size_subtrees.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
#include <functional>
 
// lal includes
#include <lal/graphs/rooted_tree.hpp>
#include <lal/graphs/free_tree.hpp>
#include <lal/internal/macros.hpp>
 
namespace lal {
namespace internal {
 
namespace __lal {
 
/*
 * @brief Calculate the size of every subtree of the tree @e t.
 *
 * @param t Input tree.
 * @param u Parent node (the first call should be an invalid value (e.g., n+1)).
 * @param v Next node in the exploration of the tree.
 * @param sizes The size of the subtree rooted at every reachable node
 * from @e r.
 * @pre Parameter @e sizes has size the number of vertices.
 */
template<
    class T,
    std::enable_if_t<
        std::is_base_of_v<graphs::rooted_tree, T> ||
        std::is_base_of_v<graphs::free_tree, T>,
    bool> = true
>
void get_size_subtrees
(const T& t, const node u, const node v, uint32_t * const sizes)
{
    sizes[v] = 1;
 
    if constexpr (std::is_base_of_v<graphs::rooted_tree, T>) {
        for (const node w : t.get_out_neighbours(v)) {
            if (w == u) { continue; }
            get_size_subtrees(t, v, w, sizes);
            sizes[v] += sizes[w];
        }
        for (const node w : t.get_in_neighbours(v)) {
            if (w == u) { continue; }
            get_size_subtrees(t, v, w, sizes);
            sizes[v] += sizes[w];
        }
    }
    else {
        for (const node w : t.get_neighbours(v)) {
            if (w == u) { continue; }
            get_size_subtrees(t, v, w, sizes);
            sizes[v] += sizes[w];
        }
    }
}
 
} // -- namespace __lal
 
/*
 * @brief Calculate the size of every subtree of tree @e t.
 *
 * The method starts calculating the sizes at node @e r. Since rooted trees
 * have directed edges, starting at a node different from the tree's root
 * may not calculate every subtree's size.
 * @param t Input rooted tree.
 * @param r Start calculating sizes of subtrees at this node.
 * @param vis Mark nodes as visited as the algorithm goes on.
 * @param sizes The size of the subtree rooted at every reachable node from @e r.
 * @pre Parameter @e sizes has size the number of vertices.
 */
template<
    class T,
    std::enable_if_t<
        std::is_base_of_v<graphs::rooted_tree, T> ||
        std::is_base_of_v<graphs::free_tree, T>,
    bool> = true
>
void get_size_subtrees
(const T& t, node r, uint32_t * const sizes)
{
#if defined DEBUG
    assert(sizes != nullptr);
#endif
    __lal::get_size_subtrees(t, t.get_num_nodes(), r, sizes);
}
 
namespace __lal {
 
/*
 * @brief Calculates the values \f$s(u,v)\f$ for the edges \f$(s,t)\f$ reachable
 * from \f$v\f$ in the subtree \f$T^u_v\f$.
 *
 * This function calculates the 'map' relating each edge \f$(u, v)\f$ with the
 * size of the subtree rooted at \f$v\f$ with respect to the hypothetical root
 * \f$u\f$. This is an implementation of the algorithm described in
 * \cite Hochberg2003a (proof of lemma 8 (page 63), and the beginning of
 * section 6 (page 65)).
 *
 * Notice that the values are not stored in an actual map (std::map, or similar),
 * but in a vector.
 * @tparam tree_type Type of the tree. Must be 'rooted_tree' or 'free_tree'.
 * @tparam Iterated_Type The type that will store the sizes.
 * @tparam Iterator_Type Iterator type on a container of Iterated_Type that stores
 * the list of bidirectional sizes.
 * @param t Input tree.
 * @param n Size of the connected component to which edge \f$(u,v)\f$ belongs to.
 * @param u First vertex of the edge.
 * @param v Second vertex of the edge.
 * @param it An iterator to the container that holds the size values. Such
 * container must have size equal to twice the number of edges in the connected
 * component of @e u and @e v.
 * @pre Vertices @e u and @e v belong to the same connected component.
 */
template<
    class tree_type,
    typename Iterator_Type,
    std::enable_if_t<
        (
            std::is_base_of_v<graphs::rooted_tree, tree_type> ||
            std::is_base_of_v<graphs::free_tree, tree_type>
        )
        && is_pointer_iterator_v<std::pair<edge,uint32_t>, Iterator_Type>
        ,
        bool
    > = true
>
uint32_t calculate_bidirectional_sizes
(const tree_type& t, const uint32_t n, const node u, const node v, Iterator_Type& it)
{
    uint32_t s = 1;
    if constexpr (std::is_base_of_v<graphs::rooted_tree, tree_type>) {
        for (const node w : t.get_out_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, it);
        }
        for (const node w : t.get_in_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, it);
        }
    }
    else {
        for (const node w : t.get_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, it);
        }
    }
 
