// 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.
#ifndef SDSL_CONSTRUCT_SA_SE
#define SDSL_CONSTRUCT_SA_SE

#include <cmath>
#include <fstream>
#include <iostream>
#include <string>

#include <sdsl/int_vector.hpp>
#include <sdsl/io.hpp>
#include <sdsl/rank_support.hpp>
#include <sdsl/select_support.hpp>

namespace sdsl
{

template <class int_vector_type>
uint64_t _get_next_lms_position(int_vector_type & text, uint64_t i)
{
    if (i >= text.size() - 3) { return text.size() - 1; }
    // text[i] is S-TYP or L-TYP
    uint64_t ci = text[i], cip1 = text[i + 1];
    while (ci <= cip1)
    {
        ++i;
        ci = cip1;
        cip1 = text[i + 1];
    }
    // text[i] is L-TYP or S-TYP
    uint64_t candidate = i + 1;
    while (ci >= cip1)
    {
        if (ci > cip1)
        {
            if (i + 1 == text.size() - 1) { return text.size() - 1; }
            candidate = i + 1;
        }
        ++i;
        ci = cip1;
        cip1 = text[i + 1];
    }
    return candidate;
}

inline void _construct_sa_IS(int_vector<> & text,
                             int_vector<> & sa,
                             std::string & filename_sa,
                             size_t n,
                             size_t text_offset,
                             size_t sigma,
                             uint64_t recursion)
{
    uint64_t buffersize = 1024 * 1024 / 8;

    size_t name = 0;
    size_t number_of_lms_strings = 0;
    std::string filename_c_array = tmp_file(filename_sa, "_c_array" + util::to_string(recursion));
    // Phase 1
    {
        std::vector<uint64_t> bkt(sigma, 0);
        // Step 1 - Count characters into c array
        // TODO: better create this in higher recursion-level
        for (size_t i = 0; i < n; ++i) { ++bkt[text[text_offset + i]]; }

        // Step 1.5 save them into cached_external_array
        int_vector_buffer<> c_array(filename_c_array, std::ios::out, buffersize, 64);
        for (size_t c = 0; c < sigma; ++c) { c_array[c] = bkt[c]; }

        // Step 2 Calculate End-Pointer of Buckets
        bkt[0] = 0;
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + bkt[c]; }

        // Step 3 - Insert S*-positions into correct bucket of SA but not in correct order inside the buckets
        for (size_t i = n - 2, was_s_typ = 1; i < n; --i)
        {
            if (text[text_offset + i] > text[text_offset + i + 1])
            {
                if (was_s_typ)
                {
                    sa[bkt[text[text_offset + i + 1]]--] = i + 1;
                    ++number_of_lms_strings;
                    was_s_typ = 0;
                }
            }
            else if (text[text_offset + i] < text[text_offset + i + 1])
            {
                was_s_typ = 1;
            }
        }

        // Step 4 - Calculate Begin-Pointer of Buckets
        bkt[0] = 0;
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + c_array[c - 1]; }

        // Step 5 - Scan from Left-To-Right to induce L-Types
        for (size_t i = 0; i < n; ++i)
        {
            if (sa[i] > 0 and text[text_offset + sa[i]] <= text[text_offset + sa[i] - 1])
            { // faster than if(sa[i]>0 and bkt_beg[text[ sa[i]-1 ]] > i)
                sa[bkt[text[text_offset + sa[i] - 1]]++] = sa[i] - 1;
                sa[i] = 0;
            }
        }

        // Step 6 - Scan from Right-To-Left to induce S-Types
        bkt[0] = 0;
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + c_array[c]; }
        c_array.close();

        for (size_t i = n - 1, endpointer = n; i < n; --i)
        {
            if (sa[i] > 0)
            {
                if (text[text_offset + sa[i] - 1] <= text[text_offset + sa[i]])
                { // faster than if(bkt_end[text[ sa[i]-1 ]] < i)
                    sa[bkt[text[text_offset + sa[i] - 1]]--] = sa[i] - 1;
                }
                else
                {
                    sa[--endpointer] = sa[i];
                }
                sa[i] = 0;
            }
        }

