

import heapq

def 						UpperCamelCase (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__							:   Any					       =		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__							:   Optional[int]					       =		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__							:   Tuple					       =		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()

							A_	:			Tuple  	=      {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)}''')






from __future__ import annotations

def 						UpperCamelCase (lowercase_:			list[int]   ,				lowercase_:			list[int]   ,				lowercase_:			int )					->				tuple[float, list[float]]:
	A__							:   Tuple					       =		list(range(len(lowercase_ ) ) )
	A__							:   Union[str, Any]					       =		[v / w for v, w in zip(lowercase_   ,				lowercase_ )]
	index.sort(key=lambda lowercase_ : ratio[i]   ,				reverse=lowercase_ )

	A__							:   float					       =		0
	A__							:   list[float]					       =		[0] * len(lowercase_ )
	for i in index:
		if weight[i] <= capacity:
			A__							:   Optional[int]					       =		1
			max_value += value[i]
			capacity -= weight[i]
		else:
			A__							:   Union[str, Any]					       =		capacity / weight[i]
			max_value += value[i] * capacity / weight[i]
			break

	return max_value, fractions


if __name__ == "__main__":
	import doctest

	doctest.testmod()



