/*   AVL rotations pseudo-code
 *   slightly modified from Ford and Topp
 *
 */

Node singleRight ( Node p ) {
   Node lc = p.left;
   p.left = lc.right;
   lc.right = p
   p.height = max ( height (p.left),
                    height(p.right) ) +
              1;
   lc.height = max ( height(lc.left),
                     lc.height)       +
              1;
   return lc;
   }
   
   
Node singleLeft ( Node p ) {
   Node rc = p.right;
   p.right = rc.left;
   rc.left = p;
   p.height = max ( height (p.left),
                    height (p.right) ) +
              1;
   rc.height = max (height(rc.right),
                    rc.height)         +
               1;
   return rc;
   }
   
   
Node doubleRight (Node p) {
   p.left = singleLeft(p.left);
   return singleRight(p);
   }
   
              
Node doubleLeft (Node p) {
   p.right = singleRight(p.right);
   return singleLeft(p);
   }
   

Node addNode (Node t, int item) {
   if (t == null) t = new Node(item);
   else if ( (item < t.value) {
      t.left = addNode(t.left, item);
      
      if (height(t.left) - height(t.right) == 2 )
         if (item < t.left.value)
         	t = singleRight(t);
         else
         	t = doubleRight(t);
      }
   
   else if (t.value < item) {
      t.right = addNode (t.right, item);
      if (height(t.left) - height(t.right) == -2)
         if (t.right.value < item) 
            t = singleLeft(t);
         else
            t = doubleLeft(t);
         }
   
   else
   	// duplicate -- throw IllegalStateException
   	throw new IllegalStateException();
   	
   	t.height = max (height(t.lef), height(t.right) ) + 1;
   	
   	return t;
   }
   
boolean add (int item) {
   try {
      root = addNode (root, item);
      }
   catch (IllegalStateException ise) {
      return false;
      }
   
   // increment tree size
   treeSize++;
   
   // added a node to tree
   return true;
   }