// Exercise 4.3.22 4.3.33 (Solution published at http://algs4.cs.princeton.edu/)
package algs43;
import stdlib.*;
import algs13.Queue;
import algs15.WeightedUF;
import algs24.MinPQ;
/* ***********************************************************************
 * 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 final Queue<Edge> mst = new Queue<>();  // 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<>();
    for (Edge e : G.edges()) {
      pq.insert(e);
    }

    // run greedy algorithm
    WeightedUF uf = new WeightedUF(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.format("Weight of edges does not equal weight(): %f vs. %f\n", total, 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);
    KruskalMST mst = new KruskalMST(G);
    for (Edge e : mst.edges()) {
      StdOut.println(e);
    }
    StdOut.format("%.5f\n", mst.weight());
  }

}