code: 
  
  # 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     lowerCamelCase_			:
  
  
  
  
  	def __init__(    self	:    Dict				,			__A	:    int				,			__A	:    List[str]       ):
  		__A   : Optional[int]								= key
  		__A   : Optional[int]								= freq
  
  
  
  
  	def __str__(    self	:    Optional[int]       ):
  		return F"""Node(key={self.key}, freq={self.freq})"""
  
  
  
  
  
  
  def        __SCREAMING_SNAKE_CASE    (      a__						:      Tuple ,a__						:      Union[str, Any] ,a__						:      Optional[Any] ,a__						:      Tuple ,a__						:      Tuple ,a__						:      List[Any]					)				->							Tuple:
  	if i > j or i < 0 or j > len(a__					) - 1:
  		return
  
  	__A   : Optional[Any]								= 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    (      a__						:      str					)				->							Union[str, Any]:
  	nodes.sort(key=lambda a__					: node.key					)
  
  	__A   : Optional[int]								= len(a__					)
  
  	__A   : List[str]								= [nodes[i].key for i in range(a__					)]
  	__A   : List[Any]								= [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.
  	__A   : Tuple								= [[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
  	__A   : Any								= [[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
  	__A   : str								= [[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					):
  			__A   : Any								= i + interval_length - 1
  
  			__A   : Optional[int]								= sys.maxsize  # set the value to "infinity"
  			__A   : Dict								= 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
  				__A   : List[str]								= dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
  				__A   : str								= dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
  				__A   : Tuple								= left + total[i][j] + right
  
  				if dp[i][j] > cost:
  					__A   : str								= cost
  					__A   : Any								= 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    (      )				->							List[str]:
  	# A sample binary search tree
  	__A   : Optional[int]								= [Node(a__ ,randint(1 ,50					)					) for i in range(10 ,0 ,-1					)]
  	find_optimal_binary_search_tree(a__					)
  
  
  if __name__ == "__main__":
  			main()
  
  
  
  
  
  
style_context: 
  
  import os
  from typing import List, Union
  
  import tensorflow as tf
  from tensorflow_text import BertTokenizer as BertTokenizerLayer
  from tensorflow_text import FastBertTokenizer, ShrinkLongestTrimmer, case_fold_utfa, combine_segments, pad_model_inputs
  
  from .tokenization_bert import BertTokenizer
  
  
  
  
  
  
  class     lowerCamelCase_			(  tf.keras.layers.Layer  ):
  
  
  
  
  	def __init__(    self	:    int				,			__A	:    List				,			__A	:    bool				,			__A	:    int = None				,			__A	:    int = None				,			__A	:    int = None				,			__A	:    str = "longest"				,			__A	:    bool = True				,			__A	:    int = 512				,			__A	:    int = None				,			__A	:    bool = True				,			__A	:    bool = True				,			__A	:    bool = True				,			**__A	:    Any				,			):
  		super().__init__()
  		if use_fast_bert_tokenizer:
  			__A   : Optional[int]								= FastBertTokenizer(
  			    __A				,			token_out_type=tf.intaa				,			lower_case_nfd_strip_accents=__A				,			**__A       )
  		else:
  			__A   : Optional[Any]								= tf.lookup.StaticVocabularyTable(
  			    tf.lookup.KeyValueTensorInitializer(
  			        keys=__A				,			key_dtype=tf.string				,			values=tf.range(tf.size(__A				,			out_type=tf.intaa       )				,			dtype=tf.intaa       )				,			value_dtype=tf.intaa				,			)				,			num_oov_buckets=1				,			)
  			__A   : Any								= BertTokenizerLayer(
  			    __A				,			token_out_type=tf.intaa				,			lower_case=__A				,			**__A       )
  
  		__A   : Union[str, Any]								= vocab_list
  		__A   : List[str]								= do_lower_case
  		__A   : List[Any]								= cls_token_id or vocab_list.index("""[CLS]"""       )
  		__A   : Tuple								= sep_token_id or vocab_list.index("""[SEP]"""       )
  		__A   : str								= pad_token_id or vocab_list.index("""[PAD]"""       )
  		__A   : Optional[int]								= ShrinkLongestTrimmer(max_length - 3				,			axis=1       )  # Allow room for special tokens
  		__A   : Union[str, Any]								= max_length
  		__A   : List[Any]								= padding
  		__A   : Optional[int]								= truncation
  		__A   : Tuple								= pad_to_multiple_of
  		__A   : Optional[Any]								= return_token_type_ids
  		__A   : int								= return_attention_mask
  
  
  
  
  	@classmethod
  	def 					lowerCAmelCase_					(    cls	:    List[Any]				,			__A	:    "PreTrainedTokenizerBase"				,			**__A	:    List[str]       ):  # noqa: F821
  		__A   : Any								= kwargs.pop("""do_lower_case"""				,			__A       )
  		__A   : Dict								= tokenizer.do_lower_case if do_lower_case is None else do_lower_case
  		__A   : List[str]								= kwargs.pop("""cls_token_id"""				,			__A       )
  		__A   : str								= tokenizer.cls_token_id if cls_token_id is None else cls_token_id
  		__A   : str								= kwargs.pop("""sep_token_id"""				,			__A       )
  		__A   : Dict								= tokenizer.sep_token_id if sep_token_id is None else sep_token_id
  		__A   : Tuple								= kwargs.pop("""pad_token_id"""				,			__A       )
  		__A   : List[Any]								= tokenizer.pad_token_id if pad_token_id is None else pad_token_id
  