        // Step 7 - Determine length of LMS-Strings
        for (size_t i = n - 2, end = n - 2, was_s_typ = 1; i < n; --i)
        {
            if (text[text_offset + i] > text[text_offset + i + 1])
            {
                if (was_s_typ)
                {
                    sa[(i + 1) >> 1] = end - i;
                    end = i + 1;
                    was_s_typ = 0;
                }
            }
            else if (text[text_offset + i] < text[text_offset + i + 1])
            {
                was_s_typ = 1;
            }
        }

        // Step 8 - Rename
        for (size_t i = n - number_of_lms_strings + 1, cur_pos = 0, cur_len = 0, last_pos = n - 1, last_len = 1; i < n;
             ++i)
        {
            cur_pos = sa[i];
            cur_len = sa[(cur_pos >> 1)];
            if (cur_len == last_len)
            {
                size_t l = 0;
                while (l < cur_len and text[text_offset + cur_pos + l] == text[text_offset + last_pos + l]) { ++l; }
                if (l >= cur_len) { --name; }
            }
            sa[(cur_pos >> 1)] = ++name;
            last_pos = cur_pos;
            last_len = cur_len;
        }
    }

    // Step 9 - Calculate SA of new string - in most cases recursive
    if (name + 1 < number_of_lms_strings)
    {
        // Move Names to the end
        for (size_t i = 0, t = n - number_of_lms_strings; i < (n >> 1); ++i)
        {
            if (sa[i] > 0)
            {
                sa[t++] = sa[i];
                sa[i] = 0;
            }
        }
        sa[n - 1] = 0;

        // Recursive call
        std::string filename_sa_rec = tmp_file(filename_sa, "_sa_rec" + util::to_string(recursion + 1));
        _construct_sa_IS(sa,
                         sa,
                         filename_sa_rec,
                         number_of_lms_strings,
                         n - number_of_lms_strings,
                         name + 1,
                         recursion + 1);

        for (size_t i = n - 2, endpointer = n - 1, was_s_typ = 1; i < n; --i)
        {
            if (text[text_offset + i] > text[text_offset + i + 1])
            {
                if (was_s_typ)
                {
                    sa[endpointer--] = i + 1;
                    was_s_typ = 0;
                }
            }
            else if (text[text_offset + i] < text[text_offset + i + 1])
            {
                was_s_typ = 1;
            }
        }

        // Sort S*-positions in correct order into SA
        for (size_t i = 0; i < number_of_lms_strings; ++i)
        {
            size_t pos = sa[i];
            sa[i] = sa[n - number_of_lms_strings + pos];
            sa[n - number_of_lms_strings + pos] = 0;
        }
    }
    else
    {
        // Move s*-Positions to front
        sa[0] = n - 1;
        for (size_t i = 1; i < number_of_lms_strings; ++i)
        {
            sa[i] = sa[n - number_of_lms_strings + i];
            sa[n - number_of_lms_strings + i] = 0;
        }
        // Clear lex. names
        for (size_t i = number_of_lms_strings; i < (n >> 1); ++i) { sa[i] = 0; }
    }

    // Phase 3
    {
        // Step 10 - Count characters into c array

        // Step 11 - Calculate End-Pointer of Buckets
        int_vector_buffer<> c_array(filename_c_array, std::ios::in, buffersize, 64);
        std::vector<uint64_t> bkt(sigma, 0);
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + c_array[c]; }

        // Step 12 - Move S*-positions in correct order into SA
        for (size_t i = number_of_lms_strings - 1; i < n; --i)
        {
            size_t pos = sa[i];
            sa[i] = 0;
            sa[bkt[text[text_offset + pos]]--] = pos;
        }

        // Step 13 - Calculate Begin-Pointer of Buckets
        bkt[0] = 0;
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + c_array[c - 1]; }

