





'''simple docstring'''

import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


lowercase__		:     str			=							'\\n@article{hendrycksmath2021,\n  title={Measuring Mathematical Problem Solving With the MATH Dataset},\n  author={Dan Hendrycks\n    and Collin Burns\n    and Saurav Kadavath\n    and Akul Arora\n    and Steven Basart\n    and Eric Tang\n    and Dawn Song\n    and Jacob Steinhardt},\n  journal={arXiv preprint arXiv:2103.03874},\n  year={2021}\n}\n'


lowercase__		:     str			=							'\\nThis metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.\nIt first canonicalizes the inputs (e.g., converting "1/2" to "\\frac{1}{2}") and then computes accuracy.\n'


lowercase__		:     Dict			=							R'\nCalculates accuracy after canonicalizing inputs.\n\nArgs:\n    predictions: list of predictions to score. Each prediction\n        is a string that contains natural language and LaTex.\n    references: list of reference for each prediction. Each\n        reference is a string that contains natural language\n        and LaTex.\nReturns:\n    accuracy: accuracy after canonicalizing inputs\n        (e.g., converting "1/2" to "\\frac{1}{2}")\n\nExamples:\n    >>> metric = datasets.load_metric("competition_math")\n    >>> results = metric.compute(references=["\\frac{1}{2}"], predictions=["1/2"])\n    >>> print(results)\n    {\'accuracy\': 1.0}\n'
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION		,		_KWARGS_DESCRIPTION					)
class 							__lowerCAmelCase	(       datasets.Metric					):






       """simple docstring"""





       def snake_case__		(				self  :						Dict	)       ->	Any:

            '''simple docstring'''




            return datasets.MetricInfo(
                description=_DESCRIPTION			,					citation=_CITATION			,					inputs_description=_KWARGS_DESCRIPTION			,					features=datasets.Features(
                    {
                        '''predictions''': datasets.Value('''string'''	),
                        '''references''': datasets.Value('''string'''	),
                    }	)			,					homepage='''https://github.com/hendrycks/math'''			,					codebase_urls=['''https://github.com/hendrycks/math''']			,					)







       def snake_case__		(				self  :						List[Any]			,					lowerCAmelCase__  :						Dict			,					lowerCAmelCase__  :						int	)       ->	List[str]:

            '''simple docstring'''




            _UpperCamelCase							       =			0.0
            for i, j in zip(lowerCAmelCase__			,					lowerCAmelCase__	):
                 n_correct += 1.0 if math_equivalence.is_equiv(lowerCAmelCase__			,					lowerCAmelCase__	) else 0.0
            _UpperCamelCase							       =			n_correct / len(lowerCAmelCase__	)
            return {
                "accuracy": accuracy,
            }










'''simple docstring'''

def    a__							(							lowercase   :	Dict,   lowercase   :	Optional[Any] )						->						int:





     """simple docstring"""

     _UpperCamelCase							       =			0
     _UpperCamelCase							       =			len(lowercase ) - 1

     while left <= right:
          # avoid divided by 0 during interpolation
          if sorted_collection[left] == sorted_collection[right]:
               if sorted_collection[left] == item:
                    return left
               else:
                    return None

          _UpperCamelCase							       =			left + ((item - sorted_collection[left]) * (right - left)) // (
              sorted_collection[right] - sorted_collection[left]
          )

          # out of range check
          if point < 0 or point >= len(lowercase ):
               return None

          _UpperCamelCase							       =			sorted_collection[point]
          if current_item == item:
               return point
          else:
               if point < left:
                    _UpperCamelCase							       =			left
                    _UpperCamelCase							       =			point
               elif point > right:
                    _UpperCamelCase							       =			right
                    _UpperCamelCase							       =			point
               else:
                    if item < current_item:
                         _UpperCamelCase							       =			point - 1
                    else:
                         _UpperCamelCase							       =			point + 1
     return None







def    a__							(							lowercase   :	int,   lowercase   :	Optional[int],   lowercase   :	List[Any],   lowercase   :	List[Any] )						->						Dict:





     """simple docstring"""

     if sorted_collection[left] == sorted_collection[right]:
          if sorted_collection[left] == item:
               return left
          else:
               return None

     _UpperCamelCase							       =			left + ((item - sorted_collection[left]) * (right - left)) // (
         sorted_collection[right] - sorted_collection[left]
     )

     # out of range check
     if point < 0 or point >= len(lowercase ):
          return None

     if sorted_collection[point] == item:
          return point
     elif point < left:
          return interpolation_search_by_recursion(lowercase,   lowercase,   lowercase,   lowercase )
     elif point > right:
          return interpolation_search_by_recursion(lowercase,   lowercase,   lowercase,   lowercase )
     else:
          if sorted_collection[point] > item:
               return interpolation_search_by_recursion(
                   lowercase,   lowercase,   lowercase,   point - 1 )
          else:
               return interpolation_search_by_recursion(
                   lowercase,   lowercase,   point + 1,   lowercase )







def    a__							(							lowercase   :	Any )						->						List[Any]:





     """simple docstring"""

     if collection != sorted(lowercase ):
          raise ValueError('''Collection must be ascending sorted''' )
     return True


if __name__ == "__main__":
   import sys
   lowercase__		:     int			=							0
   if debug == 1:
      lowercase__		:     Optional[Any]			=							[10, 30, 40, 45, 50, 66, 77, 93]
      try:
         __assert_sorted(collection)
      except ValueError:
         sys.exit('Sequence must be ascending sorted to apply interpolation search')
      lowercase__		:     List[str]			=							67

   lowercase__		:     Optional[int]			=							interpolation_search(collection, target)
   if result is not None:
      print(F"""{target} found at positions: {result}""")
   else:
      print('Not found')



