union_find.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
#if defined DEBUG
#include <cassert>
#endif
 
// lal includes
#include <lal/definitions.hpp>
#include <lal/graphs/rooted_tree.hpp>
#include <lal/graphs/free_tree.hpp>
#include <lal/internal/graphs/traversal.hpp>
 
namespace lal {
namespace internal {
 
/* This function updates the union-find data structure of a tree after the
 * addition of the edge between the edges 'u' and 'v'.
 */
template<typename T>
void UnionFind_update_roots_after_add
(
    const T& t, node u, node v,
    node * const root_of,
    uint32_t * const root_size
)
{
    // 'u' and 'v' are not connected, so they belong to
    // (different) connected components of the tree.
 
    // 'parent' and 'child' determine a direction to be used later.
    // 'new_root' is the new root for one of the vertices
    node parent, child, new_root;
 
    const node root_u = root_of[u];
    const node root_v = root_of[v];
 
    const uint32_t size_u = root_size[root_u];
    const uint32_t size_v = root_size[root_v];
    const uint32_t new_size = size_u + size_v;
 
    if (size_u < size_v) {
        root_of[root_u] = root_v;
        root_of[u] = root_v;
 
        new_root = root_v;
        root_size[new_root] = new_size;
 
        // update roots in the direction of v -> u
        parent = v; child = u;
    }
    else {
        root_of[root_v] = root_u;
        root_of[v] = root_u;
 
        new_root = root_u;
        root_size[new_root] = new_size;
 
        // update roots in the direction of u -> v
        parent = u; child = v;
    }
 
    // update roots of the smaller component,
    // in the direction parent -> child
    internal::BFS<T> bfs(t);
    bfs.set_use_rev_edges(t.is_directed());
    bfs.set_process_current(
    [&](const auto&, node w) -> void { root_of[w] = new_root; }
    );
    bfs.set_visited(parent, 1); // avoid going backwards
    bfs.start_at(child);
}
 
/* This function updates the union-find data structure of a tree after the
 * removal of the edge between the edges 'u' and 'v'.
 */
template<typename T>
void UnionFind_update_roots_after_remove
(
    const T& t, node u, node v,
    node * const root_of,
    uint32_t * const root_size
)
{
    // 'u' and 'v' are connected
#if defined DEBUG
    assert(root_of[u] == root_of[v]);
#endif
 
    const uint32_t size_uv = root_size[root_of[u]];
 
    internal::BFS<T> bfs(t);
 
    // --- update u's info ---
 
    // Update the root of the vertices reachable from 'u'.
    //   (also calculate the size of u's component)
    uint32_t size_u = 0;
    bfs.set_use_rev_edges(t.is_directed());
    bfs.set_process_current(
    [&](const auto&, node w) -> void { root_of[w] = u; ++size_u; }
    );
    bfs.start_at(u);
    root_of[u] = u;
    root_size[u] = size_u;
 
    // --- update v's info ---
 
    // Update the root of the vertices reachable from 'v'.
    //   (there is no need to reset the BFS object)
    bfs.set_process_current(
    [&](const auto&, node w) -> void { root_of[w] = v; }
    );
    bfs.start_at(v);
    root_of[v] = v;
    root_size[v] = size_uv - size_u;
}
 
// -----------------------------------------------------------------------------
 
namespace __lal {
 
/* This function updates the union-find data structure of a tree prior to the
 * removal of the edge (u,v).
 *
 * This function is called by the function
 *      lal::internal::UnionFind_update_roots_before_remove_all_incident_to
 *
 * In particular, it updates the information associated to the vertices found
 * in the direction (u,v).
 */
template<typename T>
void UnionFind_update_roots_before_remove_all_incident_to
(
    const T& t, node u, node v,
    node * const root_of,
    uint32_t * const root_size
)
{
    internal::BFS<T> bfs(t);
    bfs.set_use_rev_edges(t.is_directed());
    // avoid going 'backwards', we need to go 'onwards'
    bfs.set_visited(u, 1);
 
    uint32_t size_cc_v = 0;
    bfs.set_process_current(
    [&](const auto&, node w) -> void { root_of[w] = v; ++size_cc_v; }
    );
    bfs.start_at(v);
 
    root_of[v] = v;
    root_size[v] = size_cc_v;
}
 
} // -- namespace __lal
 
/* This function updates the union-find data structure of a tree prior to the
 * removal of the edges incidents to vertex 'u'.
 */
template<typename T>
void UnionFind_update_roots_before_remove_all_incident_to
(
    const T& t, node u,
    node * const root_of,
    uint32_t * const root_size
)
{
    if constexpr (std::is_base_of_v<graphs::free_tree, T>) {
        for (node v : t.get_neighbours(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            __lal::UnionFind_update_roots_before_remove_all_incident_to(
                t, u, v, root_of, root_size
            );
        }
    }
    else {
        for (node v : t.get_in_neighbours(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            __lal::UnionFind_update_roots_before_remove_all_incident_to(
                t, u, v, root_of, root_size
            );
        }
        for (node v : t.get_out_neighbours(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            __lal::UnionFind_update_roots_before_remove_all_incident_to(
                t, u, v, root_of, root_size
            );
        }
    }
 
    root_of[u] = u;
    root_size[u] = 1;
}
 
} // -- namespace internal
} // -- namespace lal