


def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						List[Any]:




      """simple docstring"""

      _enforce_args(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
      if n == 0:
            return 0
      snake_case_ =   float('''-inf'''      )
      for i in range(1      ,      n + 1      ):
            snake_case_ =   max(
                SCREAMING_SNAKE_CASE      ,      prices[i - 1] + naive_cut_rod_recursive(n - i      ,      SCREAMING_SNAKE_CASE      )      )

      return max_revue






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						Optional[Any]:




      """simple docstring"""

      _enforce_args(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
      snake_case_ =   [float('''-inf'''      ) for _ in range(n + 1      )]
      return _top_down_cut_rod_recursive(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						List[Any]:




      """simple docstring"""

      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            snake_case_ =   float('''-inf'''      )
            for i in range(1      ,      n + 1      ):
                  snake_case_ =   max(
                      SCREAMING_SNAKE_CASE      ,      prices[i - 1] + _top_down_cut_rod_recursive(n - i      ,      SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )      ,      )

            snake_case_ =   max_revenue

      return max_rev[n]






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						Any:




      """simple docstring"""

      _enforce_args(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )

      # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
      # length 0.
      snake_case_ =   [float('''-inf'''      ) for _ in range(n + 1      )]
      snake_case_ =   0

      for i in range(1      ,      n + 1      ):
            snake_case_ =   max_rev[i]
            for j in range(1      ,      i + 1      ):
                  snake_case_ =   max(SCREAMING_SNAKE_CASE      ,      prices[j - 1] + max_rev[i - j]      )

            snake_case_ =   max_revenue_i

      return max_rev[n]






def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )->						Tuple:




      """simple docstring"""

      if n < 0:
            snake_case_ =   f'''n must be greater than or equal to 0. Got n = {n}'''
            raise ValueError(SCREAMING_SNAKE_CASE      )

      if n > len(SCREAMING_SNAKE_CASE      ):
            snake_case_ =   (
                '''Each integral piece of rod must have a corresponding price. '''
                f'''Got n = {n} but length of prices = {len(SCREAMING_SNAKE_CASE      )}'''
            )
            raise ValueError(SCREAMING_SNAKE_CASE      )






def  __lowerCAmelCase					()->						List[str]:




      """simple docstring"""

      snake_case_ =   [6, 10, 12, 15, 20, 23]
      snake_case_ =   len(SCREAMING_SNAKE_CASE      )

      # the best revenue comes from cutting the rod into 6 pieces, each
      # of length 1 resulting in a revenue of 6 * 6 = 36.
      snake_case_ =   36

      snake_case_ =   top_down_cut_rod(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
      snake_case_ =   bottom_up_cut_rod(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )
      snake_case_ =   naive_cut_rod_recursive(SCREAMING_SNAKE_CASE      ,      SCREAMING_SNAKE_CASE      )

      assert expected_max_revenue == max_rev_top_down
      assert max_rev_top_down == max_rev_bottom_up
      assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
   main()



import numpy as np

import datasets


UpperCAmelCase    =					"""
Compute the Mahalanobis Distance

Mahalonobis distance is the distance between a point and a distribution.
And not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.
It was introduced by Prof. P. C. Mahalanobis in 1936
and has been used in various statistical applications ever since
[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]
"""

UpperCAmelCase    =					"""\
@article{de2000mahalanobis,
  title={The mahalanobis distance},
  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},
  journal={Chemometrics and intelligent laboratory systems},
  volume={50},
  number={1},
  pages={1--18},
  year={2000},
  publisher={Elsevier}
}
"""

UpperCAmelCase    =					"""
Args:
    X: List of datapoints to be compared with the `reference_distribution`.
    reference_distribution: List of datapoints from the reference distribution we want to compare to.
Returns:
    mahalanobis: The Mahalonobis distance for each datapoint in `X`.
Examples:

    >>> mahalanobis_metric = datasets.load_metric(\"mahalanobis\")
    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])
    >>> print(results)
    {'mahalanobis': array([0.5])}
"""







@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION      ,		_KWARGS_DESCRIPTION )
class lowerCAmelCase_		(				datasets.Metric ):

 '''simple docstring'''

 def 		UpperCamelCase__  (			self      ):
       return datasets.MetricInfo(
           description=_DESCRIPTION	,   citation=_CITATION	,   inputs_description=_KWARGS_DESCRIPTION	,   features=datasets.Features(
               {
                   '''X''': datasets.Sequence(datasets.Value('''float'''	,   id='''sequence'''      )	,   id='''X'''      ),
               }      )	,   )





 def 		UpperCamelCase__  (			self	,   _UpperCAmelCase	,   _UpperCAmelCase      ):
       # convert to numpy arrays
       snake_case_ =   np.array(_UpperCAmelCase      )
       snake_case_ =   np.array(_UpperCAmelCase      )

       # Assert that arrays are 2D
       if len(X.shape      ) != 2:
             raise ValueError('''Expected `X` to be a 2D vector'''      )
       if len(reference_distribution.shape      ) != 2:
             raise ValueError('''Expected `reference_distribution` to be a 2D vector'''      )
       if reference_distribution.shape[0] < 2:
             raise ValueError(
                 '''Expected `reference_distribution` to be a 2D vector with more than one element in the first dimension'''      )

       # Get mahalanobis distance for each prediction
       snake_case_ =   X - np.mean(_UpperCAmelCase      )
       snake_case_ =   np.cov(reference_distribution.T      )
       try:
             snake_case_ =   np.linalg.inv(_UpperCAmelCase      )
       except np.linalg.LinAlgError:
             snake_case_ =   np.linalg.pinv(_UpperCAmelCase      )
       snake_case_ =   np.dot(_UpperCAmelCase	,   _UpperCAmelCase      )
       snake_case_ =   np.dot(_UpperCAmelCase	,   X_minus_mu.T      ).diagonal()

       return {"mahalanobis": mahal_dist}