is_tree.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
 
// lal includes
#include <lal/internal/graphs/traversal.hpp>
 
namespace lal {
namespace internal {
 
/*
 * @brief Returns true if, and only if, the graph is a tree.
 *
 * By definition, an undirected graph is a tree if it does not contain
 * cycles and has one single connected component. Note that isloated nodes
 * count as single connected components. Directed graphs are allowed.
 * @param g Input graph.
 */
template<class G>
bool is_graph_a_tree(const G& g) {
    const auto n = g.get_num_nodes();
 
    // simple cases
    if (n <= 1) { return true; }
    if (n == 2) { return g.get_num_edges() == 1; }
    if (n == 3) { return g.get_num_edges() == 2; }
 
    // check exact amount of edges
    if (g.get_num_edges() != g.get_num_nodes() - 1) { return false; }
 
    // visit all vertices, if all vertices
    // were visited then the graph is a tree
    BFS<G> bfs(g);
    bfs.set_use_rev_edges(g.is_directed());
    bfs.start_at(0);
    return bfs.all_visited();
}
 
} // -- namespace internal
} // -- namespace lal