



def        a						(      _UpperCAmelCase							:					str						):







		'''simple docstring'''





		__UpperCAmelCase    :     List[str]													=	[0 for i in range(len(_UpperCAmelCase						)						)]

		# initialize interval's left pointer and right pointer
		__UpperCAmelCase							,					__UpperCAmelCase    :     Optional[Any]													=	0, 0

		for i in range(1 ,   len(_UpperCAmelCase						)						):
				# case when current index is inside the interval
				if i <= right_pointer:
						__UpperCAmelCase    :     Optional[int]													=	min(right_pointer - i + 1 ,   z_result[i - left_pointer]						)
						__UpperCAmelCase    :     Tuple													=	min_edge

				while go_next(_UpperCAmelCase ,   _UpperCAmelCase ,   _UpperCAmelCase						):
						z_result[i] += 1

				# if new index's result gives us more right interval,
				# we've to update left_pointer and right_pointer
				if i + z_result[i] - 1 > right_pointer:
						__UpperCAmelCase							,					__UpperCAmelCase    :     List[str]													=	i, i + z_result[i] - 1

		return z_result

def        a						(      _UpperCAmelCase							:					int ,   _UpperCAmelCase							:					list[int] ,   _UpperCAmelCase							:					str						):







		'''simple docstring'''





		return i + z_result[i] < len(_UpperCAmelCase						) and s[z_result[i]] == s[i + z_result[i]]

def        a						(      _UpperCAmelCase							:					str ,   _UpperCAmelCase							:					str						):







		'''simple docstring'''





		__UpperCAmelCase    :     Dict													=	0
		# concatenate 'pattern' and 'input_str' and call z_function
		# with concatenated string
		__UpperCAmelCase    :     int													=	z_function(pattern + input_str						)

		for val in z_result:
				# if value is greater then length of the pattern string
				# that means this index is starting position of substring
				# which is equal to pattern string
				if val >= len(_UpperCAmelCase						):
						answer += 1

		return answer


if __name__ == "__main__":
				import doctest

				doctest.testmod()










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						(      _UpperCAmelCase							:					Tuple ,   _UpperCAmelCase							:					Optional[int]						):







		'''simple docstring'''





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

def        a						(      _UpperCAmelCase							:					Optional[int] ,   _UpperCAmelCase							:					Any ,   _UpperCAmelCase							:					List[Any]						):







		'''simple docstring'''





		__UpperCAmelCase							,					__UpperCAmelCase    :     Union[str, Any]													=	image.shape[0], image.shape[1]
		# dst image height and width
		__UpperCAmelCase    :     str													=	height - k_size + 1
		__UpperCAmelCase    :     Optional[int]													=	width - k_size + 1

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

		#  turn the kernel into shape(k*k, 1)
		__UpperCAmelCase    :     Tuple													=	gen_gaussian_kernel(_UpperCAmelCase ,   _UpperCAmelCase						)
		__UpperCAmelCase    :     List[Any]													=	ravel(_UpperCAmelCase						)

		# reshape and get the dst image
		__UpperCAmelCase    :     Optional[Any]													=	dot(_UpperCAmelCase ,   _UpperCAmelCase						).reshape(_UpperCAmelCase ,   _UpperCAmelCase						).astype(_UpperCAmelCase						)

		return dst


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

				# get values with two different mask size
				__A   			=gaussian_filter(gray, 3, sigma=1)
				__A   			=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()





