traversal.hpp

/*********************************************************************
 *
 *  Linear Arrangement Library - A library that implements a collection
 *  algorithms for linear arrangments of graphs.
 *
 *  Copyright (C) 2019 - 2021
 *
 *  This file is part of Linear Arrangement Library. To see the full code
 *  visit the webpage:
 *      https://github.com/lluisalemanypuig/linear-arrangement-library.git
 *
 *  Linear Arrangement Library is free software: you can redistribute it
 *  and/or modify it under the terms of the GNU Affero General Public License
 *  as published by the Free Software Foundation, either version 3 of the
 *  License, or (at your option) any later version.
 *
 *  Linear Arrangement Library 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 Affero General Public License for more details.
 *
 *  You should have received a copy of the GNU Affero General Public License
 *  along with Linear Arrangement Library.  If not, see <http://www.gnu.org/licenses/>.
 *
 *  Contact:
 *
 *      Lluís Alemany Puig (lalemany@cs.upc.edu)
 *          LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)
 *          CQL (Complexity and Quantitative Linguistics Lab)
 *          Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *          Webpage: https://cqllab.upc.edu/people/lalemany/
 *
 *      Ramon Ferrer i Cancho (rferrericancho@cs.upc.edu)
 *          LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)
 *          CQL (Complexity and Quantitative Linguistics Lab)
 *          Office S124, Omega building
 *          Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *          Webpage: https://cqllab.upc.edu/people/rferrericancho/
 *
 ********************************************************************/
 
#pragma once
 
// C++ includes
#include <functional>
#include <queue>
 
// lal includes
#include <lal/definitions.hpp>
#include <lal/graphs/directed_graph.hpp>
#include <lal/graphs/undirected_graph.hpp>
#include <lal/internal/data_array.hpp>
 
namespace lal {
namespace internal {
 
/* This class implements an abstract graph breadth-first traversal.
 *
 * Users of this class can control the traversal by setting custom control-flow
 * functions. The user can set:
 * - a function used for early termination of the traversal
 * (see @ref set_terminate),
 * - a function that processes the current node in the traversal
 * (see @ref set_process_current),
 * - a function that processes the current edge in the traversal
 * (see @ref set_process_neighbour),
 * - a function that can decide when to add another node to the queue of the
 * traversal (see @ref set_node_add).
 *
 * This graph_traversal traversal can also use "reversed edges" when doing traversals on
 * directed graphs. A back edge in a directed graph of a node u is a node
 * that points to u, namely, the directed edge is of the form (v,u), for another
 * node v of the graph. This can be set via the @ref set_use_back_edges method.
 */
template<
    typename G,
    bool is_directed = std::is_base_of_v<graphs::directed_graph, G>,
    std::enable_if_t<
        std::is_base_of_v<graphs::directed_graph, G> ||
        std::is_base_of_v<graphs::undirected_graph, G>
        , bool
    > = true
>
class BFS {
public:
    typedef std::function<void (const BFS<G>&, node)> BFS_process_one;
    typedef std::function<void (const BFS<G>&, node, node, bool)> BFS_process_two;
    typedef std::function<bool (const BFS<G>&, node)> BFS_bool_one;
    typedef std::function<bool (const BFS<G>&, node, node)> BFS_bool_two;
 
public:
    // Constructor
    BFS(const G& g) : m_G(g), m_vis(m_G.get_num_nodes()) {
        reset();
    }
    // Destructor
    ~BFS() { }
 
    // Set the graph_traversal to its default state.
    void reset() {
        reset_visited();
        clear_structure();
 
        set_use_rev_edges(false);
        set_process_visited_neighbours(false);
 
        set_terminate_default();
        set_process_current_default();
        set_process_neighbour_default();
        set_node_add_default();
    }
 
    void start_at(node source) {
        m_X.push(source);
        m_vis[source] = 1;
        do_traversal();
    }
 
    void start_at(const std::vector<node>& sources) {
        for (const node& u : sources) {
            m_X.push(u);
            m_vis[u] = 1;
        }
        do_traversal();
    }
 
