



'''simple docstring'''

import heapq






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						str							)      ->						List[Any]:







	"""simple docstring"""
	lowerCAmelCase   =     []

	# 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
	lowerCAmelCase   =     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
		lowerCAmelCase   =     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]:
				lowerCAmelCase   =     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()

		UpperCAmelCase     		=   {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'''

class __snake_case(				_lowerCAmelCase ):


						'''simple docstring'''



						pass







class __snake_case(				_lowerCAmelCase ):


						'''simple docstring'''



						pass







class __snake_case:


						'''simple docstring'''



						def __init__( self				)     ->     int:
							lowerCAmelCase   =     [
							    [],
							    [],
							    [],
							]


						def     __snake_case   ( self     ,	A_     ,	A_				)     ->     None:
							try:
								if len(self.queues[priority]				) >= 100:
									raise OverflowError("""Maximum queue size is 100"""				)
								self.queues[priority].append(A_				)
							except IndexError:
								raise ValueError("""Valid priorities are 0, 1, and 2"""				)


						def     __snake_case   ( self				)     ->     int:
							for queue in self.queues:
								if queue:
									return queue.pop(0				)
							raise UnderFlowError("""All queues are empty"""				)




						def __str__( self				)     ->     str:
							return "\n".join(f'Priority {i}: {q}' for i, q in enumerate(self.queues				)				)







class __snake_case:


						'''simple docstring'''



						def __init__( self				)     ->     Dict:
							lowerCAmelCase   =     []


						def     __snake_case   ( self     ,	A_				)     ->     None:
							if len(self.queue				) == 100:
								raise OverFlowError("""Maximum queue size is 100"""				)
							self.queue.append(A_				)


						def     __snake_case   ( self				)     ->     int:
							if not self.queue:
								raise UnderFlowError("""The queue is empty"""				)
							else:
								lowerCAmelCase   =     min(self.queue				)
								self.queue.remove(A_				)
								return data




						def __str__( self				)     ->     str:
							return str(self.queue				)







def 		_snake_case		( )      ->						Tuple:







	"""simple docstring"""
	lowerCAmelCase   =     FixedPriorityQueue()
	fpq.enqueue(0							,		10							)
	fpq.enqueue(1							,		70							)
	fpq.enqueue(0							,		100							)
	fpq.enqueue(2							,		1							)
	fpq.enqueue(2							,		5							)
	fpq.enqueue(1							,		7							)
	fpq.enqueue(2							,		4							)
	fpq.enqueue(1							,		64							)
	fpq.enqueue(0							,		128							)
	print(_SCREAMING_SNAKE_CASE							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(_SCREAMING_SNAKE_CASE							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)






def 		_snake_case		( )      ->						Optional[Any]:







	"""simple docstring"""
	lowerCAmelCase   =     ElementPriorityQueue()
	epq.enqueue(10							)
	epq.enqueue(70							)
	epq.enqueue(100							)
	epq.enqueue(1							)
	epq.enqueue(5							)
	epq.enqueue(7							)
	epq.enqueue(4							)
	epq.enqueue(64							)
	epq.enqueue(128							)
	print(_SCREAMING_SNAKE_CASE							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(_SCREAMING_SNAKE_CASE							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)


if __name__ == "__main__":
				fixed_priority_queue()
				element_priority_queue()