# 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 					__snake_case    :




					def __init__(  self       ,			__UpperCamelCase       ,			__UpperCamelCase						)	->    Optional[int]:



									'''simple docstring'''







									snake_case__   :      Optional[Any]   				= key
									snake_case__   :      int   				= freq




					def __str__(  self						)	->    int:



									'''simple docstring'''







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




def 					UpperCamelCase__		(							A__     ,					A__     ,					A__     ,					A__     ,					A__     ,					A__       )  ->   Optional[Any]:
				if i > j or i < 0 or j > len(A__       ) - 1:
								return

				snake_case__   :      Tuple   				= 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 					UpperCamelCase__		(							A__       )  ->   Union[str, Any]:
				nodes.sort(key=lambda A__       : node.key       )

				snake_case__   :      Optional[Any]   				= len(A__       )

				snake_case__   :      Union[str, Any]   				= [nodes[i].key for i in range(A__       )]
				snake_case__   :      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.
				snake_case__   :      Union[str, Any]   				= [[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
				snake_case__   :      Optional[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
				snake_case__   :      List[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       ):
												snake_case__   :      Optional[int]   				= i + interval_length - 1

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

																if dp[i][j] > cost:
																				snake_case__   :      Union[str, Any]   				= cost
																				snake_case__   :      List[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 					UpperCamelCase__		(							)  ->   Optional[Any]:
				# A sample binary search tree
				snake_case__   :      Tuple   				= [Node(A__     ,					randint(1     ,					50       )       ) for i in range(10     ,					0     ,					-1       )]
				find_optimal_binary_search_tree(A__       )


if __name__ == "__main__":
				main()



import os
import unittest

from transformers import RealmTokenizerFast
from transformers.models.bert.tokenization_bert import (
    VOCAB_FILES_NAMES,
    BasicTokenizer,
    WordpieceTokenizer,
    _is_control,
    _is_punctuation,
    _is_whitespace,
)
from transformers.models.realm.tokenization_realm import RealmTokenizer
from transformers.testing_utils import require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin, filter_non_english





@require_tokenizers
class 					__snake_case    (     _lowerCamelCase       ,unittest.TestCase      ):
					__lowerCamelCase			   =  RealmTokenizer
					__lowerCamelCase			   =  RealmTokenizerFast
					__lowerCamelCase			   =  True
					__lowerCamelCase			   =  True
					__lowerCamelCase			   =  filter_non_english




					def      __a     (  self						)	->    Optional[Any]:



									'''simple docstring'''







									super().setUp()

									snake_case__   :      Any   				= [
									    '[UNK]',
									    '[CLS]',
									    '[SEP]',
									    '[PAD]',
									    '[MASK]',
									    'want',
									    '##want',
									    '##ed',
									    'wa',
									    'un',
									    'runn',
									    '##ing',
									    ',',
									    'low',
									    'lowest',
									]
									snake_case__   :      int   				= os.path.join(self.tmpdirname       ,			VOCAB_FILES_NAMES['vocab_file']						)
									with open(self.vocab_file       ,			'w'       ,			encoding='utf-8'						) as vocab_writer:
													vocab_writer.write(''.join([x + '\n' for x in vocab_tokens]						)						)




					def      __a     (  self       ,			__UpperCamelCase						)	->    Optional[Any]:



									'''simple docstring'''







									snake_case__   :      Optional[int]   				= 'UNwant\u00E9d,running'
									snake_case__   :      Optional[Any]   				= 'unwanted, running'
									return input_text, output_text




					def      __a     (  self						)	->    Union[str, Any]:



									'''simple docstring'''







									snake_case__   :      Optional[Any]   				= self.tokenizer_class(self.vocab_file						)

									snake_case__   :      Any   				= tokenizer.tokenize('UNwant\u00E9d,running'						)
									self.assertListEqual(__UpperCamelCase       ,			['un', '##want', '##ed', ',', 'runn', '##ing']						)
									self.assertListEqual(tokenizer.convert_tokens_to_ids(__UpperCamelCase						)       ,			[9, 6, 7, 12, 10, 11]						)




					def      __a     (  self						)	->    Union[str, Any]:



