// Textbook fragment 13.05
  /** Execute a depth first search traversal on graph g, starting
    * from a start vertex s, passing in an information object (in) */
  public R execute(Graph<V, E> g, Vertex<V> s, I in) {
    graph = g;
    start = s;
    info = in;
    for(Vertex<V> v: graph.vertices()) unVisit(v); // mark vertices as unvisited
    for(Edge<E> e: graph.edges()) unVisit(e);      // mark edges as unvisited
    setup();           // perform any necessary setup prior to DFS traversal
    return finalResult(dfsTraversal(start));
  }
  /** Recursive template method for a generic DFS traversal.  */
  protected R dfsTraversal(Vertex<V> v) {
    initResult();
    if (!isDone())
      startVisit(v);
    if (!isDone()) {
      visit(v);
      for (Edge<E> e: graph.incidentEdges(v)) {
        if (!isVisited(e)) {
          // found an unexplored edge, explore it
          visit(e);
          Vertex<V> w = graph.opposite(v, e);
          if (!isVisited(w)) {
            // w is unexplored, this is a discovery edge
            traverseDiscovery(e, v);
            if (isDone()) break;
            visitResult = dfsTraversal(w); // get result from DFS-tree child
            if (isDone()) break;
          }
          else {
            // w is explored, this is a back edge
            traverseBack(e, v);
            if (isDone()) break;
          }
        }
      }
    }
    if(!isDone())
      finishVisit(v);
    return result();
  }