예제 #1
0
  /**
   * This method will return a list of vertices which represents the Eulerian circuit of the graph.
   *
   * @param g The graph to find an Eulerian circuit
   * @return null if no Eulerian circuit exists, or a list of vertices representing the Eulerian
   *     circuit if one does exist
   */
  public static <V, E> List<V> getEulerianCircuitVertices(UndirectedGraph<V, E> g) {
    // If the graph is not Eulerian then just return a null since no
    // Eulerian circuit exists
    if (!isEulerian(g)) {
      return null;
    }

    // The circuit will be represented by a linked list
    List<V> path = new LinkedList<V>();
    UndirectedGraph<V, E> sg = new UndirectedSubgraph<V, E>(g, null, null);
    path.add(sg.vertexSet().iterator().next());

    // Algorithm for finding an Eulerian circuit Basically this will find an
    // arbitrary circuit, then it will find another arbitrary circuit until
    // every edge has been traversed
    while (sg.edgeSet().size() > 0) {
      V v = null;

      // Find a vertex which has an edge that hasn't been traversed yet,
      // and keep its index position in the circuit list
      int index = 0;
      for (Iterator<V> iter = path.iterator(); iter.hasNext(); index++) {
        v = iter.next();
        if (sg.degreeOf(v) > 0) {
          break;
        }
      }

      // Finds an arbitrary circuit of the current vertex and
      // appends this into the circuit list
      while (sg.degreeOf(v) > 0) {
        for (Iterator<V> iter = sg.vertexSet().iterator(); iter.hasNext(); ) {
          V temp = iter.next();
          if (sg.containsEdge(v, temp)) {
            path.add(index, temp);
            sg.removeEdge(v, temp);
            v = temp;
            break;
          }
        }
      }
    }
    return path;
  }
예제 #2
0
  /**
   * This method will check whether the graph passed in is Eulerian or not.
   *
   * @param g The graph to be checked
   * @return true for Eulerian and false for non-Eulerian
   */
  public static <V, E> boolean isEulerian(UndirectedGraph<V, E> g) {
    // If the graph is not connected, then no Eulerian circuit exists
    if (!(new ConnectivityInspector<V, E>(g)).isGraphConnected()) {
      return false;
    }

    // A graph is Eulerian if and only if all vertices have even degree
    // So, this code will check for that
    Iterator<V> iter = g.vertexSet().iterator();
    while (iter.hasNext()) {
      V v = iter.next();
      if ((g.degreeOf(v) % 2) == 1) {
        return false;
      }
    }
    return true;
  }