// Exercise 4.3.43 (Solution published at http://algs4.cs.princeton.edu/)
package algs43;
import stdlib.*;
import algs13.Bag;
import algs15.WeightedUF;
/* ***********************************************************************
 *  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 final Bag<Edge> mst = new Bag<>();    // edges in MST
  private double weight;                      // weight of MST

  // Boruvka's algorithm
  public BoruvkaMST(EdgeWeightedGraph G) {
    WeightedUF uf = new WeightedUF(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.format("Weight of edges does not equal weight(): %f vs. %f\n", totalWeight, weight());
      return false;
    }

    // check that it is acyclic
    WeightedUF uf = new WeightedUF(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 WeightedUF(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.format("%.5f\n", mst.weight());
  }

}