def test_union_on_three_nodes_as_1_2_and_1_3(self):
value1 = 1
value2 = 2
value3 = 3
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
self.structure.make_set(node1)
self.structure.make_set(node2)
self.structure.make_set(node3)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
self.structure.union(node1, node2)
self.assert_node(node1, value1, node1, 1)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node3, 0)
self.structure.union(node1, node3)
self.assert_node(node1, value1, node1, 1)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 0)
def test_repr_with_parent_and_rank(self):
parent = union_find.Node(1)
node = union_find.Node(2)
node.parent = parent
node.rank = 123
self.assertEqual('[2, parent=1, rank=123]', repr(node))
def test_make_set_on_three_nodes(self):
value1 = 1
value2 = 2
value3 = 3
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
self.structure.make_set(node1)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, None, None)
self.assert_node(node3, value3, None, None)
self.structure.make_set(node2)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, None, None)
self.structure.make_set(node3)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
def test_find_on_on_three_nodes(self):
value1 = 1
value2 = 2
value3 = 3
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
self.structure.make_set(node1)
self.structure.make_set(node2)
self.structure.make_set(node3)
result = self.structure.find(node1)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
result = self.structure.find(node2)
self.assertEqual(node2, result)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
result = self.structure.find(node3)
self.assertEqual(node3, result)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
def test_union_on_two_nodes_before_make_set(self):
value1 = 1
value2 = 2
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
with self.assertRaisesRegex(ValueError,
'1 not in the set.'):
self.structure.union(node1, node2)
with self.assertRaisesRegex(ValueError,
'2 not in the set.'):
self.structure.union(node2, node1)
def test_find_on_four_node_set_of_two_ranks(self):
value1 = 1
value2 = 2
value3 = 3
value4 = 4
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
node4 = union_find.Node(value4)
self.structure.make_set(node1)
self.structure.make_set(node2)
self.structure.make_set(node3)
self.structure.make_set(node4)
self.structure.union(node1, node2)
self.structure.union(node3, node4)
self.structure.union(node1, node3)
result = self.structure.find(node1)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 2)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
result = self.structure.find(node2)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 2)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
result = self.structure.find(node3)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 2)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
result = self.structure.find(node4)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 2)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
def test_make_set_on_two_nodes(self):
value1 = 1
value2 = 2
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
self.structure.make_set(node1)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, None, None)
self.structure.make_set(node2)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
def test_make_set_on_one_node(self):
value = 1
node = union_find.Node(value)
self.structure.make_set(node)
self.assert_node(node, value, node, 0)
def test_constructor(self):
value = 1
node = union_find.Node(value)
self.assertEqual(value, node.value)
self.assertEqual(None, node.parent)
self.assertEqual(None, node.rank)
def test_find_on_one_node(self):
value = 1
node = union_find.Node(value)
self.structure.make_set(node)
result = self.structure.find(node)
self.assertEqual(node, result)
self.assert_node(node, value, node, 0)
def test_union_on_four_nodes_as_1_2_and_3_4_and_1_3(self):
value1 = 1
value2 = 2
value3 = 3
value4 = 4
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
node4 = union_find.Node(value4)
self.structure.make_set(node1)
self.structure.make_set(node2)
self.structure.make_set(node3)
self.structure.make_set(node4)
self.assert_node(node1, value1, node1, 0)
self.assert_node(node2, value2, node2, 0)
self.assert_node(node3, value3, node3, 0)
self.assert_node(node4, value4, node4, 0)
self.structure.union(node1, node2)
self.assert_node(node1, value1, node1, 1)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node3, 0)
self.assert_node(node4, value4, node4, 0)
self.structure.union(node3, node4)
self.assert_node(node1, value1, node1, 1)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node3, 1)
self.assert_node(node4, value4, node3, 0)
self.structure.union(node1, node3)
self.assert_node(node1, value1, node1, 2)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
def kruskal(self, graph):
"""
Given a connected undirected graph G = (V, E) with positive edge
weights, computes a minimum spanning tree that consists of a subset
of edges E′ ⊆ E of minimum total weight such that the graph (V, E′)
is connected.
Greedy Strategy: Repeatedly adds the next lightest edge if this
doesn’t produce a cycle.
Note: The graph does not have to be undirected.
