int GetBalanceHeight(AvlTreeNode node)
{
if (node == null)
{
return(0);
}
return(GetNodeHeight(node.Left) - GetNodeHeight(node.Right));
}
int GetNodeHeight(AvlTreeNode avlTreeNode)
{
if (avlTreeNode == null)
{
return(0);
}
return(avlTreeNode.Height);
}
public List <AvlTreeNode> GetPostOrder(AvlTreeNode node)
{
List <AvlTreeNode> avlTreeNodes = new List <AvlTreeNode>();
if (node != null)
{
avlTreeNodes.AddRange(GetPostOrder(node.Left));
avlTreeNodes.AddRange(GetPostOrder(node.Right));
avlTreeNodes.Add(node);
}
return(avlTreeNodes);
}
public AvlTreeNode LeftRotate(AvlTreeNode x)
{
AvlTreeNode y = x.Right;
AvlTreeNode t2 = y.Left;
y.Left = x;
x.Right = t2;
x.Height = (Math.Max(x.Left.Height, x.Right.Height)) + 1;
y.Height = (Math.Max(y.Left.Height, y.Right.Height)) + 1;
return(y);
}
public AvlTreeNode GetMinimum(AvlTreeNode node)
{
AvlTreeNode currentNode = node;
if (currentNode != null)
{
while (currentNode.Left != null)
{
currentNode = currentNode.Left;
}
}
return(currentNode);
}
// T1, T2 and T3 are subtrees of the tree
// rooted with y(on the left side) or x(on
// the right side)
// y x
// / \ Right Rotation / \
// x T3 – – – – – – – > T1 y
// / \ < - - - - - - - / \
// T1 T2 Left Rotation T2 T3
//Keys in both of the above trees follow the
//following order
// keys(T1) < key(x) < keys(T2) < key(y) < keys(T3)
//So BST property is not violated anywhere.
public AvlTreeNode RightRotate(AvlTreeNode y)
{
AvlTreeNode x = y.Left;
AvlTreeNode t2 = x.Right;
x.Right = y;
y.Left = t2;
x.Height = (Math.Max(x.Left.Height, x.Right.Height)) + 1;
y.Height = (Math.Max(y.Left.Height, y.Right.Height)) + 1;
//Return the new root
return(x);
}
public AvlTreeNode Insert(AvlTreeNode node, int key)
{
/* 1. Perform the normal BST insertion */
if (node == null)
{
return(new AvlTreeNode(key));
}
if (key < node.Data)
{
node.Left = Insert(node.Left, key);
}
else if (key > node.Data)
{
node.Right = Insert(node.Right, key);
}
else // Node with same key cannot be inserted into the tree.
{
return(node);
}
/* 2. Update height of this ancestor node */
node.Height = (Math.Max(GetNodeHeight(node.Left), GetNodeHeight(node.Right))) + 1;
/* 3. Get the balance factor of this ancestor
* node to check whether this node became
* unbalanced */
int balance = GetBalanceHeight(node);
// If this node becomes unbalanced, then there
// are 4 cases
//Left left case
if (balance > 1 && key < node.Left.Data)
{
return(RightRotate(node));
}
//Right right case
if (balance < -1 && key > node.Right.Data)
{
return(LeftRotate(node));
}
//Left Right case
if (balance > 1 && key > node.Left.Data)
{
node.Left = LeftRotate(node.Left);
return(RightRotate(node));
}
//Right Left case
if (balance < -1 && key < node.Right.Data)
{
node.Right = RightRotate(node.Right);
return(LeftRotate(node));
}
//return unchanged node pointer
return(node);
}
//public AvlTreeNode InsertFixUp(AvlTreeNode z)
//{
//}
public AvlTreeNode Delete(AvlTreeNode node, int key)
{
if (node == null)
{
return(node);
}
if (key < node.Data)
{
node.Left = Delete(node.Left, key);
}
else if (key > node.Data)
{
node.Right = Delete(node.Right, key);
}
if (node.Left == null && node.Right == null)
{
return(null);
}
if (node.Left == null)
{
AvlTreeNode temp = node.Right;
node.Right = null;
return(temp);
}
if (node.Right == null)
{
AvlTreeNode temp = node.Left;
node.Left = null;
return(temp);
}
AvlTreeNode successor = GetMinimum(node.Right);
node.Data = successor.Data;
node.Right = Delete(node.Right, successor.Data);
//Recalculate the height of node
node.Height = Math.Max(node.Left.Height, node.Right.Height) + 1;
//Check the Height Balance
int balance = GetBalanceHeight(node);
//Left Left case
if (balance > 1 && GetBalanceHeight(node.Left) >= 0)
{
node = RightRotate(node);
}
//Left Right case
if (balance > 1 && GetBalanceHeight(node.Left) < 0)
{
node.Left = LeftRotate(node.Left);
node = RightRotate(node);
}
//Right Right case
if (balance < 1 && GetBalanceHeight(node.Right) <= 0)
{
node = LeftRotate(node);
}
//Right Left case
if (balance < 1 && GetBalanceHeight(node.Right) > 0)
{
node.Right = RightRotate(node.Right);
node = LeftRotate(node);
}
return(node);
}