


"""simple docstring"""






import heapq
def       A_   (   _lowerCAmelCase     :					dict       ):






     """simple docstring"""

     _a    	=				[]

     # 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(_lowerCAmelCase,     [-1 * len(_lowerCAmelCase       ), (key, value)]       )

     # chosen_vertices = set of chosen vertices
     _a    	=				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
          _a    	=				heapq.heappop(_lowerCAmelCase       )[1][0]
          chosen_vertices.add(_lowerCAmelCase       )

          # 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]:
                    _a    	=				elem[1][1].index(_lowerCAmelCase       )
                    del elem[1][1][index]
                    elem[0] += 1
        # re-order the queue
          heapq.heapify(_lowerCAmelCase       )
     return chosen_vertices


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   __snake_case		=       {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 . import __version__

# Backward compatibility imports, to make sure all those objects can be found in file_utils
from .utils import (
    CLOUDFRONT_DISTRIB_PREFIX,
    CONFIG_NAME,
    DISABLE_TELEMETRY,
    DUMMY_INPUTS,
    DUMMY_MASK,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    FEATURE_EXTRACTOR_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_PREFIX,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    MODEL_CARD_NAME,
    MULTIPLE_CHOICE_DUMMY_INPUTS,
    PYTORCH_PRETRAINED_BERT_CACHE,
    PYTORCH_TRANSFORMERS_CACHE,
    S3_BUCKET_PREFIX,
    SENTENCEPIECE_UNDERLINE,
    SPIECE_UNDERLINE,
    TF2_WEIGHTS_NAME,
    TF_WEIGHTS_NAME,
    TORCH_FX_REQUIRED_VERSION,
    TRANSFORMERS_CACHE,
    TRANSFORMERS_DYNAMIC_MODULE_NAME,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
    ContextManagers,
    DummyObject,
    EntryNotFoundError,
    ExplicitEnum,
    ModelOutput,
    PaddingStrategy,
    PushToHubMixin,
    RepositoryNotFoundError,
    RevisionNotFoundError,
    TensorType,
    _LazyModule,
    add_code_sample_docstrings,
    add_end_docstrings,
    add_start_docstrings,
    add_start_docstrings_to_model_forward,
    cached_property,
    copy_func,
    default_cache_path,
    define_sagemaker_information,
    get_cached_models,
    get_file_from_repo,
    get_full_repo_name,
    get_torch_version,
    has_file,
    http_user_agent,
    is_apex_available,
    is_bsa_available,
    is_coloredlogs_available,
    is_datasets_available,
    is_detectrona_available,
    is_faiss_available,
    is_flax_available,
    is_ftfy_available,
    is_in_notebook,
    is_ipex_available,
    is_librosa_available,
    is_offline_mode,
    is_onnx_available,
    is_pandas_available,
    is_phonemizer_available,
    is_protobuf_available,
    is_psutil_available,
    is_pyanvml_available,
    is_pyctcdecode_available,
    is_pytesseract_available,
    is_pytorch_quantization_available,
    is_rjieba_available,
    is_sagemaker_dp_enabled,
    is_sagemaker_mp_enabled,
    is_scipy_available,
    is_sentencepiece_available,
    is_seqio_available,
    is_sklearn_available,
    is_soundfile_availble,
    is_spacy_available,
    is_speech_available,
    is_tensor,
    is_tensorflow_probability_available,
    is_tfaonnx_available,
    is_tf_available,
    is_timm_available,
    is_tokenizers_available,
    is_torch_available,
    is_torch_bfaa_available,
    is_torch_cuda_available,
    is_torch_fx_available,
    is_torch_fx_proxy,
    is_torch_mps_available,
    is_torch_tfaa_available,
    is_torch_tpu_available,
    is_torchaudio_available,
    is_training_run_on_sagemaker,
    is_vision_available,
    replace_return_docstrings,
    requires_backends,
    to_numpy,
    to_py_obj,
    torch_only_method,
)