/******************************************************************************
 *  Compilation:  javac BreadthFirstDirectedPaths.java
 *  Execution:    java BreadthFirstDirectedPaths digraph.txt s
 *  Dependencies: Digraph.java Queue.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
 *
 *  Run breadth-first search on a digraph.
 *  Runs in O(E + V) time.
 *
 *  % java BreadthFirstDirectedPaths tinyDG.txt 3
 *  3 to 0 (2):  3->2->0
 *  3 to 1 (3):  3->2->0->1
 *  3 to 2 (1):  3->2
 *  3 to 3 (0):  3
 *  3 to 4 (2):  3->5->4
 *  3 to 5 (1):  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 BreadthDirectedFirstPaths} class represents a data type for
 *  finding shortest paths (number of edges) from a source vertex <em>s</em>
 *  (or set of source vertices) to every other vertex in the digraph.
 *  <p>
 *  This implementation uses breadth-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>
 *  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 BreadthFirstDirectedPaths {
    private static final int INFINITY = Integer.MAX_VALUE;
    private boolean[] marked;  // marked[v] = is there an s->v path?
    private int[] edgeTo;      // edgeTo[v] = last edge on shortest s->v path
    private int[] distTo;      // distTo[v] = length of shortest s->v path

    /**
     * Computes the shortest path from {@code s} and every other vertex in graph {@code G}.
     * @param G the digraph
     * @param s the source vertex
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public BreadthFirstDirectedPaths(Digraph G, int s) {
        marked = new boolean[G.V()];
        distTo = new int[G.V()];
        edgeTo = new int[G.V()];
        for (int v = 0; v < G.V(); v++)
            distTo[v] = INFINITY;
        validateVertex(s);
        bfs(G, s);
    }

    /**
     * Computes the shortest path from any one of the source vertices in {@code sources}
     * to every other vertex in graph {@code G}.
     * @param G the digraph
     * @param sources the source vertices
     * @throws IllegalArgumentException if {@code sources} is {@code null}
     * @throws IllegalArgumentException if {@code sources} contains no vertices
     * @throws IllegalArgumentException unless each vertex {@code v} in
     *         {@code sources} satisfies {@code 0 <= v < V}
     */
    public BreadthFirstDirectedPaths(Digraph G, Iterable<Integer> sources) {
        marked = new boolean[G.V()];
        distTo = new int[G.V()];
        edgeTo = new int[G.V()];
        for (int v = 0; v < G.V(); v++)
            distTo[v] = INFINITY;
        validateVertices(sources);
        bfs(G, sources);
    }

    // BFS from single source
    private void bfs(Digraph G, int s) {
        Queue<Integer> q = new Queue<Integer>();
        marked[s] = true;
        distTo[s] = 0;
        q.enqueue(s);
        while (!q.isEmpty()) {
            int v = q.dequeue();
            for (int w : G.adj(v)) {
                if (!marked[w]) {
                    edgeTo[w] = v;
                    distTo[w] = distTo[v] + 1;
                    marked[w] = true;
                    q.enqueue(w);
                }
            }
        }
    }

    // BFS from multiple sources
    private void bfs(Digraph G, Iterable<Integer> sources) {
        Queue<Integer> q = new Queue<Integer>();
        for (int s : sources) {
            marked[s] = true;
            distTo[s] = 0;
            q.enqueue(s);
        }
        while (!q.isEmpty()) {
            int v = q.dequeue();
            for (int w : G.adj(v)) {
                if (!marked[w]) {
                    edgeTo[w] = v;
                    distTo[w] = distTo[v] + 1;
                    marked[w] = true;
                    q.enqueue(w);
                }
            }
        }
    }

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

    /**
     * Returns the number of edges in a shortest path from the source {@code s}
     * (or sources) to vertex {@code v}?
     * @param v the vertex
     * @return the number of edges in such a shortest path
     *         (or {@code Integer.MAX_VALUE} if there is no such path)
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public int distTo(int v) {
        validateVertex(v);
        return distTo[v];
    }

    /**
     * Returns a shortest path from {@code s} (or sources) to {@code v}, or
     * {@code null} if no such path.
     * @param v the vertex
     * @return the sequence of vertices on a shortest path, 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>();
        int x;
        for (x = v; distTo[x] != 0; x = edgeTo[x])
            path.push(x);
        path.push(x);
        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));
    }

    // throw an IllegalArgumentException if vertices is null, has zero vertices,
    // or has a vertex not between 0 and V-1
    private void validateVertices(Iterable<Integer> vertices) {
        if (vertices == null) {
            throw new IllegalArgumentException("argument is null");
        }
        int vertexCount = 0;
        for (Integer v : vertices) {
            vertexCount++;
            if (v == null) {
                throw new IllegalArgumentException("vertex is null");
            }
            validateVertex(v);
        }
        if (vertexCount == 0) {
            throw new IllegalArgumentException("zero vertices");
        }
    }

    /**
     * Unit tests the {@code BreadthFirstDirectedPaths} 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]);
        BreadthFirstDirectedPaths bfs = new BreadthFirstDirectedPaths(G, s);

        for (int v = 0; v < G.V(); v++) {
            if (bfs.hasPathTo(v)) {
                StdOut.printf("%d to %d (%d):  ", s, v, bfs.distTo(v));
                for (int x : bfs.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);
            }

        }
    }


}