



import heapq






def      lowerCAmelCase__		(   lowerCamelCase_		:		dict):





				'''simple docstring'''

				lowerCAmelCase__					:    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
				lowerCAmelCase__					:    int												=					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__					:    str												=					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]:
																lowerCAmelCase__					:    Optional[int]												=					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()

							__snake_case    :		List[str]  ={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)}""")






def      lowerCAmelCase__		(   lowerCamelCase_		:		int	,lowerCamelCase_		:		int):





				'''simple docstring'''

				while b:
								lowerCAmelCase__						,		lowerCAmelCase__					:    Optional[Any]												=					b, a % b
				return a






def      lowerCAmelCase__		(   lowerCamelCase_		:		int	,lowerCamelCase_		:		int):





				'''simple docstring'''

				return a if b == 0 else euclidean_gcd_recursive(lowerCamelCase_	,a % b)






def      lowerCAmelCase__		(   ):





				'''simple docstring'''

				print(f"""euclidean_gcd(3, 5) = {euclidean_gcd(3	,5)}""")
				print(f"""euclidean_gcd(5, 3) = {euclidean_gcd(5	,3)}""")
				print(f"""euclidean_gcd(1, 3) = {euclidean_gcd(1	,3)}""")
				print(f"""euclidean_gcd(3, 6) = {euclidean_gcd(3	,6)}""")
				print(f"""euclidean_gcd(6, 3) = {euclidean_gcd(6	,3)}""")

				print(f"""euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3	,5)}""")
				print(f"""euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5	,3)}""")
				print(f"""euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1	,3)}""")
				print(f"""euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3	,6)}""")
				print(f"""euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6	,3)}""")


if __name__ == "__main__":
							main()

