// 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 : 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()) {
      int v = e.either(), w = e.other(v);

      // 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;
  }
Example #2
0
  public PrimMST(EdgeWeightedGraph G) {
    edgeTo = new Edge[G.V()];
    distTo = new double[G.V()];
    marked = new boolean[G.V()];

    for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY;
    pq = new IndexMinPQ<Double>(G.V());

    distTo[0] = 0.0;
    pq.insert(0, 0.0); // Initialize pq with 0, weight 0.
    while (!pq.isEmpty()) visit(G, pq.delMin()); // Add closest vertex to tree.
  }
 /**
  * Initializes a new edge-weighted graph that is a deep copy of <tt>G</tt>.
  *
  * @param G the edge-weighted graph to copy
  */
 public EdgeWeightedGraph(EdgeWeightedGraph G) {
   this(G.V());
   this.E = G.E();
   for (int v = 0; v < G.V(); v++) {
     // reverse so that adjacency list is in same order as original
     Stack<Edge> reverse = new Stack<Edge>();
     for (Edge e : G.adj[v]) {
       reverse.push(e);
     }
     for (Edge e : reverse) {
       adj[v].add(e);
     }
   }
 }
Example #4
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
    }
  }
Example #5
0
 public MyPrimMST(EdgeWeightedGraph G) {
   this.G = G;
   pq = new IndexMinPQ<Double>(G.V());
   disTo = new double[G.V()];
   edges = new Bag<Edge>();
   for (int i = 0; i < G.V(); ++i) disTo[i] = Double.POSITIVE_INFINITY;
   edgeTo = new int[G.V()];
   marked = new boolean[G.V()];
   disTo[0] = 0.0;
   visit(0);
   while (!pq.isEmpty()) {
     int v = pq.delMin();
     weight += disTo[v];
     edges.add(new Edge(v, edgeTo[v], disTo[v]));
     visit(v);
   }
 }
Example #6
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;
 }
  // 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);
  }
Example #8
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);
  }
Example #9
0
  public LazyPrimMST(EdgeWeightedGraph G) {
    pq = new PriorityQueue<>(Collections.reverseOrder());
    marked = new boolean[G.V()];

    mst = new LinkedList<>();
    visit(G, 0);
    while (!pq.isEmpty()) {
      Edge e = pq.poll();
      int v = e.either();
      int w = e.other(v);
      if (marked[v] && marked[w]) continue;
      mst.offer(e);

      if (!marked[v]) visit(G, v);

      if (!marked[w]) visit(G, w);
    }
  }
Example #10
0
  public LazyPrimMST(EdgeWeightedGraph G) {
    pq = new MinPQ<Edge>();
    marked = new boolean[G.V()];
    mst = new Queue<Edge>();

    visit(G, 0); // assumes G is connected (see ex. 4.3.22)
    while (!pq.isEmpty()) {
      Edge e = pq.delMin(); // Get lowest-weight from pq.
      int v = e.either();
      int w = e.other(v);
      if (marked[v] && marked[w]) {
        continue; // Skip if ineligible
      }
      mst.enqueue(e); // Add edge to tree
      if (!marked[v]) { // Add vertex to tree (either v or w).
        visit(G, v);
      }

      if (!marked[w]) {
        visit(G, w);
      }
    }
  }