






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

import datasets


__A      =				'\\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'


__A      =				'\\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'


__A      =				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 						SCREAMING_SNAKE_CASE				( datasets.Metric					):





							"""simple docstring"""

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











def      __A					(     _lowercase					,			_lowercase					,			_lowercase					,			_lowercase ):

					'''simple docstring'''







					global f  # a global dp table for knapsack
					if f[i][j] < 0:
										if j < wt[i - 1]:
															_A								= mf_knapsack(i - 1					,			_lowercase					,			_lowercase					,			_lowercase )
										else:
															_A								= max(
															    mf_knapsack(i - 1					,			_lowercase					,			_lowercase					,			_lowercase )					,			mf_knapsack(i - 1					,			_lowercase					,			_lowercase					,			j - wt[i - 1] ) + val[i - 1]					,			)
										_A								= val
					return f[i][j]




def      __A					(     _lowercase					,			_lowercase					,			_lowercase					,			_lowercase ):

					'''simple docstring'''







					_A								= [[0] * (w + 1) for _ in range(n + 1 )]

					for i in range(1					,			n + 1 ):
										for w_ in range(1					,			w + 1 ):
															if wt[i - 1] <= w_:
																				_A								= max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]					,			dp[i - 1][w_] )
															else:
																				_A								= dp[i - 1][w_]

					return dp[n][w_], dp




def      __A					(     _lowercase					,			_lowercase					,			_lowercase ):

					'''simple docstring'''







					if not (isinstance(_lowercase					,			(list, tuple) ) and isinstance(_lowercase					,			(list, tuple) )):
										raise ValueError(
										    '''Both the weights and values vectors must be either lists or tuples''' )

					_A								= len(_lowercase )
					if num_items != len(_lowercase ):
										_A								= (
										    '''The number of weights must be the same as the number of values.\n'''
										    f"""But got {num_items} weights and {len(_lowercase )} values"""
										)
										raise ValueError(_lowercase )
					for i in range(_lowercase ):
										if not isinstance(wt[i]					,			_lowercase ):
															_A								= (
															    '''All weights must be integers but got weight of '''
															    f"""type {type(wt[i] )} at index {i}"""
															)
															raise TypeError(_lowercase )

					_A							,_A								= knapsack(_lowercase					,			_lowercase					,			_lowercase					,			_lowercase )
					_A								= set()
					_construct_solution(_lowercase					,			_lowercase					,			_lowercase					,			_lowercase					,			_lowercase )

					return optimal_val, example_optional_set




def      __A					(     _lowercase					,			_lowercase					,			_lowercase					,			_lowercase					,			_lowercase ):

					'''simple docstring'''







					if i > 0 and j > 0:
										if dp[i - 1][j] == dp[i][j]:
															_construct_solution(_lowercase					,			_lowercase					,			i - 1					,			_lowercase					,			_lowercase )
										else:
															optimal_set.add(_lowercase )
															_construct_solution(_lowercase					,			_lowercase					,			i - 1					,			j - wt[i - 1]					,			_lowercase )


if __name__ == "__main__":
				__A      =				[3, 2, 4, 4]
				__A      =				[4, 3, 2, 3]
				__A      =				4
				__A      =				6
				__A      =				[[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
				__A ,  __A      =				knapsack(w, wt, val, n)
				print(optimal_solution)
				print(mf_knapsack(n, wt, val, w))  # switched the n and w

				# testing the dynamic programming problem with example
				# the optimal subset for the above example are items 3 and 4
				__A ,  __A      =				knapsack_with_example_solution(w, wt, val)
				assert optimal_solution == 8
				assert optimal_subset == {3, 4}
				print('optimal_value = ', optimal_solution)
				print('An optimal subset corresponding to the optimal value', optimal_subset)



