from typing import List

from .keymap import KEYMAP, get_character



def A__  (			lowercase:     str					)				->		List[str]:

       def decorator(lowercase:     int					):
              A						:     Tuple         =getattr(lowercase,		'handle_key',		[]					)
              handle += [key]
              setattr(lowercase,		'handle_key',		lowercase					)
              return func

       return decorator



def A__  (			*lowercase:     List[str]					)				->		Dict:

       def decorator(lowercase:     Union[str, Any]					):
              A						:     Optional[int]         =getattr(lowercase,		'handle_key',		[]					)
              handle += keys
              setattr(lowercase,		'handle_key',		lowercase					)
              return func

       return decorator



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


  def __new__(				cls    :					List[str]      ,	SCREAMING_SNAKE_CASE__    :					Optional[Any]      ,	SCREAMING_SNAKE_CASE__    :					List[Any]      ,	SCREAMING_SNAKE_CASE__    :					List[str]     )    ->				Any:
         A						:     Dict         =super().__new__(cls      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__     )
         if not hasattr(SCREAMING_SNAKE_CASE__      ,	'key_handler'     ):
                setattr(SCREAMING_SNAKE_CASE__      ,	'key_handler'      ,	{}     )
         setattr(SCREAMING_SNAKE_CASE__      ,	'handle_input'      ,	KeyHandler.handle_input     )

         for value in attrs.values():
                A						:     Optional[Any]         =getattr(SCREAMING_SNAKE_CASE__      ,	'handle_key'      ,	[]     )
                for key in handled_keys:
                       A						:     str         =value
         return new_cls







  @staticmethod
  def 		SCREAMING_SNAKE_CASE_		(				cls    :					str     )    ->				Any:
         A						:     str         =get_character()
         if char != KEYMAP["undefined"]:
                A						:     List[str]         =ord(SCREAMING_SNAKE_CASE__     )
         A						:     List[str]         =cls.key_handler.get(SCREAMING_SNAKE_CASE__     )
         if handler:
                A						:     List[str]         =char
                return handler(cls     )
         else:
                return None







def A__  (			cls:     Optional[int]					)				->		str:
       return KeyHandler(cls.__name__,		cls.__bases__,		cls.__dict__.copy()					)







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)}''')






