content: /*************************************************************************
   *  Compilation:  javac LazyPrimMST.java
   *  Execution:    java LazyPrimMST filename.txt
   *  Dependencies: EdgeWeightedGraph.java Edge.java Queue.java
   *                MinPQ.java UF.java In.java StdOut.java
   *  Data files:   http://algs4.cs.princeton.edu/43mst/tinyEWG.txt
   *                http://algs4.cs.princeton.edu/43mst/mediumEWG.txt
   *                http://algs4.cs.princeton.edu/43mst/largeEWG.txt
   *
   *  Compute a minimum spanning forest using a lazy version of Prim's 
   *  algorithm.
   *
   *  %  java LazyPrimMST tinyEWG.txt 
   *  0-7 0.16000
   *  1-7 0.19000
   *  0-2 0.26000
   *  2-3 0.17000
   *  5-7 0.28000
   *  4-5 0.35000
   *  6-2 0.40000
   *  1.81000
   *
   *  % java LazyPrimMST mediumEWG.txt
   *  0-225   0.02383
   *  49-225  0.03314
   *  44-49   0.02107
   *  44-204  0.01774
   *  49-97   0.03121
   *  202-204 0.04207
   *  176-202 0.04299
   *  176-191 0.02089
   *  68-176  0.04396
   *  58-68   0.04795
   *  10.46351
   *
   *  % java LazyPrimMST largeEWG.txt
   *  ...
   *  647.66307
   *
   *************************************************************************/
  
  public class LazyPrimMST {
      private double weight;       // total weight of MST
      private Queue<Edge> mst;     // edges in the MST
      private boolean[] marked;    // marked[v] = true if v on tree
      private MinPQ<Edge> pq;      // edges with one endpoint in tree
  
      // compute minimum spanning forest of G
      public LazyPrimMST(EdgeWeightedGraph G) {
          mst = new Queue<Edge>();
          pq = new MinPQ<Edge>();
          marked = new boolean[G.V()];
          for (int v = 0; v < G.V(); v++)     // run Prim from all vertices to
              if (!marked[v]) prim(G, v);     // get a minimum spanning forest
  
          // check optimality conditions
          assert check(G);
      }
  
      // run Prim's algorithm
      private void prim(EdgeWeightedGraph G, int s) {
          scan(G, s);
          while (!pq.isEmpty()) {                        // better to stop when mst has V-1 edges
              Edge e = pq.delMin();                      // smallest edge on pq
              int v = e.either(), w = e.other(v);        // two endpoints
              assert marked[v] || marked[w];
              if (marked[v] && marked[w]) continue;      // lazy, both v and w already scanned
              mst.enqueue(e);                            // add e to MST
              weight += e.weight();
              if (!marked[v]) scan(G, v);               // v becomes part of tree
              if (!marked[w]) scan(G, w);               // w becomes part of tree
          }
      }
  
      // add all edges e incident to v onto pq if the other endpoint has not yet been scanned
      private void scan(EdgeWeightedGraph G, int v) {
          assert !marked[v];
          marked[v] = true;
          for (Edge e : G.adj(v))
              if (!marked[e.other(v)]) pq.insert(e);
      }
          
      // return edges in MST as an Iterable
      public Iterable<Edge> edges() {
          return mst;
      }
  
      // return weight of MST
      public double weight() {
          return weight;
      }
  
      // check optimality conditions (takes time proportional to E V lg* V)
      private boolean check(EdgeWeightedGraph G) {
  
          // check weight
          double totalWeight = 0.0;
          for (Edge e : edges()) {
              totalWeight += e.weight();
          }
          double EPSILON = 1E-12;
          if (Math.abs(totalWeight - weight()) > EPSILON) {
              System.err.printf("Weight of edges does not equal weight(): %f vs. %f\n", totalWeight, 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;
      }
      
      
      public static void main(String[] args) {
          In in = new In(args[0]);
          EdgeWeightedGraph G = new EdgeWeightedGraph(in);
          LazyPrimMST mst = new LazyPrimMST(G);
          for (Edge e : mst.edges()) {
              StdOut.println(e);
          }
          StdOut.printf("%.5f\n", mst.weight());
      }
  
  }
  