/******************************************************************************
 *  Compilation:  javac EdgeWeightedDirectedCycle.java
 *  Execution:    java EdgeWeightedDirectedCycle V E F
 *  Dependencies: EdgeWeightedDigraph.java DirectedEdge.java Stack.java
 *
 *  Finds a directed cycle in an edge-weighted digraph.
 *  Runs in O(E + V) time.
 *
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

/**
 *  The {@code EdgeWeightedDirectedCycle} class represents a data type for
 *  determining whether an edge-weighted digraph has a directed cycle.
 *  The <em>hasCycle</em> operation determines whether the edge-weighted
 *  digraph has a directed cycle and, if so, the <em>cycle</em> operation
 *  returns one.
 *  <p>
 *  This implementation uses <em>depth-first search</em>.
 *  The constructor takes &Theta;(<em>V</em> + <em>E</em>) time in the
 *  worst case, where <em>V</em> is the number of vertices and
 *  <em>E</em> is the number of edges.
 *  Each instance method takes &Theta;(1) time.
 *  It uses &Theta;(<em>V</em>) extra space (not including the
 *  edge-weighted digraph).
 *  <p>
 *  See {@link Topological} to compute a topological order if the
 *  edge-weighted digraph is acyclic.
 *  <p>
 *  For additional documentation,
 *  see <a href="https://algs4.cs.princeton.edu/44sp">Section 4.4</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class EdgeWeightedDirectedCycle {
    private boolean[] marked;             // marked[v] = has vertex v been marked?
    private DirectedEdge[] edgeTo;        // edgeTo[v] = previous edge on path to v
    private boolean[] onStack;            // onStack[v] = is vertex on the stack?
    private Stack<DirectedEdge> cycle;    // directed cycle (or null if no such cycle)

    /**
     * Determines whether the edge-weighted digraph {@code G} has a directed cycle and,
     * if so, finds such a cycle.
     * @param G the edge-weighted digraph
     */
    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();
    }

    // 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<DirectedEdge>();

                DirectedEdge f = e;
                while (f.from() != w) {
                    cycle.push(f);
                    f = edgeTo[f.from()];
                }
                cycle.push(f);

                return;
            }
        }

        onStack[v] = false;
    }

    /**
     * Does the edge-weighted digraph have a directed cycle?
     * @return {@code true} if the edge-weighted digraph has a directed cycle,
     * {@code false} otherwise
     */
    public boolean hasCycle() {
        return cycle != null;
    }

    /**
     * Returns a directed cycle if the edge-weighted digraph has a directed cycle,
     * and {@code null} otherwise.
     * @return a directed cycle (as an iterable) if the edge-weighted digraph
     *    has a directed cycle, and {@code null} otherwise
     */
    public Iterable<DirectedEdge> cycle() {
        return cycle;
    }


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

        // 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.printf("cycle edges %s and %s not incident\n", last, e);
                        return false;
                    }
                }
                last = e;
            }

            // cycle() contains no edges
            if (first == null || last == null) {
                System.err.printf("cycle contains no edges\n");
                return false;
            }

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


        return true;
    }

    /**
     * Unit tests the {@code EdgeWeightedDirectedCycle} data type.
     *
     * @param args the command-line arguments
     */
    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.uniformInt(V);
                w = StdRandom.uniformInt(V);
            } while (v >= w);
            double weight = StdRandom.uniformDouble(0.0, 1.0);
            G.addEdge(new DirectedEdge(v, w, weight));
        }

        // add F extra edges
        for (int i = 0; i < F; i++) {
            int v = StdRandom.uniformInt(V);
            int w = StdRandom.uniformInt(V);
            double weight = StdRandom.uniformDouble(0.0, 1.0);
            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 topological sort
        else {
            StdOut.println("No directed cycle");
        }
    }

}

/******************************************************************************
 *  Copyright 2002-2022, Robert Sedgewick and Kevin Wayne.
 *
 *  This file is part of algs4.jar, which accompanies the textbook
 *
 *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
 *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
 *      http://algs4.cs.princeton.edu
 *
 *
 *  algs4.jar is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  algs4.jar is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with algs4.jar.  If not, see http://www.gnu.org/licenses.
 ******************************************************************************/