/******************************************************************************
 *  Compilation:  javac DepthFirstDirectedPaths.java
 *  Execution:    java DepthFirstDirectedPaths digraph.txt s
 *  Dependencies: Digraph.java Stack.java
 *  Data files:   https://algs4.cs.princeton.edu/42digraph/tinyDG.txt
 *                https://algs4.cs.princeton.edu/42digraph/mediumDG.txt
 *                https://algs4.cs.princeton.edu/42digraph/largeDG.txt
 *
 *  Determine reachability in a digraph from a given vertex using
 *  depth-first search.
 *  Runs in O(E + V) time.
 *
 *  % java DepthFirstDirectedPaths tinyDG.txt 3
 *  3 to 0:  3-5-4-2-0
 *  3 to 1:  3-5-4-2-0-1
 *  3 to 2:  3-5-4-2
 *  3 to 3:  3
 *  3 to 4:  3-5-4
 *  3 to 5:  3-5
 *  3 to 6:  not connected
 *  3 to 7:  not connected
 *  3 to 8:  not connected
 *  3 to 9:  not connected
 *  3 to 10:  not connected
 *  3 to 11:  not connected
 *  3 to 12:  not connected
 *
 ******************************************************************************/

/**
 *  The {@code DepthFirstDirectedPaths} class represents a data type for
 *  finding directed paths from a source vertex <em>s</em> to every
 *  other vertex in the digraph.
 *  <p>
 *  This implementation uses depth-first search.
 *  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 digraph).
 *  <p>
 *  See {@link DepthFirstDirectedPaths} for a nonrecursive implementation.
 *  For additional documentation,
 *  see <a href="https://algs4.cs.princeton.edu/42digraph">Section 4.2</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class DepthFirstDirectedPaths {
    private boolean[] marked;  // marked[v] = true iff v is reachable from s
    private int[] edgeTo;      // edgeTo[v] = last edge on path from s to v
    private final int s;       // source vertex

    /**
     * Computes a directed path from {@code s} to every other vertex in digraph {@code G}.
     * @param  G the digraph
     * @param  s the source vertex
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     */
    public DepthFirstDirectedPaths(Digraph G, int s) {
        marked = new boolean[G.V()];
        edgeTo = new int[G.V()];
        this.s = s;
        validateVertex(s);
        dfs(G, s);
    }

    private void dfs(Digraph G, int v) {
        marked[v] = true;
        for (int w : G.adj(v)) {
            if (!marked[w]) {
                edgeTo[w] = v;
                dfs(G, w);
            }
        }
    }

    /**
     * Is there a directed path from the source vertex {@code s} to vertex {@code v}?
     * @param  v the vertex
     * @return {@code true} if there is a directed path from the source
     *         vertex {@code s} to vertex {@code v}, {@code false} otherwise
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public boolean hasPathTo(int v) {
        validateVertex(v);
        return marked[v];
    }


    /**
     * Returns a directed path from the source vertex {@code s} to vertex {@code v}, or
     * {@code null} if no such path.
     * @param  v the vertex
     * @return the sequence of vertices on a directed path from the source vertex
     *         {@code s} to vertex {@code v}, as an Iterable
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public Iterable<Integer> pathTo(int v) {
        validateVertex(v);
        if (!hasPathTo(v)) return null;
        Stack<Integer> path = new Stack<Integer>();
        for (int x = v; x != s; x = edgeTo[x])
            path.push(x);
        path.push(s);
        return path;
    }

    // throw an IllegalArgumentException unless {@code 0 <= v < V}
    private void validateVertex(int v) {
        int V = marked.length;
        if (v < 0 || v >= V)
            throw new IllegalArgumentException("vertex " + v + " is not between 0 and " + (V-1));
    }

    /**
     * Unit tests the {@code DepthFirstDirectedPaths} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        In in = new In(args[0]);
        Digraph G = new Digraph(in);
        // StdOut.println(G);

        int s = Integer.parseInt(args[1]);
        DepthFirstDirectedPaths dfs = new DepthFirstDirectedPaths(G, s);

        for (int v = 0; v < G.V(); v++) {
            if (dfs.hasPathTo(v)) {
                StdOut.printf("%d to %d:  ", s, v);
                for (int x : dfs.pathTo(v)) {
                    if (x == s) StdOut.print(x);
                    else        StdOut.print("-" + x);
                }
                StdOut.println();
            }

            else {
                StdOut.printf("%d to %d:  not connected\n", s, v);
            }

        }
    }

}