content: /*************************************************************************
   *  Compilation:  javac BoruvkaMST.java
   *  Execution:    java BoruvkaMST filename.txt
   *  Dependencies: EdgeWeightedGraph.java Edge.java Bag.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 Boruvka's algorithm.
   *
   *  % java BoruvkaMST tinyEWG.txt 
   *  0-2 0.26000
   *  6-2 0.40000
   *  5-7 0.28000
   *  4-5 0.35000
   *  2-3 0.17000
   *  1-7 0.19000
   *  0-7 0.16000
   *  1.81000
   *
   *************************************************************************/
  
  
  public class BoruvkaMST {
      private Bag<Edge> mst = new Bag<Edge>();    // edges in MST
      private double weight;                      // weight of MST
  
      // Boruvka's algorithm
      public BoruvkaMST(EdgeWeightedGraph G) {
          UF uf = new UF(G.V());
  
          // repeat at most log V times or until we have V-1 edges
          for (int t = 1; t < G.V() && mst.size() < G.V() - 1; t = t + t) {
  
              // foreach tree in forest, find closest edge
              // if edge weights are equal, ties are broken in favor of first edge in G.edges()
              Edge[] closest = new Edge[G.V()];
              for (Edge e : G.edges()) {
                  int v = e.either(), w = e.other(v);
                  int i = uf.find(v), j = uf.find(w);
                  if (i == j) continue;   // same tree
                  if (closest[i] == null || less(e, closest[i])) closest[i] = e;
                  if (closest[j] == null || less(e, closest[j])) closest[j] = e;
              }
  
              // add newly discovered edges to MST
              for (int i = 0; i < G.V(); i++) {
                  Edge e = closest[i];
                  if (e != null) {
                      int v = e.either(), w = e.other(v);
                      // don't add the same edge twice
                      if (!uf.connected(v, w)) {
                          mst.add(e);
                          weight += e.weight();
                          uf.union(v, w);
                      }
                  }
              }
          }
  
          // 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;
      }
  
      // is the weight of edge e strictly less than that of edge f?
      private static boolean less(Edge e, Edge f) {
          return e.weight() < f.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);
          BoruvkaMST mst = new BoruvkaMST(G);
          for (Edge e : mst.edges()) {
              StdOut.println(e);
          }
          StdOut.printf("%.5f\n", mst.weight());
      }
  
  }
  