private void RebalancePostInsertion(RBTreeNode newNode)
{
/**
* Insert function places newNode as an appropriate leaf for a regular BST but
* not necessarily a Red-black tree. Check if newNode's parent is RED (ie. if it
* breaks a only red-black tree condition). If so, use the RED and BLACK labels
* of newNode's parent, grandparent, and/or pibling (aunt/uncle) to balance.
*
* Note on conceptualizing this process:
* At this point, newNode is a RED leaf whose addition may cause the tree to
* not meet the required RED-BLACK conditions (noted in class description)
* such that it is imbalanced beyond the red-black tree threshold. In order
* to correct for this, we re-balance and/or recolor the subtree rooted at
* newNode's grandparent. We perform this process iteratively, reassigning
* newNode to its decendants (parents/grandparents), until we reach the root.
* At no point do we consider ancestors of newNode.
*
* See this page for a more detailed overview of the process:
* https://www.geeksforgeeks.org/red-black-tree-set-2-insert/ */
if (newNode.GrandParent() == null)
{
return;
}
RBTreeNode u; // Will represent pibling (aunt/uncle) or parent of newNode.
// ie. given newNode's grandparent (gP), u can be either gP's
// left or right child
while (newNode.Parent().IsRed())
{
// Case: p is the RIGHT child of gP:
if (newNode.Parent() == newNode.GrandParent().Right())
{
// Set u as the (LEFT) pibling of newNode
u = newNode.GrandParent().Left();
// Case: u exists and is RED: set both u & p to BLACK, set gP to RED,
// assign newNode = gP
if (u != null && u.IsRed())
{
u.SetBlack();
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
newNode = newNode.GrandParent();
}
else // Case: the (LEFT) pibling of newNode is BLACK
// Case: newNode is the left child of p: assign newNode = p and
// right rotate newNode
{
if (newNode == newNode.Parent().Left())
{
newNode = newNode.Parent();
RotateRight(newNode);
}
// Set p to BLACK and gP to RED. Then left rotate gP.
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
RotateLeft(newNode.GrandParent());
}
}
else // Case: p is the LEFT child of gP:
// Assign u as the (RIGHT) pibling of newNode
{
u = newNode.GrandParent().Right();
// Case: u is RED: set the color of both children of gP to BLACK, set
// gp to RED. Assign gP = newNode.
if (u != null && u.IsRed())
{
u.SetBlack();
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
newNode = newNode.GrandParent();
}
else
{
// Case: newNode is the right child of p then: set p = newNode.
// Then left rotate newNode.
if (newNode == newNode.Parent().Right())
{
newNode = newNode.Parent();
RotateLeft(newNode);
}
// Set color of p as BLACK and color of gP as RED. Then right
// rotate gP.
newNode.Parent().SetBlack();
newNode.GrandParent().SetRed();
RotateRight(newNode.GrandParent());
}
}
if (newNode == Root)
{
break;
}
}
Root.SetBlack();
}
private void RebalancePostDeletion(RBTreeNode node)
{
// Very similar to RebalancePostInsertion function
// node is the node in the location of/closest to the node just deleted
RBTreeNode s; // represents sibbling of node
while (node != Root && node.IsBlack())
{
if (node == node.Parent().Left())
{
s = node.Parent().Right();
if (s.IsRed()) // case 1
{
s.SetBlack();
node.Parent().SetRed();
RotateLeft(node.Parent());
s = node.Parent().Right();
}
if (s.Left().IsBlack() && s.Right().IsBlack()) // case 2
{
s.SetRed();
node = node.Parent();
}
else
{
if (s.Right().IsBlack()) // case 3
{
s.Left().SetBlack();
s.SetRed();
RotateRight(s);
s = node.Parent().Right();
}
if (s.Parent().IsRed())
{
s.SetRed();
}
else
{
s.SetBlack();
}
node.Parent().SetBlack();
s.Right().SetBlack();
RotateLeft(s.Parent());
node = Root;
}
}
else
{
s = node.Parent().Left();
if (s.IsRed())
{
s.SetBlack();
node.Parent().SetRed();
RotateRight(node.Parent());
s = node.Parent().Left();
}
if (s.Right() == null)
{
s.SetRight(Leaf);
}
if (s.Left() == null)
{
s.SetLeft(Leaf);
}
if (s.Right().IsBlack() && s.Left().IsBlack())
{
s.SetRed();
node = node.Parent();
}
else
{
if (s.Left().IsBlack())
{
s.Right().SetBlack();
s.SetRed();
RotateLeft(s);
s = node.Parent().Left();
}
if (s.Parent().IsRed())
{
s.SetRed();
}
else
{
s.SetBlack();
}
node.Parent().SetBlack();
s.Left().SetBlack();
RotateRight(node.Parent());
node = Root;
}
}
}
node.SetBlack();
}