        // Step 14 - Scan from Left-To-Right to induce L-Types
        for (size_t i = 0; i < n; ++i)
        {
            if (sa[i] > 0 and text[text_offset + sa[i]] <= text[text_offset + sa[i] - 1])
            { // faster than if(sa[i]>0 and bkt_beg[text[ sa[i]-1 ]] > i)
                sa[bkt[text[text_offset + sa[i] - 1]]++] = sa[i] - 1;
            }
        }

        // Step 15 - Scan from Right-To-Left to induce S-Types
        bkt[0] = 0;
        for (size_t c = 1; c < sigma; ++c) { bkt[c] = bkt[c - 1] + c_array[c]; }
        for (size_t i = n - 1; i < n; --i)
        {
            if (sa[i] > 0 and text[text_offset + sa[i] - 1] <= text[text_offset + sa[i]])
            {
                sa[bkt[text[text_offset + sa[i] - 1]]--] = sa[i] - 1;
            }
        }
        c_array.close(true);
    }
}

template <class int_vector_type>
void _construct_sa_se(int_vector_type & text, std::string filename_sa, uint64_t sigma, uint64_t recursion)
{
    std::string filename_text = tmp_file(filename_sa, "_text_rec" + util::to_string(recursion));
    store_to_file(text, filename_text);
    uint64_t n = text.size();
    uint64_t nsize = bits::hi(n) + 1;
    uint8_t int_width = bits::hi(n - 1) + 1;
    uint64_t buffersize = 1024 * 1024 / 8;

    // Step 1 - Scan Text from right to left and count LMS, S and L characters and store lms_positions

    // Define variables
    size_t first_lms_pos = 0;
    size_t number_of_lms_strings = 0;
    size_t bkt_s_last = 0, bkt_s_sum = 0, bound_s = 0, bkt_l_sum = 0;
    int_vector<> C(sigma, 0, int_width);
    int_vector<> bkt_lms(sigma, 0, int_width);
    int_vector<> bkt_s(sigma, 0, int_width);
    int_vector<> bkt_l(sigma, 0, int_width);
    std::string filename_lms_pos_b = tmp_file(filename_sa, "_lms_pos_b" + util::to_string(recursion));
    size_t parts = 10;

    {
        int_vector_buffer<1> lms_pos_b(filename_lms_pos_b, std::ios::out, buffersize, 1);
        uint64_t ci = text[n - 1];
        ++C[ci];
        bool was_s_typ = 1;
        for (size_t i = n - 2; i < n; --i)
        {
            uint64_t cip1 = ci;
            ci = text[i];
            ++C[ci];
            if (was_s_typ)
            {
                ++bkt_s[text[i + 1]];
                if (ci > cip1)
                {
                    ++bkt_lms[cip1];
                    lms_pos_b[i + 1] = 1;
                    ++number_of_lms_strings;
                    first_lms_pos = i + 1;
                    was_s_typ = 0;
                }
            }
            else if (ci < cip1)
            {
                was_s_typ = 1;
            }
        }
        if (was_s_typ) { ++bkt_s[ci]; }
        bkt_l[0] = C[0] - bkt_s[0];
        for (size_t i = 1; i < C.size(); ++i)
        {
            bkt_l[i] = C[i] - bkt_s[i];
            C[i] = C[i] + C[i - 1];
        }
        lms_pos_b.close();
    }

