




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







class 						A:



 '''simple docstring'''


 def __init__(       self      :						List[str]		,							A_      :						Optional[Any]						)     ->			Dict:

       """simple docstring"""






       lowerCamelCase_	  =					str(id_						)
       lowerCamelCase_	  =					None
       lowerCamelCase_	  =					None
       lowerCamelCase_	  =					[]
       lowerCamelCase_	  =					{}  # {vertex:distance}

 def __lt__(       self      :						Dict		,							A_      :						Optional[Any]						)     ->			Optional[int]:

       """simple docstring"""






       return self.key < other.key

 def __repr__(       self      :						Optional[Any]						)     ->			Dict:

       """simple docstring"""






       return self.id

 def        a__				(       self      :						int		,							A_      :						Optional[Any]						)     ->			List[str]:

       """simple docstring"""






       self.neighbors.append(A_						)





 def        a__				(       self      :						Optional[Any]		,							A_      :						Any		,							A_      :						Any						)     ->			List[Any]:

       """simple docstring"""






       lowerCamelCase_	  =					weight

def     _SCREAMING_SNAKE_CASE    (							lowercase			: Dict			,							lowercase			: Tuple			,							lowercase			: Optional[int]			,							lowercase			: Optional[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]			,							lowercase  )
      graph[b - 1].add_edge(graph[a - 1]			,							lowercase  )

def     _SCREAMING_SNAKE_CASE    (							lowercase			: list			,							lowercase			: Vertex  ):


      '''simple docstring'''



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

def     _SCREAMING_SNAKE_CASE    (							lowercase			: list			,							lowercase			: Vertex  ):


      '''simple docstring'''



      for u in graph:
            lowerCamelCase_	  =					math.inf
            lowerCamelCase_	  =					None
      lowerCamelCase_	  =					0

      lowerCamelCase_	  =					list(lowercase  )
      hq.heapify(lowercase  )

      while h:
            lowerCamelCase_	  =					hq.heappop(lowercase  )
            for v in u.neighbors:
                  if (v in h) and (u.edges[v.id] < v.key):
                        lowerCamelCase_	  =					u
                        lowerCamelCase_	  =					u.edges[v.id]
                        hq.heapify(lowercase  )

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

def     _SCREAMING_SNAKE_CASE    (							):


      '''simple docstring'''





if __name__ == "__main__":
 import doctest

 doctest.testmod()









import unittest

from transformers import is_tf_available
from transformers.testing_utils import require_tf


if is_tf_available():
 import tensorflow as tf
 from tensorflow.python.eager import context
 from tensorflow.python.framework import ops

 from transformers import GradientAccumulator, create_optimizer







@require_tf
class 						A(		unittest.TestCase     ):



 '''simple docstring'''


 def        a__				(       self      :						Optional[int]		,							A_      :						Tuple		,							A_      :						str		,							A_      :						int						)     ->			Any:

       """simple docstring"""






       self.assertEqual(len(A_						)		,							len(A_						)						)
       for a, b in zip(A_		,							A_						):
             self.assertAlmostEqual(A_		,							A_		,							delta=A_						)

 def        a__				(       self      :						int						)     ->			str:

       """simple docstring"""






       lowerCamelCase_	  =					GradientAccumulator()
       accumulator([tf.constant([1.0, 2.0]						)]						)
       accumulator([tf.constant([-2.0, 1.0]						)]						)
       accumulator([tf.constant([-1.0, 2.0]						)]						)
       with self.assertRaises(A_						):
             accumulator([tf.constant([1.0, 1.0]						), tf.constant([2.0, 2.0]						)]						)
       self.assertEqual(accumulator.step		,							3						)
       self.assertEqual(len(accumulator.gradients						)		,							1						)
       self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()		,							[-2.0, 5.0]		,							tol=1E-2						)
       accumulator.reset()
       self.assertEqual(accumulator.step		,							0						)
       self.assertListAlmostEqual(accumulator.gradients[0].numpy().tolist()		,							[0.0, 0.0]		,							tol=1E-2						)





 def        a__				(       self      :						List[Any]						)     ->			List[Any]:

       """simple docstring"""






       lowerCamelCase_	  =					None
       ops.enable_eager_execution_internal()
       lowerCamelCase_	  =					tf.config.list_physical_devices('CPU'						)
       if len(A_						) == 1:
             tf.config.set_logical_device_configuration(
                 physical_devices[0]		,							[tf.config.LogicalDeviceConfiguration(), tf.config.LogicalDeviceConfiguration()]						)
       lowerCamelCase_	  =					tf.config.list_logical_devices(device_type='CPU'						)
       lowerCamelCase_	  =					tf.distribute.MirroredStrategy(devices=devices[:2]						)

       with strategy.scope():
             lowerCamelCase_	  =					GradientAccumulator()
             lowerCamelCase_	  =					tf.Variable([4.0, 3.0]						)
             lowerCamelCase_  ,       lowerCamelCase_	  =					create_optimizer(5E-5		,							10		,							5						)
             lowerCamelCase_	  =					tf.Variable([0.0, 0.0]		,							trainable=A_						)

       def accumulate_on_replica(A_      :						Any						):
             accumulator([gradient]						)

       def apply_on_replica():
             optimizer.apply_gradients(list(zip(accumulator.gradients		,							[variable]						)						)						)

       @tf.function
       def accumulate(A_      :						List[Any]		,							A_      :						Tuple						):
             with strategy.scope():
                   lowerCamelCase_	  =					strategy.experimental_local_results(A_						)
                   local_variables[0].assign(A_						)
                   local_variables[1].assign(A_						)
                   strategy.run(A_		,							args=(gradient_placeholder,)						)

       @tf.function
       def apply_grad():
             with strategy.scope():
                   strategy.run(A_						)

       def _check_local_values(A_      :						List[Any]		,							A_      :						str						):
             lowerCamelCase_	  =					strategy.experimental_local_results(accumulator._gradients[0]						)
             self.assertListAlmostEqual(values[0].value()		,							A_		,							tol=1E-2						)
             self.assertListAlmostEqual(values[1].value()		,							A_		,							tol=1E-2						)

       accumulate([1.0, 2.0]		,							[-1.0, 1.0]						)
       accumulate([3.0, -1.0]		,							[-1.0, -1.0]						)
       accumulate([-2.0, 2.0]		,							[3.0, -2.0]						)
       self.assertEqual(accumulator.step		,							3						)
       _check_local_values([2.0, 3.0]		,							[1.0, -2.0]						)
       apply_grad()
       self.assertListAlmostEqual(variable.value()		,							[4.0, 3.0]		,							tol=1E-2						)
       accumulator.reset()
       self.assertEqual(accumulator.step		,							0						)
       _check_local_values([0.0, 0.0]		,							[0.0, 0.0]						)



