TopologicalX.java


Below is the syntax highlighted version of TopologicalX.java.


/******************************************************************************
 *  Compilation:  javac TopologicalX.java
 *  Execution:    java TopologicalX V E F
 *  Dependencies: Queue.java Digraph.java
 *
 *  Compute topological ordering of a DAG using queue-based algorithm.
 *  Runs in O(E + V) time.
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

/**
 *  The {@code TopologicalX} class represents a data type for 
 *  determining a topological order of a directed acyclic graph (DAG).
 *  Recall, a digraph has a topological order if and only if it is a DAG.
 *  The <em>hasOrder</em> operation determines whether the digraph has
 *  a topological order, and if so, the <em>order</em> operation
 *  returns one.
 *  <p>
 *  This implementation uses a nonrecursive, queue-based algorithm.
 *  The constructor takes time proportional to <em>V</em> + <em>E</em>
 *  (in the worst case),
 *  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
 *  Afterwards, the <em>hasOrder</em> and <em>rank</em> operations takes constant time;
 *  the <em>order</em> operation takes time proportional to <em>V</em>.
 *  <p>
 *  See {@link DirectedCycle}, {@link DirectedCycleX}, and
 *  {@link EdgeWeightedDirectedCycle} to compute a
 *  directed cycle if the digraph is not a DAG.
 *  See {@link Topological} for a recursive version that uses depth-first search.
 *  <p>
 *  For additional documentation,
 *  see <a href="http://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 TopologicalX {
    private Queue<Integer> order;     // vertices in topological order
    private int[] ranks;              // ranks[v] = order where vertex v appers in order

    /**
     * Determines whether the digraph {@code G} has a topological order and, if so,
     * finds such a topological order.
     * @param G the digraph
     */
    public TopologicalX(Digraph G) {

        // indegrees of remaining vertices
        int[] indegree = new int[G.V()];
        for (int v = 0; v < G.V(); v++) {
            indegree[v] = G.indegree(v);
        }

        // initialize 
        ranks = new int[G.V()]; 
        order = new Queue<Integer>();
        int count = 0;

        // initialize queue to contain all vertices with indegree = 0
        Queue<Integer> queue = new Queue<Integer>();
        for (int v = 0; v < G.V(); v++)
            if (indegree[v] == 0) queue.enqueue(v);

        while (!queue.isEmpty()) {
            int v = queue.dequeue();
            order.enqueue(v);
            ranks[v] = count++;
            for (int w : G.adj(v)) {
                indegree[w]--;
                if (indegree[w] == 0) queue.enqueue(w);
            }
        }

        // there is a directed cycle in subgraph of vertices with indegree >= 1.
        if (count != G.V()) {
            order = null;
        }

        assert check(G);
    }

    /**
     * Determines whether the edge-weighted digraph {@code G} has a
     * topological order and, if so, finds such a topological order.
     * @param G the digraph
     */
    public TopologicalX(EdgeWeightedDigraph G) {

        // indegrees of remaining vertices
        int[] indegree = new int[G.V()];
        for (int v = 0; v < G.V(); v++) {
            indegree[v] = G.indegree(v);
        }

        // initialize 
        ranks = new int[G.V()]; 
        order = new Queue<Integer>();
        int count = 0;

        // initialize queue to contain all vertices with indegree = 0
        Queue<Integer> queue = new Queue<Integer>();
        for (int v = 0; v < G.V(); v++)
            if (indegree[v] == 0) queue.enqueue(v);

        while (!queue.isEmpty()) {
            int v = queue.dequeue();
            order.enqueue(v);
            ranks[v] = count++;
            for (DirectedEdge e : G.adj(v)) {
                int w = e.to();
                indegree[w]--;
                if (indegree[w] == 0) queue.enqueue(w);
            }
        }

        // there is a directed cycle in subgraph of vertices with indegree >= 1.
        if (count != G.V()) {
            order = null;
        }

        assert check(G);
    }

    /**
     * Returns a topological order if the digraph has a topologial order,
     * and {@code null} otherwise.
     * @return a topological order of the vertices (as an interable) if the
     *    digraph has a topological order (or equivalently, if the digraph is a DAG),
     *    and {@code null} otherwise
     */
    public Iterable<Integer> order() {
        return order;
    }

    /**
     * Does the digraph have a topological order?
     * @return {@code true} if the digraph has a topological order (or equivalently,
     *    if the digraph is a DAG), and {@code false} otherwise
     */
    public boolean hasOrder() {
        return order != null;
    }

