"""simple docstring"""






from scipy.stats import spearmanr

import datasets


lowerCAmelCase__						:						Any		  =			'\nThe Spearman rank-order correlation coefficient is a measure of the\nrelationship between two datasets. Like other correlation coefficients,\nthis one varies between -1 and +1 with 0 implying no correlation.\nPositive correlations imply that as data in dataset x increases, so\ndoes data in dataset y. Negative correlations imply that as x increases,\ny decreases. Correlations of -1 or +1 imply an exact monotonic relationship.\n\nUnlike the Pearson correlation, the Spearman correlation does not\nassume that both datasets are normally distributed.\n\nThe p-value roughly indicates the probability of an uncorrelated system\nproducing datasets that have a Spearman correlation at least as extreme\nas the one computed from these datasets. The p-values are not entirely\nreliable but are probably reasonable for datasets larger than 500 or so.\n'

lowerCAmelCase__						:						Any		  =			'\nArgs:\n    predictions (`List[float]`): Predicted labels, as returned by a model.\n    references (`List[float]`): Ground truth labels.\n    return_pvalue (`bool`): If `True`, returns the p-value. If `False`, returns\n            only the spearmanr score. Defaults to `False`.\nReturns:\n    spearmanr (`float`): Spearman correlation coefficient.\n    p-value (`float`): p-value. **Note**: is only returned if `return_pvalue=True` is input.\nExamples:\n    Example 1:\n        >>> spearmanr_metric = datasets.load_metric("spearmanr")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])\n        >>> print(results)\n        {\'spearmanr\': -0.7}\n\n    Example 2:\n        >>> spearmanr_metric = datasets.load_metric("spearmanr")\n        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5],\n        ...                                     predictions=[10, 9, 2.5, 6, 4],\n        ...                                     return_pvalue=True)\n        >>> print(results[\'spearmanr\'])\n        -0.7\n        >>> print(round(results[\'spearmanr_pvalue\'], 2))\n        0.19\n'

lowerCAmelCase__						:						List[str]		  =			r'\\n@book{kokoska2000crc,\n  title={CRC standard probability and statistics tables and formulae},\n  author={Kokoska, Stephen and Zwillinger, Daniel},\n  year={2000},\n  publisher={Crc Press}\n}\n@article{2020SciPy-NMeth,\n  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and\n            Haberland, Matt and Reddy, Tyler and Cournapeau, David and\n            Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and\n            Bright, Jonathan and {van der Walt}, St{\'e}fan J. and\n            Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and\n            Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and\n            Kern, Robert and Larson, Eric and Carey, C J and\n            Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and\n            {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and\n            Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and\n            Harris, Charles R. and Archibald, Anne M. and\n            Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and\n            {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\n  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n            Computing in Python}},\n  journal = {Nature Methods},\n  year    = {2020},\n  volume  = {17},\n  pages   = {261--272},\n  adsurl  = {https://rdcu.be/b08Wh},\n  doi     = {10.1038/s41592-019-0686-2},\n}\n'
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION   ,					_KWARGS_DESCRIPTION       )
class        snake_case (				datasets.Metric       ):




					"""simple docstring"""

					def 	__lowerCAmelCase		(       self     :			Any    ):
									return datasets.MetricInfo(
									    description=_DESCRIPTION					,citation=_CITATION					,inputs_description=_KWARGS_DESCRIPTION					,features=datasets.Features(
									        {
									            'predictions': datasets.Value('float'    ),
									            'references': datasets.Value('float'    ),
									        }    )					,reference_urls=['https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html']					,)







					def 	__lowerCAmelCase		(       self     :			List[Any]					,lowerCamelCase__     :			Tuple					,lowerCamelCase__     :			Optional[int]					,lowerCamelCase__     :			int=False    ):
									UpperCAmelCase__    =							spearmanr(lowerCamelCase__					,lowerCamelCase__    )
									if return_pvalue:
													return {"spearmanr": results[0], "spearmanr_pvalue": results[1]}
									else:
													return {"spearmanr": results[0]}




"""simple docstring"""






from __future__ import annotations

from math import ceil, floor, sqrt



def 						a_		(      lowerCamelCase = 2_0_0_0_0_0_0 ):
				UpperCAmelCase__    =							[0]
				UpperCAmelCase__    =							42

				for idx in range(1      ,    ceil(sqrt(target * 2 ) * 1.1 ) ):
								triangle_numbers.append(triangle_numbers[-1] + idx )

				# we want this to be as close as possible to target
				UpperCAmelCase__    =							0
				# the area corresponding to the grid that gives the product closest to target
				UpperCAmelCase__    =							0
				# an estimate of b, using the quadratic formula
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_floor
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_ceil
				UpperCAmelCase__    =							42

				for idx_a, triangle_a in enumerate(triangle_numbers[1:]      ,    1 ):
								UpperCAmelCase__    =							(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
								UpperCAmelCase__    =							floor(lowerCamelCase )
								UpperCAmelCase__    =							ceil(lowerCamelCase )
								UpperCAmelCase__    =							triangle_numbers[b_floor]
								UpperCAmelCase__    =							triangle_numbers[b_ceil]

								if abs(target - triangle_b_first_guess * triangle_a ) < abs(
								    target - best_product ):
												UpperCAmelCase__    =							triangle_b_first_guess * triangle_a
												UpperCAmelCase__    =							idx_a * b_floor

								if abs(target - triangle_b_second_guess * triangle_a ) < abs(
								    target - best_product ):
												UpperCAmelCase__    =							triangle_b_second_guess * triangle_a
												UpperCAmelCase__    =							idx_a * b_ceil

				return area


if __name__ == "__main__":
						print(F"""{solution() = }""")



