


def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






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



     """simple docstring"""






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

     return dp[n][w_], dp
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






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

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

     snake_case			,  snake_case					=    knapsack(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )
     snake_case					=    set()
     _construct_solution(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    )

     return optimal_val, example_optional_set
def       UpperCAmelCase__						(UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_							,UpperCamelCase_    ):



     """simple docstring"""






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


if __name__ == "__main__":
 _SCREAMING_SNAKE_CASE      :			Tuple      				=   [3, 2, 4, 4]
 _SCREAMING_SNAKE_CASE      :			Dict      				=   [4, 3, 2, 3]
 _SCREAMING_SNAKE_CASE      :			Optional[int]      				=   4
 _SCREAMING_SNAKE_CASE      :			str      				=   6
 _SCREAMING_SNAKE_CASE      :			str      				=   [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE      :			Union[str, 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
 _SCREAMING_SNAKE_CASE				,       _SCREAMING_SNAKE_CASE      :			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 TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


_SCREAMING_SNAKE_CASE      :			Dict      				=   {"configuration_van": ["VAN_PRETRAINED_CONFIG_ARCHIVE_MAP", "VanConfig"]}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _SCREAMING_SNAKE_CASE      :			Dict      				=   [
     "VAN_PRETRAINED_MODEL_ARCHIVE_LIST",
     "VanForImageClassification",
     "VanModel",
     "VanPreTrainedModel",
 ]

if TYPE_CHECKING:
 from .configuration_van import VAN_PRETRAINED_CONFIG_ARCHIVE_MAP, VanConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_van import (
      VAN_PRETRAINED_MODEL_ARCHIVE_LIST,
      VanForImageClassification,
      VanModel,
      VanPreTrainedModel,
  )

else:
 import sys

 _SCREAMING_SNAKE_CASE      :			str      				=   _LazyModule(__name__, globals()["__file__"], _import_structure)




