



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

import datasets


UpperCAmelCase__   =       """\
@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}
}
"""


UpperCAmelCase__   =       """\
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.
"""


UpperCAmelCase__   =       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   :  Tuple)   ->    int:



						"""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     _lowerCamelCase       (						self   :  int ,		A   :  Union[str, Any] ,		A   :  Dict)   ->    str:



						"""simple docstring"""






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


from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass

@dataclass
class __snake_case		:
    _a		:						int
    _a		:						TreeNode | None=				None
    _a		:						TreeNode | None=				None






lowercase  :					Dict						    =							namedtuple("""CoinsDistribResult""", """moves excess""")







def 						_snake_case(  SCREAMING_SNAKE_CASE__				) ->    int:

       if root is None:
              return 0

       # Validation
       def count_nodes(SCREAMING_SNAKE_CASE__				) -> int:
              if node is None:
                     return 0

              return count_nodes(node.left				) + count_nodes(node.right				) + 1

       def count_coins(SCREAMING_SNAKE_CASE__				) -> int:
              if node is None:
                     return 0

              return count_coins(node.left				) + count_coins(node.right				) + node.data

       if count_nodes(SCREAMING_SNAKE_CASE__				) != count_coins(SCREAMING_SNAKE_CASE__				):
              raise ValueError("""The nodes number should be same as the number of coins"""				)

       # Main calculation
       def get_distrib(SCREAMING_SNAKE_CASE__				) -> CoinsDistribResult:

              if node is None:
                     return CoinsDistribResult(0					,	1				)

              lowercase	,			lowercase							:     int       	=      get_distrib(node.left				)
              lowercase	,			lowercase							:     List[Any]       	=      get_distrib(node.right				)

              lowercase							:     Optional[Any]       	=      1 - left_distrib_excess
              lowercase							:     Union[str, Any]       	=      1 - right_distrib_excess

              lowercase							:     List[Any]       	=      (
                  left_distrib_moves
                  + right_distrib_moves
                  + abs(SCREAMING_SNAKE_CASE__				)
                  + abs(SCREAMING_SNAKE_CASE__				)
              )
              lowercase							:     Any       	=      node.data - coins_to_left - coins_to_right

              return CoinsDistribResult(SCREAMING_SNAKE_CASE__					,	SCREAMING_SNAKE_CASE__				)

       return get_distrib(SCREAMING_SNAKE_CASE__				)[0]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