  		__A   : Union[str, Any]								= tokenizer.get_vocab()
  		__A   : Any								= sorted([(wordpiece, idx) for wordpiece, idx in vocab.items()]				,			key=lambda __A       : x[1]       )
  		__A   : int								= [entry[0] for entry in vocab]
  		return cls(
  		    vocab_list=__A				,			do_lower_case=__A				,			cls_token_id=__A				,			sep_token_id=__A				,			pad_token_id=__A				,			**__A				,			)
  
  
  
  
  	@classmethod
  	def 					lowerCAmelCase_					(    cls	:    List[str]				,			__A	:    Union[str, os.PathLike]				,			*__A	:    Tuple				,			**__A	:    Optional[int]       ):
  		try:
  			__A   : int								= BertTokenizer.from_pretrained(__A				,			*__A				,			**__A       )
  		except:  # noqa: E722
  			from .tokenization_bert_fast import BertTokenizerFast
  
  			__A   : Optional[int]								= BertTokenizerFast.from_pretrained(__A				,			*__A				,			**__A       )
  		return cls.from_tokenizer(__A				,			**__A       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Optional[int]				,			__A	:    Optional[Any]       ):
  		if self.do_lower_case:
  			__A   : Tuple								= case_fold_utfa(__A       )
  		__A   : Optional[int]								= self.tf_tokenizer.tokenize(__A       )
  		return tokens.merge_dims(1				,			-1       )
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Any				,			__A	:    Optional[Any]				,			__A	:    Dict=None				,			__A	:    List[Any]=None				,			__A	:    str=None				,			__A	:    Union[str, Any]=None				,			__A	:    Union[str, Any]=None				,			__A	:    int=None				,			__A	:    Any=None				,			):
  		if padding is None:
  			__A   : List[Any]								= self.padding
  		if padding not in ("longest", "max_length"):
  			raise ValueError("""Padding must be either 'longest' or 'max_length'!"""       )
  		if max_length is not None and text_pair is not None:
  			# Because we have to instantiate a Trimmer to do it properly
  			raise ValueError("""max_length cannot be overridden at call time when truncating paired texts!"""       )
  		if max_length is None:
  			__A   : Any								= self.max_length
  		if truncation is None:
  			__A   : int								= self.truncation
  		if pad_to_multiple_of is None:
  			__A   : List[str]								= self.pad_to_multiple_of
  		if return_token_type_ids is None:
  			__A   : int								= self.return_token_type_ids
  		if return_attention_mask is None:
  			__A   : Any								= self.return_attention_mask
  		if not isinstance(__A				,			tf.Tensor       ):
  			__A   : str								= tf.convert_to_tensor(__A       )
  		if text_pair is not None and not isinstance(__A				,			tf.Tensor       ):
  			__A   : Optional[Any]								= tf.convert_to_tensor(__A       )
  		if text_pair is not None:
  			if text.shape.rank > 1:
  				raise ValueError("""text argument should not be multidimensional when a text pair is supplied!"""       )
  			if text_pair.shape.rank > 1:
  				raise ValueError("""text_pair should not be multidimensional!"""       )
  		if text.shape.rank == 2:
  			__A						,							__A   : Optional[int]								= text[:, 0], text[:, 1]
  		__A   : List[Any]								= self.unpaired_tokenize(__A       )
  		if text_pair is None:  # Unpaired text
  			if truncation:
  				__A   : Union[str, Any]								= text[:, : max_length - 2]  # Allow room for special tokens
  			__A						,							__A   : List[Any]								= combine_segments(
  			    (text,)				,			start_of_sequence_id=self.cls_token_id				,			end_of_segment_id=self.sep_token_id       )
  		else:  # Paired text
  			__A   : Tuple								= self.unpaired_tokenize(__A       )
  			if truncation:
  				__A						,							__A   : Optional[int]								= self.paired_trimmer.trim([text, text_pair]       )
  			__A						,							__A   : int								= combine_segments(
  			    (text, text_pair)				,			start_of_sequence_id=self.cls_token_id				,			end_of_segment_id=self.sep_token_id       )
  		if padding == "longest":
  			__A   : str								= input_ids.bounding_shape(axis=1       )
  			if pad_to_multiple_of is not None:
  				# No ceiling division in tensorflow, so we negate floordiv instead
  				__A   : Optional[Any]								= pad_to_multiple_of * (-tf.math.floordiv(-pad_length				,			__A       ))
  		else:
  			__A   : Dict								= max_length
  
  		__A						,							__A   : str								= pad_model_inputs(__A				,			max_seq_length=__A				,			pad_value=self.pad_token_id       )
  		__A   : List[str]								= {"""input_ids""": input_ids}
  		if return_attention_mask:
  			__A   : Any								= attention_mask
  		if return_token_type_ids:
  			__A						,							__A   : Tuple								= pad_model_inputs(
  			    __A				,			max_seq_length=__A				,			pad_value=self.pad_token_id       )
  			__A   : List[str]								= token_type_ids
  		return output
  
  
  
  
  	def 					lowerCAmelCase_					(    self	:    Optional[int]       ):
  		return {
  		    "vocab_list": self.vocab_list,
  		    "do_lower_case": self.do_lower_case,
  		    "cls_token_id": self.cls_token_id,
  		    "sep_token_id": self.sep_token_id,
  		    "pad_token_id": self.pad_token_id,
  		}
  
  
  
  
  
  