    // Step 2 - Scan Text from right to left and detect LMS-Positions. Sort and write them to disk
    int_vector_buffer<> right(tmp_file(filename_sa, "_right" + util::to_string(recursion)),
                              std::ios::out,
                              buffersize,
                              nsize);
    size_t right_pointer = 0;
    int_vector_buffer<> left(tmp_file(filename_sa, "_left" + util::to_string(recursion)),
                             std::ios::out,
                             buffersize,
                             nsize);
    size_t left_pointer = 0;
    {
        for (size_t i = 0, tmp2 = 0, tmp = 0; i < sigma; ++i)
        {
            tmp += bkt_lms[i];
            bkt_lms[i] = tmp2;
            tmp2 = tmp;
        }
        int_vector_buffer<> lms_positions(tmp_file(filename_sa, "_lms_positions" + util::to_string(recursion)),
                                          std::ios::out,
                                          buffersize,
                                          nsize);
        for (size_t i = n - 2, was_s_typ = 1, ci = text[n - 1]; i < n; --i)
        {
            uint64_t cip1 = ci;
            ci = text[i];
            if (ci > cip1)
            {
                if (was_s_typ)
                {
                    lms_positions.push_back(bkt_lms[cip1]);
                    lms_positions.push_back(i + 1);
                    ++bkt_lms[cip1];
                    was_s_typ = 0;
                }
            }
            else if (ci < cip1)
            {
                was_s_typ = 1;
            }
        }
        util::clear(text);
        {
            // Order lms_positions according to first character
            int_vector<> lms_strings(number_of_lms_strings, 0, int_width);
            for (size_t i = 0; i < lms_positions.size();)
            {
                size_t idx = lms_positions[i++];
                size_t val = lms_positions[i++];
                lms_strings[idx] = val;
            }
            lms_positions.close(true);
            // Store it to file
            left_pointer = 0;
            for (size_t i = 0; i < number_of_lms_strings; ++i)
            {
                left[left_pointer++] = lms_strings[number_of_lms_strings - i - 1];
            }
        }
        load_from_file(text, filename_text);
    }
    left_pointer--;

    // Step 3 - Scan virtual array from left to right
    {
        // prepare bkt_l and backup it into bkt_lms
        for (size_t i = 0, tmp = 0; i < sigma; ++i)
        {
            tmp = bkt_l[i];
            bkt_l[i] = bkt_l_sum;
            bkt_l_sum += tmp;
            bkt_lms[i] = bkt_l[i];
        }

        size_t partsize = bkt_l_sum / parts + 1;

        int_vector<> array(partsize, 0, int_width);
        std::vector<int_vector_buffer<>> cached_array(parts - 1);
        for (size_t i = 0; i < cached_array.size(); ++i)
        {
            cached_array[i] = int_vector_buffer<>(tmp_file(filename_sa,
                                                           "_rightbuffer" + util::to_string(i) + "_" + util::to_string(recursion)),
                                                  std::ios::out,
                                                  buffersize,
                                                  nsize);
        }

        for (size_t c = 0, pos = 0, offset = 0; c < sigma; ++c)
        {
            // begin with array
            for (; pos < bkt_l[c]; ++pos)
            {
                // Load lazy values
                if (pos - offset >= partsize)
                {
                    offset += partsize;
                    for (size_t i = 0, cur_part = pos / partsize - 1; i < cached_array[cur_part].size();)
                    {
                        size_t src = cached_array[cur_part][i++];
                        size_t val = cached_array[cur_part][i++];
                        array[src - offset] = val;
                    }
                    cached_array[pos / partsize - 1].reset();
                }

                size_t idx = array[pos - offset];
                if (idx == 0) { right[right_pointer++] = idx; }
                else
                {
                    size_t symbol = text[idx - 1];
                    if (symbol >= c)
                    {
                        size_t val = idx - 1;
                        size_t src = bkt_l[symbol];
                        bkt_l[symbol] = bkt_l[symbol] + 1;
                        if ((src - offset) / partsize == 0) { array[src - offset] = val; }
                        else
                        {
                            size_t part = src / partsize - 1;
                            cached_array[part].push_back(src);
                            cached_array[part].push_back(val);
                        }
                    }
                    else
                    {
                        right[right_pointer++] = idx;
                    }
                }
            }
            // continue with stack
            while (left_pointer < number_of_lms_strings and text[left[left_pointer]] == c)
            {
                size_t idx = left[left_pointer--];
                --idx;
                size_t symbol = text[idx];

                size_t val = idx;
                size_t src = bkt_l[symbol];
                bkt_l[symbol] = bkt_l[symbol] + 1;
                if ((src - offset) / partsize == 0) { array[src - offset] = val; }
                else
                {
                    size_t part = src / partsize - 1;
                    cached_array[part].push_back(src);
                    cached_array[part].push_back(val);
                }
            }
        }
        for (size_t i = 0; i < cached_array.size(); ++i) { cached_array[i].close(true); }

