// Textbook fragment 13.08
/** Class specializing DFS to find a path between a start vertex and a target
  * vertex. It assumes the target vertex is passed as the info object to the
  * execute method. It returns an iterable list of the vertices and edges
  * comprising the path from start to info. The returned path is empty if
  * info is unreachable from start.  */
public class FindPathDFS<V, E>
    extends DFS<V, E, Vertex<V>, Iterable<Position>> {
  protected PositionList<Position> path;
  protected boolean done;
  /** Setup method to initialize the path. */
  public void setup() {
    path = new NodePositionList<Position>();
    done = false;
  }
  protected void startVisit(Vertex<V> v) {
    path.addLast(v); // add vertex v to path
    if (v == info)
      done = true;
  }
  protected void finishVisit(Vertex<V> v) {
    path.remove(path.last());   // remove v from path
    if(!path.isEmpty())         // if v is not the start vertex
      path.remove(path.last()); // remove discovery edge into v from path
  }
  protected void traverseDiscovery(Edge<E> e, Vertex<V> from) {
    path.addLast(e); // add edge e to the path
  }
  protected boolean isDone() {
    return done;
  }
  public Iterable<Position> finalResult(Iterable<Position> r) {
    return path;
  }
}