





'''simple docstring'''






import functools
from typing import Any






def      __A						(							a_						:  str      ,a_						:  list[str]	):

  # Validation
  if not isinstance(a_      ,a_	) or len(a_	) == 0:
    raise ValueError("the string should be not empty string"	)

  if not isinstance(a_      ,a_	) or not all(
      isinstance(a_      ,a_	) and len(a_	) > 0 for item in words	):
    raise ValueError("the words should be a list of non-empty strings"	)

  # Build trie
  lowerCAmelCase     :    dict[str, Any]						=   {}
  lowerCAmelCase     :    List[str]						=   "WORD_KEEPER"

  for word in words:
    lowerCAmelCase     :    List[str]						=   trie
    for c in word:
      if c not in trie_node:
        lowerCAmelCase     :    Optional[Any]						=   {}

      lowerCAmelCase     :    Dict						=   trie_node[c]

    lowerCAmelCase     :    Dict						=   True

  lowerCAmelCase     :    int						=   len(a_	)

  # Dynamic programming method
  @functools.cache
  def is_breakable(a_						:  int	) -> bool:
    if index == len_string:
      return True

    lowerCAmelCase     :    Any						=   trie
    for i in range(a_      ,a_	):
      lowerCAmelCase     :    Optional[int]						=   trie_node.get(string[i]      ,a_	)

      if trie_node is None:
        return False

      if trie_node.get(a_      ,a_	) and is_breakable(i + 1	):
        return True

    return False

  return is_breakable(0	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()










'''simple docstring'''






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

import datasets


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


lowerCAmelCase       		=      """\
This metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.
It first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.
"""


lowerCAmelCase       		=      R"""
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")

Examples:
    >>> metric = datasets.load_metric(\"competition_math\")
    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])
    >>> print(results)
    {'accuracy': 1.0}
"""
@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION      ,   _KWARGS_DESCRIPTION       )
class 		lowerCamelCase  (      datasets.Metric       ):



	def   _lowerCamelCase    (   self	):
			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   _lowerCamelCase    (   self		,      a_		,      a_	):
			lowerCAmelCase     :    Any						=   0.0
			for i, j in zip(a_		,      a_	):
					n_correct += 1.0 if math_equivalence.is_equiv(a_		,      a_	) else 0.0
			lowerCAmelCase     :    List[str]						=   n_correct / len(a_	)
			return {
			    "accuracy": accuracy,
			}



