def test_find_pom_tree(self):
n = random.randint(1, 30)
tree = RedBlackTree(sentinel=IntervalPomNode(None))
intervals = []
node_pairs = []
for _ in range(n):
low_endpoint = random.randint(0, 899)
high_endpoint = low_endpoint + random.randint(0, 100)
interval = Interval(low_endpoint, high_endpoint)
intervals.append(interval)
node_pair = interval_pom_insert(tree, interval)
node_pairs.append(node_pair)
assert_interval_pom_tree(tree)
while node_pairs:
actual_pom = find_pom(tree)
expected_poms = get_expected_poms(intervals)
assert_that(actual_pom, is_in(expected_poms))
node_pair = random.choice(node_pairs)
node_pairs.remove(node_pair)
interval_to_delete = Interval(node_pair[0].key, node_pair[1].key)
intervals.remove(interval_to_delete)
interval_pom_delete(tree, *node_pair)
assert_interval_pom_tree(tree)
def test_joinable_rb_insert(self):
keys = [random.randrange(1000) for _ in range(20)]
tree = RedBlackTree(sentinel=None)
tree.bh = 0
for key in keys:
joinable_rb_insert(tree, Node(key))
assert_red_black_tree(tree)
assert_parent_pointers_consistent(tree)
actual_keys = get_binary_tree_keys(tree)
assert_that(actual_keys, contains_inanyorder(*keys))
actual_black_height = calculate_black_height(tree.root)
assert_that(tree.bh, is_(equal_to(actual_black_height)))
def test_effective_os_tree(self):
_, keys = get_random_array()
tree = RedBlackTree(sentinel=OSNode(None))
tree.nil.min = tree.nil.max = tree.nil.pred = tree.nil.succ = tree.nil
for key in keys:
effective_os_insert(tree, OSNode(key))
nodes = get_binary_tree_nodes(tree, sentinel=tree.nil)
while nodes:
actual_minimum = effective_os_minimum(tree)
actual_maximum = effective_os_maximum(tree)
expected_minimum = rb_minimum(tree.root, sentinel=tree.nil)
expected_maximum = rb_maximum(tree.root, sentinel=tree.nil)
assert_that(actual_minimum, is_(expected_minimum))
assert_that(actual_maximum, is_(expected_maximum))
node = random.choice(nodes)
actual_predecessor = effective_os_predecessor(tree, node)
actual_successor = effective_os_successor(tree, node)
expected_predecessor = rb_predecessor(node, sentinel=tree.nil)
expected_successor = rb_successor(node, sentinel=tree.nil)
assert_that(actual_predecessor, is_(expected_predecessor))
assert_that(actual_successor, is_(expected_successor))
effective_os_delete(tree, node)
nodes = get_binary_tree_nodes(tree, sentinel=tree.nil)
def test_min_gap_tree(self):
_, keys = get_random_unique_array()
tree = RedBlackTree()
tree.nil.min_key = tree.nil.min_gap = math.inf
tree.nil.max_key = -math.inf
for key in keys:
min_gap_insert(tree, Node(key))
nodes = get_binary_tree_nodes(tree, sentinel=tree.nil)
while nodes:
node = random.choice(nodes)
key = node.key
keys.remove(key)
actual_found = min_gap_search(tree, key)
assert_that(actual_found.key, is_(equal_to(key)))
min_gap_delete(tree, node)
actual_found = min_gap_search(tree, key)
assert_that(actual_found, is_(tree.nil))
actual_min_gap = min_gap(tree)
expected_min_gap = get_expected_min_gap(keys)
assert_that(actual_min_gap, is_(equal_to(expected_min_gap)))
nodes = get_binary_tree_nodes(tree, sentinel=tree.nil)
def test_joinable_rb_insert(self):
keys = [random.randrange(1000) for _ in range(20)]
tree = RedBlackTree(sentinel=None)
tree.bh = 0
for key in keys:
joinable_rb_insert(tree, Node(key))
assert_red_black_tree(tree)
assert_parent_pointers_consistent(tree)
actual_keys = get_binary_tree_keys(tree)
assert_that(actual_keys, contains_inanyorder(*keys))
actual_black_height = calculate_black_height(tree.root)
assert_that(tree.bh, is_(equal_to(actual_black_height)))
def os_count_inversions(A):
n = A.length
inversions = 0
tree = RedBlackTree(sentinel=OSNode(None))
