def spanning_tree(g: Graph) -> {(str, str, int)}:
answer = set()
edges = sorted((e[2], e[0], e[1]) for e in g if len(e) != 1)
components = EquivalenceClass(g.all_nodes())
n = len(g.all_nodes())
for v, o, d in edges:
if n == 1:
return answer
if not components.in_same_class(o, d):
answer.add((o, d, v))
components.merge_classes_containing(o, d)
n -= 1
return answer
def setup(size):
global ec
ec = EquivalenceClass([i for i in range(size)])