

def      a      (			A__	:   Optional[Any]      ,   A__	:   str      ,   A__	:   List[Any]      ,   A__	:   Union[str, Any]     )    ->      Optional[int]:





      """simple docstring"""



      global f  # a global dp table for knapsack
      if f[i][j] < 0:
            if j < wt[i - 1]:
                  _lowercase	       =mf_knapsack(i - 1      ,   A__      ,   A__      ,   A__     )
            else:
                  _lowercase	       =max(
                      mf_knapsack(i - 1      ,   A__      ,   A__      ,   A__     )      ,   mf_knapsack(i - 1      ,   A__      ,   A__      ,   j - wt[i - 1]     ) + val[i - 1]      ,   )
            _lowercase	       =val
      return f[i][j]
def      a      (			A__	:   Tuple      ,   A__	:   Tuple      ,   A__	:   int      ,   A__	:   Dict     )    ->      Optional[Any]:





      """simple docstring"""



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

      return dp[n][w_], dp
def      a      (			A__	:   int      ,   A__	:   list      ,   A__	:   list     )    ->      str:





      """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'     )

      _lowercase	       =len(A__     )
      if num_items != len(A__     ):
            _lowercase	       =(
                '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__     ):
                  _lowercase	       =(
                      'All weights must be integers but got weight of '
                      F'''type {type(wt[i]     )} at index {i}'''
                  )
                  raise TypeError(A__     )

      _lowercase       ,       _lowercase	       =knapsack(A__      ,   A__      ,   A__      ,   A__     )
      _lowercase	       =set()
      _construct_solution(A__      ,   A__      ,   A__      ,   A__      ,   A__     )

      return optimal_val, example_optional_set
def      a      (			A__	:   list      ,   A__	:   list      ,   A__	:   int      ,   A__	:   int      ,   A__	:   set     )    ->      str:





      """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__":
  lowercase_									=   [3, 2, 4, 4]
  lowercase_									=   [4, 3, 2, 3]
  lowercase_									=   4
  lowercase_									=   6
  lowercase_									=   [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
  lowercase_				,						lowercase_									=   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
  lowercase_				,						lowercase_									=   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 .imports import is_tqdm_available


if is_tqdm_available():
  from tqdm.auto import tqdm as _tqdm

from ..state import PartialState
def      a      (			A__	:   bool = True      ,   *A__	:   int      ,   **A__	:   Union[str, Any]     )    ->      List[str]:





      """simple docstring"""



      if not is_tqdm_available():
            raise ImportError('Accelerate\'s `tqdm` module requires `tqdm` to be installed. Please run `pip install tqdm`.'     )
      _lowercase	       =False
      if main_process_only:
            _lowercase	       =PartialState().local_process_index == 0
      return _tqdm(*A__      ,   **A__      ,   disable=A__     )


