
"""simple docstring"""


def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_					)->				List[Any]:







       """simple docstring"""
       global f  # a global dp table for knapsack
       if f[i][j] < 0:
              if j < wt[i - 1]:
                     UpperCamelCase       			=		mf_knapsack(i - 1		,   snake_case__		,   snake_case__		,   snake_case__					)
              else:
                     UpperCamelCase       			=		max(
                         mf_knapsack(i - 1		,   snake_case__		,   snake_case__		,   snake_case__					)		,   mf_knapsack(i - 1		,   snake_case__		,   snake_case__		,   j - wt[i - 1]					) + val[i - 1]		,   )
              UpperCamelCase       			=		val
       return f[i][j]



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_					)->				Dict:







       """simple docstring"""
       UpperCamelCase       			=		[[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_:
                            UpperCamelCase       			=		max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]		,   dp[i - 1][w_]					)
                     else:
                            UpperCamelCase       			=		dp[i - 1][w_]

       return dp[n][w_], dp



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_					)->				str:







       """simple docstring"""
       if not (isinstance(snake_case__		,   (list, tuple)					) and isinstance(snake_case__		,   (list, tuple)					)):
              raise ValueError(
                  "Both the weights and values vectors must be either lists or tuples"					)

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

       UpperCamelCase       			=		knapsack(snake_case__		,   snake_case__		,   snake_case__		,   snake_case__					)
       UpperCamelCase       			=		set()
       _construct_solution(snake_case__		,   snake_case__		,   snake_case__		,   snake_case__		,   snake_case__					)

       return optimal_val, example_optional_set



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_					)->				Optional[Any]:







       """simple docstring"""
       # 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(snake_case__		,   snake_case__		,   i - 1		,   snake_case__		,   snake_case__					)
              else:
                     optimal_set.add(snake_case__					)
                     _construct_solution(snake_case__		,   snake_case__		,   i - 1		,   j - wt[i - 1]		,   snake_case__					)


if __name__ == "__main__":
      SCREAMING_SNAKE_CASE			  =  [3, 2, 4, 4]
      SCREAMING_SNAKE_CASE			  =  [4, 3, 2, 3]
      SCREAMING_SNAKE_CASE			  =  4
      SCREAMING_SNAKE_CASE			  =  6
      SCREAMING_SNAKE_CASE			  =  [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
      SCREAMING_SNAKE_CASE  ,   SCREAMING_SNAKE_CASE			  =  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			  =  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"""
import torch
import torch.nn as nn
from transformers.modeling_utils import ModuleUtilsMixin
from transformers.models.ta.modeling_ta import TaBlock, TaConfig, TaLayerNorm

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin



class   SCREAMING_SNAKE_CASE	(					_SCREAMING_SNAKE_CASE							,							_SCREAMING_SNAKE_CASE							,							_SCREAMING_SNAKE_CASE    ):





	"""simple docstring"""




	@register_to_config
	def __init__(self  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_  ,  lowerCAmelCase_ = False  ,  ):
		super().__init__()

		A_		:    Tuple						     = nn.Embedding(lowerCAmelCase_  ,  lowerCAmelCase_				)

		A_		:    List[str]						     = nn.Embedding(lowerCAmelCase_  ,  lowerCAmelCase_				)
		A_		:    Any						     = False

		A_		:    Tuple						     = nn.Dropout(p=lowerCAmelCase_				)

		A_		:    List[str]						     = TaConfig(
		    vocab_size=lowerCAmelCase_  ,  d_model=lowerCAmelCase_  ,  num_heads=lowerCAmelCase_  ,  d_kv=lowerCAmelCase_  ,  d_ff=lowerCAmelCase_  ,  dropout_rate=lowerCAmelCase_  ,  feed_forward_proj=lowerCAmelCase_  ,  is_decoder=lowerCAmelCase_  ,  is_encoder_decoder=lowerCAmelCase_  ,  )

		A_		:    Optional[Any]						     = nn.ModuleList()
		for lyr_num in range(lowerCAmelCase_				):
			A_		:    Tuple						     = TaBlock(lowerCAmelCase_				)
			self.encoders.append(lowerCAmelCase_				)

		A_		:    Any						     = TaLayerNorm(lowerCAmelCase_				)
		A_		:    Union[str, Any]						     = nn.Dropout(p=lowerCAmelCase_				)





	def  lowerCamelCase(self  ,  lowerCAmelCase_  ,  lowerCAmelCase_				):
		A_		:    List[Any]						     = self.token_embedder(lowerCAmelCase_				)

		A_		:    Optional[Any]						     = encoder_input_tokens.shape[1]
		A_		:    Any						     = torch.arange(lowerCAmelCase_  ,  device=encoder_input_tokens.device				)
		x += self.position_encoding(lowerCAmelCase_				)

		A_		:    Optional[Any]						     = self.dropout_pre(lowerCAmelCase_				)

		# inverted the attention mask
		A_		:    int						     = encoder_input_tokens.size()
		A_		:    Optional[Any]						     = self.get_extended_attention_mask(lowerCAmelCase_  ,  lowerCAmelCase_				)

		for lyr in self.encoders:
			A_		:    int						     = lyr(lowerCAmelCase_  ,  lowerCAmelCase_				)[0]
		A_		:    List[str]						     = self.layer_norm(lowerCAmelCase_				)

		return self.dropout_post(lowerCAmelCase_				), encoder_inputs_mask

