// Copyright (c) 2016, the SDSL Project Authors.  All rights reserved.
// Please see the AUTHORS file for details.  Use of this source code is governed
// by a BSD license that can be found in the LICENSE file.
/*!\file k2_tree.hpp
 * \brief k2_tree.hpp contains a compact k^2-tree.
 * \author Francisco Montoto
 */
#ifndef INCLUDED_SDSL_K2_TREE
#define INCLUDED_SDSL_K2_TREE

#include <algorithm>
#include <assert.h>
#include <cmath>
#include <cstdint>
#include <deque>
#include <iosfwd>
#include <memory>
#include <queue>
#include <stdexcept>
#include <string>
#include <tuple>
#include <type_traits>
#include <vector>

#include <sdsl/cereal.hpp>
#include <sdsl/int_vector.hpp>
#include <sdsl/int_vector_buffer.hpp>
#include <sdsl/io.hpp>
#include <sdsl/k2_tree_helper.hpp>
#include <sdsl/structure_tree.hpp>
#include <sdsl/util.hpp>

//! Namespace for the succint data structure library
namespace sdsl
{
//! A k^2-tree
/*! A k^2-tree is a compact tree structure to represent a web graph. The
 *  structure takes advantage of large empty areas of the adjacency matrix of
 *  the graph.
 *
 *  \par References
 *      [1] Brisaboa, N. R., Ladra, S., & Navarro, G. (2009, August):
 *          k2-trees for compact web graph representation. In International
 *          Symposium on String Processing and Information Retrieval
 *          (pp. 18-30). Springer Berlin Heidelberg.
 */

template <uint8_t k, typename t_bv = bit_vector, typename t_rank = typename t_bv::rank_1_type>
class k2_tree
{
public:
    typedef k2_tree_ns::idx_type idx_type;
    typedef k2_tree_ns::size_type size_type;

private:
    //! Bit array to store all the bits of the tree, except those in the
    //! last level.
    t_bv k_t;
    //! Bit array to store the last level of the tree.
    t_bv k_l;

    t_rank k_t_rank;

    uint8_t k_k;
    uint16_t k_height;

protected:
    void build_from_matrix(std::vector<std::vector<int>> const & matrix)
    {
        // Makes the size a power of k.
        int simulated_size = std::pow(k, k_height);
        std::vector<std::deque<bit_vector>> acc(k_height + 1);

        k2_tree_ns::_build_from_matrix<bit_vector>(matrix, k, simulated_size, k_height, 1, 0, 0, acc);

        size_type t_size = 0;
        size_type l_size = 0;
        for (int i = 1; i < k_height; i++)
            for (auto it = acc[i].begin(); it != acc[i].end(); it++)
                t_size += (*it).size();

        for (auto it = acc[k_height].begin(); it != acc[k_height].end(); it++)
            l_size += (*it).size();

        bit_vector k_t_(t_size, 0);
        bit_vector k_l_(l_size, 0);

        int n = 0;
        for (int j = 1; j < k_height; j++)
            for (auto it = acc[j].begin(); it != acc[j].end(); it++)
                for (unsigned i = 0; i < (*it).size(); i++)
                {
                    // TODO there should be a better way to do this
                    k_t_.set_int(n, (*it).get_int(i, 1), 1);
                    n++;
                }
        n = 0;
        for (auto it = acc[k_height].begin(); it != acc[k_height].end(); it++)
            for (unsigned i = 0; i < (*it).size(); i++)
            {
                // TODO there should be a better way to do this
                k_l_.set_int(n * 1, (*it).get_int(i, 1), 1);
                n++;
            }

        k2_tree_ns::build_template_vector<t_bv>(k_t_, k_l_, k_t, k_l);
    }

    /*! Recursive function to retrieve list of neighbors.
     *
     *  \param n Size of the submatrix in the next recursive step.
     *  \param row Row of interest in the current submatrix, this is the
     *      row corresponding the node we are looking neighbors for.
     *  \param col Column offset of the current submatrix in the global
     *      matrix.
     *  \param level Position in k_t:k_l (k_l appended to k_t) of the node
     *      or leaf being processed at this step.
     *  \param acc Accumulator to store the neighbors found.
     */
    void _neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector<idx_type> & acc) const
    {
        if (level >= k_t.size())
        { // Last level
            if (k_l[level - k_t.size()] == 1)
                acc.push_back(col);
            return;
        }

        if (k_t[level] == 1)
        {
            idx_type y = k_t_rank(level + 1) * std::pow(k_k, 2) + k_k * std::floor(row / static_cast<double>(n));
            for (unsigned j = 0; j < k_k; j++)
                _neigh(n / k_k, row % n, col + n * j, y + j, acc);
        }
    }

