implements PeekingIterator<T> {
    private final Queue<T> queue;

    BreadthFirstIterator(T root) {
      this.queue = new ArrayDeque<>();
      queue.add(root);
    }

    @Override
    public boolean hasNext() {
      return !queue.isEmpty();
    }

    @Override
    public T peek() {
      return queue.element();
    }

    @Override
    public T next() {

    // contract.
    // This is somewhat annoying, but turns out to be very fast in practice. Alternatively, we could
    // drop the contract on the method that enforces this queue like behavior since depending on it
    // is likely to be a bug anyway.

    // N.B. All writes to the list and the next pointers must have happened before the above