    /**
     * The the rank of vertex {@code v} in the topological order;
     * -1 if the digraph is not a DAG
     *
     * @param v vertex
     * @return the position of vertex {@code v} in a topological order
     *    of the digraph; -1 if the digraph is not a DAG
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    public int rank(int v) {
        validateVertex(v);
        if (hasOrder()) return ranks[v];
        else            return -1;
    }

    // certify that digraph is acyclic
    private boolean check(Digraph G) {

        // digraph is acyclic
        if (hasOrder()) {
            // check that ranks are a permutation of 0 to V-1
            boolean[] found = new boolean[G.V()];
            for (int i = 0; i < G.V(); i++) {
                found[rank(i)] = true;
            }
            for (int i = 0; i < G.V(); i++) {
                if (!found[i]) {
                    System.err.println("No vertex with rank " + i);
                    return false;
                }
            }

            // check that ranks provide a valid topological order
            for (int v = 0; v < G.V(); v++) {
                for (int w : G.adj(v)) {
                    if (rank(v) > rank(w)) {
                        System.err.printf("%d-%d: rank(%d) = %d, rank(%d) = %d\n",
                                          v, w, v, rank(v), w, rank(w));
                        return false;
                    }
                }
            }

            // check that order() is consistent with rank()
            int r = 0;
            for (int v : order()) {
                if (rank(v) != r) {
                    System.err.println("order() and rank() inconsistent");
                    return false;
                }
                r++;
            }
        }


        return true;
    }

    // certify that digraph is acyclic
    private boolean check(EdgeWeightedDigraph G) {

        // digraph is acyclic
        if (hasOrder()) {
            // check that ranks are a permutation of 0 to V-1
            boolean[] found = new boolean[G.V()];
            for (int i = 0; i < G.V(); i++) {
                found[rank(i)] = true;
            }
            for (int i = 0; i < G.V(); i++) {
                if (!found[i]) {
                    System.err.println("No vertex with rank " + i);
                    return false;
                }
            }

            // check that ranks provide a valid topological order
            for (int v = 0; v < G.V(); v++) {
                for (DirectedEdge e : G.adj(v)) {
                    int w = e.to();
                    if (rank(v) > rank(w)) {
                        System.err.printf("%d-%d: rank(%d) = %d, rank(%d) = %d\n",
                                          v, w, v, rank(v), w, rank(w));
                        return false;
                    }
                }
            }

            // check that order() is consistent with rank()
            int r = 0;
            for (int v : order()) {
                if (rank(v) != r) {
                    System.err.println("order() and rank() inconsistent");
                    return false;
                }
                r++;
            }
        }


        return true;
    }

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

    /**
     * Unit tests the {@code TopologicalX} 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]);

        Digraph G1 = DigraphGenerator.dag(V, E);

        // corresponding edge-weighted digraph
        EdgeWeightedDigraph G2 = new EdgeWeightedDigraph(V);
        for (int v = 0; v < G1.V(); v++)
            for (int w : G1.adj(v))
                G2.addEdge(new DirectedEdge(v, w, 0.0));

        // add F extra edges
        for (int i = 0; i < F; i++) {
            int v = StdRandom.uniform(V);
            int w = StdRandom.uniform(V);
            G1.addEdge(v, w);
            G2.addEdge(new DirectedEdge(v, w, 0.0));
        }

        StdOut.println(G1);
        StdOut.println();
        StdOut.println(G2);

        // find a directed cycle
        TopologicalX topological1 = new TopologicalX(G1);
        if (!topological1.hasOrder()) {
            StdOut.println("Not a DAG");
        }

        // or give topologial sort
        else {
            StdOut.print("Topological order: ");
            for (int v : topological1.order()) {
                StdOut.print(v + " ");
            }
            StdOut.println();
        }

        // find a directed cycle
        TopologicalX topological2 = new TopologicalX(G2);
        if (!topological2.hasOrder()) {
            StdOut.println("Not a DAG");
        }

        // or give topologial sort
        else {
            StdOut.print("Topological order: ");
            for (int v : topological2.order()) {
                StdOut.print(v + " ");
            }
            StdOut.println();
        }
    }

}

/******************************************************************************
 *  Copyright 2002-2016, 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.
 ******************************************************************************/


Last updated: Tue May 9 03:21:46 EDT 2017.