Topological Sort

Given a digraph, put the vertices in order such that all its directed edges point from a vertex earlier in the order to a vertex later in the order (or report that doing so is not possible).

Directed Graph

Topological Sort

/******************************************************************************
 *  Compilation:  javac Topological.java
 *  Execution:    java  Topological filename.txt delimiter
 *  Dependencies: Digraph.java DepthFirstOrder.java DirectedCycle.java
 *                EdgeWeightedDigraph.java EdgeWeightedDirectedCycle.java
 *                SymbolDigraph.java
 *  Data files:   https://algs4.cs.princeton.edu/42digraph/jobs.txt
 *
 *  Compute topological ordering of a DAG or edge-weighted DAG.
 *  Runs in O(E + V) time.
 *
 *  % java Topological jobs.txt "/"
 *  Calculus
 *  Linear Algebra
 *  Introduction to CS
 *  Advanced Programming
 *  Algorithms
 *  Theoretical CS
 *  Artificial Intelligence
 *  Robotics
 *  Machine Learning
 *  Neural Networks
 *  Databases
 *  Scientific Computing
 *  Computational Biology
 *
 ******************************************************************************/

/**
 *  The {@code Topological} class represents a data type for 
 *  determining a topological order of a <em>directed acyclic graph</em> (DAG).
 *  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 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 DirectedCycle}, {@link DirectedCycleX}, and
 *  {@link EdgeWeightedDirectedCycle} for computing a directed cycle
 *  if the digraph is not a DAG.
 *  See {@link TopologicalX} for a nonrecursive queue-based algorithm
 *  for computing a topological order of a DAG.
 *  <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 Topological {
    private Iterable<Integer> order;  // topological order
    private int[] rank;               // rank[v] = rank of vertex v 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 Topological(Digraph G) {
        DirectedCycle finder = new DirectedCycle(G);
        if (!finder.hasCycle()) {
            DepthFirstOrder dfs = new DepthFirstOrder(G);
            order = dfs.reversePost();
            rank = new int[G.V()];
            int i = 0;
            for (int v : order)
                rank[v] = i++;
        }
    }

    /**
     * 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;
    }

    /**
     * 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
     * @deprecated Replaced by {@link #hasOrder()}.
     */
    @Deprecated
    public boolean isDAG() {
        return hasOrder();
    }

    /**
     * The the rank of vertex {@code v} in the topological order;
     * -1 if the digraph is not a DAG
     *
     * @param v the 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 rank[v];
        else            return -1;
    }

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

    /**
     * Unit tests the {@code Topological} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) {
        String filename  = args[0];
        String delimiter = args[1];
        SymbolDigraph sg = new SymbolDigraph(filename, delimiter);
        Topological topological = new Topological(sg.digraph());
        for (int v : topological.order()) {
            StdOut.println(sg.nameOf(v));
        }
    }

}

https://algs4.cs.princeton.edu/42digraph/Topological.java.html