


'''simple docstring'''


import warnings
from dataclasses import dataclass, field
from typing import Optional, Tuple

from .training_args import TrainingArguments
from .utils import cached_property, is_tf_available, logging, requires_backends


_UpperCamelCase          =     logging.get_logger(__name__)

if is_tf_available():
      import tensorflow as tf







@dataclass
class        __magic_name__  (					lowerCAmelCase   ):

     """simple docstring"""






     lowerCamelCase__						=							'tf'
     lowerCamelCase__						=							field(
         default=lowerCAmelCase						,		metadata={'help': 'Name of TPU'}						,		)

     lowerCamelCase__						=							field(
         default=lowerCAmelCase						,		metadata={'help': 'Zone of TPU'}						,		)

     lowerCamelCase__						=							field(
         default=lowerCAmelCase						,		metadata={'help': 'Name of Cloud TPU-enabled project'}						,		)

     lowerCamelCase__						=							field(
         default=1.0						,		metadata={'help': 'Power for the Polynomial decay LR scheduler.'}						,		)

     lowerCamelCase__						=							field(default=lowerCAmelCase						,		metadata={'help': 'Whether to activate the XLA compilation or not'}   )


     @cached_property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          requires_backends(self ,    ["tf"]		)
          logger.info("Tensorflow: setting up strategy"		)

          __A  :					List[Any]						     =       tf.config.list_physical_devices("GPU"		)

          # Set to float16 at first
          if self.fpaa:
               tf.keras.mixed_precision.set_global_policy("mixed_float16"		)

          if self.no_cuda:
               __A  :					Union[str, Any]						     =       tf.distribute.OneDeviceStrategy(device="/cpu:0"		)
          else:
               try:
                    if self.tpu_name:
                         __A  :					Optional[Any]						     =       tf.distribute.cluster_resolver.TPUClusterResolver(
                             self.tpu_name ,    zone=self.tpu_zone ,    project=self.gcp_project		)
                    else:
                         __A  :					Union[str, Any]						     =       tf.distribute.cluster_resolver.TPUClusterResolver()
               except ValueError:
                    if self.tpu_name:
                         raise RuntimeError(f"Couldn't connect to TPU {self.tpu_name}!"		)
                    else:
                         __A  :					Any						     =       None

               if tpu:
                    # Set to bfloat16 in case of TPU
                    if self.fpaa:
                         tf.keras.mixed_precision.set_global_policy("mixed_bfloat16"		)

                    tf.config.experimental_connect_to_cluster(lowerCamelCase		)
                    tf.tpu.experimental.initialize_tpu_system(lowerCamelCase		)

                    __A  :					Dict						     =       tf.distribute.TPUStrategy(lowerCamelCase		)

               elif len(lowerCamelCase		) == 0:
                    __A  :					str						     =       tf.distribute.OneDeviceStrategy(device="/cpu:0"		)
               elif len(lowerCamelCase		) == 1:
                    __A  :					Any						     =       tf.distribute.OneDeviceStrategy(device="/gpu:0"		)
               elif len(lowerCamelCase		) > 1:
                    # If you only want to use a specific subset of GPUs use `CUDA_VISIBLE_DEVICES=0`
                    __A  :					str						     =       tf.distribute.MirroredStrategy()
               else:
                    raise ValueError("Cannot find the proper strategy, please check your environment properties."		)

          return strategy


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          requires_backends(self ,    ["tf"]		)
          return self._setup_strategy


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          requires_backends(self ,    ["tf"]		)
          return self._setup_strategy.num_replicas_in_sync


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          return False  # TF Logging is handled by Keras not the Trainer


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          if self.per_gpu_train_batch_size:
               logger.warning(
                   "Using deprecated `--per_gpu_train_batch_size` argument which will be removed in a future "
                   "version. Using `--per_device_train_batch_size` is preferred."		)
          __A  :					Any						     =       self.per_gpu_train_batch_size or self.per_device_train_batch_size
          return per_device_batch_size * self.n_replicas


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          if self.per_gpu_eval_batch_size:
               logger.warning(
                   "Using deprecated `--per_gpu_eval_batch_size` argument which will be removed in a future "
                   "version. Using `--per_device_eval_batch_size` is preferred."		)
          __A  :					Optional[Any]						     =       self.per_gpu_eval_batch_size or self.per_device_eval_batch_size
          return per_device_batch_size * self.n_replicas


     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          requires_backends(self ,    ["tf"]		)
          warnings.warn(
              "The n_gpu argument is deprecated and will be removed in a future version, use n_replicas instead." ,    lowerCamelCase ,    )
          return self._setup_strategy.num_replicas_in_sync






'''simple docstring'''


from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_UpperCamelCase          =     {
    """1""": ["""2""", """3""", """4""", """5"""],
    """2""": ["""1""", """3""", """4""", """5"""],
    """3""": ["""1""", """2""", """4""", """5""", """10"""],
    """4""": ["""1""", """2""", """3""", """5""", """6"""],
    """5""": ["""1""", """2""", """3""", """4""", """7"""],
    """6""": ["""7""", """8""", """9""", """10""", """4"""],
    """7""": ["""6""", """8""", """9""", """10""", """5"""],
    """8""": ["""6""", """7""", """9""", """10"""],
    """9""": ["""6""", """7""", """8""", """10"""],
    """10""": ["""6""", """7""", """8""", """9""", """3"""],
}


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					Any						     =       {node: {node} for node in graph}

     __A  :					List[str]						     =       {node: graph[node][:] for node in graph}

     while len(SCREAMING_SNAKE_CASE       ) > 2:
          # Choose a random edge.
          __A  :					Tuple						     =       random.choice(list(graph_copy.keys()       )       )
          __A  :					Any						     =       random.choice(graph_copy[u]       )

          # Contract edge (u, v) to new node uv
          __A  :					str						     =       u + v
          __A  :					Any						     =       list(set(graph_copy[u] + graph_copy[v]       )       )
          uv_neighbors.remove(SCREAMING_SNAKE_CASE       )
          uv_neighbors.remove(SCREAMING_SNAKE_CASE       )
          __A  :					Any						     =       uv_neighbors
          for neighbor in uv_neighbors:
               graph_copy[neighbor].append(SCREAMING_SNAKE_CASE       )

          __A  :					str						     =       set(contracted_nodes[u].union(contracted_nodes[v]       )       )

          # Remove nodes u and v.
          del graph_copy[u]
          del graph_copy[v]
          for neighbor in uv_neighbors:
               if u in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE       )
               if v in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE       )

    # Find cutset.
     __A  :					int						     =       [contracted_nodes[node] for node in graph_copy]
     return {
         (node, neighbor)
         for node in groups[0]
         for neighbor in graph[node]
         if neighbor in groups[1]
     }


if __name__ == "__main__":
      print(partition_graph(TEST_GRAPH))