"""
minimum_spanning_tree = Graph()
set = union_find.UnionFind()
node_to_wrapper_node_map = {}
priority_queue = heap.BinHeap(heap.HeapMode.min)
for node in graph.nodes():
minimum_spanning_tree.add_node(node)
wrapper_node = union_find.Node(node)
node_to_wrapper_node_map[node] = wrapper_node
set.make_set(wrapper_node)
for u, v in graph.edges():
edge = (node_to_wrapper_node_map[u], node_to_wrapper_node_map[v])
priority_queue.insert(heap.HeapItem(graph.weight((u, v)), edge))
while priority_queue.size > 0:
min_item = priority_queue.extract()
u_node, v_node = min_item.datum
if set.find(u_node) != set.find(v_node):
minimum_spanning_tree.add_undirected_edge(
u_node.value, v_node.value, min_item.priority)
set.union(u_node, v_node)
return minimum_spanning_tree
def test_lt(self):
node1 = union_find.Node(1)
node2 = union_find.Node(2)
self.assertEqual(True, node1 < node2)
self.assertEqual(False, node2 < node1)
def test_eq(self):
node1 = union_find.Node(1)
node2 = union_find.Node(2)
self.assertEqual(False, node1 == node2)
self.assertEqual(False, node2 == node1)
def test_str(self):
node = union_find.Node(1)
self.assertEqual('1', str(node))
def test_gt_on_diff_type(self):
node = union_find.Node(1)
self.assertEqual(False, 'diff-type' > node)
self.assertEqual(False, node > 'diff-type')
def test_gt_on_none(self):
node = union_find.Node(1)
self.assertEqual(False, None > node)
self.assertEqual(False, node > None)
def test_eq_on_diff_type(self):
node = union_find.Node(1)
self.assertEqual(False, 'diff-type' == node)
self.assertEqual(False, node == 'diff-type')
def test_find_on_eight_node_set_of_three_ranks(self):
value1 = 1
value2 = 2
value3 = 3
value4 = 4
value5 = 5
value6 = 6
value7 = 7
value8 = 8
node1 = union_find.Node(value1)
node2 = union_find.Node(value2)
node3 = union_find.Node(value3)
node4 = union_find.Node(value4)
node5 = union_find.Node(value5)
node6 = union_find.Node(value6)
node7 = union_find.Node(value7)
node8 = union_find.Node(value8)
self.structure.make_set(node1)
self.structure.make_set(node2)
self.structure.make_set(node3)
self.structure.make_set(node4)
self.structure.make_set(node5)
self.structure.make_set(node6)
self.structure.make_set(node7)
self.structure.make_set(node8)
self.structure.union(node1, node2)
self.structure.union(node3, node4)
self.structure.union(node1, node3)
self.structure.union(node5, node6)
self.structure.union(node7, node8)
self.structure.union(node5, node7)
self.structure.union(node1, node5)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node1)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node2)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node3)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node3, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node4)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node5)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node5, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node6)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node1, 0)
self.assert_node(node7, value7, node5, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node7)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node1, 0)
self.assert_node(node7, value7, node1, 1)
self.assert_node(node8, value8, node7, 0)
result = self.structure.find(node8)
self.assertEqual(node1, result)
self.assert_node(node1, value1, node1, 3)
self.assert_node(node2, value2, node1, 0)
self.assert_node(node3, value3, node1, 1)
self.assert_node(node4, value4, node1, 0)
self.assert_node(node5, value5, node1, 2)
self.assert_node(node6, value6, node1, 0)
self.assert_node(node7, value7, node1, 1)
self.assert_node(node8, value8, node1, 0)
def test_eq_on_none(self):
node = union_find.Node(1)
self.assertEqual(False, None == node)
self.assertEqual(False, node == None)
def test_lt_on_none(self):
node = union_find.Node(1)
self.assertEqual(False, None < node)
self.assertEqual(False, node < None)
def test_gt_on_self(self):
node = union_find.Node(1)
self.assertEqual(False, node > node)
def test_eq_on_self(self):
node = union_find.Node(1)
self.assertEqual(True, node == node)
def test_repr(self):
node = union_find.Node(1)
self.assertEqual('[1, parent=None, rank=None]', repr(node))
def test_find_before_make_set(self):
node = union_find.Node(1)
with self.assertRaisesRegex(ValueError,
'1 not in the set.'):
self.structure.find(node)
