


'''simple docstring'''

# 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 :	Tuple,					a_ :	Any,					a_ :	int					):





    """simple docstring"""



    UpperCamelCase__ 						=						key
    UpperCamelCase__ 						=						freq

 def __str__( self :	str					):





    """simple docstring"""



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







def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[int]    ,		_UpperCamelCase      :				Optional[int]    ,		_UpperCamelCase      :				str    ,		_UpperCamelCase      :				List[str]    ,		_UpperCamelCase      :				str    ,		_UpperCamelCase      :				List[str]   ):





   '''simple docstring'''







   if i > j or i < 0 or j > len(_A   ) - 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(_A    ,		_A    ,		_A    ,		node - 1    ,		key[node]    ,		_A   )
   print_binary_search_tree(_A    ,		_A    ,		node + 1    ,		_A    ,		key[node]    ,		_A   )



def        SCREAMING_SNAKE_CASE__(		_UpperCamelCase      :				Optional[Any]   ):





   '''simple docstring'''







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

   UpperCamelCase__ 						=						len(_A   )

   UpperCamelCase__ 						=						[nodes[i].key for i in range(_A   )]
   UpperCamelCase__ 						=						[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.
   UpperCamelCase__ 						=						[[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
   UpperCamelCase__ 						=						[[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
   UpperCamelCase__ 						=						[[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   ):
         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(_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        SCREAMING_SNAKE_CASE__(		):





   '''simple docstring'''







   UpperCamelCase__ 						=						[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 transformers import SqueezeBertTokenizer, SqueezeBertTokenizerFast
from transformers.testing_utils import require_tokenizers, slow

from ..bert.test_tokenization_bert import BertTokenizationTest







@require_tokenizers
class  UpperCAmelCase (       SCREAMING_SNAKE_CASE__):
 _lowerCamelCase :					Optional[int]    					=					SqueezeBertTokenizer
 _lowerCamelCase :					List[Any]    					=					SqueezeBertTokenizerFast
 _lowerCamelCase :					int    					=					True

 def 		lowercase_						( self :	List[str],					**a_ :	str					):





    """simple docstring"""



    return SqueezeBertTokenizerFast.from_pretrained(self.tmpdirname,					**a_					)

 @slow
 def 		lowercase_						( self :	int					):





    """simple docstring"""



    UpperCamelCase__ 						=						SqueezeBertTokenizer.from_pretrained("squeezebert/squeezebert-mnli-headless"					)

    UpperCamelCase__ 						=						tokenizer.encode("sequence builders",					add_special_tokens=a_					)
    UpperCamelCase__ 						=						tokenizer.encode("multi-sequence build",					add_special_tokens=a_					)

    UpperCamelCase__ 						=						tokenizer.build_inputs_with_special_tokens(a_					)
    UpperCamelCase__ 						=						tokenizer.build_inputs_with_special_tokens(a_,					a_					)

    assert encoded_sentence == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id]
    assert encoded_pair == [tokenizer.cls_token_id] + text + [tokenizer.sep_token_id] + text_a + [
        tokenizer.sep_token_id
    ]