





def 							UpperCAmelCase_  (						__lowerCamelCase : List[str]     ,__lowerCamelCase : List[Any]     ,__lowerCamelCase : Dict     ,__lowerCamelCase : List[str]			):
   global f  # a global dp table for knapsack
   if f[i][j] < 0:
      if j < wt[i - 1]:
         lowercase_      :Optional[int]         =			mf_knapsack(i - 1     ,__A     ,__A     ,__A			)
      else:
         lowercase_      :Optional[Any]         =			max(
             mf_knapsack(i - 1     ,__A     ,__A     ,__A			)     ,mf_knapsack(i - 1     ,__A     ,__A     ,j - wt[i - 1]			) + val[i - 1]     ,)
      lowercase_      :str         =			val
   return f[i][j]
def 							UpperCAmelCase_  (						__lowerCamelCase : Optional[Any]     ,__lowerCamelCase : int     ,__lowerCamelCase : Tuple     ,__lowerCamelCase : int			):
   lowercase_      :str         =			[[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_      :List[str]         =			max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]     ,dp[i - 1][w_]			)
         else:
            lowercase_      :Tuple         =			dp[i - 1][w_]

   return dp[n][w_], dp
def 							UpperCAmelCase_  (						__lowerCamelCase : int     ,__lowerCamelCase : list     ,__lowerCamelCase : list			):


   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_      :Optional[Any]         =			len(__A			)
   if num_items != len(__A			):
      lowercase_      :Dict         =			(
          "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_      :Union[str, Any]         =			(
             "All weights must be integers but got weight of "
             F'type {type(wt[i]			)} at index {i}'
         )
         raise TypeError(__A			)

   lowercase_      ,							lowercase_      :List[Any]         =			knapsack(__A     ,__A     ,__A     ,__A			)
   lowercase_      :Dict         =			set()
   _construct_solution(__A     ,__A     ,__A     ,__A     ,__A			)

   return optimal_val, example_optional_set
def 							UpperCAmelCase_  (						__lowerCamelCase : list     ,__lowerCamelCase : list     ,__lowerCamelCase : int     ,__lowerCamelCase : int     ,__lowerCamelCase : set			):


   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 :					str 							=[3, 2, 4, 4]
 lowerCAmelCase :					Optional[Any] 							=[4, 3, 2, 3]
 lowerCAmelCase :					str 							=4
 lowerCAmelCase :					Any 							=6
 lowerCAmelCase :					List[Any] 							=[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 lowerCAmelCase :					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
 lowerCAmelCase :					List[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)









'''simple docstring'''


# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase :					Dict 							={
    '''configuration_xmod''': [
        '''XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''XmodConfig''',
        '''XmodOnnxConfig''',
    ],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase :					Union[str, Any] 							=[
     '''XMOD_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''XmodForCausalLM''',
     '''XmodForMaskedLM''',
     '''XmodForMultipleChoice''',
     '''XmodForQuestionAnswering''',
     '''XmodForSequenceClassification''',
     '''XmodForTokenClassification''',
     '''XmodModel''',
     '''XmodPreTrainedModel''',
 ]

if TYPE_CHECKING:
 from .configuration_xmod import XMOD_PRETRAINED_CONFIG_ARCHIVE_MAP, XmodConfig, XmodOnnxConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_xmod import (
      XMOD_PRETRAINED_MODEL_ARCHIVE_LIST,
      XmodForCausalLM,
      XmodForMaskedLM,
      XmodForMultipleChoice,
      XmodForQuestionAnswering,
      XmodForSequenceClassification,
      XmodForTokenClassification,
      XmodModel,
      XmodPreTrainedModel,
  )

else:
 import sys

 lowerCAmelCase :					Optional[Any] 							=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


