



"""simple docstring"""
import datasets

from .evaluate import evaluate


_lowerCAmelCase       :str	=   '\\n@inproceedings{Rajpurkar2016SQuAD10,\n  title={SQuAD: 100, 000+ Questions for Machine Comprehension of Text},\n  author={Pranav Rajpurkar and Jian Zhang and Konstantin Lopyrev and Percy Liang},\n  booktitle={EMNLP},\n  year={2016}\n}\n'

_lowerCAmelCase       :Dict	=   '\nThis metric wrap the official scoring script for version 1 of the Stanford Question Answering Dataset (SQuAD).\n\nStanford Question Answering Dataset (SQuAD) is a reading comprehension dataset, consisting of questions posed by\ncrowdworkers on a set of Wikipedia articles, where the answer to every question is a segment of text, or span,\nfrom the corresponding reading passage, or the question might be unanswerable.\n'

_lowerCAmelCase       :List[str]	=   '\nComputes SQuAD scores (F1 and EM).\nArgs:\n    predictions: List of question-answers dictionaries with the following key-values:\n        - \'id\': id of the question-answer pair as given in the references (see below)\n        - \'prediction_text\': the text of the answer\n    references: List of question-answers dictionaries with the following key-values:\n        - \'id\': id of the question-answer pair (see above),\n        - \'answers\': a Dict in the SQuAD dataset format\n            {\n                \'text\': list of possible texts for the answer, as a list of strings\n                \'answer_start\': list of start positions for the answer, as a list of ints\n            }\n            Note that answer_start values are not taken into account to compute the metric.\nReturns:\n    \'exact_match\': Exact match (the normalized answer exactly match the gold answer)\n    \'f1\': The F-score of predicted tokens versus the gold answer\nExamples:\n\n    >>> predictions = [{\'prediction_text\': \'1976\', \'id\': \'56e10a3be3433e1400422b22\'}]\n    >>> references = [{\'answers\': {\'answer_start\': [97], \'text\': [\'1976\']}, \'id\': \'56e10a3be3433e1400422b22\'}]\n    >>> squad_metric = datasets.load_metric(\"squad\")\n    >>> results = squad_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'exact_match\': 100.0, \'f1\': 100.0}\n'
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION						,_KWARGS_DESCRIPTION )
class 				_UpperCAmelCase				(					datasets.Metric ):





     '''simple docstring'''



     def 					__lowerCAmelCase      (   self						)				->   Optional[Any]:
         return datasets.MetricInfo(
             description=_DESCRIPTION			,      citation=_CITATION			,      inputs_description=_KWARGS_DESCRIPTION			,      features=datasets.Features(
                 {
                     '''predictions''': {'''id''': datasets.Value('''string'''						), '''prediction_text''': datasets.Value('''string'''						)},
                     '''references''': {
                         '''id''': datasets.Value('''string'''						),
                         '''answers''': datasets.features.Sequence(
                             {
                                 '''text''': datasets.Value('''string'''						),
                                 '''answer_start''': datasets.Value('''int32'''						),
                             }						),
                     },
                 }						)			,      codebase_urls=['''https://rajpurkar.github.io/SQuAD-explorer/''']			,      reference_urls=['''https://rajpurkar.github.io/SQuAD-explorer/''']			,      )





     def 					__lowerCAmelCase      (   self			,      A			,      A						)				->   Tuple:
         _UpperCAmelCase				:    Tuple											=       {prediction['''id''']: prediction['''prediction_text'''] for prediction in predictions}
         _UpperCAmelCase				:    Dict											=       [
             {
                 '''paragraphs''': [
                     {
                         '''qas''': [
                             {
                                 '''answers''': [{'''text''': answer_text} for answer_text in ref['''answers''']['''text''']],
                                 '''id''': ref['''id'''],
                             }
                             for ref in references
                         ]
                     }
                 ]
             }
         ]
         _UpperCAmelCase				:    Optional[Any]											=       evaluate(dataset=__UpperCAmelCase			,      predictions=__UpperCAmelCase						)
         return score







from __future__ import annotations

from math import ceil, floor, sqrt





def 		a__      (		_UpperCamelCase      :			int = 2_00_00_00				):
   __lowerCamelCase    				=     [0]
   __lowerCamelCase    				=     42

   for idx in range(1			,ceil(sqrt(target * 2				) * 1.1				)				):
      triangle_numbers.append(triangle_numbers[-1] + idx				)

   # we want this to be as close as possible to target
   __lowerCamelCase    				=     0
   # the area corresponding to the grid that gives the product closest to target
   __lowerCamelCase    				=     0
   # an estimate of b, using the quadratic formula
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the largest integer less than b_estimate
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_floor
   __lowerCamelCase    				=     42
   # the triangle number corresponding to b_ceil
   __lowerCamelCase    				=     42

   for idx_a, triangle_a in enumerate(triangle_numbers[1:]			,1				):
      __lowerCamelCase    				=     (-1 + sqrt(1 + 8 * target / triangle_a				)) / 2
      __lowerCamelCase    				=     floor(_UpperCamelCase				)
      __lowerCamelCase    				=     ceil(_UpperCamelCase				)
      __lowerCamelCase    				=     triangle_numbers[b_floor]
      __lowerCamelCase    				=     triangle_numbers[b_ceil]

      if abs(target - triangle_b_first_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_first_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_floor

      if abs(target - triangle_b_second_guess * triangle_a				) < abs(
          target - best_product				):
         __lowerCamelCase    				=     triangle_b_second_guess * triangle_a
         __lowerCamelCase    				=     idx_a * b_ceil

   return area


if __name__ == "__main__":
  print(f"{solution() = }")






