





from math import factorial






def 	a_		(	__lowercase       :     int	, __lowercase       :     int			)			->  int:

			# If either of the conditions are true, the function is being asked
			# to calculate a factorial of a negative number, which is not possible
			if n < k or k < 0:
						raise ValueError('Please enter positive integers for n and k where n >= k'			)
			return factorial(__lowercase			) // (factorial(__lowercase			) * factorial(n - k			))


if __name__ == "__main__":
			print(
			    '''The number of five-card hands possible from a standard''',
			    F'fifty-two card deck is: {combinations(52, 5)}\n',
			)

			print(
			    '''If a class of 40 students must be arranged into groups of''',
			    F'4 for group projects, there are {combinations(40, 4)} ways',
			    '''to arrange them.\n''',
			)

			print(
			    '''If 10 teams are competing in a Formula One race, there''',
			    F'are {combinations(10, 3)} ways that first, second and',
			    '''third place can be awarded.''',
			)

from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt






def 	a_		(	__lowercase       :     np.ndarray	, __lowercase       :     np.ndarray	, __lowercase       :     np.ndarray	, __lowercase       :     int	, __lowercase       :     int			)			->  np.ndarray:
			_snake_case          =      cva.getAffineTransform(__lowercase	, __lowercase			)
			return cva.warpAffine(__lowercase	, __lowercase	, (rows, cols)			)


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

			# set different points to rotate image
			_lowerCamelCase	:    str          =      np.array([[50, 50], [200, 50], [50, 200]], np.floataa)
			_lowerCamelCase	:    Optional[Any]          =      np.array([[10, 100], [200, 50], [100, 250]], np.floataa)
			_lowerCamelCase	:    List[str]          =      np.array([[50, 50], [150, 50], [120, 200]], np.floataa)
			_lowerCamelCase	:    Dict          =      np.array([[10, 100], [80, 50], [180, 250]], np.floataa)

			# add all rotated images in a list
			_lowerCamelCase	:    int          =      [
			    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	:    Any          =      plt.figure(1)
			_lowerCamelCase	:    List[Any]          =      ['''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=0.0_5, right=1.0, top=0.9_5)
			plt.show()