// 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());
	}

}