public static int height (Heap heap) {
    if (heap == null) return 0;
    int left = height (heap.left) + 1;
    int right = height (heap.right) + 1;
    if (left > right) return left;
    return right;
  }


  public static void printHeap (Heap heap) {

    int height = height (heap);

    for (int i = 0; i<height; i++) {
      printLevel (heap, i, 0);
      System.out.println ("");
    }
  }

  public static void printLevel(Heap heap, int level, int sofar){
    if (sofar == level) {
      if (heap == null) {
	System.out.print ("n ");
      } else {
	System.out.print (heap.value + " ");
      }

    } else if (heap != null) {
      printLevel (heap.left, level, sofar+1);
      printLevel (heap.right, level, sofar+1);
    }
  }