def N(val, left=None, right=None, color=B):
node = make_node(val, left=left, right=right, color=color)
if left:
left.parent = node
if right:
right.parent = node
return node
def N(val, left=None, right=None, color=B):
node = make_node(val, left=left, right=right, color=color)
if left:
left.parent = node
if right:
right.parent = node
return node
def sample_tree():
'''
Tree for rotation - the pivot is 4
4
|
-------
/ \
2 (6)
| |
----- -----
/ \ / \
(1) (3) 5 7
'''
return assign_parents(make_node(4,color=B,
left = make_node(2, color=B,
left=make_node(1),
right = make_node(3)),
right = make_node(6,
left=make_node(5, color=B),
right=make_node(7, color=B))))
def sample_tree():
'''
Tree for rotation - the pivot is 4
4
|
-------
/ \
2 (6)
| |
----- -----
/ \ / \
(1) (3) 5 7
'''
return assign_parents(
make_node(4,
color=B,
left=make_node(2,
color=B,
left=make_node(1),
right=make_node(3)),
right=make_node(6,
left=make_node(5, color=B),
right=make_node(7, color=B))))
def valid_trunk_2_children():
return assign_parents(make_node(2, color=B, left=make_node(1), right = make_node(3)))
def valid_trunk_1_child():
return assign_parents(make_node(2, color=B, left=make_node(1)))
def should_delete_corner_cases():
'''
delete 4 in this tree
Example 1:
3 3
/ \ / \
2 (5) => 2 (7)
/ / \ / / \
(1) 4 7 (1) 5 8
/ \ X \
(6) (8) (4) (6)
Example 2:
sibling black with single red child.
Rotate to romve zig zag (if any) and rotate left.
3 3 3
/ \ / \ / \
2 (5) rotate right 2 (5) left 2 (6)
/ / \ => / / \ => / / \
(1) 4 7 (1) 4 6 (1) 5 7
/ \ X
(6) (7) (4)
Ex 3:
black node, black parent but one of sibling or sibling's children is red
3
|
3 -------
/ \ / \
1 5 1 7
/ \ / \ => / \ / \
1 2 4 (7) 1 2 5 8
/ \ X \
6 8 (4) (6)
3 3
| |
3 ------- -------
/ \ / \ => / \
1 5 1 5 1 6
/ \ / \ => / \ / \ / \ / \
1 2 4 7 1 2 4 6 1 2 5 7
/ \ X
(6) (7) (4)
'''
for tree in [
make_node(3, color=B,
left=make_node(2, color=B, left=make_node(1)),
right = make_node(5,
left=make_node(4, color=B),
right = make_node(7, color=B,
left=make_node(6),
right = make_node(8)))),
make_node(3, color=B,
left=make_node(1, color=B, left=make_node(1)),
right = make_node(5,
left=make_node(4, color=B),
right = make_node(7, color=B, left=make_node(6)))),
make_node(3, color=B,
left=make_node(1, color=B,
left=make_node(1, color=B),
right = make_node(2, color =B)),
right = make_node(5, color=B,
left=make_node(4, color=B),
right = make_node(7, color=B,
left=make_node(6),
right = make_node(8)))),
make_node(3, color=B,
left=make_node(1, color=B,
left=make_node(1, color=B),
right = make_node(2, color =B)),
right = make_node(5, color=B,
left=make_node(4, color=B),
right = make_node(7, color=B,
left=make_node(6))))]:
tree = assign_parents(tree)
assert is_valid(tree) # ensure test data is valid
vals = inorder(tree)
print strify(tree)
tree = delete(4, tree)
print strify(tree)
assert is_valid(tree)
vals.remove(4)
assert vals == inorder(tree)
def should_satisfy_invariant():
assert is_valid(valid_trunk_2_children())
assert is_valid(valid_trunk_1_child())
tree = valid_trunk_2_children()
tree.left.left = make_node(-1, R)
assert not is_valid(tree)
tree.left.left = make_node(-1, B)
tree = valid_trunk_2_children()
tree.left.value = tree.value + 1
assert not is_valid(tree)
tree = valid_trunk_2_children()
tree.right.value = tree.value - 1
assert not is_valid(tree)
tree = assign_parents(make_node(4, color = B,
left = make_node(2,
left=make_node(1, color=B),
right=make_node(3, color=B)),
right = make_node(6, color = B,
left = make_node(5),
right = make_node(7))))
assert is_valid(tree)
tree.left.right.value = tree.value + 1
assert not is_valid(tree)
tree = assign_parents(make_node(8, color = B,
left = make_node(4,
left=make_node(2, color=B,
left = make_node(1, color=B),
right = make_node(3, color=B)),
right=make_node(6, color=B,
left = make_node(5, color=B),
right = make_node(7, color=B))),
right = make_node(10, color = B,
left = make_node(9, color = B),
right = make_node(11, color = B))))
assert is_valid(tree)
def valid_trunk_2_children():
return assign_parents(
make_node(2, color=B, left=make_node(1), right=make_node(3)))
def valid_trunk_1_child():
return assign_parents(make_node(2, color=B, left=make_node(1)))
def should_delete_corner_cases():
'''
delete 4 in this tree
Example 1:
3 3
/ \ / \
2 (5) => 2 (7)
/ / \ / / \
(1) 4 7 (1) 5 8
/ \ X \
(6) (8) (4) (6)
Example 2:
sibling black with single red child.
