






'''simple docstring'''







import heapq





def 		_UpperCAmelCase   (							__A							:   Any      ):
				a_		:  Optional[Any]											=      []

				# 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(__snake_case						,		[-1 * len(__snake_case      ), (key, value)]      )

				# chosen_vertices = set of chosen vertices
				a_		:  List[str]											=      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_		:  Tuple											=      heapq.heappop(__snake_case      )[1][0]
								chosen_vertices.add(__snake_case      )

								# 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_		:  int											=      elem[1][1].index(__snake_case      )
																del elem[1][1][index]
																elem[0] += 1
        # re-order the queue
								heapq.heapify(__snake_case      )
				return chosen_vertices


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		__lowerCAmelCase       		=      {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'''







from __future__ import annotations





def 		_UpperCAmelCase   (							__A							:   list[int]      ):
				a_		:  int											=      len(__A      ) // 2

				# choose the middle 3 elements
				a_		:  Dict											=      lst[m - 1 : m + 2]

				# if middle element is peak
				if three[1] > three[0] and three[1] > three[2]:
								return three[1]

				# if increasing, recurse on right
				elif three[0] < three[2]:
								if len(lst[:m]      ) == 2:
												m -= 1
								return peak(lst[m:]      )

				# decreasing
				else:
								if len(lst[:m]      ) == 2:
												m += 1
								return peak(lst[:m]      )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




