utils.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/
 *
 *     Juan Luis Esteban (esteban@cs.upc.edu)
 *         LOGPROG: Logics and Programming Research Group
 *         Office 110, Omega building
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://www.cs.upc.edu/~esteban/
 *
 *     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 <optional>
#include <cassert>
#endif
#include <vector>
 
// lal includes
#include <lal/linear_arrangement.hpp>
#include <lal/graphs/rooted_tree.hpp>
#include <lal/detail/array.hpp>
#include <lal/iterators/E_iterator.hpp>
#include <lal/detail/graphs/size_subtrees.hpp>
#include <lal/detail/sorting/counting_sort.hpp>
#include <lal/detail/properties/tree_centroid.hpp>
#include <lal/detail/macros/basic_convert.hpp>
#include <lal/detail/linarr/D/Dopt_utils.hpp>
 
namespace lal {
namespace detail {
 
namespace Dmin_utils {
 
/* ************************************************************************** */
/* ---------------------- INTERVAL-based methods ---------------------------- */
 
/* The following namespace contains functions for the interval-based algorithms
 * to calculate the planar and projective minimum sum of edge lengths.
 */
 
template <bool make_arrangement>
[[nodiscard]] uint64_t arrange
(
    const std::vector<std::vector<node_size>>& L,
    const node r,
    const Dopt_utils::place r_place,
    position ini,
    position fin,
    linear_arrangement& arr
)
noexcept
{
#if defined DEBUG
    assert(ini <= fin);
#endif
 
    // the children and the sizes of the subtrees of 'r'
    const auto& children_size_of_r = L[r];
 
    // -- place the children --
 
    // work out the starting side of the first-largest subtree
    Dopt_utils::side roots_side =
        r_place == Dopt_utils::PLACE_RIGHT_OF ?
            Dopt_utils::RIGHT_SIDE :
            Dopt_utils::LEFT_SIDE;
 
    // size of the intervals from the root to the left end
    uint64_t acc_size_left = 0;
    // size of the intervals from the root to the right end
    uint64_t acc_size_right = 0;
 
    // number of intervals to the left of the root
    uint64_t n_intervals_left = 0;
    // number of intervals to the right of the root
    uint64_t n_intervals_right = 0;
 
    // sum of the optimal D for every subtree +
    // the length of the edge from 'r' to its parent (if any)
    uint64_t D = 0;
    // total sum of lengths of edges from 'r' to 'vi' without the anchor
    uint64_t d = 0;
 
#if defined DEBUG
    // store the size of the previous subtree (previous in the lists's sorted)
    std::optional<uint64_t> previous_size;
#endif
 
    // while placing the children calculate the
    // length of the edge from 'r' to vertex 'vi'
    // LARGEST to SMALLEST
    for (const auto& [vi, ni] : children_size_of_r) {
 
#if defined DEBUG
        // ensure that the list is sorted non-increasingly
        if (previous_size) {
            assert(*previous_size >= ni);
        }
        previous_size = {ni};
#endif
 
        // recursive call: make the interval of 'vi'
        D +=
        arrange<make_arrangement>(
            L, vi,
            (roots_side == Dopt_utils::LEFT_SIDE ? Dopt_utils::PLACE_LEFT_OF : Dopt_utils::PLACE_RIGHT_OF),
            (make_arrangement ? (roots_side == Dopt_utils::LEFT_SIDE ? ini : fin - ni + 1) : 0),
            (make_arrangement ? (roots_side == Dopt_utils::LEFT_SIDE ? ini + ni - 1 : fin) : 0),
            arr
        );
 
        // accumulate size of interval
        d += ni*(roots_side == Dopt_utils::LEFT_SIDE ? n_intervals_left : n_intervals_right);
        // add length of edge over root 'r'
        d += 1;
 
        // number of intervals to the left and right of the root
        n_intervals_left += roots_side;
        n_intervals_right += Dopt_utils::other_side(roots_side);
 
        // accumulate size of subtree rooted at vi
        acc_size_left += roots_side*ni;
        acc_size_right += Dopt_utils::other_side(roots_side)*ni;
 
        // update limits of the embedding
        if constexpr (make_arrangement) {
        ini += roots_side*ni;
        fin -= Dopt_utils::other_side(roots_side)*ni;
        }
 
        // change side
        roots_side = Dopt_utils::other_side(roots_side);
    }
 
#if defined DEBUG
    if constexpr (make_arrangement) {
    assert(ini == fin);
    }
#endif
    if constexpr (make_arrangement) {
    arr.assign(r, ini);
    }
 
