

'''simple docstring'''



import sys
from random import randint







class 		lowerCAmelCase__     :



 """simple docstring"""



 def __init__(	self      : Optional[int]      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]      ,							__SCREAMING_SNAKE_CASE      : Optional[int]    )						->				Any:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   key
      __SCREAMING_SNAKE_CASE						     =   freq


 def __str__(	self      : Optional[Any]    )						->				List[Any]:


      """simple docstring"""




      return f'Node(key={self.key}, freq={self.freq})'







def      a__ (						a__   ,					a__   ,					a__   ,					a__   ,					a__   ,					a__		):




     """simple docstring"""


     if i > j or i < 0 or j > len(a__		) - 1:
          return

     __SCREAMING_SNAKE_CASE						     =   root[i][j]
     if parent == -1:  # root does not have a parent
          print(F'{key[node]} is the root of the binary search tree.'		)
     elif is_left:
          print(F'{key[node]} is the left child of key {parent}.'		)
     else:
          print(F'{key[node]} is the right child of key {parent}.'		)

     print_binary_search_tree(a__   ,					a__   ,					a__   ,					node - 1   ,					key[node]   ,					a__		)
     print_binary_search_tree(a__   ,					a__   ,					node + 1   ,					a__   ,					key[node]   ,					a__		)







def      a__ (						a__		):




     """simple docstring"""


     nodes.sort(key=lambda a__		: node.key		)

     __SCREAMING_SNAKE_CASE						     =   len(a__		)

     __SCREAMING_SNAKE_CASE						     =   [nodes[i].key for i in range(a__		)]
     __SCREAMING_SNAKE_CASE						     =   [nodes[i].freq for i in range(a__		)]

     # This 2D array stores the overall tree cost (which's as minimized as possible);
     # for a single key, cost is equal to frequency of the key.
     __SCREAMING_SNAKE_CASE						     =   [[freqs[i] if i == j else 0 for j in range(a__		)] for i in range(a__		)]
     # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
     # array
     __SCREAMING_SNAKE_CASE						     =   [[freqs[i] if i == j else 0 for j in range(a__		)] for i in range(a__		)]
     # stores tree roots that will be used later for constructing binary search tree
     __SCREAMING_SNAKE_CASE						     =   [[i if i == j else 0 for j in range(a__		)] for i in range(a__		)]

     for interval_length in range(2   ,					n + 1		):
          for i in range(n - interval_length + 1		):
               __SCREAMING_SNAKE_CASE						     =   i + interval_length - 1

               __SCREAMING_SNAKE_CASE						     =   sys.maxsize  # set the value to "infinity"
               __SCREAMING_SNAKE_CASE						     =   total[i][j - 1] + freqs[j]

               # Apply Knuth's optimization
               # Loop without optimization: for r in range(i, j + 1):
               for r in range(root[i][j - 1]   ,					root[i + 1][j] + 1		):  # r is a temporal root
                    __SCREAMING_SNAKE_CASE						     =   dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                    __SCREAMING_SNAKE_CASE						     =   dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
                    __SCREAMING_SNAKE_CASE						     =   left + total[i][j] + right

                    if dp[i][j] > cost:
                         __SCREAMING_SNAKE_CASE						     =   cost
                         __SCREAMING_SNAKE_CASE						     =   r

     print("""Binary search tree nodes:"""		)
     for node in nodes:
          print(a__		)

     print(F'\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'		)
     print_binary_search_tree(a__   ,					a__   ,					0   ,					n - 1   ,					-1   ,					a__		)







def      a__ (						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   [Node(a__   ,					randint(1   ,					50		)		) for i in range(10   ,					0   ,					-1		)]
     find_optimal_binary_search_tree(a__		)


if __name__ == "__main__":
  main()









'''simple docstring'''



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


UpperCAmelCase				: Union[str, Any]         =  logging.get_logger(__name__)

UpperCAmelCase				: Optional[int]         =  {
    'bert-base-uncased': 'https://huggingface.co/bert-base-uncased/resolve/main/config.json',
    # QDQBERT models can be loaded from any BERT checkpoint, available at https://huggingface.co/models?filter=bert
}







class 		lowerCAmelCase__     (   a      ):



 """simple docstring"""



 lowerCAmelCase__						      =   "qdqbert"
 def __init__(	self      : str      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=30_522      ,							__SCREAMING_SNAKE_CASE      : str=768      ,							__SCREAMING_SNAKE_CASE      : Union[str, Any]=12      ,							__SCREAMING_SNAKE_CASE      : Any=12      ,							__SCREAMING_SNAKE_CASE      : Any=3_072      ,							__SCREAMING_SNAKE_CASE      : List[str]="gelu"      ,							__SCREAMING_SNAKE_CASE      : Any=0.1      ,							__SCREAMING_SNAKE_CASE      : Any=0.1      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=512      ,							__SCREAMING_SNAKE_CASE      : List[str]=2      ,							__SCREAMING_SNAKE_CASE      : Dict=0.02      ,							__SCREAMING_SNAKE_CASE      : List[str]=1E-12      ,							__SCREAMING_SNAKE_CASE      : str=True      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=1      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=0      ,							__SCREAMING_SNAKE_CASE      : Dict=2      ,							**__SCREAMING_SNAKE_CASE      : Union[str, Any]      ,							)						->				str:


      """simple docstring"""




      super().__init__(pad_token_id=__SCREAMING_SNAKE_CASE      ,							bos_token_id=__SCREAMING_SNAKE_CASE      ,							eos_token_id=__SCREAMING_SNAKE_CASE      ,							**__SCREAMING_SNAKE_CASE    )

      __SCREAMING_SNAKE_CASE						     =   vocab_size
      __SCREAMING_SNAKE_CASE						     =   max_position_embeddings
      __SCREAMING_SNAKE_CASE						     =   hidden_size
      __SCREAMING_SNAKE_CASE						     =   num_hidden_layers
      __SCREAMING_SNAKE_CASE						     =   num_attention_heads
      __SCREAMING_SNAKE_CASE						     =   intermediate_size
      __SCREAMING_SNAKE_CASE						     =   hidden_act
      __SCREAMING_SNAKE_CASE						     =   hidden_dropout_prob
      __SCREAMING_SNAKE_CASE						     =   attention_probs_dropout_prob
      __SCREAMING_SNAKE_CASE						     =   initializer_range
      __SCREAMING_SNAKE_CASE						     =   type_vocab_size
      __SCREAMING_SNAKE_CASE						     =   layer_norm_eps
      __SCREAMING_SNAKE_CASE						     =   use_cache






