/** Calculates the matrix of all shortest paths, but does not populate the paths map. */
  private void lazyCalculateMatrix() {
    if (d != null) {
      // already done
      return;
    }

    int n = vertices.size();

    // init the backtrace matrix
    backtrace = new int[n][n];
    for (int i = 0; i < n; i++) {
      Arrays.fill(backtrace[i], -1);
    }

    // initialize matrix, 0
    d = new double[n][n];
    for (int i = 0; i < n; i++) {
      Arrays.fill(d[i], Double.POSITIVE_INFINITY);
    }

    // initialize matrix, 1
    for (int i = 0; i < n; i++) {
      d[i][i] = 0.0;
    }

    // initialize matrix, 2
    Set<E> edges = graph.edgeSet();
    for (E edge : edges) {
      V v1 = graph.getEdgeSource(edge);
      V v2 = graph.getEdgeTarget(edge);

      int v_1 = vertices.indexOf(v1);
      int v_2 = vertices.indexOf(v2);

      d[v_1][v_2] = graph.getEdgeWeight(edge);
      if (!(graph instanceof DirectedGraph<?, ?>)) {
        d[v_2][v_1] = graph.getEdgeWeight(edge);
      }
    }

    // run fw alg
    for (int k = 0; k < n; k++) {
      for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
          double ik_kj = d[i][k] + d[k][j];
          if (ik_kj < d[i][j]) {
            d[i][j] = ik_kj;
            backtrace[i][j] = k;
          }
        }
      }
    }
  }
 private void shortestPathRecur(List<E> edges, int v_a, int v_b) {
   int k = backtrace[v_a][v_b];
   if (k == -1) {
     E edge = graph.getEdge(vertices.get(v_a), vertices.get(v_b));
     if (edge != null) {
       edges.add(edge);
     }
   } else {
     shortestPathRecur(edges, v_a, k);
     shortestPathRecur(edges, k, v_b);
   }
 }
  private GraphPath<V, E> getShortestPathImpl(V a, V b) {
    int v_a = vertices.indexOf(a);
    int v_b = vertices.indexOf(b);

    List<E> edges = new ArrayList<E>();
    shortestPathRecur(edges, v_a, v_b);

    // no path, return null
    if (edges.size() < 1) {
      return null;
    }

    double weight = 0.;
    for (E e : edges) {
      weight += graph.getEdgeWeight(e);
    }

    GraphPathImpl<V, E> path = new GraphPathImpl<V, E>(graph, a, b, edges, weight);

    return path;
  }
 public FloydWarshallShortestPaths(Graph<V, E> graph) {
   this.graph = graph;
   this.vertices = new ArrayList<V>(graph.vertexSet());
 }