

'''simple docstring'''

import colorsys

from PIL import Image  # type: ignore







def  a__    (    lowercase :					float, lowercase :					float, lowercase :					int				)		->		float:





     """simple docstring"""

     _UpperCamelCase       =	x
     _UpperCamelCase       =	y
     for step in range(lowercase				):  # noqa: B007
          _UpperCamelCase       =	a * a - b * b + x
          _UpperCamelCase       =	2 * a * b + y
          _UpperCamelCase       =	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  a__    (    lowercase :					float				)		->		tuple:





     """simple docstring"""

     if distance == 1:
          return (0, 0, 0)
     else:
          return (255, 255, 255)







def  a__    (    lowercase :					float				)		->		tuple:





     """simple docstring"""

     if distance == 1:
          return (0, 0, 0)
     else:
          return tuple(round(i * 255				) for i in colorsys.hsv_to_rgb(lowercase, 1, 1				)				)







def  a__    (    lowercase :					int = 800, lowercase :					int = 600, lowercase :					float = -0.6, lowercase :					float = 0, lowercase :					float = 3.2, lowercase :					int = 50, lowercase :					bool = True, )		->		Image.Image:





     """simple docstring"""

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

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

               _UpperCamelCase       =	get_distance(lowercase, lowercase, lowercase				)

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

     return img


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # colored version, full figure
   lowercase__						:      Union[str, Any]	=    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()










'''simple docstring'''

from __future__ import annotations







def  a__    (    lowercase :					list[int], lowercase :					list[int], lowercase :					int				)		->		tuple[float, list[float]]:





     """simple docstring"""

     _UpperCamelCase       =	list(range(len(lowercase				)				)				)
     _UpperCamelCase       =	[v / w for v, w in zip(lowercase, lowercase				)]
     index.sort(key=lambda lowercase				: ratio[i], reverse=lowercase				)

     _UpperCamelCase       =	0
     _UpperCamelCase       =	[0] * len(lowercase				)
     for i in index:
          if weight[i] <= capacity:
               _UpperCamelCase       =	1
               max_value += value[i]
               capacity -= weight[i]
          else:
               _UpperCamelCase       =	capacity / weight[i]
               max_value += value[i] * capacity / weight[i]
               break

     return max_value, fractions


if __name__ == "__main__":
   import doctest

   doctest.testmod()



