DepthFirstPaths.h

#ifndef CH4_DEPTHFIRSTPATHS_H
#define CH4_DEPTHFIRSTPATHS_H

#include "../head/Graph.h"

/**
 *  The {@code DepthFirstPaths} class represents a data type for finding
 *  paths from a source vertex <em>s</em> to every other vertex
 *  in an undirected graph.
 *  <p>
 *  This implementation uses depth-first search.
 *  The constructor takes time proportional to <em>V</em> + <em>E</em>,
 *  where <em>V</em> is the number of vertices and <em>E</em> is the number of edges.
 *  Each call to {@link #hasPathTo(int)} takes constant time;
 *  each call to {@link #pathTo(int)} takes time proportional to the length
 *  of the path.
 *  It uses extra space (not including the graph) proportional to <em>V</em>.
 *  <p>
 *  For additional documentation, see <a href="https://algs4.cs.princeton.edu/41graph">Section 4.1</a>
 *  of <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
class DepthFirstPaths {
public:
    /**
     * Computes a path between {@code s} and every other vertex in graph {@code G}.
     * @param G the graph
     * @param s the source vertex
     * @throws IllegalArgumentException unless {@code 0 <= s < V}
     */
    DepthFirstPaths(Graph &G, int s) : s(s), edgeTo(G.getV()), marked(G.getV()) {
        validateVertex(s);
        dfs(G, s);
    }

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

    /**
     * Returns a path between the source vertex {@code s} and vertex {@code v}, or
     * {@code null} if no such path.
     * @param  v the vertex
     * @return the sequence of vertices on a path between the source vertex
     *         {@code s} and vertex {@code v}, as an Iterable
     * @throws IllegalArgumentException unless {@code 0 <= v < V}
     */
    decltype(auto) pathTo(int v) {
        validateVertex(v);
        if (!hasPathTo(v)) throw runtime_error("No path to this vertex");
        forward_list<int> path;
        for (int x = v; x != s; x = edgeTo[x])
            path.push_front(x);
        path.push_front(s);
        return path;
    }

private:
    // depth first search from v
    void dfs(Graph &G, int v) {
        marked[v] = true;
        for (int w : G.getadj(v)) {
            if (!marked[w]) {
                edgeTo[w] = v;
                dfs(G, w);
            }
        }
    }

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

private:
    vector<bool> marked;  // marked[v] = is there an s-v path?
    vector<int> edgeTo;   // edgeTo[v] = last edge on s-v path
    int s;                // source vertex
};


#endif //CH4_DEPTHFIRSTPATHS_H