





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



def A_     (		A__		,				A__		,				A__		,				A__    )  ->		int:
       a__						:     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_:
                            a__						:     Dict			=    max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]		,				dp[i - 1][w_]    )
                     else:
                            a__						:     Any			=    dp[i - 1][w_]

       return dp[n][w_], dp



def A_     (		A__		,				A__		,				A__    )  ->		Union[str, Any]:
       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'    )

       a__						:     str			=    len(A__    )
       if num_items != len(A__    ):
              a__						:     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__    ):
                     a__						:     Optional[Any]			=    (
                         'All weights must be integers but got weight of '
                         F'type {type(wt[i]    )} at index {i}'
                     )
                     raise TypeError(A__    )

       a__			,							a__						:     str			=    knapsack(A__		,				A__		,				A__		,				A__    )
       a__						:     set			=    set()
       _construct_solution(A__		,				A__		,				A__		,				A__		,				A__    )

       return optimal_val, example_optional_set



def A_     (		A__		,				A__		,				A__		,				A__		,				A__    )  ->		Any:
       # 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(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__":
    lowercase				:	Optional[Any]      						=  [3, 2, 4, 4]
    lowercase				:	Optional[int]      						=  [4, 3, 2, 3]
    lowercase				:	Tuple      						=  4
    lowercase				:	Optional[Any]      						=  6
    lowercase				:	Tuple      						=  [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
    lowercase						, lowercase				:	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
    lowercase						, lowercase				:	Dict      						=  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)









import json
from typing import List, Optional, Tuple

from tokenizers import pre_tokenizers, processors

from ...tokenization_utils_base import AddedToken, BatchEncoding
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_mvp import MvpTokenizer


lowercase				:	List[Any]      						=  logging.get_logger(__name__)


lowercase				:	Any      						=  {"""vocab_file""": """vocab.json""", """merges_file""": """merges.txt""", """tokenizer_file""": """tokenizer.json"""}

# See all MVP models at https://huggingface.co/models?filter=mvp
lowercase				:	Optional[Any]      						=  {
    """vocab_file""": {
        """RUCAIBox/mvp""": """https://huggingface.co/RUCAIBox/mvp/resolve/main/vocab.json""",
    },
    """added_tokens.json""": {
        """RUCAIBox/mvp""": """https://huggingface.co/RUCAIBox/mvp/resolve/main/added_tokens.json""",
    },
    """merges_file""": {
        """RUCAIBox/mvp""": """https://huggingface.co/RUCAIBox/mvp/resolve/main/merges.txt""",
    },
    """tokenizer_file""": {
        """RUCAIBox/mvp""": """https://huggingface.co/RUCAIBox/mvp/resolve/main/tokenizer.json""",
    },
}

lowercase				:	List[str]      						=  {
    """RUCAIBox/mvp""": 1_0_2_4,
}





class 			A__   (							__UpperCAmelCase     ):




   """simple docstring"""



   __A       :    Dict	  =  VOCAB_FILES_NAMES
   __A       :    str	  =  PRETRAINED_VOCAB_FILES_MAP
   __A       :    Tuple	  =  PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
   __A       :    Any	  =  ['''input_ids''', '''attention_mask''']
   __A       :    Tuple	  =  MvpTokenizer

   def __init__( self ,  lowercase=None ,  lowercase=None ,  lowercase=None ,  lowercase="replace" ,  lowercase="<s>" ,  lowercase="</s>" ,  lowercase="</s>" ,  lowercase="<s>" ,  lowercase="<unk>" ,  lowercase="<pad>" ,  lowercase="<mask>" ,  lowercase=False ,  lowercase=True ,  **lowercase ,  )      ->						str:







