def test_mst_random(self):
graph = WeightedGraph()
number_of_vertices = 10 ** 3
max_value = number_of_vertices + 10 ** 2
number_of_chords = number_of_vertices // 2
branching_factor = 4
delta_weight = 30
vs = sample(range(max_value), number_of_vertices)
trees = [[v] for v in vs]
guaranteed = set()
possible = set()
min_weight, max_weight = 0, 0
while len(trees) > 1: # spanning tree of the graph
min_weight, max_weight = max_weight, max_weight + delta_weight # in each iteration weight is increased
nodes_on_level = max(len(trees) // branching_factor, 1)
trees, tail = trees[:nodes_on_level], trees[nodes_on_level:]
for (tree, t) in ((choice(trees), t) for t in tail): # Cut property:
[u], [v] = sample(tree, 1), sample(t, 1) # Let S be any subset of vertices,
w = randrange(min_weight, max_weight) # and let e be the min cost edge
graph.add_direct_link(u, v, w) # with exactly one endpoint in S.
tree.extend(t) # Then the MST contains e.
e = tuple(sorted((u, v)))
if nodes_on_level > 1: # So the lightest edges must be present in the graph's MST
guaranteed.add(e)
else: # There will be more edges within the last range
possible.add(e)
i = 0
extralarge_weight = max_weight + delta_weight
while i < number_of_chords:
(u, v) = sorted(sample(vs, 2))
if (u, v) not in graph._edge:
if getrandbits(1): # Here they are
graph.add_direct_link(u, v, randrange(min_weight, max_weight)) # Cycle property:
possible.add((u, v)) # Let C be any cycle in G,
else: # and let f be the max cost
graph.add_direct_link(u, v, randrange(max_weight, extralarge_weight)) # edge belonging to C.
i += 1 # Then the MST
mst = graph.mst() # does not contain f.
result = set(mst._edge)
self.check_spanning(mst, graph)
self.assertTrue(guaranteed <= result) # Cut property: contains all min edges of spanning forest
self.assertTrue(result - guaranteed <= possible) # Cycle property: contains no heavy chords
def test_mst_manually(self):
graph = WeightedGraph()
graph.add_direct_link(1, 2, 1).add_direct_link(1, 3, 1).add_direct_link(1, 4, 1).add_direct_link(
2, 3, 1
).add_direct_link(2, 4, 1).add_direct_link(3, 4, 1)
mst = graph.mst()
self.check_spanning(mst, graph)
self.assertEqual(mst.weight(), 3)
graph = WeightedGraph()
graph.add_direct_link(2, 3, 1).add_direct_link(2, 4, 2).add_direct_link(3, 4, 3).add_direct_link(
1, 2, 3
).add_direct_link(1, 3, 2).add_direct_link(1, 4, 1)
mst = graph.mst() # 1-4, 2-3, 2-4 or 1-3, 1-4, 2-3
self.check_spanning(mst, graph)
self.assertEqual(mst.weight(), 4)
self.assertTrue(
set(mst._edge.items()) == {((1, 4), 1), ((2, 3), 1), ((2, 4), 2)}
or set(mst._edge.items()) == {((1, 3), 2), ((1, 4), 1), ((2, 3), 1)}
)
