




"""simple docstring"""

import os
import pickle
import tempfile
import unittest
from typing import Callable, Optional

import numpy as np

from transformers import (
    BatchEncoding,
    BertTokenizer,
    BertTokenizerFast,
    PreTrainedTokenizer,
    PreTrainedTokenizerFast,
    TensorType,
    TokenSpan,
    is_tokenizers_available,
)
from transformers.models.gpta.tokenization_gpta import GPTaTokenizer
from transformers.testing_utils import CaptureStderr, require_flax, require_tf, require_tokenizers, require_torch, slow


if is_tokenizers_available():
						from tokenizers import Tokenizer
						from tokenizers.models import WordPiece



class  _snake_case				(							unittest.TestCase       ):

				'''simple docstring'''




				def 				snake_case_ (							self      :  Any					,							snake_case      :  Any     ):
								UpperCAmelCase_					:str      			=      list(tokenizer_class.max_model_input_sizes.keys()     )
								for model_name in sa_models[:1]:
												UpperCAmelCase_					:Tuple      			=      tokenizer_class.from_pretrained(snake_case     )
												self.assertIsNotNone(snake_case     )
												self.assertIsInstance(snake_case					,							snake_case     )
												self.assertIsInstance(snake_case					,							snake_case     )

												for special_tok in tokenizer.all_special_tokens:
																self.assertIsInstance(snake_case					,							snake_case     )
																UpperCAmelCase_					:Optional[Any]      			=      tokenizer.convert_tokens_to_ids(snake_case     )
																self.assertIsInstance(snake_case					,							snake_case     )





				def 				snake_case_ (							self      :  List[Any]					,							snake_case      :  BatchEncoding					,							snake_case      :  Optional[Callable] = None     ):
								UpperCAmelCase_					:Any      			=      pickle.dumps(snake_case     )
								self.assertIsNotNone(snake_case     )

								UpperCAmelCase_					:List[Any]      			=      pickle.loads(snake_case     )

								# Ensure is_fast is correctly restored
								self.assertEqual(be_restored.is_fast					,							be_original.is_fast     )

								# Ensure encodings are potentially correctly restored
								if be_original.is_fast:
												self.assertIsNotNone(be_restored.encodings     )
								else:
												self.assertIsNone(be_restored.encodings     )

								# Ensure the keys are the same
								for original_v, restored_v in zip(be_original.values()					,							be_restored.values()     ):
												if equal_op:
																self.assertTrue(equal_op(snake_case					,							snake_case     )     )
												else:
																self.assertEqual(snake_case					,							snake_case     )





				@slow
				def 				snake_case_ (							self      :  List[Any]     ):
								self.check_tokenizer_from_pretrained(snake_case     )





				def 				snake_case_ (							self      :  Dict     ):
								self.assertEqual(TensorType('''tf'''     )					,							TensorType.TENSORFLOW     )
								self.assertEqual(TensorType('''pt'''     )					,							TensorType.PYTORCH     )
								self.assertEqual(TensorType('''np'''     )					,							TensorType.NUMPY     )





				@require_tokenizers
				def 				snake_case_ (							self      :  List[Any]     ):
								import numpy as np

								UpperCAmelCase_					:Tuple      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )
								UpperCAmelCase_					:Union[str, Any]      			=      BertTokenizerFast.from_pretrained('''bert-base-cased'''     )

								# Python no tensor
								with self.subTest('''BatchEncoding (Python, return_tensors=None)'''     ):
												self.assert_dump_and_restore(tokenizer_p('''Small example to encode'''     )     )

								with self.subTest('''BatchEncoding (Python, return_tensors=NUMPY)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_p('''Small example to encode'''					,							return_tensors=TensorType.NUMPY     )					,							np.array_equal     )

								with self.subTest('''BatchEncoding (Rust, return_tensors=None)'''     ):
												self.assert_dump_and_restore(tokenizer_r('''Small example to encode'''     )     )

								with self.subTest('''BatchEncoding (Rust, return_tensors=NUMPY)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_r('''Small example to encode'''					,							return_tensors=TensorType.NUMPY     )					,							np.array_equal     )





				@require_tf
				@require_tokenizers
				def 				snake_case_ (							self      :  Optional[int]     ):
								import tensorflow as tf

								def tf_array_equals(snake_case      :  str					,							snake_case      :  List[Any]     ):
												return tf.reduce_all(tf.equal(snake_case					,							snake_case     )     )