        // Restore bkt_l from bkt_lms
        for (size_t i = 0; i < sigma; ++i) { bkt_l[i] = bkt_lms[i]; }
    }
    right_pointer--;

    // Step 4 - Scan virtual array from right to left
    left_pointer = 0;
    left.reset();
    {
        // Prepare bkt_s and backup it into bkt_lms
        bkt_s_last = 0, bkt_s_sum = 0;
        for (size_t i = 0; i < sigma; ++i)
        {
            bkt_s_sum += bkt_s[i];
            if (bkt_s[i])
            {
                bkt_s[i] = bkt_s_sum;
                bkt_s_last = bkt_s_sum;
            }
            else
            {
                bkt_s[i] = bkt_s_sum;
            }
            bkt_lms[i] = bkt_s[i];
        }
        bound_s = bkt_s_sum;

        // Determine splitting parameters
        for (size_t i = 0; i < sigma; ++i)
        {
            if (bkt_s[i] > bkt_s_sum / 2)
            {
                bkt_s_sum = bkt_s[i];
                break;
            }
        }

        size_t partsize = bound_s / parts + 1;
        int_vector<> array(partsize, 0, int_width);
        std::vector<int_vector_buffer<>> cached_array(parts - 1);
        for (size_t i = 0; i < cached_array.size(); ++i)
        {
            cached_array[i] = int_vector_buffer<>(tmp_file(filename_sa,
                                                           "_leftbuffer" + util::to_string(i) + "_" + util::to_string(recursion)),
                                                  std::ios::out,
                                                  buffersize,
                                                  nsize);
        }
        for (size_t c = sigma - 1, pos = bkt_s_last - 1, offset = partsize * (parts - 1); c < sigma; --c)
        {
            // begin with array
            for (; pos + 1 > bkt_s[c]; --pos)
            {
                while (pos < offset)
                {
                    // Load buffered values
                    offset -= partsize;
                    for (size_t i = 0, cur_part = offset / partsize; i < cached_array[cur_part].size();)
                    {
                        size_t src = cached_array[cur_part][i++];
                        size_t val = cached_array[cur_part][i++];
                        array[src - offset] = val;
                    }
                    cached_array[offset / partsize].reset();
                }

                size_t idx = array[pos - offset];
                if (idx == 0) { idx = n; }
                --idx;
                size_t symbol = text[idx];
                if (symbol <= c)
                {
                    bkt_s[symbol] = bkt_s[symbol] - 1;
                    size_t val = idx;
                    size_t src = bkt_s[symbol];
                    if (src >= offset) { array[src - offset] = val; }
                    else
                    {
                        size_t part = src / partsize;
                        cached_array[part].push_back(src);
                        cached_array[part].push_back(val);
                    }
                }
                else
                {
                    left[left_pointer++] = array[pos - offset];
                }
            }

            // continue with stack
            while (right_pointer < number_of_lms_strings and text[right[right_pointer]] == c)
            {
                size_t idx = right[right_pointer--];
                if (idx == 0) { idx = n; }
                --idx;
                size_t symbol = text[idx];
                bkt_s[symbol] = bkt_s[symbol] - 1;

                size_t val = idx;
                size_t src = bkt_s[symbol];
                if (src >= offset) { array[src - offset] = val; }
                else
                {
                    size_t part = src / partsize;
                    cached_array[part].push_back(src);
                    cached_array[part].push_back(val);
                }
            }
        }
        for (size_t i = 0; i < cached_array.size(); ++i) { cached_array[i].close(true); }
        // Restore bkt_s from bkt_lms
        for (size_t i = 0; i < sigma; ++i) { bkt_s[i] = bkt_lms[i]; }
    }
    right.buffersize(0);
    right.reset();
    right_pointer = 0;
    --left_pointer;

