




"""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 							lowercase   :







				def __init__(				self :       Optional[int]   ,  _lowerCamelCase :       str   ,  _lowerCamelCase :       Optional[Any]							):



					"""simple docstring"""

					A_	:					Union[str, Any]						 =		key
					A_	:					str						 =		freq







				def __str__(				self :       Optional[Any]							):



					"""simple docstring"""

					return F"""Node(key={self.key}, freq={self.freq})"""

def 		lowercase_   (		_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase						):




	"""simple docstring"""






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

	A_	:					Union[str, 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(_UpperCAmelCase	,   _UpperCAmelCase	,   _UpperCAmelCase	,   node - 1	,   key[node]	,   _UpperCAmelCase						)
	print_binary_search_tree(_UpperCAmelCase	,   _UpperCAmelCase	,   node + 1	,   _UpperCAmelCase	,   key[node]	,   _UpperCAmelCase						)

def 		lowercase_   (		_UpperCAmelCase						):




	"""simple docstring"""






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

	A_	:					Any						 =		len(_UpperCAmelCase						)

	A_	:					int						 =		[nodes[i].key for i in range(_UpperCAmelCase						)]
	A_	:					List[str]						 =		[nodes[i].freq for i in range(_UpperCAmelCase						)]

	# 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_	:					List[str]						 =		[[freqs[i] if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]
	# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
	# array
	A_	:					Optional[int]						 =		[[freqs[i] if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]
	# stores tree roots that will be used later for constructing binary search tree
	A_	:					List[Any]						 =		[[i if i == j else 0 for j in range(_UpperCAmelCase						)] for i in range(_UpperCAmelCase						)]

	for interval_length in range(2	,   n + 1						):
		for i in range(n - interval_length + 1						):
			A_	:					List[Any]						 =		i + interval_length - 1

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

				if dp[i][j] > cost:
					A_	:					Dict						 =		cost
					A_	:					List[str]						 =		r

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

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

def 		lowercase_   (		):




	"""simple docstring"""






	A_	:					List[Any]						 =		[Node(_UpperCAmelCase	,   randint(1	,   50						)						) for i in range(10	,   0	,   -1						)]
	find_optimal_binary_search_tree(_UpperCAmelCase						)


if __name__ == "__main__":
		main()











"""simple docstring"""

import os
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
		from .tokenization_xglm import XGLMTokenizer
else:
		_lowerCamelCase	:      Union[str, Any]   =							None


_lowerCamelCase	:      Optional[Any]   =							logging.get_logger(__name__)

_lowerCamelCase	:      Tuple   =							{'vocab_file': 'sentencepiece.bpe.model', 'tokenizer_file': 'tokenizer.json'}

_lowerCamelCase	:      Union[str, Any]   =							{
    'vocab_file': {
        'facebook/xglm-564M': 'https://huggingface.co/facebook/xglm-564M/resolve/main/sentencepiece.bpe.model',
    },
    'tokenizer_file': {
        'facebook/xglm-564M': 'https://huggingface.co/facebook/xglm-564M/resolve/main/tokenizer.json',
    },
}

_lowerCamelCase	:      Dict   =							{
    'facebook/xglm-564M': 2048,
}

class 							lowercase   (     __UpperCAmelCase):
				__lowerCAmelCase     :     Optional[int]								= VOCAB_FILES_NAMES
				__lowerCAmelCase     :     Tuple								= PRETRAINED_VOCAB_FILES_MAP
				__lowerCAmelCase     :     List[Any]								= PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
				__lowerCAmelCase     :     Union[str, Any]								= ["""input_ids""", """attention_mask"""]
				__lowerCAmelCase     :     List[str]								= XGLMTokenizer







				def __init__(				self :       str   ,  _lowerCamelCase :       int=None   ,  _lowerCamelCase :       Any=None   ,  _lowerCamelCase :       List[str]="<s>"   ,  _lowerCamelCase :       int="</s>"   ,  _lowerCamelCase :       Any="</s>"   ,  _lowerCamelCase :       Optional[int]="<s>"   ,  _lowerCamelCase :       List[Any]="<unk>"   ,  _lowerCamelCase :       Optional[int]="<pad>"   ,  **_lowerCamelCase :       List[Any]   ,  ):



					"""simple docstring"""

					A_	:					Tuple						 =		7
					A_	:					Dict						 =		[F"""<madeupword{i}>""" for i in range(self.num_madeup_words							)]

					A_	:					str						 =		kwargs.get('''additional_special_tokens'''   ,  []							)
					kwargs["additional_special_tokens"] += [
					    word for word in madeup_words if word not in kwargs["additional_special_tokens"]
					]

					super().__init__(
					    _lowerCamelCase   ,  tokenizer_file=_lowerCamelCase   ,  bos_token=_lowerCamelCase   ,  eos_token=_lowerCamelCase   ,  sep_token=_lowerCamelCase   ,  cls_token=_lowerCamelCase   ,  unk_token=_lowerCamelCase   ,  pad_token=_lowerCamelCase   ,  **_lowerCamelCase   ,  )

					A_	:					Tuple						 =		vocab_file
					A_	:					str						 =		False if not self.vocab_file else True







				def        a_	(				self :       List[Any]   ,  _lowerCamelCase :       List[int]   ,  _lowerCamelCase :       Optional[List[int]] = None							):



					"""simple docstring"""

					if token_ids_a is None:
						return [self.sep_token_id] + token_ids_a
					A_	:					List[Any]						 =		[self.sep_token_id]
					return sep + token_ids_a + sep + sep + token_ids_a







				def        a_	(				self :       List[str]   ,  _lowerCamelCase :       List[int]   ,  _lowerCamelCase :       Optional[List[int]] = None							):



					"""simple docstring"""

					A_	:					Dict						 =		[self.sep_token_id]

					if token_ids_a is None:
						return len(sep + token_ids_a							) * [0]
					return len(sep + token_ids_a + sep + sep + token_ids_a							) * [0]







				def        a_	(				self :       List[str]   ,  _lowerCamelCase :       str   ,  _lowerCamelCase :       Optional[str] = None							):



					"""simple docstring"""

					if not self.can_save_slow_tokenizer:
						raise ValueError(
						    '''Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '''
						    '''tokenizer.'''							)

					if not os.path.isdir(_lowerCamelCase							):
						logger.error(F"""Vocabulary path ({save_directory}) should be a directory."""							)
						return
					A_	:					Tuple						 =		os.path.join(
					    _lowerCamelCase   ,  (filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file''']							)

					if os.path.abspath(self.vocab_file							) != os.path.abspath(_lowerCamelCase							):
						copyfile(self.vocab_file   ,  _lowerCamelCase							)

					return (out_vocab_file,)