									'''simple docstring'''







									if not self.test_rust_tokenizer:
													return

									snake_case__   :      Any   				= self.get_tokenizer()
									snake_case__   :      Tuple   				= self.get_rust_tokenizer()

									snake_case__   :      Tuple   				= 'UNwant\u00E9d,running'

									snake_case__   :      Optional[int]   				= tokenizer.tokenize(__UpperCamelCase						)
									snake_case__   :      Dict   				= rust_tokenizer.tokenize(__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)

									snake_case__   :      Optional[int]   				= tokenizer.encode(__UpperCamelCase       ,			add_special_tokens=__UpperCamelCase						)
									snake_case__   :      int   				= rust_tokenizer.encode(__UpperCamelCase       ,			add_special_tokens=__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)

									snake_case__   :      Optional[int]   				= self.get_rust_tokenizer()
									snake_case__   :      Optional[Any]   				= tokenizer.encode(__UpperCamelCase						)
									snake_case__   :      Union[str, Any]   				= rust_tokenizer.encode(__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)

									# With lower casing
									snake_case__   :      Union[str, Any]   				= self.get_tokenizer(do_lower_case=__UpperCamelCase						)
									snake_case__   :      Union[str, Any]   				= self.get_rust_tokenizer(do_lower_case=__UpperCamelCase						)

									snake_case__   :      str   				= 'UNwant\u00E9d,running'

									snake_case__   :      List[Any]   				= tokenizer.tokenize(__UpperCamelCase						)
									snake_case__   :      str   				= rust_tokenizer.tokenize(__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)

									snake_case__   :      Union[str, Any]   				= tokenizer.encode(__UpperCamelCase       ,			add_special_tokens=__UpperCamelCase						)
									snake_case__   :      str   				= rust_tokenizer.encode(__UpperCamelCase       ,			add_special_tokens=__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)

									snake_case__   :      Any   				= self.get_rust_tokenizer()
									snake_case__   :      int   				= tokenizer.encode(__UpperCamelCase						)
									snake_case__   :      List[str]   				= rust_tokenizer.encode(__UpperCamelCase						)
									self.assertListEqual(__UpperCamelCase       ,			__UpperCamelCase						)




					def      __a     (  self						)	->    Optional[int]:



									'''simple docstring'''







									snake_case__   :      Optional[int]   				= BasicTokenizer()

									self.assertListEqual(tokenizer.tokenize('ah\u535A\u63A8zz'						)       ,			['ah', '\u535A', '\u63A8', 'zz']						)




					def      __a     (  self						)	->    str:



									'''simple docstring'''







									snake_case__   :      Any   				= BasicTokenizer(do_lower_case=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHeLLo!how  \n Are yoU?  '						)       ,			['hello', '!', 'how', 'are', 'you', '?']						)
									self.assertListEqual(tokenizer.tokenize('H\u00E9llo'						)       ,			['hello']						)




					def      __a     (  self						)	->    Union[str, Any]:



									'''simple docstring'''







									snake_case__   :      Optional[Any]   				= BasicTokenizer(do_lower_case=__UpperCamelCase       ,			strip_accents=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHäLLo!how  \n Are yoU?  '						)       ,			['hällo', '!', 'how', 'are', 'you', '?']						)
									self.assertListEqual(tokenizer.tokenize('H\u00E9llo'						)       ,			['h\u00E9llo']						)




					def      __a     (  self						)	->    Dict:



									'''simple docstring'''







									snake_case__   :      int   				= BasicTokenizer(do_lower_case=__UpperCamelCase       ,			strip_accents=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHäLLo!how  \n Are yoU?  '						)       ,			['hallo', '!', 'how', 'are', 'you', '?']						)
									self.assertListEqual(tokenizer.tokenize('H\u00E9llo'						)       ,			['hello']						)




					def      __a     (  self						)	->    Dict:



									'''simple docstring'''







									snake_case__   :      Any   				= BasicTokenizer(do_lower_case=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHäLLo!how  \n Are yoU?  '						)       ,			['hallo', '!', 'how', 'are', 'you', '?']						)
									self.assertListEqual(tokenizer.tokenize('H\u00E9llo'						)       ,			['hello']						)




					def      __a     (  self						)	->    List[Any]:



									'''simple docstring'''







									snake_case__   :      List[str]   				= BasicTokenizer(do_lower_case=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHeLLo!how  \n Are yoU?  '						)       ,			['HeLLo', '!', 'how', 'Are', 'yoU', '?']						)




					def      __a     (  self						)	->    int:



									'''simple docstring'''







									snake_case__   :      Optional[Any]   				= BasicTokenizer(do_lower_case=__UpperCamelCase       ,			strip_accents=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHäLLo!how  \n Are yoU?  '						)       ,			['HäLLo', '!', 'how', 'Are', 'yoU', '?']						)




					def      __a     (  self						)	->    Optional[int]:



									'''simple docstring'''







									snake_case__   :      Dict   				= BasicTokenizer(do_lower_case=__UpperCamelCase       ,			strip_accents=__UpperCamelCase						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHäLLo!how  \n Are yoU?  '						)       ,			['HaLLo', '!', 'how', 'Are', 'yoU', '?']						)




					def      __a     (  self						)	->    str:



									'''simple docstring'''







									snake_case__   :      Union[str, Any]   				= BasicTokenizer(do_lower_case=__UpperCamelCase       ,			never_split=['[UNK]']						)

									self.assertListEqual(
									    tokenizer.tokenize(' \tHeLLo!how  \n Are yoU? [UNK]'						)       ,			['HeLLo', '!', 'how', 'Are', 'yoU', '?', '[UNK]']						)




					def      __a     (  self						)	->    Tuple:



									'''simple docstring'''







									snake_case__   :      List[str]   				= ['[UNK]', '[CLS]', '[SEP]', 'want', '##want', '##ed', 'wa', 'un', 'runn', '##ing']

									snake_case__   :      List[str]   				= {}
									for i, token in enumerate(__UpperCamelCase						):
													snake_case__   :      Union[str, Any]   				= i
									snake_case__   :      List[Any]   				= WordpieceTokenizer(vocab=__UpperCamelCase       ,			unk_token='[UNK]'						)

									self.assertListEqual(tokenizer.tokenize(''						)       ,			[]						)

									self.assertListEqual(tokenizer.tokenize('unwanted running'						)       ,			['un', '##want', '##ed', 'runn', '##ing']						)

									self.assertListEqual(tokenizer.tokenize('unwantedX running'						)       ,			['[UNK]', 'runn', '##ing']						)




					def      __a     (  self						)	->    int:



									'''simple docstring'''







									self.assertTrue(_is_whitespace(' '						)						)
									self.assertTrue(_is_whitespace('\t'						)						)
									self.assertTrue(_is_whitespace('\r'						)						)
									self.assertTrue(_is_whitespace('\n'						)						)
									self.assertTrue(_is_whitespace('\u00A0'						)						)

									self.assertFalse(_is_whitespace('A'						)						)
									self.assertFalse(_is_whitespace('-'						)						)




					def      __a     (  self						)	->    List[Any]:



									'''simple docstring'''







									self.assertTrue(_is_control('\u0005'						)						)

									self.assertFalse(_is_control('A'						)						)
									self.assertFalse(_is_control(' '						)						)
									self.assertFalse(_is_control('\t'						)						)
									self.assertFalse(_is_control('\r'						)						)




					def      __a     (  self						)	->    Optional[Any]:



									'''simple docstring'''







									self.assertTrue(_is_punctuation('-'						)						)
									self.assertTrue(_is_punctuation('$'						)						)
									self.assertTrue(_is_punctuation('`'						)						)
									self.assertTrue(_is_punctuation('.'						)						)

									self.assertFalse(_is_punctuation('A'						)						)
									self.assertFalse(_is_punctuation(' '						)						)




					def      __a     (  self						)	->    Optional[int]:



									'''simple docstring'''







									snake_case__   :      List[str]   				= self.get_tokenizer()

									# Example taken from the issue https://github.com/huggingface/tokenizers/issues/340
									self.assertListEqual([tokenizer.tokenize(__UpperCamelCase						) for t in ['Test', '\xad', 'test']]       ,			[['[UNK]'], [], ['[UNK]']]						)

									if self.test_rust_tokenizer:
													snake_case__   :      int   				= self.get_rust_tokenizer()
													self.assertListEqual(
													    [rust_tokenizer.tokenize(__UpperCamelCase						) for t in ['Test', '\xad', 'test']]       ,			[['[UNK]'], [], ['[UNK]']]						)




					@slow
					def      __a     (  self						)	->    Tuple:



									'''simple docstring'''







									snake_case__   :      Any   				= self.tokenizer_class.from_pretrained('bert-base-uncased'						)

									snake_case__   :      Optional[int]   				= tokenizer.encode('sequence builders'       ,			add_special_tokens=__UpperCamelCase						)
									snake_case__   :      Optional[int]   				= tokenizer.encode('multi-sequence build'       ,			add_special_tokens=__UpperCamelCase						)

									snake_case__   :      str   				= tokenizer.build_inputs_with_special_tokens(__UpperCamelCase						)
									snake_case__   :      Tuple   				= tokenizer.build_inputs_with_special_tokens(__UpperCamelCase       ,			__UpperCamelCase						)

									assert encoded_sentence == [101] + text + [102]
									assert encoded_pair == [101] + text + [102] + text_a + [102]




					def      __a     (  self						)	->    Dict:



