from ..utils import DummyObject, requires_backends



class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     int            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					Any      ,	*SCREAMING_SNAKE_CASE__    :					str      ,	**SCREAMING_SNAKE_CASE__    :					Optional[int]     )    ->				Any:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					int      ,	*SCREAMING_SNAKE_CASE__    :					Any      ,	**SCREAMING_SNAKE_CASE__    :					str     )    ->				List[Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Tuple      ,	*SCREAMING_SNAKE_CASE__    :					Any      ,	**SCREAMING_SNAKE_CASE__    :					int     )    ->				Union[str, Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Optional[int]            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					Optional[int]      ,	*SCREAMING_SNAKE_CASE__    :					str      ,	**SCREAMING_SNAKE_CASE__    :					str     )    ->				int:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Tuple      ,	*SCREAMING_SNAKE_CASE__    :					Dict      ,	**SCREAMING_SNAKE_CASE__    :					int     )    ->				Union[str, Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					int      ,	*SCREAMING_SNAKE_CASE__    :					List[Any]      ,	**SCREAMING_SNAKE_CASE__    :					Optional[int]     )    ->				Union[str, Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Tuple            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					Dict      ,	*SCREAMING_SNAKE_CASE__    :					Optional[Any]      ,	**SCREAMING_SNAKE_CASE__    :					Union[str, Any]     )    ->				Tuple:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					List[str]      ,	*SCREAMING_SNAKE_CASE__    :					Optional[Any]      ,	**SCREAMING_SNAKE_CASE__    :					str     )    ->				List[Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Any      ,	*SCREAMING_SNAKE_CASE__    :					int      ,	**SCREAMING_SNAKE_CASE__    :					List[str]     )    ->				Dict:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     List[Any]            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					List[Any]      ,	*SCREAMING_SNAKE_CASE__    :					List[Any]      ,	**SCREAMING_SNAKE_CASE__    :					List[str]     )    ->				Any:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					List[str]      ,	*SCREAMING_SNAKE_CASE__    :					List[Any]      ,	**SCREAMING_SNAKE_CASE__    :					Dict     )    ->				Dict:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Tuple      ,	*SCREAMING_SNAKE_CASE__    :					List[str]      ,	**SCREAMING_SNAKE_CASE__    :					Union[str, Any]     )    ->				List[str]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     List[str]            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					Optional[int]      ,	*SCREAMING_SNAKE_CASE__    :					Union[str, Any]      ,	**SCREAMING_SNAKE_CASE__    :					Optional[int]     )    ->				Any:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Optional[int]      ,	*SCREAMING_SNAKE_CASE__    :					str      ,	**SCREAMING_SNAKE_CASE__    :					Any     )    ->				Dict:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Optional[Any]      ,	*SCREAMING_SNAKE_CASE__    :					Dict      ,	**SCREAMING_SNAKE_CASE__    :					Tuple     )    ->				Optional[int]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







class  SCREAMING_SNAKE_CASE_ (					metaclass=lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Union[str, Any]            =				["torch", "transformers", "onnx"]







  def __init__(				self    :					Any      ,	*SCREAMING_SNAKE_CASE__    :					Tuple      ,	**SCREAMING_SNAKE_CASE__    :					List[Any]     )    ->				Union[str, Any]:
         requires_backends(self      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Tuple      ,	*SCREAMING_SNAKE_CASE__    :					List[Any]      ,	**SCREAMING_SNAKE_CASE__    :					Optional[int]     )    ->				List[Any]:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







  @classmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					Dict      ,	*SCREAMING_SNAKE_CASE__    :					Optional[Any]      ,	**SCREAMING_SNAKE_CASE__    :					List[str]     )    ->				Dict:
         requires_backends(cls      ,	['torch', 'transformers', 'onnx']     )







import heapq



def A__  (			lowercase:     dict					)				->		set[int]:
       A						:     list[list]         =[]

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

       # chosen_vertices = set of chosen vertices
       A						:     Dict         =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						:     List[str]         =heapq.heappop(lowercase					)[1][0]
              chosen_vertices.add(lowercase					)

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    _lowercase							:      List[Any]      							={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)}''')






