




"""simple docstring"""

def      UpperCamelCase__   (						lowercase__     :   Optional[Any]				,   lowercase__     :   Optional[Any]				,   lowercase__     :   Union[str, Any]				,   lowercase__     :   Optional[int]      ):
		global f  # a global dp table for knapsack
		if f[i][j] < 0:
				if j < wt[i - 1]:
						snake_case						:  Optional[Any]    	= mf_knapsack(i - 1				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__      )
				else:
						snake_case						:  Any    	= max(
						    mf_knapsack(i - 1				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__      )				,   mf_knapsack(i - 1				,   UpperCamelCase__				,   UpperCamelCase__				,   j - wt[i - 1]      ) + val[i - 1]				,   )
				snake_case						:  int    	= val
		return f[i][j]



def      UpperCamelCase__   (						lowercase__     :   Tuple				,   lowercase__     :   str				,   lowercase__     :   int				,   lowercase__     :   Dict      ):
		snake_case						:  Optional[int]    	= [[0] * (w + 1) for _ in range(n + 1      )]

		for i in range(1				,   n + 1      ):
				for w_ in range(1				,   w + 1      ):
						if wt[i - 1] <= w_:
								snake_case						:  int    	= max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]				,   dp[i - 1][w_]      )
						else:
								snake_case						:  Any    	= dp[i - 1][w_]

		return dp[n][w_], dp



def      UpperCamelCase__   (						lowercase__     :   Dict				,   lowercase__     :   Tuple				,   lowercase__     :   Tuple      ):
		if not (isinstance(UpperCamelCase__				,   (list, tuple)      ) and isinstance(UpperCamelCase__				,   (list, tuple)      )):
				raise ValueError(
				    "Both the weights and values vectors must be either lists or tuples"      )

		snake_case						:  Union[str, Any]    	= len(UpperCamelCase__      )
		if num_items != len(UpperCamelCase__      ):
				snake_case						:  Union[str, Any]    	= (
				    """The number of weights must be the same as the number of values.\n"""
				    F'''But got {num_items} weights and {len(UpperCamelCase__      )} values'''
				)
				raise ValueError(UpperCamelCase__      )
		for i in range(UpperCamelCase__      ):
				if not isinstance(wt[i]				,   UpperCamelCase__      ):
						snake_case						:  Tuple    	= (
						    """All weights must be integers but got weight of """
						    F'''type {type(wt[i]      )} at index {i}'''
						)
						raise TypeError(UpperCamelCase__      )

		snake_case						:  List[Any]    	= knapsack(UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__      )
		snake_case						:  set    	= set()
		_construct_solution(UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__      )

		return optimal_val, example_optional_set



def      UpperCamelCase__   (						lowercase__     :   int				,   lowercase__     :   int				,   lowercase__     :   str				,   lowercase__     :   Optional[int]				,   lowercase__     :   Optional[Any]      ):
		# for the current item i at a maximum weight j to be part of an optimal subset,
		# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
		# where i - 1 means considering only the previous items at the given maximum weight
		if i > 0 and j > 0:
				if dp[i - 1][j] == dp[i][j]:
						_construct_solution(UpperCamelCase__				,   UpperCamelCase__				,   i - 1				,   UpperCamelCase__				,   UpperCamelCase__      )
				else:
						optimal_set.add(UpperCamelCase__      )
						_construct_solution(UpperCamelCase__				,   UpperCamelCase__				,   i - 1				,   j - wt[i - 1]				,   UpperCamelCase__      )


if __name__ == "__main__":
							__A       						=	[3, 2, 4, 4]
							__A       						=	[4, 3, 2, 3]
							__A       						=	4
							__A       						=	6
							__A       						=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
							__A						,				__A       						=	knapsack(w, wt, val, n)
							print(optimal_solution)
							print(mf_knapsack(n, wt, val, w))  # switched the n and w

							# testing the dynamic programming problem with example
							# the optimal subset for the above example are items 3 and 4
							__A						,				__A       						=	knapsack_with_example_solution(w, wt, val)
							assert optimal_solution == 8
							assert optimal_subset == {3, 4}
							print("optimal_value = ", optimal_solution)
							print("An optimal subset corresponding to the optimal value", optimal_subset)









"""simple docstring"""




import cva
import numpy as np






class        UpperCamelCase			:


 def __init__(     self		:						Optional[int]							,						UpperCAmelCase__		:						float							,						UpperCAmelCase__		:						int							)					->       Dict:

   if k in (0.0_4, 0.0_6):
     _a  :       List[str]             =	k
     _a  :       List[Any]             =	window_size
   else:
     raise ValueError("""invalid k value"""							)


 def __str__(     self		:						Dict							)					->       str:
   return str(self.k							)







 def _lowercase	(     self		:						int							,						UpperCAmelCase__		:						str							)					->       tuple[cva.Mat, list[list[int]]]:
   _a  :       Dict             =	cva.imread(UpperCAmelCase__							,						0							)
   _a      ,  _a  :       List[Any]             =	img.shape
   _a  :       list[list[int]]             =	[]
   _a  :       List[Any]             =	img.copy()
   _a  :       int             =	cva.cvtColor(UpperCAmelCase__							,						cva.COLOR_GRAY2RGB							)
   _a      ,  _a  :       Any             =	np.gradient(UpperCAmelCase__							)
   _a  :       Tuple             =	dx**2
   _a  :       Union[str, Any]             =	dy**2
   _a  :       Union[str, Any]             =	dx * dy
   _a  :       int             =	0.0_4
   _a  :       List[str]             =	self.window_size // 2
   for y in range(UpperCAmelCase__							,						h - offset							):
     for x in range(UpperCAmelCase__							,						w - offset							):
       _a  :       str             =	ixx[
           y - offset : y + offset + 1, x - offset : x + offset + 1
       ].sum()
       _a  :       List[Any]             =	iyy[
           y - offset : y + offset + 1, x - offset : x + offset + 1
       ].sum()
       _a  :       Tuple             =	ixy[
           y - offset : y + offset + 1, x - offset : x + offset + 1
       ].sum()

       _a  :       Any             =	(wxx * wyy) - (wxy**2)
       _a  :       Tuple             =	wxx + wyy
       _a  :       Any             =	det - k * (trace**2)
       # Can change the value
       if r > 0.5:
         corner_list.append([x, y, r]							)
         color_img.itemset((y, x, 0)							,						0							)
         color_img.itemset((y, x, 1)							,						0							)
         color_img.itemset((y, x, 2)							,						255							)
   return color_img, corner_list


if __name__ == "__main__":
 _snake_case          =   HarrisCorner(0.04, 3)
 _snake_case      , _snake_case          =   edge_detect.detect('path_to_image')
 cva.imwrite('detect.png', color_img)

