cycles.hpp

/*********************************************************************
 *
 * Linear Arrangement Library - A library that implements a collection
 * algorithms for linear arrangments of graphs.
 *
 * Copyright (C) 2019 - 2024
 *
 * This file is part of Linear Arrangement Library. The full code is available
 * at:
 *      https://github.com/LAL-project/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 (lluis.alemany.puig@upc.edu)
 *         LQMC (Quantitative, Mathematical, and Computational Linguisitcs)
 *         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)
 *         LQMC (Quantitative, Mathematical, and Computational Linguisitcs)
 *         CQL (Complexity and Quantitative Linguistics Lab)
 *         Office 220, Omega building
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://cqllab.upc.edu/people/rferrericancho/
 *
 ********************************************************************/
 
#pragma once
 
// lal includes
#include <lal/graphs/directed_graph.hpp>
#include <lal/detail/graphs/traversal.hpp>
#include <lal/detail/array.hpp>
 
namespace lal {
namespace detail {
 
[[nodiscard]] inline bool find_cycle
(
    const graphs::directed_graph& g,
    const node u,
    char * const __restrict__ visited,
    char * const __restrict__ in_stack
)
noexcept
{
    if (visited[u]) { return false; }
    visited[u] = 1;
 
    in_stack[u] = 1;
    for (const node v : g.get_out_neighbors(u)) {
        if (in_stack[v]) {
            return true;
        }
        if (visited[v] == 0 and find_cycle(g,v,visited,in_stack)) {
            return true;
        }
    }
 
    in_stack[u] = 0;
    return false;
}
 
[[nodiscard]] inline bool has_directed_cycles(
    const graphs::directed_graph& g,
    char * const __restrict__ vis,
    char * const __restrict__ in_stack
)
noexcept
{
    const uint64_t n = g.get_num_nodes();
    std::fill(&vis[0], &vis[n], 0);
    std::fill(&in_stack[0], &in_stack[n], 0);
    bool has_cycle = false;
    for (node u = 0; u < n and not has_cycle; ++u) {
        if (vis[u] == 0) {
            has_cycle = find_cycle(g, u, vis, in_stack);
        }
    }
    return has_cycle;
}
 
[[nodiscard]] inline bool has_directed_cycles
(const graphs::directed_graph& g)
noexcept
{
    const uint64_t n = g.get_num_nodes();
    array<char> all_mem(2*n);
    char * const __restrict__ vis = all_mem.begin();
    char * const __restrict__ in_stack = all_mem.at(n);
    return has_directed_cycles(g, vis, in_stack);
}
 
template <class graph_t>
[[nodiscard]] bool has_undirected_cycles
(const graph_t& g, BFS<graph_t>& bfs)
noexcept
{
    const auto n = g.get_num_nodes();
 
    // parent[s] = t <->
    // (in the traversal) s was reached from t (NOTE THE DIFFERENT ORDER).
    // Note that read operations "if (parent[s] != t)" always come after
    // the first write "parent[t] = s".
    array<node> parent(n, n+1);
    // a cycle was found
    bool cycle_found = false;
 
    // we need to traverse "reversed edges" in directed graphs
    bfs.set_use_rev_edges( BFS<graph_t>::is_graph_directed );
    // we need this to detect cycles
    bfs.set_process_visited_neighbors(true);
    // -- functions for the traversal
    bfs.set_terminate(
    [&](const BFS<graph_t>&, const node) -> bool { return cycle_found; }
    );
    bfs.set_process_neighbour(
    [&](const auto& _bfs, node s, node t, bool) -> void {
        // Since we want to do the traversal on the directed graphs likewise on
        // the undirected graphs, the direction is ignored. We do not want to
        // treat the nodes 's' and 't' as in the edge "t->s" but as in the
        // edge "s->t" so as to mimic an "undirected traversal" on directed
        // graphs.
 
        if (_bfs.node_was_visited(t)) {
            // if t was visted before then
            //     "s -> t" and later "t -> s"
            // or
            //     "s -> ..." and later "... -> s"
            //     where '...' does not contain 't'
            if (parent[s] != t) {
                // node 't' was reached from some node
                // other than 's' in previous iterations
                cycle_found = true;
            }
        }
        parent[t] = s;
    }
    );
 
    // find cycles
    for (node u = 0; u < n and not cycle_found; ++u) {
        if (not bfs.node_was_visited(u)) {
            bfs.clear_queue();
            bfs.start_at(u);
        }
    }
    return cycle_found;
}
 
template <class graph_t>
[[nodiscard]] bool has_undirected_cycles
(const graph_t& g)
noexcept
{
    // BFS traversal object
    BFS<graph_t> bfs(g);
    return has_undirected_cycles(g, bfs);
}
 
} // -- namespace detail
} // -- namespace lal