								UpperCAmelCase_					:Any      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )
								UpperCAmelCase_					:Union[str, Any]      			=      BertTokenizerFast.from_pretrained('''bert-base-cased'''     )

								with self.subTest('''BatchEncoding (Python, return_tensors=TENSORFLOW)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_p('''Small example to encode'''					,							return_tensors=TensorType.TENSORFLOW     )					,							snake_case     )

								with self.subTest('''BatchEncoding (Rust, return_tensors=TENSORFLOW)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_r('''Small example to encode'''					,							return_tensors=TensorType.TENSORFLOW     )					,							snake_case     )





				@require_torch
				@require_tokenizers
				def 				snake_case_ (							self      :  Union[str, Any]     ):
								import torch

								UpperCAmelCase_					:Any      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )
								UpperCAmelCase_					:List[str]      			=      BertTokenizerFast.from_pretrained('''bert-base-cased'''     )

								with self.subTest('''BatchEncoding (Python, return_tensors=PYTORCH)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_p('''Small example to encode'''					,							return_tensors=TensorType.PYTORCH     )					,							torch.equal     )

								with self.subTest('''BatchEncoding (Rust, return_tensors=PYTORCH)'''     ):
												self.assert_dump_and_restore(
												    tokenizer_r('''Small example to encode'''					,							return_tensors=TensorType.PYTORCH     )					,							torch.equal     )





				@require_tokenizers
				def 				snake_case_ (							self      :  Optional[int]     ):
								UpperCAmelCase_					:str      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )
								UpperCAmelCase_					:Union[str, Any]      			=      BertTokenizerFast.from_pretrained('''bert-base-cased'''     )

								with self.subTest('''Python Tokenizer'''     ):
												self.assertFalse(tokenizer_p('''Small example to_encode'''     ).is_fast     )

								with self.subTest('''Rust Tokenizer'''     ):
												self.assertTrue(tokenizer_r('''Small example to_encode'''     ).is_fast     )





				@require_tokenizers
				def 				snake_case_ (							self      :  Dict     ):
								UpperCAmelCase_					:Tuple      			=      BertTokenizerFast.from_pretrained('''bert-base-cased'''     )
								UpperCAmelCase_					:List[str]      			=      tokenizer_r(['''Test''', '''\xad''', '''test''']					,							is_split_into_words=snake_case     )

								self.assertEqual(encoded.word_to_tokens(0     )					,							TokenSpan(start=1					,							end=2     )     )
								self.assertEqual(encoded.word_to_tokens(1     )					,							snake_case     )
								self.assertEqual(encoded.word_to_tokens(2     )					,							TokenSpan(start=2					,							end=3     )     )





				def 				snake_case_ (							self      :  List[Any]     ):
								UpperCAmelCase_					:int      			=      BatchEncoding({'''inputs''': [[1, 2, 3], [4, 5, 6]], '''labels''': [0, 1]}     )
								UpperCAmelCase_					:Union[str, Any]      			=      batch.convert_to_tensors(tensor_type='''np'''     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(2, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(2,)     )
								# test converting the converted
								with CaptureStderr() as cs:
												UpperCAmelCase_					:Optional[Any]      			=      batch.convert_to_tensors(tensor_type='''np'''     )
								self.assertFalse(len(cs.err     )					,							msg=f'should have no warning, but got {cs.err}'     )

								UpperCAmelCase_					:Optional[int]      			=      BatchEncoding({'''inputs''': [1, 2, 3], '''labels''': 0}     )
								UpperCAmelCase_					:List[Any]      			=      batch.convert_to_tensors(tensor_type='''np'''					,							prepend_batch_axis=snake_case     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(1, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(1,)     )





				@require_torch
				def 				snake_case_ (							self      :  Union[str, Any]     ):
								UpperCAmelCase_					:List[Any]      			=      BatchEncoding({'''inputs''': [[1, 2, 3], [4, 5, 6]], '''labels''': [0, 1]}     )
								UpperCAmelCase_					:List[str]      			=      batch.convert_to_tensors(tensor_type='''pt'''     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(2, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(2,)     )
								# test converting the converted
								with CaptureStderr() as cs:
												UpperCAmelCase_					:str      			=      batch.convert_to_tensors(tensor_type='''pt'''     )
								self.assertFalse(len(cs.err     )					,							msg=f'should have no warning, but got {cs.err}'     )

