





def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''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  ,    lowercase__  ,    lowercase__  ,    lowercase__  )
      else:
         UpperCAmelCase_											=max(
             mf_knapsack(i - 1  ,    lowercase__  ,    lowercase__  ,    lowercase__  )  ,    mf_knapsack(i - 1  ,    lowercase__  ,    lowercase__  ,    j - wt[i - 1]  ) + val[i - 1]  ,    )
      UpperCAmelCase_											=val
   return f[i][j]




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''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     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






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

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

   UpperCAmelCase_											=knapsack(lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  )
   UpperCAmelCase_											=set()
   _construct_solution(lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  )

   return optimal_val, example_optional_set




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






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


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

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowercase  :   Any						      ={
    """configuration_upernet""": ["""UperNetConfig"""],
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     __lowercase  :   Tuple						      =[
         """UperNetForSemanticSegmentation""",
         """UperNetPreTrainedModel""",
     ]


if TYPE_CHECKING:
     from .configuration_upernet import UperNetConfig

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_upernet import UperNetForSemanticSegmentation, UperNetPreTrainedModel


else:
     import sys

     __lowercase  :   Any						      =_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)




