




from collections.abc import Sequence
from queue import Queue

class     __a:






    """simple docstring"""





    def __init__( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE=None  ,_SCREAMING_SNAKE_CASE=None    )					->						Tuple:
         UpperCAmelCase_     :				Optional[int]  =     start
         UpperCAmelCase_     :				Optional[int]  =     end
         UpperCAmelCase_     :				Any  =     val
         UpperCAmelCase_     :				Tuple  =     (start + end) // 2
         UpperCAmelCase_     :				int  =     left
         UpperCAmelCase_     :				Dict  =     right





    def __repr__( self    )					->						Union[str, Any]:
         return f'''SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})'''


class     __a:






    """simple docstring"""





    def __init__( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Any:
         UpperCAmelCase_     :				int  =     collection
         UpperCAmelCase_     :				int  =     function
         if self.collection:
              UpperCAmelCase_     :				Optional[Any]  =     self._build_tree(0  ,len(_SCREAMING_SNAKE_CASE    ) - 1    )





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Any:
         self._update_tree(self.root  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Any:
         return self._query_range(self.root  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						List[Any]:
         if start == end:
              return SegmentTreeNode(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,self.collection[start]    )
         UpperCAmelCase_     :				Optional[int]  =     (start + end) // 2
         UpperCAmelCase_     :				str  =     self._build_tree(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Optional[int]  =     self._build_tree(mid + 1  ,_SCREAMING_SNAKE_CASE    )
         return SegmentTreeNode(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,self.fn(left.val  ,right.val    )  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Dict:
         if node.start == i and node.end == i:
              UpperCAmelCase_     :				Optional[Any]  =     val
              return
         if i <= node.mid:
              self._update_tree(node.left  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         else:
              self._update_tree(node.right  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Any  =     self.fn(node.left.val  ,node.right.val    )





    def 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Tuple:
         if node.start == i and node.end == j:
              return node.val

         if i <= node.mid:
              if j <= node.mid:
                   # range in left child tree
                   return self._query_range(node.left  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
              else:
                   # range in left child tree and right child tree
                   return self.fn(
                       self._query_range(node.left  ,_SCREAMING_SNAKE_CASE  ,node.mid    )  ,self._query_range(node.right  ,node.mid + 1  ,_SCREAMING_SNAKE_CASE    )  ,)
         else:
              # range in right child tree
              return self._query_range(node.right  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )





    def 				a__ ( self    )					->						int:
         if self.root is not None:
              UpperCAmelCase_     :				int  =     Queue()
              queue.put(self.root    )
              while not queue.empty():
                   UpperCAmelCase_     :				Tuple  =     queue.get()
                   yield node

                   if node.left is not None:
                        queue.put(node.left    )

                   if node.right is not None:
                        queue.put(node.right    )


if __name__ == "__main__":
     import operator

     for fn in [operator.add, max, min]:
          print('*' * 50)
          __a							     =					SegmentTree([2, 1, 5, 3, 4], fn)
          for node in arr.traverse():
               print(node)
          print()

          arr.update(1, 5)
          for node in arr.traverse():
               print(node)
          print()

          print(arr.query_range(3, 4))  # 7
          print(arr.query_range(2, 2))  # 5
          print(arr.query_range(1, 3))  # 13
          print()





import numpy as np

import datasets


__a							     =					'\nCompute the Mahalanobis Distance\n\nMahalonobis distance is the distance between a point and a distribution.\nAnd not between two distinct points. It is effectively a multivariate equivalent of the Euclidean distance.\nIt was introduced by Prof. P. C. Mahalanobis in 1936\nand has been used in various statistical applications ever since\n[source: https://www.machinelearningplus.com/statistics/mahalanobis-distance/]\n'

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

__a							     =					'\nArgs:\n    X: List of datapoints to be compared with the `reference_distribution`.\n    reference_distribution: List of datapoints from the reference distribution we want to compare to.\nReturns:\n    mahalanobis: The Mahalonobis distance for each datapoint in `X`.\nExamples:\n\n    >>> mahalanobis_metric = datasets.load_metric("mahalanobis")\n    >>> results = mahalanobis_metric.compute(reference_distribution=[[0, 1], [1, 0]], X=[[0, 1]])\n    >>> print(results)\n    {\'mahalanobis\': array([0.5])}\n'

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






    """simple docstring"""





    def 				a__ ( self    )					->						Union[str, Any]:
         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 				a__ ( self  ,_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )					->						Any:
         # convert to numpy arrays
         UpperCAmelCase_     :				str  =     np.array(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				List[Any]  =     np.array(_SCREAMING_SNAKE_CASE    )

         # 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
         UpperCAmelCase_     :				List[str]  =     X - np.mean(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Dict  =     np.cov(reference_distribution.T    )
         try:
              UpperCAmelCase_     :				Any  =     np.linalg.inv(_SCREAMING_SNAKE_CASE    )
         except np.linalg.LinAlgError:
              UpperCAmelCase_     :				List[str]  =     np.linalg.pinv(_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				Union[str, Any]  =     np.dot(_SCREAMING_SNAKE_CASE  ,_SCREAMING_SNAKE_CASE    )
         UpperCAmelCase_     :				List[Any]  =     np.dot(_SCREAMING_SNAKE_CASE  ,X_minus_mu.T    ).diagonal()

         return {"mahalanobis": mahal_dist}