Rotate to romve zig zag (if any) and rotate left.
3 3 3
/ \ / \ / \
2 (5) rotate right 2 (5) left 2 (6)
/ / \ => / / \ => / / \
(1) 4 7 (1) 4 6 (1) 5 7
/ \ X
(6) (7) (4)
Ex 3:
black node, black parent but one of sibling or sibling's children is red
3
|
3 -------
/ \ / \
1 5 1 7
/ \ / \ => / \ / \
1 2 4 (7) 1 2 5 8
/ \ X \
6 8 (4) (6)
3 3
| |
3 ------- -------
/ \ / \ => / \
1 5 1 5 1 6
/ \ / \ => / \ / \ / \ / \
1 2 4 7 1 2 4 6 1 2 5 7
/ \ X
(6) (7) (4)
'''
for tree in [
make_node(3,
color=B,
left=make_node(2, color=B, left=make_node(1)),
right=make_node(5,
left=make_node(4, color=B),
right=make_node(7,
color=B,
left=make_node(6),
right=make_node(8)))),
make_node(3,
color=B,
left=make_node(1, color=B, left=make_node(1)),
right=make_node(5,
left=make_node(4, color=B),
right=make_node(7,
color=B,
left=make_node(6)))),
make_node(3,
color=B,
left=make_node(1,
color=B,
left=make_node(1, color=B),
right=make_node(2, color=B)),
right=make_node(5,
color=B,
left=make_node(4, color=B),
right=make_node(7,
color=B,
left=make_node(6),
right=make_node(8)))),
make_node(3,
color=B,
left=make_node(1,
color=B,
left=make_node(1, color=B),
right=make_node(2, color=B)),
right=make_node(5,
color=B,
left=make_node(4, color=B),
right=make_node(7,
color=B,
left=make_node(6))))
]:
tree = assign_parents(tree)
assert is_valid(tree) # ensure test data is valid
vals = inorder(tree)
print strify(tree)
tree = delete(4, tree)
print strify(tree)
assert is_valid(tree)
vals.remove(4)
assert vals == inorder(tree)
def should_satisfy_invariant():
assert is_valid(valid_trunk_2_children())
assert is_valid(valid_trunk_1_child())
tree = valid_trunk_2_children()
tree.left.left = make_node(-1, R)
assert not is_valid(tree)
tree.left.left = make_node(-1, B)
tree = valid_trunk_2_children()
tree.left.value = tree.value + 1
assert not is_valid(tree)
tree = valid_trunk_2_children()
tree.right.value = tree.value - 1
assert not is_valid(tree)
tree = assign_parents(
make_node(4,
color=B,
left=make_node(2,
left=make_node(1, color=B),
right=make_node(3, color=B)),
right=make_node(6,
color=B,
left=make_node(5),
right=make_node(7))))
assert is_valid(tree)
tree.left.right.value = tree.value + 1
assert not is_valid(tree)
tree = assign_parents(
make_node(8,
color=B,
left=make_node(4,
left=make_node(2,
color=B,
left=make_node(1, color=B),
right=make_node(3, color=B)),
right=make_node(6,
color=B,
left=make_node(5, color=B),
right=make_node(7, color=B))),
right=make_node(10,
color=B,
left=make_node(9, color=B),
right=make_node(11, color=B))))
assert is_valid(tree)