


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


def      _snake_case						(						_snake_case				:			List[Any] ,   _snake_case				:			Optional[int] ,   _snake_case				:			List[str]			):
      lowerCAmelCase,      lowerCAmelCase					:	str       =   image.shape[0], image.shape[1]
      # dst image height and width
      lowerCAmelCase					:	Optional[Any]       =   height - k_size + 1
      lowerCAmelCase					:	Any       =   width - k_size + 1

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

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

      # reshape and get the dst image
      lowerCAmelCase					:	str       =   dot(_snake_case ,   _snake_case			).reshape(_snake_case ,   _snake_case			).astype(_snake_case			)

      return dst


if __name__ == "__main__":
 # read original image
 snake_case__		:     List[str]    				=				imread(R'''../image_data/lena.jpg''')
 # turn image in gray scale value
 snake_case__		:     Union[str, Any]    				=				cvtColor(img, COLOR_BGR2GRAY)

 # get values with two different mask size
 snake_case__		:     List[str]    				=				gaussian_filter(gray, 3, sigma=1)
 snake_case__		:     Any    				=				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"""





# using dfs for finding eulerian path traversal


def      _snake_case						(						_snake_case				:			Optional[Any] ,   _snake_case				:			List[Any] ,   _snake_case				:			str ,   _snake_case				:			List[Any]=None			):
      lowerCAmelCase					:	Any       =   (path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  lowerCAmelCase,      lowerCAmelCase					:	Union[str, Any]       =   True, True
                  lowerCAmelCase					:	int       =   dfs(_snake_case ,   _snake_case ,   _snake_case ,   _snake_case			)
      return path


def      _snake_case						(						_snake_case				:			Optional[int] ,   _snake_case				:			Dict			):
      lowerCAmelCase					:	Tuple       =   0
      lowerCAmelCase					:	Optional[Any]       =   -1
      for i in range(_snake_case			):
            if i not in graph.keys():
                  continue
            if len(graph[i]			) % 2 == 1:
                  odd_degree_nodes += 1
                  lowerCAmelCase					:	Optional[Any]       =   i
      if odd_degree_nodes == 0:
            return 1, odd_node
      if odd_degree_nodes == 2:
            return 2, odd_node
      return 3, odd_node


def      _snake_case						(						_snake_case				:			Tuple ,   _snake_case				:			List[Any]			):
      lowerCAmelCase					:	Any       =   [[False for _ in range(max_node + 1			)] for _ in range(max_node + 1			)]
      lowerCAmelCase,      lowerCAmelCase					:	Optional[int]       =   check_circuit_or_path(_snake_case ,   _snake_case			)
      if check == 3:
            print('''graph is not Eulerian'''			)
            print('''no path'''			)
            return
      lowerCAmelCase					:	Dict       =   1
      if check == 2:
            lowerCAmelCase					:	int       =   odd_node
            print('''graph has a Euler path'''			)
      if check == 1:
            print('''graph has a Euler cycle'''			)
      lowerCAmelCase					:	List[str]       =   dfs(_snake_case ,   _snake_case ,   _snake_case			)
      print(_snake_case			)


def      _snake_case						(						):
      lowerCAmelCase					:	Optional[Any]       =   {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      lowerCAmelCase					:	Union[str, Any]       =   {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      lowerCAmelCase					:	List[Any]       =   {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      lowerCAmelCase					:	Optional[Any]       =   {1: [2, 3], 2: [1, 3], 3: [1, 2]}
      lowerCAmelCase					:	Any       =   {
          1: [],
          2: []
          # all degree is zero
      }
      lowerCAmelCase					:	List[str]       =   10
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)


if __name__ == "__main__":
 main()