    *it++ = std::make_pair(edge(u,v), s);
    *it++ = std::make_pair(edge(v,u), n - s);
    return s;
}
 
/*
 * @brief Calculates the values \f$s(u,v)\f$ for the edges \f$(s,t)\f$ reachable
 * from \f$v\f$ in the subtree \f$T^u_v\f$.
 *
 * This function calculates the 'map' relating each edge \f$(u, v)\f$ with the
 * size of the subtree rooted at \f$v\f$ with respect to the hypothetical root
 * \f$u\f$. This is an implementation of the algorithm described in
 * \cite Hochberg2003a (proof of lemma 8 (page 63), and the beginning of
 * section 6 (page 65)).
 *
 * Notice that the values are not stored in an actual map (std::map, or similar),
 * but in a vector.
 * @tparam tree_type Type of the tree. Must be 'rooted_tree' or 'free_tree'.
 * @tparam Iterated_Type The type that will store the sizes.
 * @tparam Iterator_Type Iterator type on a container of Iterated_Type that stores
 * the list of bidirectional sizes.
 * @param t Input tree.
 * @param n Size of the connected component to which edge \f$(u,v)\f$ belongs to.
 * @param u First vertex of the edge.
 * @param v Second vertex of the edge.
 * @param F Function to assign the edge and the size to the Iterated_Type pointed
 * by @e it.
 * @param it An iterator to the container that holds the size values. Such
 * container must have size equal to twice the number of edges in the connected
 * component of @e u and @e v.
 * @pre Vertices @e u and @e v belong to the same connected component.
 */
template<
    class tree_type,
    typename Iterated_Type,
    typename Iterator_Type,
    std::enable_if_t<
        (
            std::is_base_of_v<graphs::rooted_tree, tree_type> ||
            std::is_base_of_v<graphs::free_tree, tree_type>
        )
        &&
        is_pointer_iterator_v<Iterated_Type, Iterator_Type>
        ,
        bool
    > = true
>
uint32_t calculate_bidirectional_sizes(
    const tree_type& t,
    const uint32_t n,
    const node u, const node v,
    const std::function<void (Iterated_Type&, const edge&, uint32_t)> F,
    Iterator_Type& it
)
{
    uint32_t s = 1;
    if constexpr (std::is_base_of_v<graphs::rooted_tree, tree_type>) {
        for (const node w : t.get_out_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, F, it);
        }
        for (const node w : t.get_in_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, F, it);
        }
    }
    else {
        for (const node w : t.get_neighbours(v)) {
            if (w == u) { continue; }
            s += calculate_bidirectional_sizes(t,n, v, w, F, it);
        }
    }
 
    F(*it, edge(u,v), s);
    ++it;
    F(*it, edge(v,u), n - s);
    ++it;
    return s;
}
 
