




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        __UpperCAmelCase						(							lowerCamelCase_ :     Any  ,							lowerCamelCase_ :     Tuple  )       ->  Tuple:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : List[Any]					  =      k_size // 2
			SCREAMING_SNAKE_CASE_  ,    SCREAMING_SNAKE_CASE_   : List[str]					  =      mgrid[0 - center : k_size - center, 0 - center : k_size - center]
			SCREAMING_SNAKE_CASE_   : int					  =      1 / (2 * pi * sigma) * exp(-(square(lowerCamelCase_  ) + square(lowerCamelCase_  )) / (2 * square(lowerCamelCase_  ))  )
			return g





def        __UpperCAmelCase						(							lowerCamelCase_ :     Tuple  ,							lowerCamelCase_ :     Any  ,							lowerCamelCase_ :     Dict  )       ->  List[str]:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_  ,    SCREAMING_SNAKE_CASE_   : List[str]					  =      image.shape[0], image.shape[1]
			# dst image height and width
			SCREAMING_SNAKE_CASE_   : Dict					  =      height - k_size + 1
			SCREAMING_SNAKE_CASE_   : List[Any]					  =      width - k_size + 1

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

			#  turn the kernel into shape(k*k, 1)
			SCREAMING_SNAKE_CASE_   : int					  =      gen_gaussian_kernel(lowerCamelCase_  ,							lowerCamelCase_  )
			SCREAMING_SNAKE_CASE_   : str					  =      ravel(lowerCamelCase_  )

			# reshape and get the dst image
			SCREAMING_SNAKE_CASE_   : Dict					  =      dot(lowerCamelCase_  ,							lowerCamelCase_  ).reshape(lowerCamelCase_  ,							lowerCamelCase_  ).astype(lowerCamelCase_  )

			return dst


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

						# get values with two different mask size
						UpperCamelCase__ :   Dict						=							gaussian_filter(gray, 3, sigma=1)
						UpperCamelCase__ :   Dict						=							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 __future__ import annotations





def 		UpperCamelCase							(				_lowerCamelCase   :   list[int]			):  # This function is recursive
    A__							=     len(_lowerCamelCase			)
    # If the array contains only one element, we return it (it's the stop condition of
    # recursion)
    if array_length <= 1:
        return array
        # Else
    A__							=     array[0]
    A__							=     False
    A__							=     1
    A__							=     []
    while not is_found and i < array_length:
        if array[i] < pivot:
            A__							=     True
            A__							=     [element for element in array[i:] if element >= array[i]]
            A__							=     longest_subsequence(_lowerCamelCase			)
            if len(_lowerCamelCase			) > len(_lowerCamelCase			):
                A__							=     temp_array
        else:
            i += 1

    A__							=     [element for element in array[1:] if element >= pivot]
    A__							=     [pivot, *longest_subsequence(_lowerCamelCase			)]
    if len(_lowerCamelCase			) > len(_lowerCamelCase			):
        return temp_array
    else:
        return longest_subseq


if __name__ == "__main__":
  import doctest

  doctest.testmod()



