


'''simple docstring'''


import colorsys

from PIL import Image  # type: ignore






def        __lowerCAmelCase       (__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase      ):
		_UpperCAmelCase						:				str	    =					x
		_UpperCAmelCase						:				Dict	    =					y
		for step in range(__lowerCAmelCase      ):  # noqa: B007
				_UpperCAmelCase						:				Optional[Any]	    =					a * a - b * b + x
				_UpperCAmelCase						:				int	    =					2 * a * b + y
				_UpperCAmelCase						:				Any	    =					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       (__lowerCAmelCase      ):
		if distance == 1:
				return (0, 0, 0)
		else:
				return (255, 255, 255)






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






def        __lowerCAmelCase       (__lowerCAmelCase = 800					,       __lowerCAmelCase = 600					,       __lowerCAmelCase = -0.6					,       __lowerCAmelCase = 0					,       __lowerCAmelCase = 3.2					,       __lowerCAmelCase = 50					,       __lowerCAmelCase = True					,       ):
		_UpperCAmelCase						:				Union[str, Any]	    =					Image.new("RGB"					,       (image_width, image_height)      )
		_UpperCAmelCase						:				Dict	    =					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
						_UpperCAmelCase						:				Dict	    =					figure_width / image_width * image_height
						_UpperCAmelCase						:				str	    =					figure_center_x + (image_x / image_width - 0.5) * figure_width
						_UpperCAmelCase						:				Any	    =					figure_center_y + (image_y / image_height - 0.5) * figure_height

						_UpperCAmelCase						:				List[Any]	    =					get_distance(__lowerCAmelCase					,       __lowerCAmelCase					,       __lowerCAmelCase      )

						# color the corresponding pixel based on the selected coloring-function
						if use_distance_color_coding:
								_UpperCAmelCase						:				Any	    =					get_color_coded_rgb(__lowerCAmelCase      )
						else:
								_UpperCAmelCase						:				Optional[Any]	    =					get_black_and_white_rgb(__lowerCAmelCase      )

		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()







'''simple docstring'''


def        __lowerCAmelCase       ():
		return [list(range(1_000 - i					,       -1_000 - i					,       -1      )      ) for i in range(1_000      )]


lowerCamelCase__					=   generate_large_matrix()
lowerCamelCase__					=   (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		assert all(row == sorted(__lowerCAmelCase					,       reverse=__lowerCAmelCase      ) for row in grid      )
		assert all(list(__lowerCAmelCase      ) == sorted(__lowerCAmelCase					,       reverse=__lowerCAmelCase      ) for col in zip(*__lowerCAmelCase      )      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				Any	    =					0
		_UpperCAmelCase						:				str	    =					len(__lowerCAmelCase      ) - 1

		# Edge cases such as no values or all numbers are negative.
		if not array or array[0] < 0:
				return 0

		while right + 1 > left:
				_UpperCAmelCase						:				Union[str, Any]	    =					(left + right) // 2
				_UpperCAmelCase						:				List[str]	    =					array[mid]

				# Num must be negative and the index must be greater than or equal to 0.
				if num < 0 and array[mid - 1] >= 0:
						return mid

				if num >= 0:
						_UpperCAmelCase						:				Tuple	    =					mid + 1
				else:
						_UpperCAmelCase						:				Optional[Any]	    =					mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
		return len(__lowerCAmelCase      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				str	    =					0
		_UpperCAmelCase						:				int	    =					len(grid[0]      )

		for i in range(len(__lowerCAmelCase      )      ):
				_UpperCAmelCase						:				Dict	    =					find_negative_index(grid[i][:bound]      )
				total += bound
		return (len(__lowerCAmelCase      ) * len(grid[0]      )) - total






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		return len([number for row in grid for number in row if number < 0]      )






def        __lowerCAmelCase       (__lowerCAmelCase      ):
		_UpperCAmelCase						:				Tuple	    =					0
		for row in grid:
				for i, number in enumerate(__lowerCAmelCase      ):
						if number < 0:
								total += len(__lowerCAmelCase      ) - i
								break
		return total






def        __lowerCAmelCase       ():
		from timeit import timeit

		print("Running benchmarks"      )
		_UpperCAmelCase						:				Tuple	    =					(
		    "from __main__ import count_negatives_binary_search, "
		    "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
		)
		for func in (
		    "count_negatives_binary_search",  # took 0.7727 seconds
		    "count_negatives_brute_force_with_break",  # took 4.6505 seconds
		    "count_negatives_brute_force",  # took 12.8160 seconds
		):
				_UpperCAmelCase						:				str	    =					timeit(F"""{func}(grid=grid)"""					,       setup=__lowerCAmelCase					,       number=500      )
				print(F"""{func}() took {time:0.4f} seconds"""      )


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						benchmark()