for i in between(1, n):
x = OSNode(A[i])
os_insert(tree, x)
inversions += i - os_rank(tree, x)
return inversions
def test_create_red_black_tree(self):
left = Node(3)
right = Node(20)
root = Node(17, left=left, right=right)
tree = RedBlackTree(root)
assert_that(tree.root, is_(root))
assert_that(root.left, is_(left))
assert_that(root.right, is_(right))
assert_parent_pointers_consistent(tree, sentinel=tree.nil)
def josephus(n, m):
T = RedBlackTree(sentinel=OSNode(None))
for j in between(1, n):
x = OSNode(j)
os_insert(T, x)
j = 1
for k in rbetween(n, 1):
j = (j + m - 1) % k + 1
x = os_select(T.root, j)
print(x.key)
os_delete(T, x)
def test_rb_parentless_insert(self):
keys = [random.randrange(1000) for _ in range(20)]
tree = RedBlackTree()
for key in keys:
parentless_rb_insert(tree, Node(key))
assert_red_black_tree(tree, sentinel=tree.nil)
actual_keys = get_binary_tree_keys(tree, sentinel=tree.nil)
assert_that(actual_keys, contains_inanyorder(*keys))
def test_persistent_rb_insert(self):
keys = [random.randrange(1000) for _ in range(20)]
tree = RedBlackTree()
for i, key in enumerate(keys):
new_tree = persistent_rb_insert(tree, ParentlessNode(key))
assert_red_black_tree(new_tree, sentinel=tree.nil)
actual_keys_before_insertion = get_binary_tree_keys(tree, sentinel=tree.nil)
actual_keys_after_insertion = get_binary_tree_keys(new_tree, sentinel=tree.nil)
assert_that(actual_keys_before_insertion, contains_inanyorder(*keys[:i]))
assert_that(actual_keys_after_insertion, contains_inanyorder(*keys[:i + 1]))
tree = new_tree
def test_rb_insert(self):
_, keys = get_random_array()
tree = RedBlackTree()
for key in keys:
rb_insert(tree, Node(key), sentinel=tree.nil)
assert_red_black_tree(tree, sentinel=tree.nil)
assert_parent_pointers_consistent(tree, sentinel=tree.nil)
actual_keys = get_binary_tree_keys(tree, sentinel=tree.nil)
assert_that(actual_keys, contains_inanyorder(*keys))
def test_os_insert(self):
keys = [random.randrange(1000) for _ in range(20)]
tree = RedBlackTree(sentinel=OSNode(None))
for i, key in enumerate(keys):
os_insert(tree, OSNode(key))
assert_os_tree(tree)
assert_that(tree.root.size, is_(equal_to(i + 1)))
assert_parent_pointers_consistent(tree, sentinel=tree.nil)
actual_keys = get_binary_tree_keys(tree, sentinel=tree.nil)
assert_that(actual_keys, contains_inanyorder(*keys))
def test_interval_insert(self):
keys = [random.randrange(949) for _ in range(20)]
tree = RedBlackTree(sentinel=IntervalNode(None, None))
for key in keys:
interval_insert(
tree,
IntervalNode(key, Interval(key, key + random.randint(0, 50))))
assert_interval_tree(tree)
assert_parent_pointers_consistent(tree, sentinel=tree.nil)
actual_keys = get_binary_tree_keys(tree, sentinel=tree.nil)
assert_that(actual_keys, contains_inanyorder(*keys))
def persistent_rb_insert(T, z):
path_length = _get_path_length_from_root_to_node(T, z)
S = Array.indexed(1, path_length + 1)
S.top = 0
y = T.nil
x = T.root
T_ = RedBlackTree(sentinel=T.nil)
y_ = T_.nil
push(S, y_)
while x is not T.nil:
y = x
x_ = rb.ParentlessNode.clone(x)
if y_ is T_.nil:
T_.root = x_
else:
if x is y_.left:
y_.left = x_
else:
y_.right = x_
y_ = x_
push(S, y_)
if z.key < x.key:
x = x.left
else:
x = x.right
if y is T.nil:
T_.root = z
else:
if z.key < y.key:
y_.left = z
else:
y_.right = z
z.left = z.right = T.nil
z.color = Red
_persistent_rb_insert_fixup(T_, S, z)
return T_
def get_random_red_black_tree(black_height=3,
min_value=0,
max_value=999,
sentinel=rb.Node(None)):
nodes = []
tree = RedBlackTree(get_random_red_black_subtree(black_height, nodes),
sentinel=sentinel)
tree_size = len(nodes)
_, keys = get_random_unique_array(min_size=tree_size,
max_size=tree_size,
