

'''simple docstring'''






from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

lowerCAmelCase__											=	TypeVar('''T''')


def 		_A     (    A__      ):






 """simple docstring"""



 return (position - 1) // 2


def 		_A     (    A__      ):






 """simple docstring"""



 return (2 * position) + 1


def 		_A     (    A__      ):






 """simple docstring"""



 return (2 * position) + 2






class 			lowercase_	(Generic[T]      ):




  """simple docstring"""




  def __init__(      self   :     Union[str, Any]			):
   __lowercase							  = []
   __lowercase							  = {}
   __lowercase							  = 0






  def __len__(      self   :     Optional[Any]			):
   return self.elements






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






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






  def 					SCREAMING_SNAKE_CASE      (      self   :     str					,lowercase__   :     T					,lowercase__   :     int			):
   # Add an element with given priority to the queue
   self.heap.append((elem, weight)			)
   __lowercase							  = self.elements
   self.elements += 1
   self._bubble_up(lowercase__			)






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






  def 					SCREAMING_SNAKE_CASE      (      self   :     Optional[Any]					,lowercase__   :     T					,lowercase__   :     int			):
   # Update the weight of the given key
   __lowercase							  = self.position_map[elem]
   __lowercase							  = (elem, weight)
   if position > 0:
    __lowercase							  = get_parent_position(lowercase__			)
    __lowercase  ,	__lowercase							  = self.heap[parent_position]
    if parent_weight > weight:
     self._bubble_up(lowercase__			)
    else:
     self._bubble_down(lowercase__			)
   else:
    self._bubble_down(lowercase__			)






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






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






  def 					SCREAMING_SNAKE_CASE      (      self   :     Optional[int]					,lowercase__   :     int					,lowercase__   :     int			):
   # Swap the nodes at the given positions
   __lowercase							  = self.heap[nodea_pos][0]
   __lowercase							  = self.heap[nodea_pos][0]
   __lowercase  ,	__lowercase							  = (
       self.heap[nodea_pos],
       self.heap[nodea_pos],
   )
   __lowercase							  = nodea_pos
   __lowercase							  = nodea_pos






class 			lowercase_	(Generic[T]      ):




  """simple docstring"""




  def __init__(      self   :     Any			):
   __lowercase							  = {}
   __lowercase							  = 0






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






  def __len__(      self   :     Any			):
   return self.nodes






  def 					SCREAMING_SNAKE_CASE      (      self   :     Dict					,lowercase__   :     T			):
   # Add a node in the graph if it is not in the graph
   if node not in self.connections:
    __lowercase							  = {}
    self.nodes += 1






  def 					SCREAMING_SNAKE_CASE      (      self   :     Optional[Any]					,lowercase__   :     T					,lowercase__   :     T					,lowercase__   :     int			):
   # Add an edge between 2 nodes in the graph
   self.add_node(lowercase__			)
   self.add_node(lowercase__			)
   __lowercase							  = weight
   __lowercase							  = weight


def 		_A     (    A__     ,				):






 """simple docstring"""



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

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

 if priority_queue.is_empty():
  return dist, parent

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

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





"""simple docstring"""




import warnings

from ..trainer import Trainer
from ..utils import logging


lowercase_			     =  logging.get_logger(__name__)
class 					__lowerCAmelCase					(   __SCREAMING_SNAKE_CASE       ):


		'''simple docstring'''



		def __init__(  self							, _a=None							, **_a      ):
				warnings.warn(
				    '''`SageMakerTrainer` is deprecated and will be removed in v5 of Transformers. You can use `Trainer` '''
				    '''instead.'''							, _a							, )
				super().__init__(args=_a							, **_a      )






