// 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());
	}

}