min_value=min_value,
max_value=max_value)
keys.sort()
fill_subtree_with_keys(tree.root, keys, tree.nil)
return tree, nodes, keys
def test_interval_search_exactly_positive(self):
_, keys = get_random_array(max_size=100, max_value=89)
tree = RedBlackTree(sentinel=IntervalNode(None, None))
intervals = []
for key in keys:
i = Interval(key, key + random.randint(0, 10))
intervals.append(i)
interval_insert_exactly(tree, IntervalNode(key, i))
assert_interval_tree(tree)
interval = random.choice(intervals)
actual_found = interval_search_exactly(tree, interval)
assert_that(actual_found.int, is_(equal_to(interval)))
def intersecting_chords(C):
n = C.length // 2
P = Array.indexed(1, n)
for k in between(1, n):
P[k] = 0
intersections = 0
T = RedBlackTree(sentinel=OSNode(None))
for k in between(1, 2 * n):
j = C[k]
if P[j] == 0:
P[j] = k
os_insert(T, OSNode(k))
else:
x = os_search(T, P[j])
intersections = intersections + T.root.size - os_rank(T, x)
os_delete(T, x)
return intersections
def rectangles_overlap(A):
T = RedBlackTree(sentinel=IntervalNode(None, None))
x_coords = [(rectangle[0].low, rectangle)
for rectangle in A] + [(rectangle[0].high, rectangle)
for rectangle in A]
x_coords.sort(key=lambda p: p[0])
for p in x_coords:
horizontal_side = p[1][0]
vertical_side = p[1][1]
if p[0] == horizontal_side.low:
if interval_search(T, vertical_side) is not T.nil:
return True
interval_insert_exactly(
T, IntervalNode(vertical_side.low, vertical_side))
else:
v = interval_search_exactly(T, vertical_side)
interval_delete(T, v)
return False
def rb_join(T1, x, T2):
T = RedBlackTree(sentinel=None)
if T1.bh >= T2.bh:
if T2.root is None:
joinable_rb_insert(T1, x)
return T1
T.root = x
T.bh = T1.bh
y = rb_join_point(T1, T2)
x.left = y
x.right = T2.root
if y is not T1.root:
if y is y.p.left:
y.p.left = x
else:
y.p.right = x
T.root = T1.root
x.p = y.p
T2.root.p = y.p = x
else:
if T1.root is None:
joinable_rb_insert(T2, x)
return T2
T.root = x
T.bh = T2.bh
y = rb_symmetric_join_point(T1, T2)
x.right = y
x.left = T1.root
if y is not T2.root:
if y is y.p.right:
y.p.right = x
else:
y.p.left = x
T.root = T2.root
x.p = y.p
T1.root.p = y.p = x
x.color = Red
joinable_rb_insert_fixup(T, x)
return T
def activity_scheduler(s, f):
n = s.length
A = Array.indexed(1, n)
F = Array(list(rbetween(n, 1)))
F.top = n
B = RedBlackTree()
# events contains triples (a, b, c) where a = 0 if the event is finish of an activity and 1 if it is start,
# b as the activity number, and c as the start time or the finish time
events = [(0, i + 1, finish_time) for i, finish_time in enumerate(f)] + \
[(1, i + 1, start_time) for i, start_time in enumerate(s)]
events.sort(key=lambda e: (e[2], e[0]))
for e in events:
if e[0] == 1:
hall_number = pop(F)
A[e[1]] = hall_number
rb_insert(B, Node(e[1], data=hall_number), sentinel=B.nil)
else:
hall = rb_search(B.root, e[1], sentinel=B.nil)
push(F, hall.data)
rb_delete(B, hall, sentinel=B.nil)
return A
def test_interval_search_exactly_random(self):
_, keys = get_random_array(max_size=100, max_value=89)
tree = RedBlackTree(sentinel=IntervalNode(None, None))
intervals = []
for key in keys:
i = Interval(key, key + random.randint(0, 10))
intervals.append(i)
interval_insert_exactly(tree, IntervalNode(key, i))
assert_interval_tree(tree)
low_endpoint = random.randint(0, 89)
high_endpoint = low_endpoint + random.randint(0, 10)
interval = Interval(low_endpoint, high_endpoint)
actual_found = interval_search_exactly(tree, interval)
if actual_found is not tree.nil:
assert_that(actual_found.int, is_(equal_to(interval)))
else:
for i in intervals:
assert_that(interval, is_not(equal_to(i)))
def rb_join(T1, x, T2):