									'''simple docstring'''







									for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
													with self.subTest(F"""{tokenizer.__class__.__name__} ({pretrained_name})"""						):
																	snake_case__   :      Union[str, Any]   				= self.rust_tokenizer_class.from_pretrained(__UpperCamelCase       ,			**__UpperCamelCase						)

																	snake_case__   :      int   				= F"""A, naïve {tokenizer_r.mask_token} AllenNLP sentence."""
																	snake_case__   :      Optional[Any]   				= tokenizer_r.encode_plus(
																	    __UpperCamelCase       ,			return_attention_mask=__UpperCamelCase       ,			return_token_type_ids=__UpperCamelCase       ,			return_offsets_mapping=__UpperCamelCase       ,			add_special_tokens=__UpperCamelCase       ,			)

																	snake_case__   :      List[str]   				= tokenizer_r.do_lower_case if hasattr(__UpperCamelCase       ,			'do_lower_case'						) else False
																	snake_case__   :      Union[str, Any]   				= (
																	    [
																	        ((0, 0), tokenizer_r.cls_token),
																	        ((0, 1), 'A'),
																	        ((1, 2), ','),
																	        ((3, 5), 'na'),
																	        ((5, 6), '##ï'),
																	        ((6, 8), '##ve'),
																	        ((9, 15), tokenizer_r.mask_token),
																	        ((16, 21), 'Allen'),
																	        ((21, 23), '##NL'),
																	        ((23, 24), '##P'),
																	        ((25, 33), 'sentence'),
																	        ((33, 34), '.'),
																	        ((0, 0), tokenizer_r.sep_token),
																	    ]
																	    if not do_lower_case
																	    else [
																	        ((0, 0), tokenizer_r.cls_token),
																	        ((0, 1), 'a'),
																	        ((1, 2), ','),
																	        ((3, 8), 'naive'),
																	        ((9, 15), tokenizer_r.mask_token),
																	        ((16, 21), 'allen'),
																	        ((21, 23), '##nl'),
																	        ((23, 24), '##p'),
																	        ((25, 33), 'sentence'),
																	        ((33, 34), '.'),
																	        ((0, 0), tokenizer_r.sep_token),
																	    ]
																	)

																	self.assertEqual(
																	    [e[1] for e in expected_results]       ,			tokenizer_r.convert_ids_to_tokens(tokens['input_ids']						)						)
																	self.assertEqual([e[0] for e in expected_results]       ,			tokens['offset_mapping']						)




					@slow
					def      __a     (  self						)	->    Tuple:



									'''simple docstring'''







									for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
													with self.subTest(F"""{tokenizer.__class__.__name__} ({pretrained_name})"""						):
																	snake_case__   :      Dict   				= self.rust_tokenizer_class.from_pretrained(__UpperCamelCase       ,			**__UpperCamelCase						)
																	snake_case__   :      Optional[Any]   				= self.tokenizer_class.from_pretrained(__UpperCamelCase       ,			**__UpperCamelCase						)
																	snake_case__   :      int   				= [['Hello world!', 'Nice to meet you!'], ['The cute cat.', 'The adorable dog.']]

																	snake_case__   :      Optional[int]   				= tokenizer_r.batch_encode_candidates(__UpperCamelCase       ,			max_length=10       ,			return_tensors='np'						)
																	snake_case__   :      Tuple   				= tokenizer_p.batch_encode_candidates(__UpperCamelCase       ,			max_length=10       ,			return_tensors='np'						)

																	snake_case__   :      Optional[int]   				= (2, 2, 10)

																	self.assertEqual(encoded_sentence_r['input_ids'].shape       ,			__UpperCamelCase						)
																	self.assertEqual(encoded_sentence_r['attention_mask'].shape       ,			__UpperCamelCase						)
																	self.assertEqual(encoded_sentence_r['token_type_ids'].shape       ,			__UpperCamelCase						)

																	self.assertEqual(encoded_sentence_p['input_ids'].shape       ,			__UpperCamelCase						)
																	self.assertEqual(encoded_sentence_p['attention_mask'].shape       ,			__UpperCamelCase						)
																	self.assertEqual(encoded_sentence_p['token_type_ids'].shape       ,			__UpperCamelCase						)