    /* SETTERS */
 
    // set whether the traversal can use reversed edges
    void set_use_rev_edges(bool use) { m_use_rev_edges = use; }
 
    // see @ref m_term
    void set_terminate_default()
    { m_term = [](const BFS<G>&, const node) -> bool { return false; }; }
    void set_terminate(const BFS_bool_one& f)
    { m_term = f; }
 
    // see @ref m_proc_cur
    void set_process_current_default()
    { m_proc_cur = [](const BFS<G>&, const node) -> void { }; }
    void set_process_current(const BFS_process_one& f)
    { m_proc_cur = f; }
 
    // see @ref m_proc_neigh
    void set_process_neighbour_default()
    { m_proc_neigh = [](const BFS<G>&, const node, const node, bool) -> void { }; }
    void set_process_neighbour(const BFS_process_two& f)
    { m_proc_neigh = f; }
 
    // see @ref m_add_node
    void set_node_add_default()
    { m_add_node = [](const BFS<G>&, const node, const node) -> bool { return true; }; }
    void set_node_add(const BFS_bool_two& f)
    { m_add_node = f; }
 
    /*
     * @brief Should the algorithm call the neighbour processing function
     * for already visited neighbours?
     * @param v Either true or false.
     */
    void set_process_visited_neighbours(bool v) { m_proc_vis_neighs = v; }
 
    // Sets all nodes to not visited.
    void reset_visited() { m_vis.fill(0); }
 
    void clear_structure() { std::queue<node> q; m_X.swap(q); }
 
    // Set node @e u as visited.
    void set_visited(node u, char vis) { m_vis[u] = vis; }
 
    /* GETTERS */
 
    // Returns the set of visited nodes.
    bool node_was_visited(node u) const { return m_vis[u]; }
 
    // have all nodes been visited?
    bool all_visited() const {
        return std::find(m_vis.begin(), m_vis.end(), 0) == m_vis.end();
    }
 
    // returns the graph
    const G& get_graph() const { return m_G; }
 
    // Return visited nodes information
    const data_array<char>& get_visited() const { return m_vis; }
 
protected:
    // ltr: is the 'natural' orientation of the vertices "s -> t"?
    //      If true, then the edge in the graph is (s,t)
    //      If false, the edge in the graph is (t,s)
    void deal_with_neighbour(node s, node t, bool ltr) {
        // Process the neighbour 't' of 's'.
        if ((m_vis[t] and m_proc_vis_neighs) or not m_vis[t]) {
            m_proc_neigh(*this, s, t, ltr);
        }
 
        if (not m_vis[t] and m_add_node(*this, s, t)) {
            m_X.push(t);
            // set node as visited
            m_vis[t] = true;
        }
    }
 
    // process neighbours
    //     when the graph is an undirected graph
    template<
        class GG = G,
        std::enable_if_t<
            std::is_base_of_v<graphs::undirected_graph, GG>, bool
        > = true
    >
    void process_neighbours(node s) {
        for (const node& t : m_G.get_neighbours(s)) {
            // Edges are processed in the direction "s -> t".
            // This is also the 'natural' orientation of the edge,
            // so this explains the 'true'.
            deal_with_neighbour(s, t, true);
        }
    }
 
    //     when the graph is a directed graph
    template<
        class GG = G,
        std::enable_if_t<
            std::is_base_of_v<graphs::directed_graph, GG>, bool
        > = true
    >
    void process_neighbours(node s) {
        for (const node& t : m_G.get_out_neighbours(s)) {
            // Edges are processed in the direction "s -> t".
            // This is also the 'natural' orientation of the edge,
            // hence the 'true'.
            deal_with_neighbour(s, t, true);
        }
        // process in-neighbours whenever appropriate
        if (m_use_rev_edges) {
            for (const node& t : m_G.get_in_neighbours(s)) {
                // Edges are processed in the direction "s -> t".
                // However, the 'natural' orientation of the edge
                // is "t -> s", hence the 'false'.
                deal_with_neighbour(s, t, false);
            }
        }
    }
 