    /*! Recursive function to retrieve list of reverse neighbors.
     *
     *  \param n Size of the submatrix in the next recursive step.
     *  \param row Row offset of the current submatrix in the global matrix.
     *  \param col Column of interest in the current submatrix, this is the
     *      column corresponding the node we are looking reverse neighbors
     *      for.
     *  \param level Position in k_t:k_l (k_l appended to k_t) of the node
     *      or leaf being processed at this step.
     *  \param acc Accumulator to store the neighbors found.
     */
    void _reverse_neigh(size_type n, idx_type row, idx_type col, size_type level, std::vector<idx_type> & acc) const
    {
        if (level >= k_t.size())
        { // Last level
            if (k_l[level - k_t.size()] == 1)
            {
                acc.push_back(row);
            }
            return;
        }

        if (k_t[level] == 1)
        {
            idx_type y = k_t_rank(level + 1) * std::pow(k_k, 2) + std::floor(col / static_cast<double>(n));
            for (unsigned j = 0; j < k_k; j++)
                _reverse_neigh(n / k_k, row + n * j, col % n, y + j * k_k, acc);
        }
    }

    //! Build a tree from an edges collection
    /*! This method takes a vector of edges describing the graph
     *  and the graph size. And takes linear time over the amount of
     *  edges to build the k_2 representation.
     *  \param edges A vector with all the edges of the graph, it can
     *               not be empty.
     *  \param size Size of the graph, all the nodes in edges must be
     *              within 0 and size ([0, size[).
     */
    void build_from_edges(std::vector<std::tuple<idx_type, idx_type>> & edges, const size_type size)
    {

        typedef std::tuple<idx_type, idx_type, size_type, idx_type, idx_type> t_part_tuple;

        k_k = k;
        k_height = std::ceil(std::log(size) / std::log(k_k));
        k_height = k_height > 1 ? k_height : 1; // If size == 0
        size_type k_2 = std::pow(k_k, 2);
        bit_vector k_t_ = bit_vector(k_2 * k_height * edges.size(), 0);
        bit_vector k_l_;

        std::queue<t_part_tuple> q;
        idx_type t = 0, last_level = 0;
        idx_type i, j, r_0, c_0, it, c, r;
        size_type l = std::pow(k_k, k_height - 1);
        std::vector<idx_type> pos_by_chunk(k_2 + 1, 0);

        q.push(t_part_tuple(0, edges.size(), l, 0, 0));

        while (!q.empty())
        {
            std::vector<idx_type> amount_by_chunk(k_2, 0);
            std::tie(i, j, l, r_0, c_0) = q.front();
            q.pop();
            // Get size for each chunk
            for (it = i; it < j; it++)
                amount_by_chunk
                    [k2_tree_ns::get_chunk_idx(std::get<0>(edges[it]), std::get<1>(edges[it]), c_0, r_0, l, k_k)] += 1;
            if (l == 1)
            {
                if (last_level == 0)
                {
                    last_level = t;
                    k_l_ = bit_vector(k_t_.size() - last_level, 0);
                    k_t_.resize(last_level);
                    k_t_.shrink_to_fit();
                    last_level = 1; // if t was 0
                    t = 0;          // Restart counter as we're storing at k_l_ now.
                }
                for (it = 0; it < k_2; it++, t++)
                    if (amount_by_chunk[it] != 0)
                        k_l_[t] = 1;
                // At l == 1 we do not put new elements at the queue.
                continue;
            }

            // Set starting position in the vector for each chunk
            pos_by_chunk[0] = i;
            for (it = 1; it < k_2; it++)
                pos_by_chunk[it] = pos_by_chunk[it - 1] + amount_by_chunk[it - 1];
            // To handle the last case when it = k_2 - 1
            pos_by_chunk[k_2] = j;
            // Push to the queue every non zero elements chunk
            for (it = 0; it < k_2; it++, t++)
                // If not empty chunk, set bit to 1
                if (amount_by_chunk[it] != 0)
                {
                    r = it / k_k;
                    c = it % k_k;
                    k_t_[t] = 1;
                    q.push(t_part_tuple(pos_by_chunk[it], pos_by_chunk[it + 1], l / k_k, r_0 + r * l, c_0 + c * l));
                }
            idx_type chunk;

            // Sort edges' vector
            for (unsigned ch = 0; ch < k_2; ch++)
            {
                idx_type be = ch == 0 ? i : pos_by_chunk[ch - 1];
                for (it = pos_by_chunk[ch]; it < be + amount_by_chunk[ch];)
                {
                    chunk = k2_tree_ns::get_chunk_idx(std::get<0>(edges[it]), std::get<1>(edges[it]), c_0, r_0, l, k_k);

                    if (pos_by_chunk[chunk] != it)
                        std::iter_swap(edges.begin() + it, edges.begin() + pos_by_chunk[chunk]);
                    else
                        it++;
                    pos_by_chunk[chunk]++;
                }
            }
        }
        k_l_.resize(t);
        k_l_.shrink_to_fit();
        k2_tree_ns::build_template_vector<t_bv>(k_t_, k_l_, k_t, k_l);

        k_t_rank = t_rank(&k_t);
    }

public:
    k2_tree() = default;

