// Exercise 4.4.12 (Solution published at http://algs4.cs.princeton.edu/)
package algs44;
import stdlib.*;
import algs13.Stack;
/* ***********************************************************************
 *  Compilation:  javac EdgeWeightedDirectedCycle.java
 *  Execution:    java EdgeWeightedDirectedCycle V E F
 *  Dependencies: EdgeWeightedDigraph.java DirectedEdge Stack.java
 *
 *  Finds a directed cycle in an edge-weighted digraph.
 *  Runs in O(E + V) time.
 *
 *
 *************************************************************************/

public class EdgeWeightedDirectedCycle {
	private final boolean[] marked;             // marked[v] = has vertex v been marked?
	private final DirectedEdge[] edgeTo;        // edgeTo[v] = previous edge on path to v
	private final boolean[] onStack;            // onStack[v] = is vertex on the stack?
	private Stack<DirectedEdge> cycle;    // directed cycle (or null if no such cycle)

	public EdgeWeightedDirectedCycle(EdgeWeightedDigraph G) {
		marked  = new boolean[G.V()];
		onStack = new boolean[G.V()];
		edgeTo  = new DirectedEdge[G.V()];
		for (int v = 0; v < G.V(); v++)
			if (!marked[v]) dfs(G, v);

		// check that digraph has a cycle
		assert check(G);
	}


	// check that algorithm computes either the topological order or finds a directed cycle
	private void dfs(EdgeWeightedDigraph G, int v) {
		onStack[v] = true;
		marked[v] = true;
		for (DirectedEdge e : G.adj(v)) {
			int w = e.to();

			// short circuit if directed cycle found
			if (cycle != null) return;

			//found new vertex, so recur
			else if (!marked[w]) {
				edgeTo[w] = e;
				dfs(G, w);
			}


			// trace back directed cycle
			else if (onStack[w]) {
				cycle = new Stack<>();
				while (e.from() != w) {
					cycle.push(e);
					e = edgeTo[e.from()];
				}
				cycle.push(e);
			}
		}

		onStack[v] = false;
	}

	public boolean hasCycle()             { return cycle != null;   }
	public Iterable<DirectedEdge> cycle() { return cycle;           }


	// certify that digraph is either acyclic or has a directed cycle
	private boolean check(EdgeWeightedDigraph G) {

		// edge-weighted digraph is cyclic
		if (hasCycle()) {
			// verify cycle
			DirectedEdge first = null, last = null;
			for (DirectedEdge e : cycle()) {
				if (first == null) first = e;
				if (last != null) {
					if (last.to() != e.from()) {
						System.err.format("cycle edges %s and %s not incident\n", last, e);
						return false;
					}
				}
				last = e;
			}

			if (last.to() != first.from()) {
				System.err.format("cycle edges %s and %s not incident\n", last, first);
				return false;
			}
		}


		return true;
	}

	public static void main(String[] args) {

		// create random DAG with V vertices and E edges; then add F random edges
		int V = Integer.parseInt(args[0]);
		int E = Integer.parseInt(args[1]);
		int F = Integer.parseInt(args[2]);
		EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
		int[] vertices = new int[V];
		for (int i = 0; i < V; i++) vertices[i] = i;
		StdRandom.shuffle(vertices);
		for (int i = 0; i < E; i++) {
			int v, w;
			do {
				v = StdRandom.uniform(V);
				w = StdRandom.uniform(V);
			} while (v >= w);
			double weight = Math.random();
			G.addEdge(new DirectedEdge(v, w, weight));
		}

		// add F extra edges
		for (int i = 0; i < F; i++) {
			int v = (int) (Math.random() * V);
			int w = (int) (Math.random() * V);
			double weight = Math.random();
			G.addEdge(new DirectedEdge(v, w, weight));
		}

		StdOut.println(G);

		// find a directed cycle
		EdgeWeightedDirectedCycle finder = new EdgeWeightedDirectedCycle(G);
		if (finder.hasCycle()) {
			StdOut.print("Cycle: ");
			for (DirectedEdge e : finder.cycle()) {
				StdOut.print(e + " ");
			}
			StdOut.println();
		}

		// or give topologial sort
		else {
			StdOut.println("No directed cycle");
		}
	}

}