






"""simple docstring"""



import math
import sys

import cva
import numpy as np



def 						lowercase    (				__snake_case				: np.ndarray		,					__snake_case				: float	):
		# For applying gaussian function for each element in matrix.
		lowercase_ : Union[str, Any]							       =   math.sqrt(__snake_case	)
		lowercase_ : Any							       =   1 / (sigma * math.sqrt(2 * math.pi	))
		return cons * np.exp(-((img / sigma) ** 2) * 0.5	)



def 						lowercase    (				__snake_case				: np.ndarray		,					__snake_case				: int		,					__snake_case				: int		,					__snake_case				: int	):
		lowercase_ : List[str]							       =   kernel_size // 2
		return img[x - half : x + half + 1, y - half : y + half + 1]



def 						lowercase    (				__snake_case				: int		,					__snake_case				: float	):
		# Creates a gaussian kernel of given dimension.
		lowercase_ : Tuple							       =   np.zeros((kernel_size, kernel_size)	)
		for i in range(0		,					__snake_case	):
				for j in range(0		,					__snake_case	):
						lowercase_ : List[str]							       =   math.sqrt(
						    abs(i - kernel_size // 2	) ** 2 + abs(j - kernel_size // 2	) ** 2	)
		return vec_gaussian(__snake_case		,					__snake_case	)



def 						lowercase    (				__snake_case				: np.ndarray		,					__snake_case				: float		,					__snake_case				: float		,					__snake_case				: int		,					):
		lowercase_ : Tuple							       =   np.zeros(img.shape	)
		lowercase_ : Union[str, Any]							       =   get_gauss_kernel(__snake_case		,					__snake_case	)
		lowercase_       ,					lowercase_ : List[Any]							       =   img.shape
		for i in range(kernel_size // 2		,					size_x - kernel_size // 2	):
				for j in range(kernel_size // 2		,					size_y - kernel_size // 2	):
						lowercase_ : str							       =   get_slice(__snake_case		,					__snake_case		,					__snake_case		,					__snake_case	)
						lowercase_ : Any							       =   img_s - img_s[kernel_size // 2, kernel_size // 2]
						lowercase_ : List[Any]							       =   vec_gaussian(__snake_case		,					__snake_case	)
						lowercase_ : List[Any]							       =   np.multiply(__snake_case		,					__snake_case	)
						lowercase_ : Union[str, Any]							       =   np.multiply(__snake_case		,					__snake_case	)
						lowercase_ : Any							       =   np.sum(__snake_case	) / np.sum(__snake_case	)
						lowercase_ : Optional[Any]							       =   val
		return imga



def 						lowercase    (				__snake_case				: list	):
		lowercase_ : Optional[Any]							       =   args[1] if args[1:] else '''../image_data/lena.jpg'''
		lowercase_ : Dict							       =   float(args[2]	) if args[2:] else 1.0
		lowercase_ : int							       =   float(args[3]	) if args[3:] else 1.0
		if args[4:]:
				lowercase_ : str							       =   int(args[4]	)
				lowercase_ : Optional[int]							       =   kernel_size + abs(kernel_size % 2 - 1	)
		else:
				lowercase_ : Dict							       =   5
		return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
						__A				,			__A				,			__A				,			__A		:       List[str]  				=		parse_args(sys.argv)
						__A		:       str  				=		cva.imread(filename, 0)
						cva.imshow('''input image''', img)

						__A		:       str  				=		img / 255
						__A		:       Any  				=		out.astype('''float32''')
						__A		:       List[Any]  				=		bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
						__A		:       Any  				=		out * 255
						__A		:       Optional[int]  				=		np.uinta(out)
						cva.imshow('''output image''', out)
						cva.waitKey(0)
						cva.destroyAllWindows()




"""simple docstring"""


from math import pow






def 			__UpperCAmelCase    (	lowercase      ,lowercase      ,lowercase      ,lowercase      ,lowercase      ,):







  """simple docstring"""
  if current_sum == needed_sum:
    # If the sum of the powers is equal to needed_sum, then we have a solution.
    solutions_count += 1
    return current_sum, solutions_count

  _UpperCAmelCase         =					int(pow(lowercase      ,lowercase						)						)
  if current_sum + i_to_n <= needed_sum:
    # If the sum of the powers is less than needed_sum, then continue adding powers.
    current_sum += i_to_n
    _UpperCAmelCase       , _UpperCAmelCase         =					backtrack(
        lowercase      ,lowercase      ,current_number + 1      ,lowercase      ,lowercase						)
    current_sum -= i_to_n
  if i_to_n < needed_sum:
    # If the power of i is less than needed_sum, then try with the next power.
    _UpperCAmelCase       , _UpperCAmelCase         =					backtrack(
        lowercase      ,lowercase      ,current_number + 1      ,lowercase      ,lowercase						)
  return current_sum, solutions_count






def 			__UpperCAmelCase    (	lowercase      ,lowercase						):







  """simple docstring"""
  if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
    raise ValueError(
        """Invalid input\n"""
        """needed_sum must be between 1 and 1000, power between 2 and 10."""						)

  return backtrack(lowercase      ,lowercase      ,1      ,0      ,0						)[1]  # Return the solutions_count


if __name__ == "__main__":
    import doctest

    doctest.testmod()
