



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

import datasets


_snake_case	=						"\\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"


_snake_case	=						"\\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"


_snake_case	=						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 						UpperCAmelCase_					( datasets.Metric):







							def      snake_case__   (     self):

														'''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,    __a,    __a):

														'''simple docstring'''

														_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  :							Dict				     =					n_correct / len(__a)
														return {
														    "accuracy": accuracy,
														}





def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							def count_of_possible_combinations(_lowerCamelCase						) -> int:
														if target < 0:
																					return 0
														if target == 0:
																					return 1
														return sum(count_of_possible_combinations(target - item						) for item in array						)

							return count_of_possible_combinations(_lowerCamelCase						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							def count_of_possible_combinations_with_dp_array(
							    _lowerCamelCase       ,				_lowerCamelCase						) -> int:
														if target < 0:
																					return 0
														if target == 0:
																					return 1
														if dp_array[target] != -1:
																					return dp_array[target]
														_lowerCAmelCase  :							Optional[int]				     =					sum(
														    count_of_possible_combinations_with_dp_array(target - item       ,				_lowerCamelCase						)
														    for item in array						)
														_lowerCAmelCase  :							Any				     =					answer
														return answer

							_lowerCAmelCase  :							List[Any]				     =					[-1] * (target + 1)
							return count_of_possible_combinations_with_dp_array(_lowerCamelCase       ,				_lowerCamelCase						)






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							List[Any]				     =					[0] * (target + 1)
							_lowerCAmelCase  :							List[str]				     =					1

							for i in range(1       ,				target + 1						):
														for j in range(_lowerCamelCase						):
																					if i - array[j] >= 0:
																												dp_array[i] += dp_array[i - array[j]]

							return dp_array[target]


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						_snake_case	=						3
						_snake_case	=						5
						_snake_case	=						[1, 2, 5]
						print(combination_sum_iv(n, array, target))
