


from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

UpperCAmelCase      =   TypeVar("""T""")






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




						"""simple docstring"""

						return (position - 1) // 2






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




						"""simple docstring"""

						return (2 * position) + 1






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




						"""simple docstring"""

						return (2 * position) + 2







class lowerCAmelCase_						(			Generic[T]	):

	'''simple docstring'''

	def __init__(     self ):
							snake_case_	=				[]
							snake_case_	=				{}
							snake_case_	=				0



	def __len__(     self ):
							return self.elements



	def __repr__(     self ):
							return str(self.heap )



	def 						UpperCamelCase__					(     self ):
							# Check if the priority queue is empty
							return self.elements == 0



	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
							# Add an element with given priority to the queue
							self.heap.append((elem, weight) )
							snake_case_	=				self.elements
							self.elements += 1
							self._bubble_up(_UpperCAmelCase )



	def 						UpperCamelCase__					(     self ):
							# Remove and return the element with lowest weight (highest priority)
							if self.elements > 1:
													self._swap_nodes(0		,				self.elements - 1 )
							snake_case_	,   snake_case_	=				self.heap.pop()
							del self.position_map[elem]
							self.elements -= 1
							if self.elements > 0:
													snake_case_	,   snake_case_	=				self.heap[0]
													self._bubble_down(_UpperCAmelCase )
							return elem



	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
							# Update the weight of the given key
							snake_case_	=				self.position_map[elem]
							snake_case_	=				(elem, weight)
							if position > 0:
													snake_case_	=				get_parent_position(_UpperCAmelCase )
													snake_case_	,   snake_case_	=				self.heap[parent_position]
													if parent_weight > weight:
																			self._bubble_up(_UpperCAmelCase )
													else:
																			self._bubble_down(_UpperCAmelCase )
							else:
													self._bubble_down(_UpperCAmelCase )



	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
							# Place a node at the proper position (upward movement) [to be used internally
							# only]
							snake_case_	=				self.position_map[elem]
							if curr_pos == 0:
													return None
							snake_case_	=				get_parent_position(_UpperCAmelCase )
							snake_case_	,   snake_case_	=				self.heap[curr_pos]
							snake_case_	,   snake_case_	=				self.heap[parent_position]
							if parent_weight > weight:
													self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
													return self._bubble_up(_UpperCAmelCase )
							return None



	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
							# Place a node at the proper position (downward movement) [to be used
							# internally only]
							snake_case_	=				self.position_map[elem]
							snake_case_	,   snake_case_	=				self.heap[curr_pos]
							snake_case_	=				get_child_left_position(_UpperCAmelCase )
							snake_case_	=				get_child_right_position(_UpperCAmelCase )
							if child_left_position < self.elements and child_right_position < self.elements:
													snake_case_	,   snake_case_	=				self.heap[child_left_position]
													snake_case_	,   snake_case_	=				self.heap[child_right_position]
													if child_right_weight < child_left_weight and child_right_weight < weight:
																			self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
																			return self._bubble_down(_UpperCAmelCase )
							if child_left_position < self.elements:
													snake_case_	,   snake_case_	=				self.heap[child_left_position]
													if child_left_weight < weight:
																			self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
																			return self._bubble_down(_UpperCAmelCase )
							else:
													return None
							if child_right_position < self.elements:
													snake_case_	,   snake_case_	=				self.heap[child_right_position]
													if child_right_weight < weight:
																			self._swap_nodes(_UpperCAmelCase		,				_UpperCAmelCase )
																			return self._bubble_down(_UpperCAmelCase )
							return None





	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
							# Swap the nodes at the given positions
							snake_case_	=				self.heap[nodea_pos][0]
							snake_case_	=				self.heap[nodea_pos][0]
							snake_case_	,   snake_case_	=				(
							    self.heap[nodea_pos],
							    self.heap[nodea_pos],
							)
							snake_case_	=				nodea_pos
							snake_case_	=				nodea_pos







class lowerCAmelCase_						(			Generic[T]	):

	'''simple docstring'''

	def __init__(     self ):
							snake_case_	=				{}
							snake_case_	=				0



	def __repr__(     self ):
							return str(self.connections )



	def __len__(     self ):
							return self.nodes



	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
							# Add a node in the graph if it is not in the graph
							if node not in self.connections:
													snake_case_	=				{}
													self.nodes += 1





	def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase		,				_UpperCAmelCase ):
							# Add an edge between 2 nodes in the graph
							self.add_node(_UpperCAmelCase )
							self.add_node(_UpperCAmelCase )
							snake_case_	=				weight
							snake_case_	=				weight






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , )->  tuple[dict[T, int], dict[T, T | None]]:




						"""simple docstring"""

						snake_case_	=				{node: maxsize for node in graph.connections}
						snake_case_	=				{node: None for node in graph.connections}

						snake_case_	=				MinPriorityQueue()
						for node, weight in dist.items():
												priority_queue.push(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )

						if priority_queue.is_empty():
												return dist, parent

						# initialization
						snake_case_	=				priority_queue.extract_min()
						snake_case_	=				0
						for neighbour in graph.connections[node]:
												if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																		snake_case_	=				dist[node] + graph.connections[node][neighbour]
																		priority_queue.update_key(SCREAMING_SNAKE_CASE , dist[neighbour] )
																		snake_case_	=				node

    # running prim's algorithm
						while not priority_queue.is_empty():
												snake_case_	=				priority_queue.extract_min()
												for neighbour in graph.connections[node]:
																		if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																								snake_case_	=				dist[node] + graph.connections[node][neighbour]
																								priority_queue.update_key(SCREAMING_SNAKE_CASE , dist[neighbour] )
																								snake_case_	=				node
						return dist, parent



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}