"""simple docstring"""




from scipy.stats import pearsonr

import datasets


_a      :		str           =   '\nPearson correlation coefficient and p-value for testing non-correlation.\nThe Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases.\nThe p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets.\n'


_a      :		List[str]           =   '\nArgs:\n    predictions (`list` of `int`): Predicted class labels, as returned by a model.\n    references (`list` of `int`): Ground truth labels.\n    return_pvalue (`boolean`): If `True`, returns the p-value, along with the correlation coefficient. If `False`, returns only the correlation coefficient. Defaults to `False`.\n\nReturns:\n    pearsonr (`float`): Pearson correlation coefficient. Minimum possible value is -1. Maximum possible value is 1. Values of 1 and -1 indicate exact linear positive and negative relationships, respectively. A value of 0 implies no correlation.\n    p-value (`float`): P-value, which roughly indicates the probability of an The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate higher probabilities.\n\nExamples:\n\n    Example 1-A simple example using only predictions and references.\n        >>> pearsonr_metric = datasets.load_metric("pearsonr")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5])\n        >>> print(round(results[\'pearsonr\'], 2))\n        -0.74\n\n    Example 2-The same as Example 1, but that also returns the `p-value`.\n        >>> pearsonr_metric = datasets.load_metric("pearsonr")\n        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5], return_pvalue=True)\n        >>> print(sorted(list(results.keys())))\n        [\'p-value\', \'pearsonr\']\n        >>> print(round(results[\'pearsonr\'], 2))\n        -0.74\n        >>> print(round(results[\'p-value\'], 2))\n        0.15\n'


_a      :		List[Any]           =   '\n@article{2020SciPy-NMeth,\nauthor  = {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, Ilhan 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, Antonio H. and Pedregosa, Fabian and\n      {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},\ntitle   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific\n      Computing in Python}},\njournal = {Nature Methods},\nyear    = {2020},\nvolume  = {17},\npages   = {261--272},\nadsurl  = {https://rdcu.be/b08Wh},\ndoi = {10.1038/s41592-019-0686-2},\n}\n'
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION    ,	_KWARGS_DESCRIPTION		)
class 						__A							( datasets.Metric		):






     def     __A  (		self  ):
       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.pearsonr.html"""]				,     )






     def     __A  (		self				,     a__				,     a__				,     a__=False  ):
       if return_pvalue:
         _lowerCAmelCase						:       List[Any]  			=     pearsonr(a__				,     a__  )
         return {"pearsonr": results[0], "p-value": results[1]}
       else:
         return {"pearsonr": float(pearsonr(a__				,     a__  )[0]  )}





'''simple docstring'''

from math import pow
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     ):
 if current_sum == needed_sum:
  # If the sum of the powers is equal to needed_sum, then we have a solution.
  solutions_count += 1
  return current_sum, solutions_count

 lowercase__				:    Optional[Any]  =					int(pow(UpperCAmelCase		,     UpperCAmelCase     )     )
 if current_sum + i_to_n <= needed_sum:
  # If the sum of the powers is less than needed_sum, then continue adding powers.
  current_sum += i_to_n
  lowercase__ ,							lowercase__				:    Dict  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
  current_sum -= i_to_n
 if i_to_n < needed_sum:
  # If the power of i is less than needed_sum, then try with the next power.
  lowercase__ ,							lowercase__				:    str  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
 return current_sum, solutions_count
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
  raise ValueError(
      '''Invalid input\n'''
      '''needed_sum must be between 1 and 1000, power between 2 and 10.'''     )

 return backtrack(UpperCAmelCase		,     UpperCAmelCase		,     1		,     0		,     0     )[1]  # Return the solutions_count


if __name__ == "__main__":
  import doctest

  doctest.testmod()

