





def 							SCREAMING_SNAKE_CASE__  (      __a				):
	snake_case_						:     str     =		0
	snake_case_						:     List[Any]     =		len(__a				)

	for i in range(n - 1				):
		for j in range(i + 1				,	__a				):
			if arr[i] > arr[j]:
				num_inversions += 1

	return num_inversions


def 							SCREAMING_SNAKE_CASE__  (      __a				):
	if len(__a				) <= 1:
		return arr, 0
	snake_case_						:     List[str]     =		len(__a				) // 2
	snake_case_						:     str     =		arr[0:mid]
	snake_case_						:     Union[str, Any]     =		arr[mid:]

	snake_case_						:     List[Any]     =		count_inversions_recursive(__a				)
	snake_case_						:     List[str]     =		count_inversions_recursive(__a				)
	snake_case_						:     int     =		_count_cross_inversions(__a				,	__a				)

	snake_case_						:     Optional[Any]     =		inversion_p + inversions_q + cross_inversions
	return c, num_inversions


def 							SCREAMING_SNAKE_CASE__  (      __a				,	__a				):
	snake_case_						:     Optional[int]     =		[]
	snake_case_						:     Optional[int]     =		0
	while i < len(__a				) and j < len(__a				):
		if p[i] > q[j]:
			# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
			# These are all inversions. The claim emerges from the
			# property that P is sorted.
			num_inversion += len(__a				) - i
			r.append(q[j]				)
			j += 1
		else:
			r.append(p[i]				)
			i += 1

	if i < len(__a				):
		r.extend(p[i:]				)
	else:
		r.extend(q[j:]				)

	return r, num_inversion


def 							SCREAMING_SNAKE_CASE__  (      ):
	snake_case_						:     int     =		[10, 2, 1, 5, 5, 2, 11]

	# this arr has 8 inversions:
	# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

	snake_case_						:     Any     =		count_inversions_bf(__a				)
	snake_case_						:     Union[str, Any]     =		count_inversions_recursive(__a				)

	assert num_inversions_bf == num_inversions_recursive == 8

	print('number of inversions = '				,	__a				)

	# testing an array with zero inversion (a sorted arr_1)

	arr_a.sort()
	snake_case_						:     Any     =		count_inversions_bf(__a				)
	snake_case_						:     Tuple     =		count_inversions_recursive(__a				)

	assert num_inversions_bf == num_inversions_recursive == 0
	print('number of inversions = '				,	__a				)

	# an empty list should also have zero inversions
	snake_case_						:     Union[str, Any]     =		[]
	snake_case_						:     Union[str, Any]     =		count_inversions_bf(__a				)
	snake_case_						:     int     =		count_inversions_recursive(__a				)

	assert num_inversions_bf == num_inversions_recursive == 0
	print('number of inversions = '				,	__a				)


if __name__ == "__main__":
					main()








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 							SCREAMING_SNAKE_CASE__  (      __a				,	__a				):
	snake_case_						:     List[Any]     =		k_size // 2
	snake_case_  ,snake_case_						:     Any     =		mgrid[0 - center : k_size - center, 0 - center : k_size - center]
	snake_case_						:     Optional[Any]     =		1 / (2 * pi * sigma) * exp(-(square(__a				) + square(__a				)) / (2 * square(__a				))				)
	return g


def 							SCREAMING_SNAKE_CASE__  (      __a				,	__a				,	__a				):
	snake_case_  ,snake_case_						:     Union[str, Any]     =		image.shape[0], image.shape[1]
	# dst image height and width
	snake_case_						:     int     =		height - k_size + 1
	snake_case_						:     Optional[int]     =		width - k_size + 1

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

	#  turn the kernel into shape(k*k, 1)
	snake_case_						:     List[Any]     =		gen_gaussian_kernel(__a				,	__a				)
	snake_case_						:     str     =		ravel(__a				)

	# reshape and get the dst image
	snake_case_						:     Optional[int]     =		dot(__a				,	__a				).reshape(__a				,	__a				).astype(__a				)

	return dst


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

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