								UpperCAmelCase_					:Dict      			=      BatchEncoding({'''inputs''': [1, 2, 3], '''labels''': 0}     )
								UpperCAmelCase_					:Union[str, Any]      			=      batch.convert_to_tensors(tensor_type='''pt'''					,							prepend_batch_axis=snake_case     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(1, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(1,)     )





				@require_tf
				def 				snake_case_ (							self      :  Tuple     ):
								UpperCAmelCase_					:Optional[Any]      			=      BatchEncoding({'''inputs''': [[1, 2, 3], [4, 5, 6]], '''labels''': [0, 1]}     )
								UpperCAmelCase_					:Union[str, Any]      			=      batch.convert_to_tensors(tensor_type='''tf'''     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(2, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(2,)     )
								# test converting the converted
								with CaptureStderr() as cs:
												UpperCAmelCase_					:Optional[int]      			=      batch.convert_to_tensors(tensor_type='''tf'''     )
								self.assertFalse(len(cs.err     )					,							msg=f'should have no warning, but got {cs.err}'     )

								UpperCAmelCase_					:int      			=      BatchEncoding({'''inputs''': [1, 2, 3], '''labels''': 0}     )
								UpperCAmelCase_					:Any      			=      batch.convert_to_tensors(tensor_type='''tf'''					,							prepend_batch_axis=snake_case     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(1, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(1,)     )





				@require_flax
				def 				snake_case_ (							self      :  Union[str, Any]     ):
								UpperCAmelCase_					:str      			=      BatchEncoding({'''inputs''': [[1, 2, 3], [4, 5, 6]], '''labels''': [0, 1]}     )
								UpperCAmelCase_					:Any      			=      batch.convert_to_tensors(tensor_type='''jax'''     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(2, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(2,)     )
								# test converting the converted
								with CaptureStderr() as cs:
												UpperCAmelCase_					:Union[str, Any]      			=      batch.convert_to_tensors(tensor_type='''jax'''     )
								self.assertFalse(len(cs.err     )					,							msg=f'should have no warning, but got {cs.err}'     )

								UpperCAmelCase_					:str      			=      BatchEncoding({'''inputs''': [1, 2, 3], '''labels''': 0}     )
								UpperCAmelCase_					:List[str]      			=      batch.convert_to_tensors(tensor_type='''jax'''					,							prepend_batch_axis=snake_case     )
								self.assertEqual(tensor_batch['''inputs'''].shape					,							(1, 3)     )
								self.assertEqual(tensor_batch['''labels'''].shape					,							(1,)     )





				def 				snake_case_ (							self      :  Optional[int]     ):
								UpperCAmelCase_					:str      			=      [{'''input_ids''': np.array([0, 1, 2]     )}, {'''input_ids''': np.array([0, 1, 2, 3]     )}]
								UpperCAmelCase_					:Any      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )

								UpperCAmelCase_					:List[str]      			=      tokenizer.pad(snake_case					,							padding=snake_case     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							np.ndarray     )     )
								self.assertEqual(batch['''input_ids'''].tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )
								UpperCAmelCase_					:List[str]      			=      tokenizer.pad(snake_case					,							padding=snake_case					,							return_tensors='''np'''     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							np.ndarray     )     )
								self.assertEqual(batch['''input_ids'''].tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )





				@require_torch
				def 				snake_case_ (							self      :  List[Any]     ):
								import torch

								UpperCAmelCase_					:int      			=      [{'''input_ids''': torch.tensor([0, 1, 2]     )}, {'''input_ids''': torch.tensor([0, 1, 2, 3]     )}]
								UpperCAmelCase_					:List[str]      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )

								UpperCAmelCase_					:int      			=      tokenizer.pad(snake_case					,							padding=snake_case     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							torch.Tensor     )     )
								self.assertEqual(batch['''input_ids'''].tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )
								UpperCAmelCase_					:Union[str, Any]      			=      tokenizer.pad(snake_case					,							padding=snake_case					,							return_tensors='''pt'''     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							torch.Tensor     )     )
								self.assertEqual(batch['''input_ids'''].tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )





				@require_tf
				def 				snake_case_ (							self      :  Union[str, Any]     ):
								import tensorflow as tf

								UpperCAmelCase_					:List[str]      			=      [{'''input_ids''': tf.constant([0, 1, 2]     )}, {'''input_ids''': tf.constant([0, 1, 2, 3]     )}]
								UpperCAmelCase_					:int      			=      BertTokenizer.from_pretrained('''bert-base-cased'''     )

