


def        lowerCAmelCase__ (			a__:		Any			,  a__:		List[str]			,  a__:		Optional[Any]			,  a__:		str       )  ->		Any:


							'''simple docstring'''





							global f  # a global dp table for knapsack
							if f[i][j] < 0:
														if j < wt[i - 1]:
																					_UpperCAmelCase 		=			mf_knapsack(i - 1			,  a__			,  a__			,  a__       )
														else:
																					_UpperCAmelCase 		=			max(
																					    mf_knapsack(i - 1			,  a__			,  a__			,  a__       )			,  mf_knapsack(i - 1			,  a__			,  a__			,  j - wt[i - 1]       ) + val[i - 1]			,  )
														_UpperCAmelCase 		=			val
							return f[i][j]

def        lowerCAmelCase__ (			a__:		List[Any]			,  a__:		Dict			,  a__:		List[str]			,  a__:		str       )  ->		List[Any]:


							'''simple docstring'''





							_UpperCAmelCase 		=			[[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_:
																												_UpperCAmelCase 		=			max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]			,  dp[i - 1][w_]       )
																					else:
																												_UpperCAmelCase 		=			dp[i - 1][w_]

							return dp[n][w_], dp

def        lowerCAmelCase__ (			a__:		int			,  a__:		list			,  a__:		list       )  ->		Tuple:


							'''simple docstring'''





							if not (isinstance(a__			,  (list, tuple)       ) and isinstance(a__			,  (list, tuple)       )):
														raise ValueError(
														    'Both the weights and values vectors must be either lists or tuples'       )

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

							_UpperCAmelCase 		=			knapsack(a__			,  a__			,  a__			,  a__       )
							_UpperCAmelCase 		=			set()
							_construct_solution(a__			,  a__			,  a__			,  a__			,  a__       )

							return optimal_val, example_optional_set

def        lowerCAmelCase__ (			a__:		list			,  a__:		list			,  a__:		int			,  a__:		int			,  a__:		set       )  ->		Union[str, Any]:


							'''simple docstring'''





							if i > 0 and j > 0:
														if dp[i - 1][j] == dp[i][j]:
																					_construct_solution(a__			,  a__			,  i - 1			,  a__			,  a__       )
														else:
																					optimal_set.add(a__       )
																					_construct_solution(a__			,  a__			,  i - 1			,  j - wt[i - 1]			,  a__       )


if __name__ == "__main__":
		lowerCAmelCase__  :str   			=							[3, 2, 4, 4]
		lowerCAmelCase__  :Any   			=							[4, 3, 2, 3]
		lowerCAmelCase__  :Optional[int]   			=							4
		lowerCAmelCase__  :List[Any]   			=							6
		lowerCAmelCase__  :str   			=							[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
		lowerCAmelCase__			,  lowerCAmelCase__  :Optional[int]   			=							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
		lowerCAmelCase__			,  lowerCAmelCase__  :int   			=							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)

from transformers import HfArgumentParser, TensorFlowBenchmark, TensorFlowBenchmarkArguments





def    __lowercase     (						):
 UpperCamelCase_					:						Optional[Any] =					HfArgumentParser(lowerCamelCase	)
 UpperCamelCase_					:						Tuple =					parser.parse_args_into_dataclasses()[0]
 UpperCamelCase_					:						Dict =					TensorFlowBenchmark(args=lowerCamelCase	)
 try:
  UpperCamelCase_					:						Any =					parser.parse_args_into_dataclasses()[0]
 except ValueError as e:
  UpperCamelCase_					:						Any =					'Arg --no_{0} is no longer used, please use --no-{0} instead.'
  UpperCamelCase_					:						Optional[int] =					' '.join(str(lowerCamelCase	).split(' '	)[:-1]	)
  UpperCamelCase_					:						Any =					''
  UpperCamelCase_					:						Any =					eval(str(lowerCamelCase	).split(' '	)[-1]	)
  UpperCamelCase_					:						List[Any] =					[]
  for arg in depreciated_args:
   # arg[2:] removes '--'
   if arg[2:] in TensorFlowBenchmark.deprecated_args:
    # arg[5:] removes '--no_'
    full_error_msg += arg_error_msg.format(arg[5:]	)
   else:
    wrong_args.append(lowerCamelCase	)
  if len(lowerCamelCase	) > 0:
   UpperCamelCase_					:						List[str] =					full_error_msg + begin_error_msg + str(lowerCamelCase	)
  raise ValueError(lowerCamelCase	)
 benchmark.run()


if __name__ == "__main__":
   main()