T = RedBlackTree(sentinel=None)
if T1.bh >= T2.bh:
if T2.root is None:
joinable_rb_insert(T1, x)
return T1
T.root = x
T.bh = T1.bh
y = rb_join_point(T1, T2)
x.left = y
x.right = T2.root
if y is not T1.root:
if y is y.p.left:
y.p.left = x
else:
y.p.right = x
T.root = T1.root
x.p = y.p
T2.root.p = y.p = x
else:
if T1.root is None:
joinable_rb_insert(T2, x)
return T2
T.root = x
T.bh = T2.bh
y = rb_symmetric_join_point(T1, T2)
x.right = y
x.left = T1.root
if y is not T2.root:
if y is y.p.right:
y.p.right = x
else:
y.p.left = x
T.root = T2.root
x.p = y.p
T1.root.p = y.p = x
x.color = Red
joinable_rb_insert_fixup(T, x)
return T
def test_create_empty_red_black_tree(self):
tree = RedBlackTree()
assert_that(tree.root, is_(tree.nil))
assert_that(tree.nil.color, is_(Black))
def persistent_rb_delete(T, z):
T_ = RedBlackTree()
T_.root = T_.nil = T.nil
if z.left is T.nil or z.right is T.nil:
y = z
else:
y = rb_successor(z, T.nil)
path_length = _get_path_length_from_root_to_node(T, y)
S = Array.indexed(1, path_length + 1)
S.top = 0
p = T.root
r = T.nil
p_ = r_ = T_.nil
push(S, p_)
z_ = T.nil
while p is not y:
p_ = rb.ParentlessNode.clone(p)
push(S, p_)
if p is z:
z_ = p_
if r_ is T_.nil:
T_.root = p_
else:
if p is r_.left:
r_.left = p_
else:
r_.right = p_
r = p
r_ = p_
if y.key < p.key:
p = p.left
else:
p = p.right
if y.left is not T.nil:
x = y.left
else:
x = y.right
if y.color == Black:
if x is not T.nil:
x_ = rb.ParentlessNode.clone(x)
else:
x_ = T.nil
if y is T.root:
T_.root = x_
else:
if y is r.left:
p_.left = x_
else:
p_.right = x_
if y is not z:
z_.key = y.key
z_.data = y.data
persistent_rb_delete_fixup(T_, S, x_)
else:
if y is r.left:
p_.left = x
else:
p_.right = x
if y is not z:
z_.key = y.key
z_.data = y.data
return T_
def setUp(self):
self.tree = RedBlackTree()
class TestRedBlackTree(unittest.TestCase):
def setUp(self):
self.tree = RedBlackTree()
def test_empty(self):
self.assertTrue(self.tree.empty())
def test_get_inorder(self):
self.assertListEqual([], self.tree.get_inorder())
self.tree.insert(3)
self.tree.insert(1)
self.tree.insert(5)
self.assertListEqual([(1, NodeColor.RED), (3, NodeColor.BLACK),
(5, NodeColor.RED)], self.tree.get_inorder())
def test_print_inorder(self):
self.assertEqual("", self.tree.print_inorder())
self.tree.insert(3)
self.tree.insert(1)
self.tree.insert(5)
self.assertEqual("1R, 3B, 5R", self.tree.print_inorder())
def test_insert(self):
self.tree.insert([10, 20, 30])
self.assertListEqual([(10, NodeColor.RED), (20, NodeColor.BLACK),
(30, NodeColor.RED)], self.tree.get_inorder())
self.tree.insert(15)
self.assertListEqual([(10, NodeColor.BLACK), (15, NodeColor.RED),
(20, NodeColor.BLACK), (30, NodeColor.BLACK)],
self.tree.get_inorder())
def test_max(self):
self.tree.insert([10, 20, 56, 78])
self.assertListEqual([(10, NodeColor.BLACK), (20, NodeColor.BLACK),
(56, NodeColor.BLACK), (78, NodeColor.RED)],
self.tree.get_inorder())
self.assertEqual(self.tree.max(), 78)
def test_min(self):
self.tree.insert([0, 20, 1, 5])
self.assertListEqual([(0, NodeColor.BLACK), (1, NodeColor.BLACK),
(5, NodeColor.RED), (20, NodeColor.BLACK)],
self.tree.get_inorder())
self.assertEqual(self.tree.min(), 0)
def test_find(self):
self.tree.insert([3, 1, 0, 5])
self.assertTrue(self.tree.find(0))
self.assertTrue(self.tree.find(5))
self.assertFalse(self.tree.find(10))
def test_contains(self):
self.assertFalse(0 in self.tree)
self.tree.insert([4, 5, 0, 2])
self.assertFalse(10 in self.tree)
self.assertTrue(0 in self.tree)
def test_create_empty_red_black_tree_without_sentinel(self):
tree = RedBlackTree(sentinel=None)
assert_that(tree.root, is_(none()))
assert_that(tree.nil, is_(none()))