


import heapq




def 	__lowercase		(  _UpperCamelCase   )			->Optional[int]:







      """simple docstring"""

      lowercase	:      Optional[Any]          =						[]

      # for each node and his adjacency list add them and the rank of the node to queue
      # using heapq module the queue will be filled like a Priority Queue
      # heapq works with a min priority queue, so I used -1*len(v) to build it
      for key, value in graph.items():
            # O(log(n))
            heapq.heappush(_UpperCamelCase,			[-1 * len(_UpperCamelCase   ), (key, value)]   )

      # chosen_vertices = set of chosen vertices
      lowercase	:      Any          =						set()

      # while queue isn't empty and there are still edges
      #   (queue[0][0] is the rank of the node with max rank)
      while queue and queue[0][0] != 0:
            # extract vertex with max rank from queue and add it to chosen_vertices
            lowercase	:      List[Any]          =						heapq.heappop(_UpperCamelCase   )[1][0]
            chosen_vertices.add(_UpperCamelCase   )

            # Remove all arcs adjacent to argmax
            for elem in queue:
                  # if v haven't adjacent node, skip
                  if elem[0] == 0:
                        continue
                  # if argmax is reachable from elem
                  # remove argmax from elem's adjacent list and update his rank
                  if argmax in elem[1][1]:
                        lowercase	:      List[str]          =						elem[1][1].index(_UpperCamelCase   )
                        del elem[1][1][index]
                        elem[0] += 1
        # re-order the queue
            heapq.heapify(_UpperCamelCase   )
      return chosen_vertices


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  __a       =					{0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
  print(F'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')


"""simple docstring"""






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


lowerCAmelCase__  :  str						     =	{
    'configuration_roc_bert': ['ROC_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'RoCBertConfig'],
    'tokenization_roc_bert': ['RoCBertTokenizer'],
}

try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						pass

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase__  :  List[str]						     =	[
						    'ROC_BERT_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'RoCBertForCausalLM',
						    'RoCBertForMaskedLM',
						    'RoCBertForMultipleChoice',
						    'RoCBertForPreTraining',
						    'RoCBertForQuestionAnswering',
						    'RoCBertForSequenceClassification',
						    'RoCBertForTokenClassification',
						    'RoCBertLayer',
						    'RoCBertModel',
						    'RoCBertPreTrainedModel',
						    'load_tf_weights_in_roc_bert',
						]

if TYPE_CHECKING:
						from .configuration_roc_bert import ROC_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP, RoCBertConfig
						from .tokenization_roc_bert import RoCBertTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												raise OptionalDependencyNotAvailable()

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_roc_bert import (
												    ROC_BERT_PRETRAINED_MODEL_ARCHIVE_LIST,
												    RoCBertForCausalLM,
												    RoCBertForMaskedLM,
												    RoCBertForMultipleChoice,
												    RoCBertForPreTraining,
												    RoCBertForQuestionAnswering,
												    RoCBertForSequenceClassification,
												    RoCBertForTokenClassification,
												    RoCBertLayer,
												    RoCBertModel,
												    RoCBertPreTrainedModel,
												    load_tf_weights_in_roc_bert,
												)


else:
						import sys

						lowerCAmelCase__  :  str						     =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