    // Step 5 - Detect same lms-Strings, write text to file
    int_vector<1> same_lms(number_of_lms_strings, false);
    size_t last_end_pos = first_lms_pos, order = number_of_lms_strings - 1;
    same_lms[number_of_lms_strings - 1] = true;
    for (size_t i = number_of_lms_strings - 2, a = 0, b = 0, last_a = left[number_of_lms_strings - 1];
         i < number_of_lms_strings;
         --i)
    {
        b = last_a;
        a = left[i];
        last_a = a;

        size_t end_pos = _get_next_lms_position(text, a);
        if (end_pos - a == last_end_pos - b)
        {
            while (a < end_pos and text[a] == text[b])
            {
                ++a;
                ++b;
            }
            if (text[a] == text[b])
            {
                same_lms[i] = true;
                --order;
            }
        }
        last_end_pos = end_pos;
    }
    util::clear(text);

    // Step 7 - Create renamed string
    int_vector<> text_rec;
    if (recursion == 0) { text_rec.width((bits::hi(order + 1) + 1)); }
    else
    {
        text_rec.width((bits::hi(number_of_lms_strings + 1) + 1));
    }
    text_rec.resize(number_of_lms_strings);
    util::_set_zero_bits(text_rec);
    {
        if (recursion == 0 and n / 2 * text_rec.width() > 8 * n)
        {
            size_t size_of_part = n / 4 + 3;
            text_rec.resize(size_of_part);
            util::_set_zero_bits(text_rec);
            order = 0;
            for (size_t i = number_of_lms_strings - 1; i < number_of_lms_strings; --i)
            {
                if (!same_lms[i]) { ++order; }
                if (left[i] / 2 >= size_of_part) { text_rec[(left[i] / 2) - size_of_part] = order; }
            }
            std::string filename_text_rec_part2 = tmp_file(filename_sa, "_text_rec_part2" + util::to_string(recursion));
            size_t pos = 0;
            for (size_t i = 0; i < size_of_part; ++i)
            {
                if (text_rec[i] > 0) { text_rec[pos++] = text_rec[i]; }
            }
            text_rec.resize(pos);
            store_to_file(text_rec, filename_text_rec_part2);
            text_rec.resize(size_of_part);
            util::_set_zero_bits(text_rec);
            order = 0;
            for (size_t i = number_of_lms_strings - 1; i < number_of_lms_strings; --i)
            {
                if (!same_lms[i]) { ++order; }
                if (left[i] / 2 < size_of_part) { text_rec[left[i] / 2] = order; }
            }
            pos = 0;
            for (size_t i = 0; i < size_of_part; ++i)
            {
                if (text_rec[i] > 0) { text_rec[pos++] = text_rec[i]; }
            }
            text_rec.resize(number_of_lms_strings);
            int_vector_buffer<> buf(filename_text_rec_part2, std::ios::in, 1024 * 1024);
            for (size_t i = 0; i < buf.size(); ++i) { text_rec[pos++] = buf[i]; }
            buf.close(true);
            text_rec[number_of_lms_strings - 1] = 0;
        }
        else
        {
            text_rec.resize(n / 2 + 1);
            util::_set_zero_bits(text_rec);
            order = 0;
            for (size_t i = number_of_lms_strings - 1; i < number_of_lms_strings; --i)
            {
                if (!same_lms[i]) { ++order; }
                text_rec[left[left_pointer--] / 2] = order;
            }
            for (size_t i = 0, pos = 0; i < text_rec.size(); ++i)
            {
                if (text_rec[i] > 0) { text_rec[pos++] = text_rec[i]; }
            }
            text_rec[number_of_lms_strings - 1] = 0;
            text_rec.resize(number_of_lms_strings);
        }
    }
    util::clear(same_lms);
    left.buffersize(0);
    left.reset();

