

def      a      (			A__	:   int      ,   A__	:   list     )    ->      int:





      """simple docstring"""



      _enforce_args(A__      ,   A__     )
      if n == 0:
            return 0
      _lowercase	       =float('-inf'     )
      for i in range(1      ,   n + 1     ):
            _lowercase	       =max(
                A__      ,   prices[i - 1] + naive_cut_rod_recursive(n - i      ,   A__     )     )

      return max_revue
def      a      (			A__	:   int      ,   A__	:   list     )    ->      Any:





      """simple docstring"""



      _enforce_args(A__      ,   A__     )
      _lowercase	       =[float('-inf'     ) for _ in range(n + 1     )]
      return _top_down_cut_rod_recursive(A__      ,   A__      ,   A__     )
def      a      (			A__	:   int      ,   A__	:   list      ,   A__	:   list     )    ->      Tuple:





      """simple docstring"""



      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            _lowercase	       =float('-inf'     )
            for i in range(1      ,   n + 1     ):
                  _lowercase	       =max(
                      A__      ,   prices[i - 1] + _top_down_cut_rod_recursive(n - i      ,   A__      ,   A__     )      ,   )

            _lowercase	       =max_revenue

      return max_rev[n]
def      a      (			A__	:   int      ,   A__	:   list     )    ->      Union[str, Any]:





      """simple docstring"""



      _enforce_args(A__      ,   A__     )

      # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
      # length 0.
      _lowercase	       =[float('-inf'     ) for _ in range(n + 1     )]
      _lowercase	       =0

      for i in range(1      ,   n + 1     ):
            _lowercase	       =max_rev[i]
            for j in range(1      ,   i + 1     ):
                  _lowercase	       =max(A__      ,   prices[j - 1] + max_rev[i - j]     )

            _lowercase	       =max_revenue_i

      return max_rev[n]
def      a      (			A__	:   int      ,   A__	:   list     )    ->      Dict:





      """simple docstring"""



      if n < 0:
            _lowercase	       =F'''n must be greater than or equal to 0. Got n = {n}'''
            raise ValueError(A__     )

      if n > len(A__     ):
            _lowercase	       =(
                'Each integral piece of rod must have a corresponding price. '
                F'''Got n = {n} but length of prices = {len(A__     )}'''
            )
            raise ValueError(A__     )
def      a      (			)    ->      Union[str, Any]:





      """simple docstring"""



      _lowercase	       =[6, 10, 12, 15, 20, 23]
      _lowercase	       =len(A__     )

      # the best revenue comes from cutting the rod into 6 pieces, each
      # of length 1 resulting in a revenue of 6 * 6 = 36.
      _lowercase	       =36

      _lowercase	       =top_down_cut_rod(A__      ,   A__     )
      _lowercase	       =bottom_up_cut_rod(A__      ,   A__     )
      _lowercase	       =naive_cut_rod_recursive(A__      ,   A__     )

      assert expected_max_revenue == max_rev_top_down
      assert max_rev_top_down == max_rev_bottom_up
      assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
  main()





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  __lowerCAmelCase     (					SCREAMING_SNAKE_CASE			,			SCREAMING_SNAKE_CASE			,			SCREAMING_SNAKE_CASE							):




  @register_to_config
  def __init__(				self							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase							,   lowerCAmelCase = False							,   )  -> Tuple:
        '''simple docstring'''






        super().__init__()

        _lowercase	       =nn.Embedding(lowerCAmelCase							,   lowerCAmelCase					)

        _lowercase	       =nn.Embedding(lowerCAmelCase							,   lowerCAmelCase					)
        _lowercase	       =False

        _lowercase	       =nn.Dropout(p=lowerCAmelCase					)

        _lowercase	       =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							,   )

        _lowercase	       =nn.ModuleList()
        for lyr_num in range(lowerCAmelCase					):
              _lowercase	       =TaBlock(lowerCAmelCase					)
              self.encoders.append(lowerCAmelCase					)

        _lowercase	       =TaLayerNorm(lowerCAmelCase					)
        _lowercase	       =nn.Dropout(p=lowerCAmelCase					)




  def   A__     (				self							,   lowerCAmelCase							,   lowerCAmelCase					)  -> Dict:
        '''simple docstring'''






        _lowercase	       =self.token_embedder(lowerCAmelCase					)

        _lowercase	       =encoder_input_tokens.shape[1]
        _lowercase	       =torch.arange(lowerCAmelCase							,   device=encoder_input_tokens.device					)
        x += self.position_encoding(lowerCAmelCase					)

        _lowercase	       =self.dropout_pre(lowerCAmelCase					)

        # inverted the attention mask
        _lowercase	       =encoder_input_tokens.size()
        _lowercase	       =self.get_extended_attention_mask(lowerCAmelCase							,   lowerCAmelCase					)

        for lyr in self.encoders:
              _lowercase	       =lyr(lowerCAmelCase							,   lowerCAmelCase					)[0]
        _lowercase	       =self.layer_norm(lowerCAmelCase					)

        return self.dropout_post(lowerCAmelCase					), encoder_inputs_mask


