branchless_paths_compute.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
 
// C++ includes
#if defined DEBUG
#include <cassert>
#endif
 
// lal includes
#include <lal/basic_types.hpp>
#include <lal/graphs/free_tree.hpp>
#include <lal/graphs/rooted_tree.hpp>
#include <lal/properties/branchless_path.hpp>
#include <lal/detail/array.hpp>
#include <lal/detail/graphs/traversal.hpp>
 
namespace lal {
namespace detail {
 
template <class tree_t>
void expand_branchless_path
(
    const tree_t& t,
    const node u, const node v,
    BFS<tree_t>& bfs,
    std::vector<properties::branchless_path>& res,
    properties::branchless_path& p
)
noexcept
{
    const uint64_t n = t.get_num_nodes();
 
    // the case of an edge...
    if (t.get_degree(u) != 2 and t.get_degree(v) != 2) {
 
        // avoid symmetric paths
        if (u > v) { return; }
 
#if defined DEBUG
        assert(t.has_edge(u, v) or t.has_edge(v, u));
#endif
        // initialize the path
        p.init(n);
        // set and add the first and second non-internal vertices
        p.add_node(u);
        p.set_h1(u);
        p.add_node(v);
        p.set_h2(v);
        // push the new path
        res.push_back(std::move(p));
        return;
    }
 
#if defined DEBUG
    assert(not bfs.node_was_visited(u));
#endif
 
    if (bfs.node_was_visited(v)) { return; }
 
    // initialize the path
    p.init(n);
    // set the first non-internal vertex and add it
    p.add_node(u);
    p.set_h1(u);
 
    // set 'u' as visited to avoid going 'back' in the tree
    bfs.set_visited(u, 1);
 
    // expand the new path
    bfs.start_at(v);
 
    // find the lowest *internal* vertex in lexicographic order
    const auto& seq = p.get_vertex_sequence();
    node lowest_lexicographic = n + 1;
    for (std::size_t i = 1; i < seq.size() - 1; ++i) {
        lowest_lexicographic = std::min(lowest_lexicographic, seq[i]);
    }
    p.set_lowest_lexicographic(lowest_lexicographic);
 
    // only let the internal vertices of the paths be visited
    bfs.set_visited(p.get_h1(), 0);
    bfs.set_visited(p.get_h2(), 0);
 
    // push the new path
    res.push_back(std::move(p));
}
 
template <class tree_t>
[[nodiscard]] std::vector<properties::branchless_path>
branchless_paths_compute(const tree_t& t)
noexcept
{
    const uint64_t n = t.get_num_nodes();
 
    // result of the function (to be returned)
    std::vector<properties::branchless_path> res;
 
    // path to be filled
    properties::branchless_path p;
 
    BFS bfs(t);
 
    // detect the last hub
    bfs.set_process_current(
    [&](const auto&, node u) {
        p.add_node(u);
        if (t.get_degree(u) != 2) {
            // The exploration will stop in the
            // next call to the 'terminate' function.
            p.set_h2(u);
        }
    }
    );
    // stop the traversal as soon as we find a vertex of degree != 2
    bfs.set_terminate(
    [&](const auto&, node u) { return t.get_degree(u) != 2; }
    );
 
    // find all paths starting at vertices of degree != 2
    for (node u = 0; u < n; ++u) {
        if (t.get_degree(u) == 2) { continue; }
 
        if constexpr (std::is_base_of_v<graphs::free_tree, tree_t>) {
            for (node v : t.get_neighbors(u)) {
                expand_branchless_path(t, u, v, bfs, res, p);
            }
        }
        else if constexpr (std::is_base_of_v<graphs::rooted_tree, tree_t>) {
            for (node v : t.get_out_neighbors(u)) {
                expand_branchless_path(t, u, v, bfs, res, p);
            }
            for (node v : t.get_in_neighbors(u)) {
                expand_branchless_path(t, u, v, bfs, res, p);
            }
        }
    }
 
    return res;
}
 
} // -- namespace detail
} // -- namespace lal