    // accumulate the length of the edge from 'r' to its parent (if any)
    D +=
    (r_place == Dopt_utils::PLACE_NONE_OF ? 0 :
     r_place == Dopt_utils::PLACE_LEFT_OF ? acc_size_right : acc_size_left);
 
    return D + d;
}
 
template <bool make_arrangement>
[[nodiscard]] inline uint64_t arrange_projective
(
    const uint64_t n,
    const std::vector<std::vector<node_size>>& L,
    const node r,
    linear_arrangement& arr
)
noexcept
{
    return arrange<make_arrangement>(L, r, Dopt_utils::PLACE_NONE_OF, 0, n-1, arr);
}
 
/* ************************************************************************** */
/* ----------------- DISPLACEMENT-based methods namespace ------------------- */
 
/* The following namespace contains functions for the interval-based algorithms
 * to calculate the planar and projective minimum sum of edge lengths.
 */
 
 
template <bool make_arrangement>
[[nodiscard]] uint64_t embed_branch
(
    const std::vector<std::vector<node_size>>& L,
    const node v,
    int64_t base,
    const int64_t dir,
    array<int64_t>& rel_pos
)
noexcept
{
    const auto& Cv = L[v];
    uint64_t cost_branch = 0;
 
    uint64_t before = 0;
    uint64_t after = 0;
    uint64_t under_anchor = 0;
 
    // LARGEST to SMALLEST
    // (only at even positions of the list, which are indexed at odd values...)
    for (std::size_t i = 1; i < Cv.size(); i += 2) {
        under_anchor += Cv[i].size;
    }
 
    if constexpr (make_arrangement) {
    base += dir*(to_int64(under_anchor) + 1);
    }
 
    cost_branch += under_anchor;
 
    // Index of the positions of Cv. The interval it iterates is [Cv.size(), 1]
    // (and not the usual [Cv.size()-1, 0]) to ensure we are using the right
    // parities (even/odd).
    uint64_t i = Cv.size();
 
    // SMALLEST to LARGEST
    for (auto it = Cv.rbegin(); it != Cv.rend(); ++it, --i) {
#if defined DEBUG
        assert(i <= Cv.size());
#endif
 
        const auto& [vi, ni] = *it;
 
        cost_branch +=
        embed_branch<make_arrangement>(
            L, vi,
            make_arrangement ?
                Dopt_utils::is_even(i) ? base - dir*to_int64(before) : base + dir*to_int64(after)
                : 0
            ,
            make_arrangement ?
                Dopt_utils::is_even(i) ? -dir : dir
                : 0
            ,
            rel_pos
        );
        cost_branch += ( Dopt_utils::is_even(i) ? before : after );
 
        before += (Dopt_utils::is_even(i) ? ni : 0);
        after += (Dopt_utils::is_even(i) ? 0 : ni);
 
        cost_branch += 1;
    }
 
    if constexpr (make_arrangement) {
        rel_pos[v] = base;
    }
    return cost_branch;
}
 
template <bool make_arrangement>
[[nodiscard]] uint64_t embed
(
    const std::vector<std::vector<node_size>>& L,
    const node r,
    linear_arrangement& arr
)
noexcept
{
    const uint64_t n = L.size();
    uint64_t D = 0;
 
    array<int64_t> rel_pos(n, 0);
    uint64_t left_sum = 0;
    uint64_t right_sum = 0;
 
    uint64_t i = L[r].size();
 
    // SMALLEST to LARGEST
    for (auto it = L[r].rbegin(); it != L[r].rend(); ++it, --i) {
        const auto& [vi, ni] = *it;
#if defined DEBUG
        assert(i <= L[r].size());
#endif
 
        D +=
        embed_branch<make_arrangement>(
            L, vi,
            make_arrangement ?
                Dopt_utils::is_even(i) ? to_int64(right_sum) : -to_int64(left_sum)
                : 0
            ,
            make_arrangement ?
                Dopt_utils::is_even(i) ? to_int64(1) : to_int64(-1)
                : 0
            ,
            rel_pos
        );
        D += ( Dopt_utils::is_even(i) ? right_sum : left_sum );
 
        right_sum += (Dopt_utils::is_even(i) ? ni : 0);
        left_sum += (Dopt_utils::is_even(i) ? 0 : ni);
 
        D += 1;
    }
 
    // the '-1' is used to offset the positions from [1,n] to [0,n-1]
    if constexpr (make_arrangement) {
    arr.assign(r, left_sum + 1 - 1);
    rel_pos[r] = 0;
    for (node v = 0; v < n; ++v) {
        const int64_t pos = to_int64(arr[node_t{r}]) + rel_pos[v];
#if defined DEBUG
        assert(pos >= 0);
#endif
        arr.assign(v, to_uint64(pos));
    }
    }
 
    return D;
}
 
} // -- namespcae Dmin_utils
} // -- namespace detail
} // -- namespace lal