          '''simple docstring'''

          super().__init__(
              lowercase ,  lowercase ,  tokenizer_file=lowercase ,  errors=lowercase ,  bos_token=lowercase ,  eos_token=lowercase ,  sep_token=lowercase ,  cls_token=lowercase ,  unk_token=lowercase ,  pad_token=lowercase ,  mask_token=lowercase ,  add_prefix_space=lowercase ,  trim_offsets=lowercase ,  **lowercase ,  )

          a__						:     Optional[int]			=    json.loads(self.backend_tokenizer.pre_tokenizer.__getstate__())
          if pre_tok_state.get('add_prefix_space' ,  lowercase) != add_prefix_space:
                 a__						:     Dict			=    getattr(lowercase ,  pre_tok_state.pop('type'))
                 a__						:     str			=    add_prefix_space
                 a__						:     Union[str, Any]			=    pre_tok_class(**lowercase)

          a__						:     List[Any]			=    add_prefix_space

          # the pre_tokenizer is already updated in the GPT2TokenizerFast `__init__`
          a__						:     Optional[int]			=    'post_processor'
          a__						:     Optional[int]			=    getattr(self.backend_tokenizer ,  lowercase ,  lowercase)
          if tokenizer_component_instance:
                 a__						:     str			=    json.loads(tokenizer_component_instance.__getstate__())

                 # The lists 'sep' and 'cls' must be cased in tuples for the object `post_processor_class`
                 if "sep" in state:
                        a__						:     Any			=    tuple(state['sep'])
                 if "cls" in state:
                        a__						:     str			=    tuple(state['cls'])

                 a__						:     List[str]			=    False

                 if state.get('add_prefix_space' ,  lowercase) != add_prefix_space:
                        a__						:     List[str]			=    add_prefix_space
                        a__						:     List[str]			=    True

                 if state.get('trim_offsets' ,  lowercase) != trim_offsets:
                        a__						:     Optional[int]			=    trim_offsets
                        a__						:     List[str]			=    True

                 if changes_to_apply:
                        a__						:     Optional[int]			=    getattr(lowercase ,  state.pop('type'))
                        a__						:     Tuple			=    component_class(**lowercase)
                        setattr(self.backend_tokenizer ,  lowercase ,  lowercase)

   @property
   def 							__lowercase		( self)      ->						str:







          '''simple docstring'''

          if self._mask_token is None:
                 if self.verbose:
                        logger.error('Using mask_token, but it is not set yet.')
                 return None
          return str(self._mask_token)

   @mask_token.setter
   def 							__lowercase		( self ,  lowercase)      ->						Any:







          '''simple docstring'''

          a__						:     Tuple			=    AddedToken(lowercase ,  lstrip=lowercase ,  rstrip=lowercase) if isinstance(lowercase ,  lowercase) else value
          a__						:     str			=    value

   def 							__lowercase		( self ,  *lowercase ,  **lowercase)      ->						BatchEncoding:







          '''simple docstring'''

          a__						:     Optional[Any]			=    kwargs.get('is_split_into_words' ,  lowercase)

          if is_split_into_words and not self.add_prefix_space:
                 raise ValueError(
                     F'You need to instantiate {self.__class__.__name__} with add_prefix_space=True '
                     'to use it with pretokenized inputs.')

          return super()._batch_encode_plus(*lowercase ,  **lowercase)

   def 							__lowercase		( self ,  *lowercase ,  **lowercase)      ->						BatchEncoding:







          '''simple docstring'''

          a__						:     List[str]			=    kwargs.get('is_split_into_words' ,  lowercase)

          if is_split_into_words and not self.add_prefix_space:
                 raise ValueError(
                     F'You need to instantiate {self.__class__.__name__} with add_prefix_space=True '
                     'to use it with pretokenized inputs.')

          return super()._encode_plus(*lowercase ,  **lowercase)

   def 							__lowercase		( self ,  lowercase ,  lowercase = None)      ->						Tuple[str]:







          '''simple docstring'''

          a__						:     List[str]			=    self._tokenizer.model.save(lowercase ,  name=lowercase)
          return tuple(lowercase)

   def 							__lowercase		( self ,  lowercase ,  lowercase=None)      ->						Union[str, Any]:







          '''simple docstring'''

          a__						:     List[Any]			=    [self.bos_token_id] + token_ids_a + [self.eos_token_id]
          if token_ids_a is None:
                 return output

          return output + [self.eos_token_id] + token_ids_a + [self.eos_token_id]

   def 							__lowercase		( self ,  lowercase ,  lowercase = None)      ->						List[int]:







          '''simple docstring'''

          a__						:     int			=    [self.sep_token_id]
          a__						:     Any			=    [self.cls_token_id]

          if token_ids_a is None:
                 return len(cls + token_ids_a + sep) * [0]
          return len(cls + token_ids_a + sep + sep + token_ids_a + sep) * [0]


