// Textbook fragment 08.10
public class ArrayListCompleteBinaryTree<E>
    implements CompleteBinaryTree<E>  {
  protected ArrayList<BTPos<E>> T;  // indexed list of tree positions
  /** Nested class for a index list-based complete binary tree node. */
  protected static class BTPos<E> implements Position<E> {
    E element; // element stored at this position
    int index;      // index of this position in the array list
    public BTPos(E elt, int i) {
      element = elt;
      index = i;
    }
    public E element() { return element; }
    public int index() { return index; }
    public E setElement(E elt) {
      E temp = element;
      element = elt;
      return temp;
    }
  }
  /** default constructor */
  public ArrayListCompleteBinaryTree() {
    T = new ArrayList<BTPos<E>>();
    T.add(0, null); // the location at rank 0 is deliberately empty
  }
  /** Returns the number of (internal and external) nodes. */
  public int size() { return T.size() - 1; }
  /** Returns whether the tree is empty. */
  public boolean isEmpty() { return (size() == 0); }