

"""simple docstring"""



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





def  _snake_case     (    UpperCAmelCase_  :					List[str]					,   UpperCAmelCase_  :					Union[str, Any]					,   UpperCAmelCase_  :					str					,   UpperCAmelCase_  :					List[str]			):
     A__										=  [[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_:
                    A__										=  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]					,   dp[i - 1][w_]			)
               else:
                    A__										=  dp[i - 1][w_]

     return dp[n][w_], dp





def  _snake_case     (    UpperCAmelCase_  :					int					,   UpperCAmelCase_  :					list					,   UpperCAmelCase_  :					list			):
     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"""			)

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

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

     return optimal_val, example_optional_set





def  _snake_case     (    UpperCAmelCase_  :					list					,   UpperCAmelCase_  :					list					,   UpperCAmelCase_  :					int					,   UpperCAmelCase_  :					int					,   UpperCAmelCase_  :					set			):
     # for the current item i at a maximum weight j to be part of an optimal subset,
     # the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
     # where i - 1 means considering only the previous items at the given maximum weight
     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_					:	int							  =						[4, 3, 2, 3]
 SCREAMING_SNAKE_CASE_					:	Optional[int]							  =						4
 SCREAMING_SNAKE_CASE_					:	List[str]							  =						6
 SCREAMING_SNAKE_CASE_					:	int							  =						[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
 SCREAMING_SNAKE_CASE_  ,SCREAMING_SNAKE_CASE_					:	str							  =						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_					:	Tuple							  =						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

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


SCREAMING_SNAKE_CASE_					:	List[str]							  =						{'configuration_mra': ['MRA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MraConfig']}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 SCREAMING_SNAKE_CASE_					:	List[Any]							  =						[
     'MRA_PRETRAINED_MODEL_ARCHIVE_LIST',
     'MraForMaskedLM',
     'MraForMultipleChoice',
     'MraForQuestionAnswering',
     'MraForSequenceClassification',
     'MraForTokenClassification',
     'MraLayer',
     'MraModel',
     'MraPreTrainedModel',
 ]


if TYPE_CHECKING:
 from .configuration_mra import MRA_PRETRAINED_CONFIG_ARCHIVE_MAP, MraConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_mra import (
      MRA_PRETRAINED_MODEL_ARCHIVE_LIST,
      MraForMaskedLM,
      MraForMultipleChoice,
      MraForQuestionAnswering,
      MraForSequenceClassification,
      MraForTokenClassification,
      MraLayer,
      MraModel,
      MraPreTrainedModel,
  )
else:
 import sys

 SCREAMING_SNAKE_CASE_					:	List[str]							  =						_LazyModule(__name__, globals()['__file__'], _import_structure)