    // Step 8 - Determine complete LMS order (recursivly)
    int_vector<> isa_rec;
    std::string filename_sa_rec = tmp_file(filename_sa, "_sa_rec" + util::to_string(recursion + 1));
    if (text_rec.size() > order + 1)
    {
        if (recursion == 0)
        {
            memory_monitor::event("begin _construct_sa");
            _construct_sa_se<int_vector<>>(text_rec, filename_sa_rec, order + 1, recursion + 1);
            memory_monitor::event("end   _construct_sa");
        }
        else
        {
            text_rec.resize(text_rec.size() * 2);
            for (size_t i = 0; i < number_of_lms_strings; ++i)
            {
                text_rec[number_of_lms_strings + i] = text_rec[i];
                text_rec[i] = 0;
            }
            memory_monitor::event("begin sa_simple");
            _construct_sa_IS(text_rec,
                             text_rec,
                             filename_sa_rec,
                             number_of_lms_strings,
                             number_of_lms_strings,
                             order + 1,
                             recursion + 1);
            memory_monitor::event("end   sa_simple");
            // SA' in first half, S' in second half
            text_rec.resize(number_of_lms_strings);
            store_to_file(text_rec, filename_sa_rec);
        }
    }
    else
    {
        isa_rec = std::move(text_rec);
    }

    // Step 9 - Initiate left for scan in step 12
    if (isa_rec.size() > 0)
    {
        // isa_rec exists //TODO test if its better to create sa_rec
        // TODO always enough memory? in memory: isa_rec, lms_pos_b, select_support, tmp_left, leftbuffer
        // load bit_vector lms_positions and create select support
        bit_vector lms_pos_b(n);
        load_from_file(lms_pos_b, filename_lms_pos_b);
        sdsl::remove(filename_lms_pos_b);
        select_support_mcl<> lms_select_support;            // select_support for bit_vector
        util::init_support(lms_select_support, &lms_pos_b); // Create select_support
        // write left
        int_vector<> tmp_left(number_of_lms_strings, 0, int_width);
        for (size_t i = number_of_lms_strings - 1; i < number_of_lms_strings; --i)
        {
            size_t idx = isa_rec[i];
            size_t val = lms_select_support.select(i + 1); // TODO test alternative without select support: look for 1
                                                           // in lms_pos_b (backwards)
            tmp_left[idx] = val;
        }
        util::clear(lms_select_support);
        util::clear(lms_pos_b);
        util::clear(isa_rec);
        // write to left
        left.buffersize(buffersize);
        left_pointer = 0;
        for (; left_pointer < number_of_lms_strings; ++left_pointer)
        {
            left[left_pointer] = tmp_left[number_of_lms_strings - left_pointer - 1];
        }
        left_pointer--;
        util::clear(tmp_left);
    }
    else
    {
        left.buffersize(buffersize);
        left_pointer = 0;
        {
            // load bit_vector lms_positions and create select support
            bit_vector lms_pos_b(n);
            load_from_file(lms_pos_b, filename_lms_pos_b);
            sdsl::remove(filename_lms_pos_b);
            select_support_mcl<> lms_select_support;            // select_support for bit_vector
            util::init_support(lms_select_support, &lms_pos_b); // create select_support
            // write to left sa_rec buffered
            int_vector_buffer<> sa_rec_buf(filename_sa_rec, std::ios::in, buffersize, nsize);
            for (uint64_t i = 0; i < sa_rec_buf.size(); ++i)
            {
                uint64_t pos = lms_select_support.select(sa_rec_buf[i] + 1);
                left[number_of_lms_strings - 1 - left_pointer++] = pos;
            }
            sa_rec_buf.close(true);
            left_pointer--;
        }
        // TODO test sa_rec unbuffered in recursion level 1 -> space still good?
    }

