





# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint




class  __UpperCamelCase						:





     def __init__(    self							,       _UpperCamelCase							,       _UpperCamelCase				):
        _UpperCAmelCase											=      key
        _UpperCAmelCase											=      freq





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




def     A__					(						SCREAMING_SNAKE_CASE_      :			List[str]							,  SCREAMING_SNAKE_CASE_      :			Any							,  SCREAMING_SNAKE_CASE_      :			Union[str, Any]							,  SCREAMING_SNAKE_CASE_      :			Union[str, Any]							,  SCREAMING_SNAKE_CASE_      :			int							,  SCREAMING_SNAKE_CASE_      :			Tuple	)     ->     List[str]:






   """simple docstring"""







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

   _UpperCAmelCase											=      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(snake_case__							,  snake_case__							,  snake_case__							,  node - 1							,  key[node]							,  snake_case__	)
   print_binary_search_tree(snake_case__							,  snake_case__							,  node + 1							,  snake_case__							,  key[node]							,  snake_case__	)
def     A__					(						SCREAMING_SNAKE_CASE_      :			int	)     ->     Optional[int]:






   """simple docstring"""







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

   _UpperCAmelCase											=      len(snake_case__	)

   _UpperCAmelCase											=      [nodes[i].key for i in range(snake_case__	)]
   _UpperCAmelCase											=      [nodes[i].freq for i in range(snake_case__	)]

   # 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.
   _UpperCAmelCase											=      [[freqs[i] if i == j else 0 for j in range(snake_case__	)] for i in range(snake_case__	)]
   # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
   # array
   _UpperCAmelCase											=      [[freqs[i] if i == j else 0 for j in range(snake_case__	)] for i in range(snake_case__	)]
   # stores tree roots that will be used later for constructing binary search tree
   _UpperCAmelCase											=      [[i if i == j else 0 for j in range(snake_case__	)] for i in range(snake_case__	)]

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

         _UpperCAmelCase											=      sys.maxsize  # set the value to "infinity"
         _UpperCAmelCase											=      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
            _UpperCAmelCase											=      dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
            _UpperCAmelCase											=      dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
            _UpperCAmelCase											=      left + total[i][j] + right

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

   print('''Binary search tree nodes:'''	)
   for node in nodes:
      print(snake_case__	)

   print(F'''\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.'''	)
   print_binary_search_tree(snake_case__							,  snake_case__							,  0							,  n - 1							,  -1							,  snake_case__	)
def     A__					(						)     ->     Optional[int]:






   """simple docstring"""







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


if __name__ == "__main__":
   main()






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


UpperCAmelCase_											=  logging.get_logger(__name__)

UpperCAmelCase_											=  {
    "tau/splinter-base": "https://huggingface.co/tau/splinter-base/resolve/main/config.json",
    "tau/splinter-base-qass": "https://huggingface.co/tau/splinter-base-qass/resolve/main/config.json",
    "tau/splinter-large": "https://huggingface.co/tau/splinter-large/resolve/main/config.json",
    "tau/splinter-large-qass": "https://huggingface.co/tau/splinter-large-qass/resolve/main/config.json",
    # See all Splinter models at https://huggingface.co/models?filter=splinter
}




class  __UpperCamelCase						(       A__						):
     __A  :     Tuple            =      """splinter"""





     def __init__(    self							,       _UpperCamelCase=30522							,       _UpperCamelCase=768							,       _UpperCamelCase=12							,       _UpperCamelCase=12							,       _UpperCamelCase=3072							,       _UpperCamelCase="gelu"							,       _UpperCamelCase=0.1							,       _UpperCamelCase=0.1							,       _UpperCamelCase=512							,       _UpperCamelCase=2							,       _UpperCamelCase=0.02							,       _UpperCamelCase=1e-12							,       _UpperCamelCase=True							,       _UpperCamelCase=0							,       _UpperCamelCase=104							,       **_UpperCamelCase							,       ):
        super().__init__(pad_token_id=_UpperCamelCase							,       **_UpperCamelCase				)

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