


class A__     :



  """simple docstring"""



  def __init__( self			:  List[Any]				,				lowerCamelCase__			:  str				,				lowerCamelCase__			:  Union[str, Any]				,				lowerCamelCase__			:  List[str]       ):
        a__	:  str     =   name
        a__	:  Optional[int]     =   value
        a__	:  Dict     =   weight

  def __repr__( self			:  Union[str, Any]       ):
        return f'''{self.__class__.__name__}({self.name}, {self.value}, {self.weight})'''

  def    _UpperCamelCase( self			:  Dict       ):
        return self.value

  def    _UpperCamelCase( self			:  Optional[Any]       ):
        return self.name

  def    _UpperCamelCase( self			:  Optional[Any]       ):
        return self.weight

  def    _UpperCamelCase( self			:  Optional[int]       ):
        return self.value / self.weight




def UpperCamelCase_				(				__a			,				__a			,				__a      )	->   Optional[Any]:
      a__	:  Optional[Any]     =   []
      for i in range(len(__a      )      ):
            menu.append(Things(name[i]			,				value[i]			,				weight[i]      )      )
      return menu



def UpperCamelCase_				(				__a			,				__a			,				__a      )	->   Union[str, Any]:
      a__	:  List[str]     =   sorted(__a			,				key=__a			,				reverse=__a      )
      a__	:  List[Any]     =   []
      a__,	a__	:  Union[str, Any]     =   0.0, 0.0
      for i in range(len(__a      )      ):
            if (total_cost + items_copy[i].get_weight()) <= max_cost:
                  result.append(items_copy[i]      )
                  total_cost += items_copy[i].get_weight()
                  total_value += items_copy[i].get_value()
      return (result, total_value)



def UpperCamelCase_				(				)	->   Union[str, Any]:
      pass


if __name__ == "__main__":
    import doctest

    doctest.testmod()







import heapq




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						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(lowerCamelCase						,  [-1 * len(lowerCamelCase ), (key, value)] )

				# chosen_vertices = set of chosen vertices
				__magic_name__						:						Tuple										=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
								__magic_name__						:						Tuple										=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]:
																__magic_name__						:						Tuple										=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()

							UpperCAmelCase_		:					Optional[int]          =  {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)}""")




