//Delete a node a balance a tree
private AVL_Node _Delete(AVL_Node root, AVL_Node node)
{
if (root == null)
{
return(root);
}
if (node.ID < root.ID)
{
root.Left = _Delete(root.Left, node);
}
else if (node.ID > root.ID)
{
root.Right = _Delete(root.Right, node);
}
else
{
if (root.Right == null)
{
return(root.Left);
}
else
{
return(_GetTheMostLeft(root.Right));
}
}
root.Height = Math.Max(root.Left.Height, root.Right.Height) + 1;
int balance = _GetBalance(root);
//Left Left case
if (balance > 1 && _GetBalance(root.Left) >= 0)
{
return(_RotateRight(root));
}
// Left Right case
if (balance > 1 && _GetBalance(root.Left) < 0)
{
root.Left = _RotateLeft(root.Left);
return(_RotateRight(root));
}
//Right Right case
if (balance < 1 && _GetBalance(root.Right) < 0)
{
return(_RotateLeft(root));
}
//Right Left case
if (balance < 1 && _GetBalance(root.Right) >= 0)
{
root.Right = _RotateRight(root.Right);
return(_RotateLeft(root));
}
return(root);
}
private AVL_Node _GetTheMostLeft(AVL_Node node)
{
if (node.Left == null)
{
return(node);
}
return(_GetTheMostLeft(node.Left));
}
private AVL_Node _RotateRight(AVL_Node node)
{
AVL_Node root = node.Left;
node.Left = root.Right;
root.Right = node;
node.Height = Math.Max(node.LeftHeight, node.RightHeight) + 1;
root.Height = Math.Max(root.LeftHeight, root.RightHeight) + 1;
return(root);
}
// Insert a node and balance a tree
private AVL_Node _Insert(AVL_Node root, AVL_Node node)
{
if (root == null)
{
return(node);
}
if (node.ID < root.ID)
{
root.Left = _Insert(root.Left, node);
}
else
{
root.Right = _Insert(root.Right, node);
}
root.Height = Math.Max(root.RightHeight, root.LeftHeight) + 1;
int balance = root.LeftHeight - root.RightHeight;
// Left Left Case
if (balance > 1 && node.ID < root.Left.ID)
{
return(_RotateRight(root));
}
// Left Right Case
if (balance > 1 && node.ID > root.Left.ID)
{
root.Left = _RotateLeft(root.Left);
return(_RotateRight(root));
}
// Right Right Case
if (balance < -1 && node.ID > root.Right.ID)
{
return(_RotateLeft(root));
}
// Right Left Case
if (balance < -1 && node.ID < root.Right.ID)
{
root.Right = _RotateRight(root.Right);
return(_RotateLeft(root));
}
return(root);
}
public AVL_Tree(AVL_Node root)
{
_root = root;
}
public void Delete(AVL_Node node)
{
_root = _Delete(_root, node);
}
private int _GetBalance(AVL_Node node)
{
return(node.LeftHeight - node.RightHeight);
}
public void Insert(AVL_Node node)
{
_root = _Insert(_root, node);
}
