				=       figure_center_y + (image_y / image_height - 0.5) * figure_height

												A__   				=       get_distance(_lowerCamelCase   ,      _lowerCamelCase   ,      _lowerCamelCase				)

												# color the corresponding pixel based on the selected coloring-function
												if use_distance_color_coding:
																A__   				=       get_color_coded_rgb(_lowerCamelCase				)
												else:
																A__   				=       get_black_and_white_rgb(_lowerCamelCase				)

				return img


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# colored version, full figure
					lowercase_			=  get_image()

					# uncomment for colored version, different section, zoomed in
					# img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
					# figure_width = 0.8)

					# uncomment for black and white version, full figure
					# img = get_image(use_distance_color_coding = False)

					# uncomment to save the image
					# img.save("mandelbrot.png")

					img.show()




import random
def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     str				)							->				tuple:





    '''simple docstring'''






    A__				,						A__				,						A__   				=       [], [], []
    for element in data:
        if element < pivot:
            less.append(SCREAMING_SNAKE_CASE__				)
        elif element > pivot:
            greater.append(SCREAMING_SNAKE_CASE__				)
        else:
            equal.append(SCREAMING_SNAKE_CASE__				)
    return less, equal, greater

def 						_snake_case(   SCREAMING_SNAKE_CASE__      :     list   ,      SCREAMING_SNAKE_CASE__      :     int				)							->				str:





    '''simple docstring'''






    if index >= len(SCREAMING_SNAKE_CASE__				) or index < 0:
        return None

    A__   				=       items[random.randint(0   ,      len(SCREAMING_SNAKE_CASE__				) - 1				)]
    A__   				=       0
    A__				,						A__				,						A__   				=       _partition(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)
    A__   				=       len(SCREAMING_SNAKE_CASE__				)

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      SCREAMING_SNAKE_CASE__				)
    # must be in larger
    else:
        return quick_select(SCREAMING_SNAKE_CASE__   ,      index - (m + count)				)

