





"""simple docstring"""
def 					__lowerCamelCase       (							a_					:		Any			,       a_					:		int			,       a_					:		Tuple			,       a_					:		Any							)      ->				int:
      global f  # a global dp table for knapsack
      if f[i][j] < 0:
            if j < wt[i - 1]:
                  __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  mf_knapsack(i - 1			,       a_			,       a_			,       a_							)
            else:
                  __SCREAMING_SNAKE_CASE       :Tuple		    =  max(
                      mf_knapsack(i - 1			,       a_			,       a_			,       a_							)			,       mf_knapsack(i - 1			,       a_			,       a_			,       j - wt[i - 1]							) + val[i - 1]			,       )
            __SCREAMING_SNAKE_CASE       :List[str]		    =  val
      return f[i][j]



def 					__lowerCamelCase       (							a_					:		Optional[Any]			,       a_					:		str			,       a_					:		Optional[Any]			,       a_					:		str							)      ->				Optional[int]:
      __SCREAMING_SNAKE_CASE       :int		    =  [[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_:
                        __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]			,       dp[i - 1][w_]							)
                  else:
                        __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  dp[i - 1][w_]

      return dp[n][w_], dp



def 					__lowerCamelCase       (							a_					:		int			,       a_					:		list			,       a_					:		list							)      ->				Dict:
      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'''							)

      __SCREAMING_SNAKE_CASE       :Dict		    =  len(a_							)
      if num_items != len(a_							):
            __SCREAMING_SNAKE_CASE       :List[str]		    =  (
                '''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_							):
                  __SCREAMING_SNAKE_CASE       :Tuple		    =  (
                      '''All weights must be integers but got weight of '''
                      f'''type {type(wt[i]							)} at index {i}'''
                  )
                  raise TypeError(a_							)

      __SCREAMING_SNAKE_CASE    ,__SCREAMING_SNAKE_CASE       :Dict		    =  knapsack(a_			,       a_			,       a_			,       a_							)
      __SCREAMING_SNAKE_CASE       :set		    =  set()
      _construct_solution(a_			,       a_			,       a_			,       a_			,       a_							)

      return optimal_val, example_optional_set



def 					__lowerCamelCase       (							a_					:		list			,       a_					:		list			,       a_					:		int			,       a_					:		int			,       a_					:		set							)      ->				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__":
  lowerCamelCase_       =		[3, 2, 4, 4]
  lowerCamelCase_       =		[4, 3, 2, 3]
  lowerCamelCase_       =		4
  lowerCamelCase_       =		6
  lowerCamelCase_       =		[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
  lowerCamelCase_      ,					lowerCamelCase_       =		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_      ,					lowerCamelCase_       =		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"""
from typing import Callable, Optional, Union

from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCamelCase_       =		logging.get_logger(__name__)

lowerCamelCase_       =		{
    "microsoft/xprophetnet-large-wiki100-cased": (
        "https://huggingface.co/microsoft/xprophetnet-large-wiki100-cased/resolve/main/config.json"
    ),
}






class  _SCREAMING_SNAKE_CASE(       A  ):
       SCREAMING_SNAKE_CASE_       :				Optional[Any]     						=  '''xlm-prophetnet'''
       SCREAMING_SNAKE_CASE_       :				Any     						=  ['''past_key_values''']
       SCREAMING_SNAKE_CASE_       :				Optional[Any]     						=  {
           '''num_attention_heads''': '''num_encoder_attention_heads''',
       }




       def __init__(						self		,SCREAMING_SNAKE_CASE__ = 0.1		,SCREAMING_SNAKE_CASE__ = "gelu"		,SCREAMING_SNAKE_CASE__ = 3_05_22		,SCREAMING_SNAKE_CASE__ = 10_24		,SCREAMING_SNAKE_CASE__ = 40_96		,SCREAMING_SNAKE_CASE__ = 12		,SCREAMING_SNAKE_CASE__ = 16		,SCREAMING_SNAKE_CASE__ = 40_96		,SCREAMING_SNAKE_CASE__ = 12		,SCREAMING_SNAKE_CASE__ = 16		,SCREAMING_SNAKE_CASE__ = 0.1		,SCREAMING_SNAKE_CASE__ = 0.1		,SCREAMING_SNAKE_CASE__ = 5_12		,SCREAMING_SNAKE_CASE__ = 0.0_2		,SCREAMING_SNAKE_CASE__ = True		,SCREAMING_SNAKE_CASE__ = True		,SCREAMING_SNAKE_CASE__ = 0		,SCREAMING_SNAKE_CASE__ = 2		,SCREAMING_SNAKE_CASE__ = 32		,SCREAMING_SNAKE_CASE__ = 1_28		,SCREAMING_SNAKE_CASE__ = False		,SCREAMING_SNAKE_CASE__ = 0.0		,SCREAMING_SNAKE_CASE__ = True		,SCREAMING_SNAKE_CASE__ = 0		,SCREAMING_SNAKE_CASE__ = 1		,SCREAMING_SNAKE_CASE__ = 2		,**SCREAMING_SNAKE_CASE__		,)      ->				Dict:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :int		    =  vocab_size
             __SCREAMING_SNAKE_CASE       :Tuple		    =  hidden_size
             __SCREAMING_SNAKE_CASE       :Optional[int]		    =  encoder_ffn_dim
             __SCREAMING_SNAKE_CASE       :Optional[int]		    =  num_encoder_layers
             __SCREAMING_SNAKE_CASE       :Tuple		    =  num_encoder_attention_heads
             __SCREAMING_SNAKE_CASE       :List[Any]		    =  decoder_ffn_dim
             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  num_decoder_layers
             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  num_decoder_attention_heads
             __SCREAMING_SNAKE_CASE       :List[str]		    =  max_position_embeddings
             __SCREAMING_SNAKE_CASE       :Dict		    =  init_std  # Normal(0, this parameter)
             __SCREAMING_SNAKE_CASE       :List[Any]		    =  activation_function

             # parameters for xlmprophetnet
             __SCREAMING_SNAKE_CASE       :Tuple		    =  ngram
             __SCREAMING_SNAKE_CASE       :int		    =  num_buckets
             __SCREAMING_SNAKE_CASE       :Optional[int]		    =  relative_max_distance
             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  disable_ngram_loss
             __SCREAMING_SNAKE_CASE       :Dict		    =  eps

             # 3 Types of Dropout
             __SCREAMING_SNAKE_CASE       :List[str]		    =  attention_dropout
             __SCREAMING_SNAKE_CASE       :Dict		    =  activation_dropout
             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  dropout

             __SCREAMING_SNAKE_CASE       :int		    =  use_cache

             super().__init__(
                 pad_token_id=SCREAMING_SNAKE_CASE__		,bos_token_id=SCREAMING_SNAKE_CASE__		,eos_token_id=SCREAMING_SNAKE_CASE__		,is_encoder_decoder=SCREAMING_SNAKE_CASE__		,add_cross_attention=SCREAMING_SNAKE_CASE__		,decoder_start_token_id=SCREAMING_SNAKE_CASE__		,**SCREAMING_SNAKE_CASE__		,)




       @property
       def    _UpperCamelCase					(						self							)      ->				int:





             """simple docstring"""






             return self.num_encoder_layers + self.num_decoder_layers




       @num_hidden_layers.setter
       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__							)      ->				Optional[int]:





             """simple docstring"""






             raise NotImplementedError(
                 '''This model does not support the setting of `num_hidden_layers`. Please set `num_encoder_layers` and'''
                 ''' `num_decoder_layers`.'''							)