






from __future__ import annotations

import math

import numpy as np
from numpy.linalg import norm






def      _snake_case     (__lowercase     ,   __lowercase):
   return math.sqrt(sum(pow(a - b     ,   2) for a, b in zip(__lowercase     ,   __lowercase)))






def      _snake_case     (__lowercase     ,   __lowercase):

   if dataset.ndim != value_array.ndim:
      UpperCamelCase_						=  (
          'Wrong input data\'s dimensions... '
          f"""dataset : {dataset.ndim}, value_array : {value_array.ndim}"""
      )
      raise ValueError(__lowercase)

   try:
      if dataset.shape[1] != value_array.shape[1]:
         UpperCamelCase_						=  (
             'Wrong input data\'s shape... '
             f"""dataset : {dataset.shape[1]}, value_array : {value_array.shape[1]}"""
         )
         raise ValueError(__lowercase)
   except IndexError:
      if dataset.ndim != value_array.ndim:
         raise TypeError('Wrong shape')

   if dataset.dtype != value_array.dtype:
      UpperCamelCase_						=  (
          'Input data have different datatype... '
          f"""dataset : {dataset.dtype}, value_array : {value_array.dtype}"""
      )
      raise TypeError(__lowercase)

   UpperCamelCase_						=  []

   for value in value_array:
      UpperCamelCase_						=  euclidean(__lowercase     ,   dataset[0])
      UpperCamelCase_						=  dataset[0].tolist()

      for dataset_value in dataset[1:]:
         UpperCamelCase_						=  euclidean(__lowercase     ,   __lowercase)

         if dist > temp_dist:
            UpperCamelCase_						=  temp_dist
            UpperCamelCase_						=  dataset_value.tolist()

      answer.append([vector, dist])

   return answer






def      _snake_case     (__lowercase     ,   __lowercase):
   return np.dot(__lowercase     ,   __lowercase) / (norm(__lowercase) * norm(__lowercase))


if __name__ == "__main__":
 import doctest

 doctest.testmod()













from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

snake_case__   :						List[str]													=   TypeVar("""T""")






def      _snake_case     (__lowercase):
   return (position - 1) // 2






def      _snake_case     (__lowercase):
   return (2 * position) + 1






def      _snake_case     (__lowercase):
   return (2 * position) + 2


class     _a							(	Generic[T]     ):






  """simple docstring"""





  def __init__(  self			)      ->			None:
     UpperCamelCase_						=  []
     UpperCamelCase_						=  {}
     UpperCamelCase_						=  0




  def __len__(  self			)      ->			int:
     return self.elements




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




  def  _UpperCAmelCase  (  self			)      ->			bool:
     # Check if the priority queue is empty
     return self.elements == 0




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Add an element with given priority to the queue
     self.heap.append((elem, weight)			)
     UpperCamelCase_						=  self.elements
     self.elements += 1
     self._bubble_up(_UpperCAmelCase			)




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




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




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			None:
     # Place a node at the proper position (downward movement) [to be used
     # internally only]
     UpperCamelCase_						=  self.position_map[elem]
     UpperCamelCase_		,   UpperCamelCase_						=  self.heap[curr_pos]
     UpperCamelCase_						=  get_child_left_position(_UpperCAmelCase			)
     UpperCamelCase_						=  get_child_right_position(_UpperCAmelCase			)
     if child_left_position < self.elements and child_right_position < self.elements:
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[child_left_position]
        UpperCamelCase_		,   UpperCamelCase_						=  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:
        UpperCamelCase_		,   UpperCamelCase_						=  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:
        UpperCamelCase_		,   UpperCamelCase_						=  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			)      ->			None:
     # Swap the nodes at the given positions
     UpperCamelCase_						=  self.heap[nodea_pos][0]
     UpperCamelCase_						=  self.heap[nodea_pos][0]
     UpperCamelCase_		,   UpperCamelCase_						=  (
         self.heap[nodea_pos],
         self.heap[nodea_pos],
     )
     UpperCamelCase_						=  nodea_pos
     UpperCamelCase_						=  nodea_pos




class     _a							(	Generic[T]     ):






  """simple docstring"""





  def __init__(  self			)      ->			None:
     UpperCamelCase_						=  {}
     UpperCamelCase_						=  0




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




  def __len__(  self			)      ->			int:
     return self.nodes




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			None:
     # Add a node in the graph if it is not in the graph
     if node not in self.connections:
        UpperCamelCase_						=  {}
        self.nodes += 1




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Add an edge between 2 nodes in the graph
     self.add_node(_UpperCAmelCase			)
     self.add_node(_UpperCAmelCase			)
     UpperCamelCase_						=  weight
     UpperCamelCase_						=  weight






def      _snake_case     (__lowercase     ,   ):
   UpperCamelCase_						=  {node: maxsize for node in graph.connections}
   UpperCamelCase_						=  {node: None for node in graph.connections}

   UpperCamelCase_						=  MinPriorityQueue()
   for node, weight in dist.items():
      priority_queue.push(__lowercase     ,   __lowercase)

   if priority_queue.is_empty():
      return dist, parent

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

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





