// Textbook fragment 13.09
/** This class specializes DFS to find a cycle. */
public class FindCycleDFS<V, E>
  extends DFS<V, E, Object, Iterable<Position>> {
  protected PositionList<Position> cycle; // sequence of edges of the cycle
  protected boolean done;
  protected Vertex<V> cycleStart;
  public void setup() {
    cycle = new NodePositionList<Position>();
    done = false;
  }
  protected void startVisit(Vertex<V> v) { cycle.addLast(v); }
  protected void finishVisit(Vertex<V> v) {
    cycle.remove(cycle.last()); // remove v from cycle
    if (!cycle.isEmpty()) cycle.remove(cycle.last()); // remove edge into v from
 cycle
  }
  protected void traverseDiscovery(Edge<E> e, Vertex<V> from) {
    cycle.addLast(e);
  }
  protected void traverseBack(Edge<E> e, Vertex<V> from) {
    cycle.addLast(e);           // back edge e creates a cycle
    cycleStart = graph.opposite(from, e);
    cycle.addLast(cycleStart);  // first vertex completes the cycle
    done = true;
  }
  protected boolean isDone() {  return done; }
  public Iterable<Position> finalResult(Iterable<Position> r) {
    // remove the vertices and edges from start to cycleStart
    if (!cycle.isEmpty()) {
      for (Position<Position> p: cycle.positions()) {
        if (p.element() == cycleStart)
          break;
        cycle.remove(p);                     // remove vertex from cycle
      }
    }
    return cycle; // list of the vertices and edges of the cycle
  }
}