
'''simple docstring'''






import heapq as hq
import math
from collections.abc import Iterator

class  UpperCAmelCase__						:



    def __init__(	self      :       Tuple,__A      :       Any     ):
          _lowerCamelCase				:   Any								=   str(id_     )
          _lowerCamelCase				:   Optional[int]								=   None
          _lowerCamelCase				:   Optional[int]								=   None
          _lowerCamelCase				:   Union[str, Any]								=   []
          _lowerCamelCase				:   Optional[Any]								=   {}  # {vertex:distance}



    def __lt__(	self      :       int,__A      :       List[Any]     ):
          return self.key < other.key



    def __repr__(	self      :       List[str]     ):
          return self.id



    def   lowerCamelCase_  (	self      :       List[str],__A      :       Optional[int]     ):
          self.neighbors.append(__A     )



    def   lowerCamelCase_  (	self      :       Optional[int],__A      :       Optional[int],__A      :       int     ):
          _lowerCamelCase				:   Optional[Any]								=   weight







def 		A_       (	_lowerCAmelCase   :    Union[str, Any]				,	_lowerCAmelCase   :    Optional[Any]				,	_lowerCAmelCase   :    Union[str, Any]				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      graph[a - 1].add_neighbor(graph[b - 1]							)
      graph[b - 1].add_neighbor(graph[a - 1]							)
      # add the edges:
      graph[a - 1].add_edge(graph[b - 1]				,	_lowerCAmelCase							)
      graph[b - 1].add_edge(graph[a - 1]				,	_lowerCAmelCase							)







def 		A_       (	_lowerCAmelCase   :    list				,	_lowerCAmelCase   :    Vertex							):



      """simple docstring"""




      _lowerCamelCase				:   str								=   []
      for u in graph:
            _lowerCamelCase				:   Any								=   math.inf
            _lowerCamelCase				:   List[str]								=   None
      _lowerCamelCase				:   Tuple								=   0
      _lowerCamelCase				:   Tuple								=   graph[:]
      while q:
            _lowerCamelCase				:   List[str]								=   min(_lowerCAmelCase							)
            q.remove(_lowerCAmelCase							)
            for v in u.neighbors:
                  if (v in q) and (u.edges[v.id] < v.key):
                        _lowerCamelCase				:   int								=   u
                        _lowerCamelCase				:   Optional[Any]								=   u.edges[v.id]
      for i in range(1				,	len(_lowerCAmelCase							)							):
            a.append((int(graph[i].id							) + 1, int(graph[i].pi.id							) + 1)							)
      return a







def 		A_       (	_lowerCAmelCase   :    list				,	_lowerCAmelCase   :    Vertex							):



      """simple docstring"""




      for u in graph:
            _lowerCamelCase				:   Any								=   math.inf
            _lowerCamelCase				:   Tuple								=   None
      _lowerCamelCase				:   int								=   0

      _lowerCamelCase				:   Dict								=   list(_lowerCAmelCase							)
      hq.heapify(_lowerCAmelCase							)

      while h:
            _lowerCamelCase				:   Dict								=   hq.heappop(_lowerCAmelCase							)
            for v in u.neighbors:
                  if (v in h) and (u.edges[v.id] < v.key):
                        _lowerCamelCase				:   List[Any]								=   u
                        _lowerCamelCase				:   List[str]								=   u.edges[v.id]
                        hq.heapify(_lowerCAmelCase							)

      for i in range(1				,	len(_lowerCAmelCase							)							):
            yield (int(graph[i].id							) + 1, int(graph[i].pi.id							) + 1)







def 		A_       (	):



      """simple docstring"""






if __name__ == "__main__":
 import doctest

 doctest.testmod()

'''simple docstring'''






import warnings

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


UpperCAmelCase_       :   Union[str, Any]   =       logging.get_logger(__name__)

class  UpperCAmelCase__						(       A ):



    def __init__(	self      :       int,__A      :       Any=None,**__A      :       Optional[Any]     ):
          warnings.warn(
              "`SageMakerTrainer` is deprecated and will be removed in v5 of Transformers. You can use `Trainer` "
              "instead.",__A,)
          super().__init__(args=__A,**__A     )