
from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		np.ndarray:
			lowerCAmelCase__      :      int         =		cva.getAffineTransform(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )
			return cva.warpAffine(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							(rows, cols)     )


if __name__ == "__main__":
					# read original image
					lowerCamelCase__          =		cva.imread(
					    str(Path(__file__).resolve().parent.parent / """image_data""" / """lena.jpg""")
					)
					# turn image in gray scale value
					lowerCamelCase__          =		cva.cvtColor(image, cva.COLOR_BGR2GRAY)
					# get image shape
					lowerCamelCase__      ,					lowerCamelCase__          =		gray_img.shape

					# set different points to rotate image
					lowerCamelCase__          =		np.array([[50, 50], [200, 50], [50, 200]], np.floataa)
					lowerCamelCase__          =		np.array([[10, 100], [200, 50], [100, 250]], np.floataa)
					lowerCamelCase__          =		np.array([[50, 50], [150, 50], [120, 200]], np.floataa)
					lowerCamelCase__          =		np.array([[10, 100], [80, 50], [180, 250]], np.floataa)

					# add all rotated images in a list
					lowerCamelCase__          =		[
					    gray_img,
					    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
					    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
					    get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
					]

					# plot different image rotations
					lowerCamelCase__          =		plt.figure(1)
					lowerCamelCase__          =		["""Original""", """Rotation 1""", """Rotation 2""", """Rotation 3"""]
					for i, image in enumerate(images):
										plt.subplot(2, 2, i + 1), plt.imshow(image, """gray""")
										plt.title(titles[i])
										plt.axis("""off""")
										plt.subplots_adjust(left=0.0, bottom=0.05, right=1.0, top=0.95)
					plt.show()

from __future__ import annotations

lowerCamelCase__          =		list[list[int]]

# assigning initial values to the grid
lowerCamelCase__          =		[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
lowerCamelCase__          =		[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		bool:
			for i in range(9     ):
						if grid[row][i] == n or grid[i][column] == n:
									return False

			for i in range(3     ):
						for j in range(3     ):
									if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
												return False

			return True
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		tuple[int, int] | None:
			for i in range(9     ):
						for j in range(9     ):
									if grid[i][j] == 0:
												return i, j
			return None
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Matrix | None:
			if location := find_empty_location(SCREAMING_SNAKE_CASE_     ):
						lowerCAmelCase__      ,				lowerCAmelCase__      :      Any         =		location
			else:
						# If the location is ``None``, then the grid is solved.
						return grid

			for digit in range(1       ,							10     ):
						if is_safe(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ):
									lowerCAmelCase__      :      Optional[Any]         =		digit

									if sudoku(SCREAMING_SNAKE_CASE_     ) is not None:
												return grid

									lowerCAmelCase__      :      List[Any]         =		0

			return None
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		None:
			for row in grid:
						for cell in row:
									print(SCREAMING_SNAKE_CASE_       ,							end=' '     )
						print()


if __name__ == "__main__":
					# make a copy of grid so that you can compare with the unmodified grid
					for example_grid in (initial_grid, no_solution):
										print("""\nExample grid:\n""" + """=""" * 20)
										print_solution(example_grid)
										print("""\nExample grid solution:""")
										lowerCamelCase__          =		sudoku(example_grid)
										if solution is not None:
															print_solution(solution)
										else:
															print("""Cannot find a solution.""")