								UpperCAmelCase_					:str      			=      tokenizer.pad(snake_case					,							padding=snake_case     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							tf.Tensor     )     )
								self.assertEqual(batch['''input_ids'''].numpy().tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )
								UpperCAmelCase_					:List[str]      			=      tokenizer.pad(snake_case					,							padding=snake_case					,							return_tensors='''tf'''     )
								self.assertTrue(isinstance(batch['''input_ids''']					,							tf.Tensor     )     )
								self.assertEqual(batch['''input_ids'''].numpy().tolist()					,							[[0, 1, 2, tokenizer.pad_token_id], [0, 1, 2, 3]]     )





				@require_tokenizers
				def 				snake_case_ (							self      :  str     ):
								UpperCAmelCase_					:str      			=      Tokenizer(WordPiece(unk_token='''[UNK]'''     )     )
								PreTrainedTokenizerFast(tokenizer_object=snake_case     )





				@require_tokenizers
				def 				snake_case_ (							self      :  str     ):
								UpperCAmelCase_					:Union[str, Any]      			=      Tokenizer(WordPiece(unk_token='''[UNK]'''     )     )
								with tempfile.TemporaryDirectory() as tmpdirname:
												bert_tokenizer.save(os.path.join(snake_case					,							'''tokenizer.json'''     )     )
												PreTrainedTokenizerFast(tokenizer_file=os.path.join(snake_case					,							'''tokenizer.json'''     )     )








"""simple docstring"""

def 				a (						__snake_case     :				list[list[int]]  ):



				'''simple docstring'''





				if len(__snake_case  ) == 0 or not all(len(__snake_case  ) == 2 for pair in coordinates  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				if len({tuple(__snake_case  ) for pair in coordinates}  ) != len(__snake_case  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				UpperCAmelCase_					:Optional[Any]      			=      {x for x, _ in coordinates}
				if len(__snake_case  ) == 1:
								return f'x={coordinates[0][0]}'

				if len(__snake_case  ) != len(__snake_case  ):
								raise ValueError('''The program cannot work out a fitting polynomial.'''  )

				UpperCAmelCase_					:List[Any]      			=      len(__snake_case  )

				UpperCAmelCase_					:str      			=      0
				UpperCAmelCase_					:list[list[float]]      			=      []
				# put the x and x to the power values in a matrix
				while count_of_line < x:
								UpperCAmelCase_					:str      			=      0
								UpperCAmelCase_					:Optional[int]      			=      coordinates[count_of_line][0]
								UpperCAmelCase_					:list[float]      			=      []
								while count_in_line < x:
												count_line.append(a ** (x - (count_in_line + 1))  )
												count_in_line += 1
								matrix.append(__snake_case  )
								count_of_line += 1

				UpperCAmelCase_					:Dict      			=      0
				# put the y values into a vector
				UpperCAmelCase_					:list[float]      			=      []
				while count_of_line < x:
								vector.append(coordinates[count_of_line][1]  )
								count_of_line += 1

				UpperCAmelCase_					:Dict      			=      0

				while count < x:
								UpperCAmelCase_					:Any      			=      0
								while zahlen < x:
												if count == zahlen:
																zahlen += 1
												if zahlen == x:
																break
												UpperCAmelCase_					:str      			=      matrix[zahlen][count] / matrix[count][count]
												for counting_columns, item in enumerate(matrix[count]  ):
																# manipulating all the values in the matrix
																matrix[zahlen][counting_columns] -= item * bruch
												# manipulating the values in the vector
												vector[zahlen] -= vector[count] * bruch
												zahlen += 1
								count += 1

				UpperCAmelCase_					:Tuple      			=      0
				# make solutions
				UpperCAmelCase_					:list[str]      			=      []
				while count < x:
								solution.append(str(vector[count] / matrix[count][count]  )  )
								count += 1

				UpperCAmelCase_					:Optional[int]      			=      0
				UpperCAmelCase_					:Optional[Any]      			=      '''f(x)='''

				while count < x:
								UpperCAmelCase_					:list[str]      			=      solution[count].split('''E'''  )
								if len(__snake_case  ) > 1:
												UpperCAmelCase_					:List[Any]      			=      f'{remove_e[0]}*10^{remove_e[1]}'
								solved += f'x^{x - (count + 1)}*{solution[count]}'
								if count + 1 != x:
												solved += "+"
								count += 1

				return solved


if __name__ == "__main__":
						print(points_to_polynomial([]))
						print(points_to_polynomial([[]]))
						print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
						print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
						print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
						print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))


