
'''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	,    lowercase_	,    lowercase_):
     snake_case_	:      Tuple            =  key
     snake_case_	:      Any            =  freq





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


def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






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

    snake_case_	:      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(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						node - 1,						key[node],						__SCREAMING_SNAKE_CASE    )
    print_binary_search_tree(__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						node + 1,						__SCREAMING_SNAKE_CASE,						key[node],						__SCREAMING_SNAKE_CASE    )

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






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

    snake_case_	:      int            =  len(__SCREAMING_SNAKE_CASE    )

    snake_case_	:      Optional[Any]            =  [nodes[i].key for i in range(__SCREAMING_SNAKE_CASE    )]
    snake_case_	:      Union[str, Any]            =  [nodes[i].freq for i in range(__SCREAMING_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.
    snake_case_	:      Optional[Any]            =  [[freqs[i] if i == j else 0 for j in range(__SCREAMING_SNAKE_CASE    )] for i in range(__SCREAMING_SNAKE_CASE    )]
    # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
    # array
    snake_case_	:      Union[str, Any]            =  [[freqs[i] if i == j else 0 for j in range(__SCREAMING_SNAKE_CASE    )] for i in range(__SCREAMING_SNAKE_CASE    )]
    # stores tree roots that will be used later for constructing binary search tree
    snake_case_	:      Tuple            =  [[i if i == j else 0 for j in range(__SCREAMING_SNAKE_CASE    )] for i in range(__SCREAMING_SNAKE_CASE    )]

    for interval_length in range(2,						n + 1    ):
        for i in range(n - interval_length + 1    ):
            snake_case_	:      Optional[int]            =  i + interval_length - 1

            snake_case_	:      int            =  sys.maxsize  # set the value to "infinity"
            snake_case_	:      Union[str, Any]            =  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
                snake_case_	:      Union[str, Any]            =  dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                snake_case_	:      int            =  dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
                snake_case_	:      Optional[Any]            =  left + total[i][j] + right

                if dp[i][j] > cost:
                    snake_case_	:      List[Any]            =  cost
                    snake_case_	:      int            =  r

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

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

def   UpperCamelCase_       (		):
    """simple docstring"""






    snake_case_	:      Optional[Any]            =  [Node(__SCREAMING_SNAKE_CASE,						randint(1,						5_0    )    ) for i in range(1_0,						0,						-1    )]
    find_optimal_binary_search_tree(__SCREAMING_SNAKE_CASE    )


if __name__ == "__main__":
  main()






'''simple docstring'''
from typing import Dict, List, Optional, Tuple

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import logging


a_     =  logging.get_logger(__name__)






class 				UpperCAmelCase_			(		snake_case__   ):
 UpperCAmelCase_						      =  ["""input_ids""", """attention_mask"""]





 def __init__(      self	,    lowercase_="[PAD]"	,    lowercase_="[BOS]"	,    lowercase_="[EOS]"	,    lowercase_="[MASK]"	,    lowercase_="[CLS]"	,    lowercase_="[SEP]"	,    lowercase_=20_48	,    **lowercase_	,    ):
     snake_case_	:      int            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else pad_token
     snake_case_	:      List[str]            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else bos_token
     snake_case_	:      Tuple            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else eos_token
     snake_case_	:      Optional[Any]            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else mask_token
     snake_case_	:      List[str]            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else cls_token
     snake_case_	:      int            =  AddedToken(lowercase_	,    lstrip=lowercase_	,    rstrip=lowercase_) if isinstance(lowercase_	,    lowercase_) else sep_token

     super().__init__(
         pad_token=lowercase_	,    bos_token=lowercase_	,    eos_token=lowercase_	,    mask_token=lowercase_	,    cls_token=lowercase_	,    sep_token=lowercase_	,    model_max_length=lowercase_	,    **lowercase_	,    )

     snake_case_	:      Dict            =  2**8  # utf is 8 bits

     # define special tokens dict
     snake_case_	:      Dict[str, int]            =  {
         self.pad_token: 0,
         self.bos_token: 1,
         self.eos_token: 2,
         self.mask_token: 3,
         self.cls_token: 4,
         self.sep_token: 5,
     }
     snake_case_	:      Dict            =  len(self.special_tokens_encoder)
     snake_case_	:      Dict[int, str]            =  {v: k for k, v in self.special_tokens_encoder.items()}





 def     snake_case__						(      self):
     snake_case_	:      str            =  self.special_tokens_encoder.copy()
     vocab.update(self.added_tokens_encoder)
     for i in range(self._utf_vocab_size):
         snake_case_	:      Tuple            =  chr(lowercase_)
         snake_case_	:      Optional[Any]            =  i + len(self.special_tokens_encoder)
     return vocab





 @property
 def     snake_case__						(      self):
     return self._utf_vocab_size + self._num_special_tokens





 def     snake_case__						(      self	,    lowercase_	,    lowercase_ = None	,    lowercase_ = False):
     if already_has_special_tokens:
         return super().get_special_tokens_mask(
             token_ids_a=lowercase_	,    token_ids_a=lowercase_	,    already_has_special_tokens=lowercase_)

     # normal case: some special tokens
     if token_ids_a is None:
         return [1] + [0] * len(lowercase_) + [1]
     return [1] + ([0] * len(lowercase_)) + [1] + ([0] * len(lowercase_)) + [1]





 def     snake_case__						(      self	,    lowercase_	,    lowercase_ = None):
     if token_ids_a is None:
         return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
     else:
         return [self.cls_token_id] + token_ids_a + [self.sep_token_id] + token_ids_a + [self.sep_token_id]





 def     snake_case__						(      self	,    lowercase_):
     snake_case_	:      Tuple            =  [chr(lowercase_) for i in text.encode("utf-8")]
     return tokens





 def     snake_case__						(      self	,    lowercase_):
     if token in self.special_tokens_encoder:
         snake_case_	:      Optional[int]            =  self.special_tokens_encoder[token]
     elif token in self.added_tokens_encoder:
         snake_case_	:      str            =  self.added_tokens_encoder[token]
     elif len(lowercase_) != 1:
         snake_case_	:      Union[str, Any]            =  self.unk_token_id
     else:
         snake_case_	:      Optional[Any]            =  ord(lowercase_) + self._num_special_tokens
     return token_id





 def     snake_case__						(      self	,    lowercase_):
     if index in self.special_tokens_decoder:
         snake_case_	:      Optional[Any]            =  self.special_tokens_decoder[index]
     elif index in self.added_tokens_decoder:
         snake_case_	:      List[str]            =  self.added_tokens_decoder[index]
     else:
         snake_case_	:      Union[str, Any]            =  chr(index - self._num_special_tokens)
     return token





 def     snake_case__						(      self	,    lowercase_):
     snake_case_	:      str            =  b""
     for token in tokens:
         if token in self.special_tokens_decoder:
             snake_case_	:      List[Any]            =  self.special_tokens_decoder[token].encode("utf-8")
         elif token in self.added_tokens_decoder:
             snake_case_	:      Any            =  self.special_tokens_decoder[token].encode("utf-8")
         elif token in self.special_tokens_encoder:
             snake_case_	:      Union[str, Any]            =  token.encode("utf-8")
         elif token in self.added_tokens_encoder:
             snake_case_	:      Any            =  token.encode("utf-8")
         else:
             snake_case_	:      Union[str, Any]            =  bytes([ord(lowercase_)])
         bstring += tok_string
     snake_case_	:      Union[str, Any]            =  bstring.decode("utf-8"	,    errors="replace")
     return string





 def     snake_case__						(      self	,    lowercase_	,    lowercase_ = None):
     return ()




