
'''simple docstring'''





import heapq

def      A (       A_							:					dict       ):
						snake_case       :     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
						snake_case       :     Optional[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
												snake_case       :     int =    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]:
																								snake_case       :     Tuple =    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()

						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'''





from __future__ import annotations

def      A (       A_							:					list[int]    ,							A_							:					int       ):
						snake_case       :     list[list[int]] =    []
						snake_case       :     list[int] =    []
						snake_case       :     int =    0
						snake_case       :     int =    sum(A_       )
						create_state_space_tree(A_    ,							A_    ,							A_    ,							A_    ,							A_    ,							A_       )
						return result

def      A (       A_							:					list[int]    ,							A_							:					int    ,							A_							:					int    ,							A_							:					list[int]    ,							A_							:					list[list[int]]    ,							A_							:					int    ,							):
						if sum(A_       ) > max_sum or (remaining_nums_sum + sum(A_       )) < max_sum:
												return
						if sum(A_       ) == max_sum:
												result.append(A_       )
												return
						for index in range(A_    ,							len(A_       )       ):
												create_state_space_tree(
												    A_    ,							A_    ,							index + 1    ,							[*path, nums[index]]    ,							A_    ,							remaining_nums_sum - nums[index]    ,							)
UpperCAmelCase    					=   [3, 34, 4, 12, 5, 2]
UpperCAmelCase    					=   9
UpperCAmelCase    					=   generate_sum_of_subsets_soln(nums, max_sum)





print(*result)

