Пример #1
0
  // check optimality conditions (takes time proportional to E V lg* V)
  private boolean check(EdgeWeightedGraph G) {

    // check total weight
    double total = 0.0;
    for (Edge e : edges()) {
      total += e.weight();
    }
    double EPSILON = 1E-12;
    if (Math.abs(total - weight()) > EPSILON) {
      System.err.printf("Weight of edges does not equal weight(): %f vs. %f\n", total, weight());
      return false;
    }

    // check that it is acyclic
    UF uf = new UF(G.V());
    for (Edge e : edges()) {
      int v = e.either(), w = e.other(v);
      if (uf.connected(v, w)) {
        System.err.println("Not a forest");
        return false;
      }
      uf.union(v, w);
    }

    // check that it is a spanning forest
    for (Edge e : G.edges()) {
      int v = e.either(), w = e.other(v);
      if (!uf.connected(v, w)) {
        System.err.println("Not a spanning forest");
        return false;
      }
    }

    // check that it is a minimal spanning forest (cut optimality conditions)
    for (Edge e : edges()) {

      // all edges in MST except e
      uf = new UF(G.V());
      for (Edge f : mst) {
        int x = f.either(), y = f.other(x);
        if (f != e) uf.union(x, y);
      }

      // check that e is min weight edge in crossing cut
      for (Edge f : G.edges()) {
        int x = f.either(), y = f.other(x);
        if (!uf.connected(x, y)) {
          if (f.weight() < e.weight()) {
            System.err.println("Edge " + f + " violates cut optimality conditions");
            return false;
          }
        }
      }
    }

    return true;
  }
Пример #2
0
  public KruskalMST(EdgeWeightedGraph G) {
    mst = new Queue<Edge>();
    MaxPQ<Edge> pq = new MaxPQ<Edge>();

    for (Edge e : G.edges()) pq.insert(e); // 将所有的边进入优先队列,按照权重升序排列

    UF uf = new UF(G.V()); // 构建union-find对象

    while (!pq.isEmpty() && mst.size() < G.V() - 1) {
      Edge e = pq.delMax(); // 从pq得到权重最小的边和他的顶点
      int v = e.either(), w = e.other(v);
      if (uf.connected(v, w)) continue; // 忽略失效的边,两个顶点已经在生成树中了

      uf.union(v, w); // 否则将两者合并,在一个树中,顶点
      mst.enqueue(e); // 将边添加到最小生成树中
    }
  }
Пример #3
0
 KruskalMST(EdgeWeightedGraph G) {
   MinPQ<Edge> pq = new MinPQ<Edge>(); // we dont need to pass a new comparator let it
   // follow the natural ordering of edges
   double temp_wt = 0;
   for (Edge e : G.edges()) pq.insert(e);
   UF set = new UF(G.V());
   while (!pq.isEmpty() && mst.size() < (G.V() - 1)) {
     Edge e = pq.delMin();
     int v = e.either();
     int w = e.other(v);
     if (!set.connected(v, w)) {
       set.union(v, w);
       mst.add(e);
       temp_wt += e.weight();
     }
   }
   this.weight = temp_wt;
 }
Пример #4
0
  public KruskalMST(EdgeWeightedGraph g) {
    mst = new Queue<Edge>();

    MinPQ<Edge> pq = new MinPQ<Edge>();

    for (Edge e : g.edges()) {
      pq.insert(e);
    }

    UnionFind uf = new UnionFind(g.vertices());

    while (!pq.isEmpty() && mst.size() < g.vertices() - 1) {
      Edge e = pq.delMin();
      int v = e.either(), w = e.other(v);

      if (uf.connected(v, w)) continue; // -- would form a cycle

      uf.union(v, w);
      mst.enqueue(e);
    }
  }
  public static void main(String[] args) {
    EdgeWeightedGraph ewg = new EdgeWeightedGraph(Integer.parseInt(args[0]));

    ewg.addEdge(new Edge(0, 1, 10));
    ewg.addEdge(new Edge(1, 2, 11));
    ewg.addEdge(new Edge(2, 3, 12));
    ewg.addEdge(new Edge(3, 4, 13));
    ewg.addEdge(new Edge(4, 5, 14));

    ewg.addEdge(new Edge(5, 6, 21));
    ewg.addEdge(new Edge(6, 7, 22));
    ewg.addEdge(new Edge(7, 8, 23));
    ewg.addEdge(new Edge(8, 9, 24));
    ewg.addEdge(new Edge(9, 0, 25));

    int count = 0;
    for (Edge e : ewg.edges()) {
      StdOut.println(count + " => " + e);
      count++;
    }
  }
Пример #6
0
  // Kruskal's algorithm
  public KruskalMST(EdgeWeightedGraph G) {
    // more efficient to build heap by passing array of edges
    MinPQ<Edge> pq = new MinPQ<Edge>();
    for (Edge e : G.edges()) {
      pq.insert(e);
    }

    // run greedy algorithm
    UF uf = new UF(G.V());
    while (!pq.isEmpty() && mst.size() < G.V() - 1) {
      Edge e = pq.delMin();
      int v = e.either();
      int w = e.other(v);
      if (!uf.connected(v, w)) { // v-w does not create a cycle
        uf.union(v, w); // merge v and w components
        mst.enqueue(e); // add edge e to mst
        weight += e.weight();
      }
    }

    // check optimality conditions
    assert check(G);
  }
Пример #7
0
  /**
   * Dado un grafo no dirigido y con pesos, ejecuta el algoritmo de Kruskal para la obtención del su
   * árbol de cobertura mínima.
   *
   * @param G Grafo no dirigido con pesos al cual se le deesea obtener su arbol de cobertura mínima.
   */
  public void minimumSpanningTree(EdgeWeightedGraph G) // By Kruskal's algorithm
      {
    LinkedList<Edge> mst = new LinkedList<>();

    MinPQ<Edge> pq = new MinPQ<>(G.E());
    for (Edge edge : G.edges()) // Bag<Edge> != Comparator<Edge> :c
    pq.insert(edge);

    UF uf = new UF(G.V());

    while (!pq.isEmpty() && mst.size() < G.V() - 1) {
      Edge edge = pq.delMin();
      int v = edge.either(), w = edge.other(v);

      if (!uf.connected(v, w)) {
        uf.union(v, w);
        mst.add(edge);
      }
    }

    System.out.println("");
    for (Edge edge : mst) System.out.println(edge);
  }