'''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   __UpperCAmelCase     (    a_:			List[Any],   a_:			List[Any]				):
   _UpperCAmelCase				:      int				=  k_size // 2
   _UpperCAmelCase				:      List[str]				=  mgrid[0 - center : k_size - center, 0 - center : k_size - center]
   _UpperCAmelCase				:      Dict				=  1 / (2 * pi * sigma) * exp(-(square(snake_case__				) + square(snake_case__				)) / (2 * square(snake_case__				))				)
   return g






def   __UpperCAmelCase     (    a_:			Tuple,   a_:			Union[str, Any],   a_:			int				):
   _UpperCAmelCase				:      str				=  image.shape[0], image.shape[1]
   # dst image height and width
   _UpperCAmelCase				:      Tuple				=  height - k_size + 1
   _UpperCAmelCase				:      List[Any]				=  width - k_size + 1

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

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

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

   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()



# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.




def    a__    (		snake_case__					:							Dict     ):
  _UpperCAmelCase		:							str							=     [False] * len(snake_case__     )
  _UpperCAmelCase		:							str							=     [-1] * len(snake_case__     )

  def dfs(snake_case__					:							Dict						,   snake_case__					:							Optional[Any]     ):
    _UpperCAmelCase		:							str							=     True
    _UpperCAmelCase		:							Optional[Any]							=     c
    for u in graph[v]:
      if not visited[u]:
        dfs(snake_case__						,   1 - c     )

  for i in range(len(snake_case__     )     ):
    if not visited[i]:
      dfs(snake_case__						,   0     )

  for i in range(len(snake_case__     )     ):
    for j in graph[i]:
      if color[i] == color[j]:
        return False

  return True


# Adjacency list of graph
SCREAMING_SNAKE_CASE__					:     Optional[Any]       =     {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}





print(check_bipartite_dfs(graph))





