content: /*************************************************************************
   * Compilation:  javac KruskalMST.java
   *  Execution:    java LazyPrimMST filename.txt
   *  Dependencies: EdgeWeightedGraph.java Edge.java Queue.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 Kruskal's algorithm.
   *
   *  %  java KruskalMST tinyEWG.txt 
   *  0-7 0.16000
   *  2-3 0.17000
   *  1-7 0.19000
   *  0-2 0.26000
   *  5-7 0.28000
   *  4-5 0.35000
   *  6-2 0.40000
   *  1.81000
   *
   *  % java KruskalMST mediumEWG.txt
   *  168-231 0.00268
   *  151-208 0.00391
   *  7-157   0.00516
   *  122-205 0.00647
   *  8-152   0.00702
   *  156-219 0.00745
   *  28-198  0.00775
   *  38-126  0.00845
   *  10-123  0.00886
   *  ...
   *  10.46351
   *
   *************************************************************************/
  
  public class KruskalMST {
      private double weight;  // weight of MST
      private Queue<Edge> mst = new Queue<Edge>();  // edges in MST
  
      // 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);
      }
  
      // edges in minimum spanning forest as an Iterable
      public Iterable<Edge> edges() {
          return mst;
      }
  
      // weight of minimum spanning forest
      public double weight() {
          return weight;
      }
      
      // 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;
      }
  
  
      public static void main(String[] args) {
          In in = new In(args[0]);
          EdgeWeightedGraph G = new EdgeWeightedGraph(in);
          KruskalMST mst = new KruskalMST(G);
          for (Edge e : mst.edges()) {
              StdOut.println(e);
          }
          StdOut.printf("%.5f\n", mst.weight());
      }
  
  }
  
  