





def 					_A	(		SCREAMING_SNAKE_CASE					:       List[Any]	,	SCREAMING_SNAKE_CASE					:       Optional[int]	,	SCREAMING_SNAKE_CASE					:       str	,	SCREAMING_SNAKE_CASE					:       Optional[Any]						):





  """simple docstring"""



  global f  # a global dp table for knapsack
  if f[i][j] < 0:
    if j < wt[i - 1]:
      a__     : Dict  =mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
    else:
      a__     : str  =max(
          mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)	,	mf_knapsack(i - 1	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	j - wt[i - 1]						) + val[i - 1]	,	)
    a__     : Optional[Any]  =val
  return f[i][j]
def 					_A	(		SCREAMING_SNAKE_CASE					:       Dict	,	SCREAMING_SNAKE_CASE					:       Dict	,	SCREAMING_SNAKE_CASE					:       List[str]	,	SCREAMING_SNAKE_CASE					:       Dict						):





  """simple docstring"""



  a__     : Tuple  =[[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_:
        a__     : Optional[Any]  =max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]	,	dp[i - 1][w_]						)
      else:
        a__     : str  =dp[i - 1][w_]

  return dp[n][w_], dp
def 					_A	(		SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       list						):





  """simple docstring"""



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

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

  a__ ,							a__     : Any  =knapsack(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
  a__     : set  =set()
  _construct_solution(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)

  return optimal_val, example_optional_set
def 					_A	(		SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       list	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       set						):





  """simple docstring"""



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


if __name__ == "__main__":
     UpperCAmelCase     :     Dict							=	[3, 2, 4, 4]
     UpperCAmelCase     :     Tuple							=	[4, 3, 2, 3]
     UpperCAmelCase     :     str							=	4
     UpperCAmelCase     :     Tuple							=	6
     UpperCAmelCase     :     Tuple							=	[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
     UpperCAmelCase					,     UpperCAmelCase     :     List[Any]							=	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
     UpperCAmelCase					,     UpperCAmelCase     :     Union[str, Any]							=	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 typing import Optional

from .. import Features, NamedSplit
from ..packaged_modules.text.text import Text
from ..utils.typing import NestedDataStructureLike, PathLike
from .abc import AbstractDatasetReader







class     __lowerCAmelCase	(   UpperCamelCase__):







      def __init__(   self		,				lowerCAmelCase__		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = None		,				lowerCAmelCase__ = False		,				lowerCAmelCase__ = False		,				lowerCAmelCase__ = None		,				**lowerCAmelCase__		,				)       ->						int:



        '''simple docstring'''




        super().__init__(
            lowerCAmelCase__		,				split=lowerCAmelCase__		,				features=lowerCAmelCase__		,				cache_dir=lowerCAmelCase__		,				keep_in_memory=lowerCAmelCase__		,				streaming=lowerCAmelCase__		,				num_proc=lowerCAmelCase__		,				**lowerCAmelCase__		,				)
        a__     : Tuple  =path_or_paths if isinstance(lowerCAmelCase__		,				lowerCAmelCase__							) else {self.split: path_or_paths}
        a__     : List[str]  =Text(
            cache_dir=lowerCAmelCase__		,				data_files=lowerCAmelCase__		,				features=lowerCAmelCase__		,				**lowerCAmelCase__		,				)







      def        _lowercase  (   self							)       ->						List[Any]:



        '''simple docstring'''




        if self.streaming:
          a__     : str  =self.builder.as_streaming_dataset(split=self.split							)
        # Build regular (map-style) dataset
        else:
          a__     : Dict  =None
          a__     : Optional[Any]  =None
          a__     : Union[str, Any]  =None
          a__     : Tuple  =None

          self.builder.download_and_prepare(
              download_config=lowerCAmelCase__		,				download_mode=lowerCAmelCase__		,				verification_mode=lowerCAmelCase__		,				base_path=lowerCAmelCase__		,				num_proc=self.num_proc		,				)
          a__     : Tuple  =self.builder.as_dataset(
              split=self.split		,				verification_mode=lowerCAmelCase__		,				in_memory=self.keep_in_memory							)
        return dataset






