Topological.h

#ifndef CH4_TOPOLOGICAL_H
#define CH4_TOPOLOGICAL_H

#include "../head/Digraph.h"
#include "../head/DirectedCycle.h"
#include "../head/EdgeWeightedDigraph.h"
#include "../head/EdgeWeightedDirectedCycle.h"
#include "../head/DepthFirstOrder.h"

/**
 *  The {@code Topological} 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 depth-first search.
 *  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 TopologicalX} for a nonrecursive queue-based algorithm
 *  to compute 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
 */
class Topological {
public:
    /**
     * Determines whether the digraph {@code G} has a topological order and, if so,
     * finds such a topological order.
     * @param G the digraph
     */
    Topological(Digraph &G) : rank(G.getV()) {
        DirectedCycle finder(G);
        if (!finder.hasCycle()) {
            DepthFirstOrder dfs(G);
            order = dfs.reversePost();
            int i = 0;
            for (int v : order)
                rank[v] = i++;
        }
    }

    /**
     * Determines whether the edge-weighted digraph {@code G} has a topological
     * order and, if so, finds such an order.
     * @param G the edge-weighted digraph
     */
    Topological(EdgeWeightedDigraph &G) {
        EdgeWeightedDirectedCycle finder(G);
        if (!finder.hasCycle()) {
            DepthFirstOrder dfs(G);
            order = dfs.reversePost();
        }
    }

    /**
     * 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
     */
    forward_list<int> getorder() {
        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
     */
    bool hasOrder() {
        return !order.empty();
    }

    /**
     * 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}
     */
    int getrank(int v) {
        validateVertex(v);
        if (hasOrder()) return rank[v];
        else return -1;
    }

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

private:
    forward_list<int> order;   // topological order
    vector<int> rank;          // rank[v] = rank of vertex v in order
};

#endif //CH4_TOPOLOGICAL_H