    //! Constructor
    /*! This constructos takes the graph adjacency matrix.
     *  The time complexity for this constructor is linear in the matrix
     *  size
     *  \param matrix Adjacency matrix of the graph. It must be a binary
     *      square matrix.
     */
    k2_tree(std::vector<std::vector<int>> & matrix)
    {
        if (matrix.size() < 1)
        {
            throw std::logic_error("Matrix has no elements");
        }
        std::vector<bit_vector> t;
        k_k = k;
        if (matrix.size() < k_k)
            k_height = 1;
        else // height = log_k n
            k_height = std::ceil(std::log(matrix.size()) / std::log(k_k));

        build_from_matrix(matrix);

        k_t_rank = t_rank(&k_t);
    }

    //! Constructor
    /*! This constructos takes a vector of edges describing the graph
     *  and the graph size. And takes linear time over the amount of
     *  edges to build the k_2 representation.
     *  \param edges A vector with all the edges of the graph, it can
     *               not be empty.
     *  \param size Size of the graph, all the nodes in edges must be
     *              within 0 and size ([0, size[).
     */
    k2_tree(std::vector<std::tuple<idx_type, idx_type>> & edges, const size_type size)
    {
        assert(size > 0);
        assert(edges.size() > 0);

        build_from_edges(edges, size);
    }

    //! Constructor
    /*! This constructos expects a filename prefix. Two serialized
     *  int_vectors have to be present at filename.x and filename.y.
     *  Each pair x,y describes an edge of the graph, from the node x
     *  to the node y.
     *  \param filename String with the prefix of the files filename.x,
     *					filename.y each of them containing a serialized
     *					int_vector<>.
     *  \param size Size of the graph, all the nodes in the edges defined
     *				by the files must be within 0 and size ([0, size[). If
     *				size==0, the size will be taken as the max node
     *				in the edges.
     */
    k2_tree(std::string filename, size_type size = 0)
    {
        int_vector_buffer<> buf_x(filename + ".x", std::ios::in);
        int_vector_buffer<> buf_y(filename + ".y", std::ios::in);

        assert(buf_x.size() == buf_y.size());
        assert(buf_x.size() > 0);

        std::vector<std::tuple<idx_type, idx_type>> edges;
        edges.reserve(buf_x.size());

        if (size == 0)
        {
            size_type max = 0;
            for (auto v : buf_x)
                max = std::max(static_cast<size_type>(v), max);
            for (auto v : buf_y)
                max = std::max(static_cast<size_type>(v), max);
            size = max + 1;
        }

        for (uint64_t i = 0; i < buf_x.size(); i++)
            edges.push_back(std::tuple<idx_type, idx_type>{buf_x[i], buf_y[i]});

        build_from_edges(edges, size);
    }

    k2_tree(k2_tree const & tr) : k_t(tr.k_t), k_l(tr.k_l), k_k(tr.k_k), k_height(tr.k_height), k_t_rank(tr.k_t_rank)
    {
        k_t_rank.set_vector(&k_t);
    }

    k2_tree(k2_tree && tr)
    {
        *this = std::move(tr);
    }

    //! Move assignment operator
    k2_tree & operator=(k2_tree && tr)
    {
        if (this != &tr)
        {
            k_t = std::move(tr.k_t);
            k_l = std::move(tr.k_l);
            k_k = std::move(tr.k_k);
            k_height = std::move(tr.k_height);
            k_t_rank = std::move(tr.k_t_rank);
            k_t_rank.set_vector(&k_t);
        }
        return *this;
    }

    //! Assignment operator
    k2_tree & operator=(k2_tree & tr)
    {
        if (this != &tr)
        {
            k2_tree tmp(tr);
            *this = std::move(tmp);
        }
        return *this;
    }

    //! Equal operator
    bool operator==(k2_tree const & tr) const
    {
        // TODO check the rank support equality?
        if (k_k != tr.k_k || k_height != tr.k_height)
            return false;
        if (k_t.size() != tr.k_t.size() || k_l.size() != tr.k_l.size())
            return false;
        for (unsigned i = 0; i < k_t.size(); i++)
            if (k_t[i] != tr.k_t[i])
                return false;
        for (unsigned i = 0; i < k_l.size(); i++)
            if (k_l[i] != tr.k_l[i])
                return false;
        return true;
    }

    t_bv get_t()
    {
        return k_t;
    }

    t_bv get_l()
    {
        return k_l;
    }

    //! Indicates wheter node j is adjacent to node i or not.
    /*!
     *  \param i Node i.
     *  \param j Node j.
     *  \returns true if there is an edge going from node i to node j,
     *           false otherwise.
     */
    bool adj(idx_type i, idx_type j) const
    {
        if (k_t.size() == 0 && k_l.size() == 0)
            return false;
        size_type n = std::pow(k_k, k_height - 1);
        size_type k_2 = std::pow(k_k, 2);
        idx_type col, row;

