


"""simple docstring"""




from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros





def       a_ (	lowercase__ :Union[str, Any],			lowercase__ :Optional[Any]     ):
			__lowerCamelCase          =      k_size // 2
			__lowerCamelCase     ,__lowerCamelCase          =      mgrid[0 - center : k_size - center, 0 - center : k_size - center]
			__lowerCamelCase          =      1 / (2 * pi * sigma) * exp(-(square(lowercase__     ) + square(lowercase__     )) / (2 * square(lowercase__     ))     )
			return g





def       a_ (	lowercase__ :Dict,			lowercase__ :Tuple,			lowercase__ :List[str]     ):
			__lowerCamelCase     ,__lowerCamelCase          =      image.shape[0], image.shape[1]
			# dst image height and width
			__lowerCamelCase          =      height - k_size + 1
			__lowerCamelCase          =      width - k_size + 1

			# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
			__lowerCamelCase          =      zeros((dst_height * dst_width, k_size * k_size)     )
			__lowerCamelCase          =      0
			for i, j in product(range(lowercase__     ),			range(lowercase__     )     ):
						__lowerCamelCase          =      ravel(image[i : i + k_size, j : j + k_size]     )
						__lowerCamelCase          =      window
						row += 1

			#  turn the kernel into shape(k*k, 1)
			__lowerCamelCase          =      gen_gaussian_kernel(lowercase__,			lowercase__     )
			__lowerCamelCase          =      ravel(lowercase__     )

			# reshape and get the dst image
			__lowerCamelCase          =      dot(lowercase__,			lowercase__     ).reshape(lowercase__,			lowercase__     ).astype(lowercase__     )

			return dst


if __name__ == "__main__":
					# read original image
					__magic_name__						: Optional[int]    =				imread(R'../image_data/lena.jpg')
					# turn image in gray scale value
					__magic_name__						: int    =				cvtColor(img, COLOR_BGR2GRAY)

					# get values with two different mask size
					__magic_name__						: List[str]    =				gaussian_filter(gray, 3, sigma=1)
					__magic_name__						: int    =				gaussian_filter(gray, 5, sigma=0.8)

					# show result images
					imshow('gaussian filter with 3x3 mask', gaussianaxa)
					imshow('gaussian filter with 5x5 mask', gaussianaxa)
					waitKey()








"""simple docstring"""




from collections import defaultdict





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(lowercase__     )
			if ret % 2 == 0:
						cuts.append(lowercase__     )
			return ret





def       a_ (	):
			dfs(1     )


if __name__ == "__main__":
					__magic_name__  , __magic_name__						: Tuple    =				1_0, 9
					__magic_name__						: Tuple    =				defaultdict(list)
					__magic_name__						: dict[int, bool]    =				{}
					__magic_name__						: list[int]    =				[]
					__magic_name__						: List[str]    =				0
					__magic_name__						: Tuple    =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)




