// Exercise 4.3.21 4.3.22 (Solution published at http://algs4.cs.princeton.edu/)
package algs43;
import stdlib.*;
import algs13.Queue;
import algs15.WeightedUF;
import algs24.IndexMinPQ;
/* ****************************************************************************
 *  Compilation:  javac PrimMST.java
 *  Execution:    java PrimMST filename.txt
 *  Dependencies: EdgeWeightedGraph.java Edge.java Queue.java
 *                IndexMinPQ.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 Prim's algorithm.
 *
 *  %  java PrimMST tinyEWG.txt
 *  1-7 0.19000
 *  0-2 0.26000
 *  2-3 0.17000
 *  4-5 0.35000
 *  5-7 0.28000
 *  6-2 0.40000
 *  0-7 0.16000
 *  1.81000
 *
 *  % java PrimMST mediumEWG.txt
 *  1-72   0.06506
 *  2-86   0.05980
 *  3-67   0.09725
 *  4-55   0.06425
 *  5-102  0.03834
 *  6-129  0.05363
 *  7-157  0.00516
 *  ...
 *  10.46351
 *
 *  % java PrimMST largeEWG.txt
 *  ...
 *  647.66307
 *
 ******************************************************************************/

public class PrimMST {
	private final Edge[] edgeTo;        // edgeTo[v] = shortest edge from tree vertex to non-tree vertex
	private final double[] distTo;      // distTo[v] = weight of shortest such edge
	private final boolean[] marked;     // marked[v] = true if v on tree, false otherwise
	private final IndexMinPQ<Double> pq;

	public PrimMST(EdgeWeightedGraph G) {
		edgeTo = new Edge[G.V()];
		distTo = new double[G.V()];
		marked = new boolean[G.V()];
		pq = new IndexMinPQ<>(G.V());
		for (int v = 0; v < G.V(); v++) distTo[v] = Double.POSITIVE_INFINITY;

		for (int v = 0; v < G.V(); v++)      // run from each vertex to find
			if (!marked[v]) prim(G, v);      // minimum spanning forest

		// check optimality conditions
		assert check(G);
	}

	// run Prim's algorithm in graph G, starting from vertex s
	private void prim(EdgeWeightedGraph G, int s) {
		distTo[s] = 0.0;
		pq.insert(s, distTo[s]);
		while (!pq.isEmpty()) {
			int v = pq.delMin();
			scan(G, v);
		}
	}

	// scan vertex v
	private void scan(EdgeWeightedGraph G, int v) {
		marked[v] = true;
		for (Edge e : G.adj(v)) {
			int w = e.other(v);
			if (marked[w]) continue;         // v-w is obsolete edge
			if (e.weight() < distTo[w]) {
				distTo[w] = e.weight();
				edgeTo[w] = e;
				if (pq.contains(w)) pq.decreaseKey(w, distTo[w]);
				else                pq.insert(w, distTo[w]);
			}
		}
	}

	// return iterator of edges in MST
	public Iterable<Edge> edges() {
		Queue<Edge> mst = new Queue<>();
		for (Edge e : edgeTo) {
			if (e != null) {
				mst.enqueue(e);
			}
		}
		return mst;
	}


	// return weight of MST
	public double weight() {
		double weight = 0.0;
		for (Edge e : edges())
			weight += e.weight();
		return 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 : edges()) {
				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) {
		args = new String[] { "data/10000EWG.txt" };
		//args = new String[] { "data/mediumEWG.txt" };
		//args = new String[] { "data/largeEWG.txt" };
		In in = new In(args[0]);
		EdgeWeightedGraph G = new EdgeWeightedGraph(in);
		PrimMST mst = new PrimMST(G);
		for (Edge e : mst.edges()) {
			StdOut.println(e);
		}
		StdOut.format("%.5f\n", mst.weight());
	}


}