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 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 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 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_