



"""simple docstring"""






def 			snake_case_    ( A_   :						Optional[int],							A_   :						Optional[int],							A_   :						Any,							A_   :						Optional[int]		):


       '''simple docstring'''





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






def 			snake_case_    ( A_   :						int,							A_   :						Any,							A_   :						List[str],							A_   :						str		):


       '''simple docstring'''





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

       return dp[n][w_], dp






def 			snake_case_    ( A_   :						int,							A_   :						list,							A_   :						list		):


       '''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'''		)

       _lowerCamelCase		:							Optional[Any]            =					len(A_		)
       if num_items != len(A_		):
              _lowerCamelCase		:							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(A_		)} values'''
              )
              raise ValueError(A_		)
       for i in range(A_		):
              if not isinstance(wt[i],							A_		):
                     _lowerCamelCase		:							int            =					(
                         '''All weights must be integers but got weight of '''
                         F'''type {type(wt[i]		)} at index {i}'''
                     )
                     raise TypeError(A_		)

       _lowerCamelCase     ,       _lowerCamelCase		:							int            =					knapsack(A_,							A_,							A_,							A_		)
       _lowerCamelCase		:							set            =					set()
       _construct_solution(A_,							A_,							A_,							A_,							A_		)

       return optimal_val, example_optional_set






def 			snake_case_    ( A_   :						list,							A_   :						list,							A_   :						int,							A_   :						int,							A_   :						set		):


       '''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__              =							[3, 2, 4, 4]
   lowerCAmelCase__              =							[4, 3, 2, 3]
   lowerCAmelCase__              =							4
   lowerCAmelCase__              =							6
   lowerCAmelCase__              =							[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
   lowerCAmelCase__       ,    lowerCAmelCase__              =							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__              =							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'''





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available


SCREAMING_SNAKE_CASE     =       {}

try:
      if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE     =       ["""GPTSw3Tokenizer"""]


if TYPE_CHECKING:
      try:
            if not is_sentencepiece_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .tokenization_gpt_swa import GPTSwaTokenizer

else:
      import sys

      SCREAMING_SNAKE_CASE     =       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