} // -- namespace __lal
 
/*
 * @brief Calculates the values \f$s(u,v)\f$ for the edges \f$(u,v)\f$ reachable
 * from vertex @e x.
 *
 * Calculates the values \f$s(u,v)\f$ for all edges \f$(u,v)\f$ in linear time.
 * This is an implementation of the algorithm described in \cite Hochberg2003a
 * (proof of lemma 8 (page 63), and the beginning of section 6 (page 65)).
 *
 * For any edge \f$(u,v)\f$ let \f$T^u\f$ be the tree \f$T\f$ rooted at \f$u\f$.
 * The value \f$s(u,v)\f$ is the size of the subtree of \f$T^u\f$ rooted at \f$v\f$,
 * i.e., \f$|V(T^u_v)|\f$.
 *
 * Example of usage (mind the vector! its initial size is \f$2*m\f$).
 *
 @code
 const free_tree t = ... ;
 vector<pair<edge,uint32_t>> sizes_edges(2*t.get_num_edges());
 auto it = sizes_edges.begin();
 internal::calculate_bidirectional_sizes(t, t.get_num_nodes(), 0, it);
 @endcode
 *
 * @tparam tree_type Type of the tree. Must be 'rooted_tree' or 'free_tree'.
 * @tparam Iterated_Type The type that will store the sizes.
 * @tparam Iterator_Type Iterator type on a container of Iterated_Type that stores
 * the list of bidirectional sizes.
 * @param t Input tree
 * @param n Number of nodes in the connected component of vertex @e x
 * @param x Node of the connected component for which we want to calculate the
 * bidirectional sizes
 * @param it An iterator to the container that holds the size values. Such
 * container must have size equal to twice the number of edges in the connected
 * component of @e u and @e v.
 */
template<
    class tree_type,
    typename Iterator_Type,
    std::enable_if_t<
        (
            std::is_base_of_v<graphs::rooted_tree, tree_type> ||
            std::is_base_of_v<graphs::free_tree, tree_type>
        )
        && is_pointer_iterator_v<std::pair<edge,uint32_t>, Iterator_Type>
        ,
        bool
    > = true
>
void calculate_bidirectional_sizes
(const tree_type& t, const uint32_t n, const node x, Iterator_Type& it)
{
    if constexpr (std::is_base_of_v<graphs::rooted_tree, tree_type>) {
        for (node y : t.get_out_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterator_Type>
            (t,n, x, y, it);
        }
        for (node y : t.get_in_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterator_Type>
            (t,n, x, y, it);
        }
    }
    else {
        for (node y : t.get_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterator_Type>
            (t,n, x, y, it);
        }
    }
}
 
/*
 * @brief Calculates the values \f$s(u,v)\f$ for the edges \f$(u,v)\f$ reachable
 * from vertex @e x.
 *
 * Calculates the values \f$s(u,v)\f$ for all edges \f$(u,v)\f$ in linear time.
 * This is an implementation of the algorithm described in \cite Hochberg2003a
 * (proof of lemma 8 (page 63), and the beginning of section 6 (page 65)).
 *
 * For any edge \f$(u,v)\f$ let \f$T^u\f$ be the tree \f$T\f$ rooted at \f$u\f$.
 * The value \f$s(u,v)\f$ is the size of the subtree of \f$T^u\f$ rooted at \f$v\f$,
 * i.e., \f$|V(T^u_v)|\f$.
 *
 * Example of usage (mind the vector! its initial size is \f$2*m\f$).
 *
 @code
 const free_tree t = ... ;
 vector<pair<edge,uint32_t>> sizes_edges(2*t.get_num_edges());
 auto it = sizes_edges.begin();
 internal::calculate_bidirectional_sizes(t, t.get_num_nodes(), 0, it);
 @endcode
 *
 * @tparam tree_type Type of the tree. Must be 'rooted_tree' or 'free_tree'.
 * @tparam Iterated_Type The type that will store the sizes.
 * @tparam Iterator_Type Iterator type on a container of Iterated_Type that stores
 * the list of bidirectional sizes.
 * @param t Input tree
 * @param n Number of nodes in the connected component of vertex @e x
 * @param x Node of the connected component for which we want to calculate the
 * bidirectional sizes
 * @param F Function to assign the edge and the size to the Iterated_Type pointed
 * by @e it.
 * @param it An iterator to the container that holds the size values. Such
 * container must have size equal to twice the number of edges in the connected
 * component of @e u and @e v.
 */
template<
    class tree_type,
    typename Iterated_Type,
    typename Iterator_Type,
    std::enable_if_t<
        (
            std::is_base_of_v<graphs::rooted_tree, tree_type> ||
            std::is_base_of_v<graphs::free_tree, tree_type>
        )
        && is_pointer_iterator_v<Iterated_Type, Iterator_Type>
        ,
        bool
    > = true
>
void calculate_bidirectional_sizes(
    const tree_type& t,
    const uint32_t n, const node x,
    const std::function<void (Iterated_Type&, const edge&, uint32_t)> F,
    Iterator_Type& it
)
{
    if constexpr (std::is_base_of_v<graphs::rooted_tree, tree_type>) {
        for (node y : t.get_out_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterated_Type, Iterator_Type>
            (t,n, x, y, F, it);
        }
        for (node y : t.get_in_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterated_Type, Iterator_Type>
            (t,n, x, y, F, it);
        }
    }
    else {
        for (node y : t.get_neighbours(x)) {
            __lal::calculate_bidirectional_sizes<tree_type, Iterated_Type, Iterator_Type>
            (t,n, x, y, F, it);
        }
    }
}
 
} // -- namespace internal
} // -- namespace lal