union_find.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/rooted_tree.hpp>
#include <lal/graphs/free_tree.hpp>
#include <lal/detail/graphs/traversal.hpp>
 
namespace lal {
namespace detail {
 
template <class tree_t>
void update_unionfind_after_add_edge
(
    const tree_t& t,
    const node u,
    const node v,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    // '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 uint64_t size_u = root_size[root_u];
    const uint64_t size_v = root_size[root_v];
    const uint64_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
    BFS<tree_t> bfs(t);
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    bfs.set_process_current(
    [&](const BFS<tree_t>&, const node w) -> void { root_of[w] = new_root; }
    );
    bfs.set_visited(parent, 1); // avoid going backwards
    bfs.start_at(child);
}
 
template <class tree_t>
void update_unionfind_after_add_edges
(
    const tree_t& t,
    const edge_list& edges,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    const auto n = t.get_num_nodes();
 
    // These two variables are used by the BFS object, but are initialized
    // in the for loop before 'start_at' is called.
    uint64_t size_current_root = n + 1;
    node current_root = n + 1;
 
    BFS<tree_t> bfs(t);
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    bfs.set_process_current(
    [&](const auto&, const node w) {
        root_of[w] = current_root;
        ++size_current_root;
    }
    );
 
    for (const auto& [u, v] : edges) {
        if (bfs.node_was_visited(u)) { continue; }
 
        current_root = u;
        size_current_root = 0;
        bfs.start_at(u);
        root_size[current_root] = size_current_root;
    }
}
 
template <class tree_t>
void update_unionfind_after_add_rem_edges_bulk
(
    const tree_t& t,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    const auto n = t.get_num_nodes();
 
    // These two variables are used by the BFS object, but are initialized
    // in the for loop before 'start_at' is called.
    uint64_t size_current_root = n + 1;
    node current_root = n + 1;
 
    BFS<tree_t> bfs(t);
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    bfs.set_process_current(
    [&](const auto&, const node w) {
        root_of[w] = current_root;
        ++size_current_root;
    }
    );
 
    for (node u = 0; u < n; ++u) {
        if (bfs.node_was_visited(u)) { continue; }
 
        current_root = u;
        size_current_root = 0;
        bfs.start_at(u);
        root_size[current_root] = size_current_root;
    }
}
 
template <class tree_t>
void update_unionfind_after_remove_edge
(
    const tree_t& t,
    const node u,
    const node v,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
        );
 
// 'u' and 'v' are connected
#if defined DEBUG
    assert(root_of[u] == root_of[v]);
#endif
 
    const uint64_t size_uv = root_size[root_of[u]];
 
    BFS<tree_t> bfs(t);
 
    // --- update u's info ---
 
    // Update the root of the vertices reachable from 'u'.
    //   (also calculate the size of u's component)
    uint64_t size_cc_u = 0;
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    bfs.set_process_current(
    [&](const auto&, const node w) -> void {
        root_of[w] = u;
        ++size_cc_u;
    }
    );
    bfs.start_at(u);
    root_of[u] = u;
    root_size[u] = size_cc_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&, const node w) -> void {
        root_of[w] = v;
    }
    );
    bfs.start_at(v);
    root_of[v] = v;
    root_size[v] = size_uv - size_cc_u;
}
 
template <class tree_t>
void update_unionfind_after_remove_edges
(
    const tree_t& t,
    [[maybe_unused]] const edge_list& edges,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    const auto n = t.get_num_nodes();
 
    // These two variables are used by the BFS object, but are initialized
    // in the for loop before 'start_at' is called.
    uint64_t size_current_cc = n + 1;
    node current_root = n + 1;
 
    BFS<tree_t> bfs(t);
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    bfs.set_process_current(
    [&](const auto&, const node w) {
        root_of[w] = current_root;
        ++size_current_cc;
    }
    );
 
    for (const auto& [u, v] : edges) {
        if (not bfs.node_was_visited(u)) {
            current_root = u;
            size_current_cc = 0;
            bfs.start_at(u);
            root_size[u] = size_current_cc;
        }
 
        if (not bfs.node_was_visited(v)) {
            current_root = v;
            size_current_cc = 0;
            bfs.start_at(v);
            root_size[v] = size_current_cc;
        }
    }
}
 
// -----------------------------------------------------------------------------
 
template <class tree_t>
void update_unionfind_before_remove_edges_incident_to
(
    BFS<tree_t>& bfs,
    const node v,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    uint64_t size_cc_v = 0;
    bfs.set_process_current(
    [&](const auto&, const node w) -> void {
        root_of[w] = v;
        ++size_cc_v;
    }
    );
    bfs.start_at(v);
 
    root_of[v] = v;
    root_size[v] = size_cc_v;
}
 
template <typename tree_t>
void update_unionfind_before_remove_edges_incident_to
(
    const tree_t& t,
    const node u,
    node * const root_of,
    uint64_t * const root_size
)
noexcept
{
    static_assert(
        std::is_base_of_v<graphs::free_tree, tree_t> or
        std::is_base_of_v<graphs::rooted_tree, tree_t>
    );
 
    BFS<tree_t> bfs(t);
    bfs.set_use_rev_edges( BFS<tree_t>::is_graph_directed );
    // avoid going 'backwards', we need to go 'onwards'
    bfs.set_visited(u, 1);
 
    if constexpr (std::is_base_of_v<graphs::free_tree, tree_t>) {
        for (const node v : t.get_neighbors(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            update_unionfind_before_remove_edges_incident_to
                (bfs, v, root_of, root_size);
        }
    }
    else {
        for (const node v : t.get_in_neighbors(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            update_unionfind_before_remove_edges_incident_to
                (bfs, v, root_of, root_size);
        }
        for (const node v : t.get_out_neighbors(u)) {
            // update size and root of the edges from v onwards
            // (onwards means "in the direction u -> v"
            update_unionfind_before_remove_edges_incident_to
                (bfs, v, root_of, root_size);
        }
    }
 
    root_of[u] = u;
    root_size[u] = 1;
}
 
} // -- namespace detail
} // -- namespace lal