

from pathlib import Path

import numpy as np
from PIL import Image






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					np.ndarray:
	__lowerCamelCase	,			__lowerCamelCase	,			__lowerCamelCase    :    int 	=			rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
	return 0.2989 * r + 0.5870 * g + 0.1140 * b






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					np.ndarray:
	return (gray > 1_2_7) & (gray <= 2_5_5)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__      )  ->					np.ndarray:
	__lowerCamelCase    :    str 	=			np.zeros_like(lowerCamelCase__      )
	__lowerCamelCase    :    Optional[int] 	=			np.zeros(
	    (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)      )

	# Copy image to padded image
	__lowerCamelCase    :    Optional[int] 	=			image

	# Iterate over image & apply kernel
	for x in range(image.shape[1]      ):
		for y in range(image.shape[0]      ):
			__lowerCamelCase    :    List[str] 	=			(
			    kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
			).sum()
			__lowerCamelCase    :    Tuple 	=			int(summation > 0      )
	return output


if __name__ == "__main__":
					# read original image
					a		=Path(__file__).resolve().parent / """image_data""" / """lena.jpg"""
					a		=np.array(Image.open(lena_path))
					# kernel to be applied
					a		=np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
					a		=dilation(gray_to_binary(rgb_to_gray(lena)), structuring_element)
					# Save the output image
					a		=Image.fromarray(output).convert("""RGB""")
					pil_img.save("""result_dilation.png""")







from __future__ import annotations






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)  ->					None:
	__lowerCamelCase    :    int 	=			len(lowerCamelCase__      )

	# If row is equal to the size of the board it means there are a queen in each row in
	# the current board (possible_board)
	if row == n:
		# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
		# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
		boards.append(['. ' * i + 'Q ' + '. ' * (n - 1 - i) for i in possible_board]      )
		return

	# We iterate each column in the row to find all possible results in each row
	for col in range(lowerCamelCase__      ):
		# We apply that we learned previously. First we check that in the current board
		# (possible_board) there are not other same value because if there is it means
		# that there are a collision in vertical. Then we apply the two formulas we
		# learned before:
		#
		# 45º: y - x = b or 45: row - col = b
		# 135º: y + x = b or row + col = b.
		#
		# And we verify if the results of this two formulas not exist in their variables
		# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
		#
		# If any or these are True it means there is a collision so we continue to the
		# next value in the for loop.
		if (
		    col in possible_board
		    or row - col in diagonal_right_collisions
		    or row + col in diagonal_left_collisions
		):
			continue

		# If it is False we call dfs function again and we update the inputs
		depth_first_search(
		    [*possible_board, col]     ,			[*diagonal_right_collisions, row - col]     ,			[*diagonal_left_collisions, row + col]     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:
	__lowerCamelCase    :    list[list[str]] 	=			[]
	depth_first_search([]     ,			[]     ,			[]     ,			lowerCamelCase__     ,			lowerCamelCase__      )

	# Print all the boards
	for board in boards:
		for column in board:
			print(lowerCamelCase__      )
		print(''      )

	print(len(lowerCamelCase__      )     ,			'solutions were found.'      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					n_queens_solution(4)




