// Textbook fragment 08.15
   /** Performs up-heap bubbling */
  protected void upHeap(Position<Entry<K,V>> v) {
    Position<Entry<K,V>> u;
    while (!heap.isRoot(v)) {
      u = heap.parent(v);
      if (comp.compare(u.element().getKey(), v.element().getKey()) <= 0) break;
      swap(u, v);
      v = u;
    }
  }
  /** Performs down-heap bubbling */
  protected void downHeap(Position<Entry<K,V>> r) {
    while (heap.isInternal(r)) {
      Position<Entry<K,V>> s;           // the position of the smaller child
      if (!heap.hasRight(r))
        s = heap.left(r);
      else if (comp.compare(heap.left(r).element().getKey(),
                            heap.right(r).element().getKey()) <=0)
        s = heap.left(r);
      else
        s = heap.right(r);
      if (comp.compare(s.element().getKey(), r.element().getKey()) < 0) {
        swap(r, s);
        r = s;
      }
      else
        break;
    }
  }
  /** Swaps the entries of the two given positions */
  protected void swap(Position<Entry<K,V>> x, Position<Entry<K,V>> y) {
    Entry<K,V> temp = x.element();
    heap.replace(x, y.element());
    heap.replace(y, temp);
  }
  /** Text visualization for debugging purposes */
  public String toString() {
    return heap.toString();
  }