

from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      if not arr:
            return None, None, 0
      if low == high:
            return low, high, arr[low]

      A_							       =		(low + high) // 2
      A_       ,A_       ,A_							       =		max_subarray(__UpperCamelCase		,				__UpperCamelCase		,				__UpperCamelCase   )
      A_       ,A_       ,A_							       =		max_subarray(__UpperCamelCase		,				mid + 1		,				__UpperCamelCase   )
      A_       ,A_       ,A_							       =		max_cross_sum(__UpperCamelCase		,				__UpperCamelCase		,				__UpperCamelCase		,				__UpperCamelCase   )
      if left_sum >= right_sum and left_sum >= cross_sum:
            return left_low, left_high, left_sum
      elif right_sum >= left_sum and right_sum >= cross_sum:
            return right_low, right_high, right_sum
      return cross_left, cross_right, cross_sum







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      A_       ,A_							       =		float('''-inf'''   ), -1
      A_       ,A_							       =		float('''-inf'''   ), -1

      A_							       =		0
      for i in range(__UpperCamelCase		,				low - 1		,				-1   ):
            summ += arr[i]
            if summ > left_sum:
                  A_							       =		summ
                  A_							       =		i

      A_							       =		0
      for i in range(mid + 1		,				high + 1   ):
            summ += arr[i]
            if summ > right_sum:
                  A_							       =		summ
                  A_							       =		i

      return max_left, max_right, (left_sum + right_sum)







def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      A_							       =		[randint(1		,				__UpperCamelCase   ) for _ in range(__UpperCamelCase   )]
      A_							       =		time.time()
      max_subarray(__UpperCamelCase		,				0		,				input_size - 1   )
      A_							       =		time.time()
      return end - start







def 							_lowerCamelCase   (			):
      '''simple docstring'''







      A_							       =		[10, 100, 1000, 10000, 50000, 100000, 200000, 300000, 400000, 500000]
      A_							       =		[time_max_subarray(__UpperCamelCase   ) for input_size in input_sizes]
      print('''No of Inputs\t\tTime Taken'''   )
      for input_size, runtime in zip(__UpperCamelCase		,				__UpperCamelCase   ):
            print(__UpperCamelCase		,				'''\t\t'''		,				__UpperCamelCase   )
      plt.plot(__UpperCamelCase		,				__UpperCamelCase   )
      plt.xlabel('''Number of Inputs'''   )
      plt.ylabel('''Time taken in seconds'''   )
      plt.show()


if __name__ == "__main__":
      from doctest import testmod

      testmod()









'''simple docstring'''
import colorsys

from PIL import Image  # type: ignore

def 					lowerCamelCase_ ( __UpperCamelCase					:       float							,    __UpperCamelCase					:       float							,    __UpperCamelCase					:       int		)					->	float:







     """simple docstring"""
     _A				=							x
     _A				=							y
     for step in range(__UpperCamelCase		):  # 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 					lowerCamelCase_ ( __UpperCamelCase					:       float		)					->	tuple:







     """simple docstring"""
     if distance == 1:
          return (0, 0, 0)
     else:
          return (2_5_5, 2_5_5, 2_5_5)

def 					lowerCamelCase_ ( __UpperCamelCase					:       float		)					->	tuple:







     """simple docstring"""
     if distance == 1:
          return (0, 0, 0)
     else:
          return tuple(round(i * 2_5_5		) for i in colorsys.hsv_to_rgb(__UpperCamelCase							,    1							,    1		)		)

def 					lowerCamelCase_ ( __UpperCamelCase					:       int = 8_0_0							,    __UpperCamelCase					:       int = 6_0_0							,    __UpperCamelCase					:       float = -0.6							,    __UpperCamelCase					:       float = 0							,    __UpperCamelCase					:       float = 3.2							,    __UpperCamelCase					:       int = 5_0							,    __UpperCamelCase					:       bool = 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(__UpperCamelCase		):
          for image_y in range(__UpperCamelCase		):
               # 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(__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase		)

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

     return img


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    # colored version, full figure
    lowerCAmelCase						=					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()





