// Textbook fragment 10.07
/**  Implementation of an AVL tree. */
public class AVLTree<K,V>
  extends BinarySearchTree<K,V> implements Dictionary<K,V> {
  public AVLTree(Comparator<K> c)  { super(c); }
  public AVLTree() { super(); }
  /** Nested class for the nodes of an AVL tree. */
  protected static class AVLNode<K,V> extends BTNode<Entry<K,V>> {
    protected int height;  // we add a height field to a BTNode
    AVLNode() {/* default constructor */}
    /** Preferred constructor */
    AVLNode(Entry<K,V> element, BTPosition<Entry<K,V>> parent,
            BTPosition<Entry<K,V>> left, BTPosition<Entry<K,V>> right) {
      super(element, parent, left, right);
      height = 0;
      if (left != null)
        height = Math.max(height, 1 + ((AVLNode<K,V>) left).getHeight());
      if (right != null)
        height = Math.max(height, 1 + ((AVLNode<K,V>) right).getHeight());
    } // we assume that the parent will revise its height if needed
    public void setHeight(int h) { height = h; }
    public int getHeight() { return height; }
  }
  /** Creates a new binary search tree node (overrides super's version). */
  protected BTPosition<Entry<K,V>> createNode(Entry<K,V> element,
      BTPosition<Entry<K,V>> parent, BTPosition<Entry<K,V>> left,
      BTPosition<Entry<K,V>> right) {
    return new AVLNode<K,V>(element,parent,left,right);  // now use AVL nodes
  }
  /** Returns the height of a node (call back to an AVLNode). */
  protected int height(Position<Entry<K,V>> p)  {
    return ((AVLNode<K,V>) p).getHeight();
  }
  /** Sets the height of an internal node (call back to an AVLNode). */
  protected void setHeight(Position<Entry<K,V>> p) {
    ((AVLNode<K,V>) p).setHeight(1+Math.max(height(left(p)), height(right(p))));
  }
  /** Returns whether a node has balance factor between -1 and 1. */
  protected boolean isBalanced(Position<Entry<K,V>> p)  {
    int bf = height(left(p)) - height(right(p));
    return ((-1 <= bf) &&  (bf <= 1));
  }