/// <summary> Internal method to find an item in a subtree.</summary>
/// <param name="x">is item to search for.
/// </param>
/// <param name="t">the node that roots the tree.
/// </param>
/// <returns> node containing the matched item.
/// </returns>
private AvlNode find(Comparable x, AvlNode t)
{
while (t != null)
{
if (x.compareTo(t.element) < 0)
{
t = t.left;
}
else if (x.compareTo(t.element) > 0)
{
t = t.right;
}
else
{
return(t); // Match
}
}
return(null); // No match
}
/// <summary> Internal method to insert into a subtree.</summary>
/// <param name="x">the item to insert.
/// </param>
/// <param name="t">the node that roots the tree.
/// </param>
/// <returns> the new root.
/// </returns>
private AvlNode insert(Comparable x, AvlNode t)
{
if (t == null)
{
t = new AvlNode(x, null, null);
}
else if (x.compareTo(t.element) < 0)
{
t.left = insert(x, t.left);
if (height(t.left) - height(t.right) == 2)
{
if (x.compareTo(t.left.element) < 0)
{
t = rotateWithLeftChild(t);
}
else
{
t = doubleWithLeftChild(t);
}
}
}
else if (x.compareTo(t.element) > 0)
{
t.right = insert(x, t.right);
if (height(t.right) - height(t.left) == 2)
{
if (x.compareTo(t.right.element) > 0)
{
t = rotateWithRightChild(t);
}
else
{
t = doubleWithRightChild(t);
}
}
}
else
{
} // Duplicate; do nothing
t.height = max(height(t.left), height(t.right)) + 1;
return(t);
}
/// <summary> Double rotate binary tree node: first right child
/// with its left child; then node k1 with new right child.
/// For AVL trees, this is a double rotation for case 3.
/// Update heights, then return new root.
/// </summary>
private static AvlNode doubleWithRightChild(AvlNode k1)
{
k1.right = rotateWithLeftChild(k1.right);
return(rotateWithRightChild(k1));
}
/// <summary> Double rotate binary tree node: first left child
/// with its right child; then node k3 with new left child.
/// For AVL trees, this is a double rotation for case 2.
/// Update heights, then return new root.
/// </summary>
private static AvlNode doubleWithLeftChild(AvlNode k3)
{
k3.left = rotateWithRightChild(k3.left);
return(rotateWithLeftChild(k3));
}
/// <summary> Return the height of node t, or -1, if null.</summary>
private static int height(AvlNode t)
{
return(t == null?-1:t.height);
}
/// <summary> Internal method to get element field.</summary>
/// <param name="t">the node.
/// </param>
/// <returns> the element field or null if t is null.
/// </returns>
private Comparable elementAt(AvlNode t)
{
return(t == null?null:t.element);
}