        // This is duplicated to avoid an extra if at the loop. As idx_type
        // is unsigned and rank has an offset of one, is not possible to run
        // k_t_rank with zero as parameter at the first iteration.
        row = std::floor(i / static_cast<double>(n));
        col = std::floor(j / static_cast<double>(n));
        i = i % n;
        j = j % n;
        idx_type level = k_k * row + col;
        n = n / k_k;

        while (level < k_t.size())
        {
            if (k_t[level] == 0)
                return false;
            row = std::floor(i / static_cast<double>(n));
            col = std::floor(j / static_cast<double>(n));
            i = i % n;
            j = j % n;
            level = k_t_rank(level + 1) * k_2 + k_k * row + col;
            n = n / k_k;
        }

        return k_l[level - k_t.size()] == 1;
    }

    //! Returns a list of neighbors of node i.
    /*!
     *  \param i Node to get neighbors from.
     *  \returns A list of neighbors of node i.
     */
    std::vector<idx_type> neigh(idx_type i) const
    {
        std::vector<idx_type> acc{};
        if (k_l.size() == 0 && k_t.size() == 0)
            return acc;
        size_type n = static_cast<size_type>(std::pow(k_k, k_height)) / k_k;
        idx_type y = k_k * std::floor(i / static_cast<double>(n));
        for (unsigned j = 0; j < k_k; j++)
            _neigh(n / k_k, i % n, n * j, y + j, acc);
        return acc;
    }

    //! Returns a list of reverse neighbors of node i.
    /*!
     *  \param i Node to get reverse neighbors from.
     *  \returns A list of reverse neighbors of node i.
     */
    std::vector<idx_type> reverse_neigh(idx_type i) const
    {
        std::vector<idx_type> acc{};
        if (k_l.size() == 0 && k_t.size() == 0)
            return acc;
        // Size of the first square division
        size_type n = static_cast<size_type>(std::pow(k_k, k_height)) / k_k;
        idx_type y = std::floor(i / static_cast<double>(n));
        for (unsigned j = 0; j < k_k; j++)
            _reverse_neigh(n / k_k, n * j, i % n, y + j * k_k, acc);

        return acc;
    }

    //! Serialize to a stream
    /*! Serialize the k2_tree data structure
     *  \param out Outstream to write the k2_tree.
     *  \param v
     *  \param string_name
     *  \returns The number of written bytes.
     */
    size_type serialize(std::ostream & out, structure_tree_node * v = nullptr, std::string name = "") const
    {
        structure_tree_node * child = structure_tree::add_child(v, name, util::class_name(*this));
        size_type written_bytes = 0;

        written_bytes += k_t.serialize(out, child, "t");
        written_bytes += k_l.serialize(out, child, "l");
        written_bytes += k_t_rank.serialize(out, child, "t_rank");
        written_bytes += write_member(k_k, out, child, "k");
        written_bytes += write_member(k_height, out, child, "height");
        structure_tree::add_size(child, written_bytes);
        return written_bytes;
    }

    //! Load from istream
    /*! Serialize the k2_tree from the given istream.
     *  \param istream Stream to load the k2_tree from.
     */
    void load(std::istream & in)
    {
        k_t.load(in);
        k_l.load(in);
        k_t_rank.load(in);
        k_t_rank.set_vector(&k_t);
        read_member(k_k, in);
        read_member(k_height, in);
    }

    //!\brief Serialise (save) via cereal
    template <typename archive_t>
    void CEREAL_SAVE_FUNCTION_NAME(archive_t & ar) const
    {
        ar(CEREAL_NVP(k_k));
        ar(CEREAL_NVP(k_height));
        ar(CEREAL_NVP(k_t));
        ar(CEREAL_NVP(k_l));
        ar(CEREAL_NVP(k_t_rank));
    }

    //!\brief Load via cereal
    template <typename archive_t>
    typename std::enable_if<cereal::traits::is_output_serializable<k2_tree, archive_t>::value, void>::type
    CEREAL_LOAD_FUNCTION_NAME(archive_t & ar)
    {
        ar(CEREAL_NVP(k_k));
        ar(CEREAL_NVP(k_height));
        ar(CEREAL_NVP(k_t));
        ar(CEREAL_NVP(k_l));
        ar(CEREAL_NVP(k_t_rank));
        k_t_rank.set_vector(&k_t);
    }
};
} // namespace sdsl

#endif