    node next_node() const { return m_X.front(); }
 
    /* The graph_traversal traversal is implemented as follows:
     *
     * <pre>
     * ProcessNeighbourhood(graph, u, Nv):
     *   1. for each w in Nv do
     *   2.     if w has not been visited before, or it has been but
     *   3.         already-visited nodes have to be processed
     *   4.     then
     *   5.         proc_neigh(u,w)
     *   6.     endif
     *   7.
     *   8.     if w not visited before and node_add(w) then
     *   9.         push w into X
     *  10.         mark w as visited in vis
     *  11.     endif
     *  12. endfor
     * </pre>
     *
     * <pre>
     * graph_traversal(graph, source):
     *   1. vis = {false}   // set of |V(graph)| bits set to false
     *   2. X = {source}    // structure of the traversal,
     *                      // initialised with the source,
     *                      // either a stack or a queue.
     *   3. while X is not empty do
     *   4.     v = X.front or X.top
     *   5.     remove X's top
     *   6.     proc_curr(v)
     *   7.     if terminate(v) then Finish traversal
     *   8.     else
     *   9.         Nv = out-neighbourhood of v
     *  10.         ProcessNeighbourhood(graph, v, Nv)
     *  11.         If graph is directed and process reverse edges then
     *  12.             Nv = in-neighbourhood of v
     *  13.             ProcessNeighbourhood(graph, v, Nv)
     *  14.         endif
     *  15.     endif
     *  16. endwhile
     * </pre>
     *
     * Note that lines (...) extend the neighbourhood of a node "Nv"
     * depending of the type of graph. If the graph is directed and
     * the user wants to process "reversed edges", then the neighbourhood
     * is not limited to "out-neighbours", but also to "in-neighbours".
     */
    void do_traversal() {
        while (not m_X.empty()) {
            const node s = next_node();
            m_X.pop();
 
            // process current node
            m_proc_cur(*this, s);
 
            // check user-defined early termination condition
            if (m_term(*this, s)) { break; }
 
            process_neighbours(s);
        }
    }
 
protected:
    // Constant reference to the graph.
    const G& m_G;
    // The structure of the traversal (either a queue or a stack).
    std::queue<node> m_X;
    // The set of visited nodes.
    data_array<char> m_vis;
    // Should we process already visitied neighbours?
    bool m_proc_vis_neighs = false;
    // Use back edges in directed graphs.
    bool m_use_rev_edges = false;
 
protected:
    /*
     * @brief graph_traversal early terminating function.
     *
     * Returns true if the @ref graph_traversal algorithm should terminate.
     *
     * For more details on when this function is called see @ref do_traversal.
     * @param graph_traversal The object containing the traversal. This also contains
     * several attributes that might be useful to guide the traversal.
     * @param s The node at the front of the queue of the algorithm.
     */
    BFS_bool_one m_term;
 
    /*
     * @brief graph_traversal node processing function.
     *
     * Processes the current node visited.
     *
     * For more details on when this function is called see @ref do_traversal.
     * @param graph_traversal The object containing the traversal. This also contains
     * several attributes that might be useful to guide the traversal.
     * @param s The node at the front of the queue of the algorithm.
     */
    BFS_process_one m_proc_cur;
 
    /*
     * @brief graph_traversal neighbour node processing function.
     *
     * Processes the next visited node. The direction of the nodes
     * visited passed as parameters is given by the boolean parameter. If
     * it is true then the edge is s -> t. If it is false then the edge is
     * t -> s.
     *
     * For more details on when this function is called see @ref do_traversal.
     * @param graph_traversal The object containing the traversal. This also contains
     * several attributes that might be useful to guide the traversal.
     * @param s The node at the front of the queue of the algorithm.
     * @param t The node neighbour of @e u visited by the algorithm.
     */
    BFS_process_two m_proc_neigh;
 
    /*
     * @brief graph_traversal node addition function.
     *
     * Determines whether a node @e s should be added to the queue or not.
     *
     * For more details on when this function is called see @ref do_traversal.
     * @param graph_traversal The object containing the traversal. This also contains
     * several attributes that might be useful to guide the traversal.
     * @param s The node candidate for addition.
     */
    BFS_bool_two m_add_node;
};
 
} // -- namespace internal
} // -- namespace lal