






"""simple docstring"""


def 				a (     UpperCamelCase_							:				list[list[int]]		)  ->		str:
 if len(UpperCamelCase_		) == 0 or not all(len(UpperCamelCase_		) == 2 for pair in coordinates		):
  raise ValueError('The program cannot work out a fitting polynomial.'		)

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

 __A	:       Tuple       =	{x for x, _ in coordinates}
 if len(UpperCamelCase_		) == 1:
  return F"x={coordinates[0][0]}"

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

 __A	:       str       =	len(UpperCamelCase_		)

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

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

 __A	:       Optional[Any]       =	0

 while count < x:
  __A	:       Dict       =	0
  while zahlen < x:
   if count == zahlen:
    zahlen += 1
   if zahlen == x:
    break
   __A	:       List[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

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

 __A	:       Dict       =	0
 __A	:       List[Any]       =	'f(x)='

 while count < x:
  __A	:       list[str]       =	solution[count].split('E'		)
  if len(UpperCamelCase_		) > 1:
   __A	:       Tuple       =	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]]))













"""simple docstring"""


import csv
import json
import os

import datasets


# TODO: Add BibTeX citation
# Find for instance the citation on arxiv or on the dataset repo/website
_UpperCamelCase   :						List[Any]     						= """\
@InProceedings{huggingface:dataset,
title = {A great new dataset},
author={huggingface, Inc.
},
year={2020}
}
"""

# TODO: Add description of the dataset here
# You can copy an official description
_UpperCamelCase   :						Any     						= """\
This new dataset is designed to solve this great NLP task and is crafted with a lot of care.
"""

# TODO: Add a link to an official homepage for the dataset here
_UpperCamelCase   :						Dict     						= """"""

# TODO: Add the licence for the dataset here if you can find it
_UpperCamelCase   :						Tuple     						= """"""

# TODO: Add link to the official dataset URLs here
# The HuggingFace Datasets library doesn't host the datasets but only points to the original files.
# This can be an arbitrary nested dict/list of URLs (see below in `_split_generators` method)
_UpperCamelCase   :						str     						= {
    """first_domain""": """https://huggingface.co/great-new-dataset-first_domain.zip""",
    """second_domain""": """https://huggingface.co/great-new-dataset-second_domain.zip""",
}






class __a   (   datasets.GeneratorBasedBuilder				):
  __lowercase    :    int						=					datasets.Version('1.1.0'				)

  # This is an example of a dataset with multiple configurations.
  # If you don't want/need to define several sub-sets in your dataset,
  # just remove the BUILDER_CONFIG_CLASS and the BUILDER_CONFIGS attributes.

  # If you need to make complex sub-parts in the datasets with configurable options
  # You can create your own builder configuration class to store attribute, inheriting from datasets.BuilderConfig
  # BUILDER_CONFIG_CLASS = MyBuilderConfig

  # You will be able to load one or the other configurations in the following list with
  # data = datasets.load_dataset('my_dataset', 'first_domain')
  # data = datasets.load_dataset('my_dataset', 'second_domain')
  __lowercase    :    Optional[Any]						=					[
      datasets.BuilderConfig(name='first_domain' ,version=snake_case_ ,description='This part of my dataset covers a first domain'				),
      datasets.BuilderConfig(name='second_domain' ,version=snake_case_ ,description='This part of my dataset covers a second domain'				),
  ]

  __lowercase    :    Any						=					'first_domain'  # It's not mandatory to have a default configuration. Just use one if it make sense.



  def 						A_				(self  :		Optional[Any]   )		->							List[Any]:
   # TODO: This method specifies the datasets.DatasetInfo object which contains informations and typings for the dataset
   if self.config.name == "first_domain":  # This is the name of the configuration selected in BUILDER_CONFIGS above
    __A	:       Dict       =	datasets.Features(
        {
            'sentence': datasets.Value('string'   ),
            'option1': datasets.Value('string'   ),
            'answer': datasets.Value('string'   )
            # These are the features of your dataset like images, labels ...
        }   )
   else:  # This is an example to show how to have different features for "first_domain" and "second_domain"
    __A	:       Optional[int]       =	datasets.Features(
        {
            'sentence': datasets.Value('string'   ),
            'option2': datasets.Value('string'   ),
            'second_domain_answer': datasets.Value('string'   )
            # These are the features of your dataset like images, labels ...
        }   )
   return datasets.DatasetInfo(
       # This is the description that will appear on the datasets page.
       description=_DESCRIPTION				,			features=lowercase_				,			homepage=_HOMEPAGE				,			license=_LICENSE				,			citation=_CITATION				,			)



  def 						A_				(self  :		Dict				,			lowercase_  :		Union[str, Any]   )		->							Union[str, Any]:
   # TODO: This method is tasked with downloading/extracting the data and defining the splits depending on the configuration
   # If several configurations are possible (listed in BUILDER_CONFIGS), the configuration selected by the user is in self.config.name

   # dl_manager is a datasets.download.DownloadManager that can be used to download and extract URLS
   # It can accept any type or nested list/dict and will give back the same structure with the url replaced with path to local files.
   # By default the archives will be extracted and a path to a cached folder where they are extracted is returned instead of the archive
   __A	:       Optional[int]       =	_URLS[self.config.name]
   __A	:       Any       =	dl_manager.download_and_extract(lowercase_   )
   return [
       datasets.SplitGenerator(
           name=datasets.Split.TRAIN				,			gen_kwargs={
               'filepath': os.path.join(lowercase_				,			'train.jsonl'   ),
               'split': 'train',
           }				,			),
       datasets.SplitGenerator(
           name=datasets.Split.VALIDATION				,			gen_kwargs={
               'filepath': os.path.join(lowercase_				,			'dev.jsonl'   ),
               'split': 'dev',
           }				,			),
       datasets.SplitGenerator(
           name=datasets.Split.TEST				,			gen_kwargs={
               'filepath': os.path.join(lowercase_				,			'test.jsonl'   ),
               'split': 'test'
           }				,			),
   ]



  def 						A_				(self  :		Tuple				,			lowercase_  :		Dict				,			lowercase_  :		Optional[Any]   )		->							Tuple:
   # TODO: This method handles input defined in _split_generators to yield (key, example) tuples from the dataset.
   # The `key` is for legacy reasons (tfds) and is not important in itself, but must be unique for each example.
   with open(lowercase_				,			encoding='utf-8'   ) as f:
    for key, row in enumerate(lowercase_   ):
     __A	:       int       =	json.loads(lowercase_   )
     if self.config.name == "first_domain":
      # Yields examples as (key, example) tuples
      yield key, {
          "sentence": data["sentence"],
          "option1": data["option1"],
          "answer": "" if split == "test" else data["answer"],
      }
     else:
      yield key, {
          "sentence": data["sentence"],
          "option2": data["option2"],
          "second_domain_answer": "" if split == "test" else data["second_domain_answer"],
      }





