


import heapq


def 				lowerCamelCase__	(      a	:   dict				)    ->	set[int]:





			"""simple docstring"""
			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(a	,  [-1 * len(a				), (key, value)]				)

			# chosen_vertices = set of chosen vertices
			a__ :List[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__ :str						  =    heapq.heappop(a				)[1][0]
						chosen_vertices.add(a				)

						# 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__ :List[str]						  =    elem[1][1].index(a				)
												del elem[1][1][index]
												elem[0] += 1
        # re-order the queue
						heapq.heapify(a				)
			return chosen_vertices


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		snake_case__			 =						{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__	(      a	:   int	,  a	:   int				)    ->	Any:





			"""simple docstring"""
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			a__ :Optional[int]						  =    (boundary[1] - boundary[0]) / steps
			a__ :str						  =    boundary[0]
			a__ :Optional[int]						  =    boundary[1]
			a__ :str						  =    make_points(a	,  a	,  a				)
			a__ :Any						  =    0.0
			y += (h / 2.0) * f(a				)
			for i in x_i:
						# print(i)
						y += h * f(a				)
			y += (h / 2.0) * f(a				)
			return y


def 				lowerCamelCase__	(      a	:   Any	,  a	:   str	,  a	:   Dict				)    ->	int:





			"""simple docstring"""
			a__ :Union[str, Any]						  =    a + h
			while x < (b - h):
						yield x
						a__ :str						  =    x + h


def 				lowerCamelCase__	(      a	:   Optional[int]				)    ->	List[Any]:  # enter your function here





			"""simple docstring"""
			a__ :Tuple						  =    (x - 0) * (x - 0)
			return y


def 				lowerCamelCase__	(      )    ->	List[str]:





			"""simple docstring"""
			a__ :Optional[Any]						  =    0.0  # Lower bound of integration
			a__ :Optional[Any]						  =    1.0  # Upper bound of integration
			a__ :List[str]						  =    1_0.0  # define number of steps or resolution
			a__ :int						  =    [a, b]  # define boundary of integration
			a__ :str						  =    method_a(a	,  a				)
			print(F'''y = {y}'''				)


if __name__ == "__main__":
		main()