    // Step 10 - Reload text
    load_from_file(text, filename_text);
    sdsl::remove(filename_text);

    // Step 12 - Scan virtual array from left to right second time
    right.buffersize(buffersize);
    right_pointer = 0;
    int_vector_buffer<> cached_sa(filename_sa, std::ios::out, buffersize, nsize);
    size_t sa_pointer = 0;
    {
        size_t partsize = bkt_l_sum / parts + 1;
        int_vector<> array(partsize, 0, int_width);
        std::vector<int_vector_buffer<>> cached_array(parts - 1);
        for (size_t i = 0; i < cached_array.size(); ++i)
        {
            cached_array[i] = int_vector_buffer<>(tmp_file(filename_sa,
                                                           "_rightbuffer" + util::to_string(i) + "_" + util::to_string(recursion)),
                                                  std::ios::out,
                                                  buffersize,
                                                  nsize);
        }

        for (size_t c = 0, pos = 0, offset = 0; c < sigma; ++c)
        {
            // begin with array
            for (; pos < bkt_l[c]; ++pos)
            {
                // Load lazy values
                if (pos - offset >= partsize)
                {
                    offset += partsize;
                    for (size_t i = 0, cur_part = pos / partsize - 1; i < cached_array[cur_part].size();)
                    {
                        size_t src = cached_array[cur_part][i++];
                        size_t val = cached_array[cur_part][i++];
                        array[src - offset] = val;
                    }
                    cached_array[pos / partsize - 1].reset();
                }
                size_t idx = array[pos - offset];
                if (idx == 0)
                {
                    cached_sa[sa_pointer++] = idx;
                    right[right_pointer++] = idx;
                }
                else
                {
                    size_t symbol = text[idx - 1];
                    cached_sa[sa_pointer++] = idx;
                    if (symbol >= c)
                    {
                        size_t val = idx - 1;
                        size_t src = bkt_l[symbol];
                        bkt_l[symbol] = bkt_l[symbol] + 1;
                        if ((src - offset) / partsize == 0) { array[src - offset] = val; }
                        else
                        {
                            size_t part = src / partsize - 1;
                            cached_array[part].push_back(src);
                            cached_array[part].push_back(val);
                        }
                    }
                    else
                    {
                        right[right_pointer++] = idx;
                    }
                }
            }
            sa_pointer = C[c];
            // continue with stack
            while (left_pointer < number_of_lms_strings and text[left[left_pointer]] == c)
            {
                size_t idx = left[left_pointer--];
                if (idx == 0) { idx = n; }
                --idx;
                size_t symbol = text[idx];
                size_t val = idx;
                size_t src = bkt_l[symbol];
                bkt_l[symbol] = bkt_l[symbol] + 1;
                if ((src - offset) / partsize == 0) { array[src - offset] = val; }
                else
                {
                    size_t part = src / partsize - 1;
                    cached_array[part].push_back(src);
                    cached_array[part].push_back(val);
                }
            }
        }
        for (size_t i = 0; i < cached_array.size(); ++i) { cached_array[i].close(true); }
    }
    left.close(true);
    right_pointer--;

    // Step 13 - Scan virtual array from right to left second time
    {
        size_t partsize = bound_s / parts + 1;

        int_vector<> array(partsize, 0, int_width);
        std::vector<int_vector_buffer<>> cached_array(parts - 1);
        for (size_t i = 0; i < cached_array.size(); ++i)
        {
            cached_array[i] = int_vector_buffer<>(tmp_file(filename_sa,
                                                           "_leftbuffer" + util::to_string(i) + "_" + util::to_string(recursion)),
                                                  std::ios::out,
                                                  buffersize,
                                                  nsize);
            //		cached_array_pointer[i] = 0;
        }
        for (size_t c = sigma - 1, pos = bkt_s_last - 1, offset = partsize * (parts - 1); c < sigma; --c)
        {
            // begin with array
            assert(c < C.size());
            sa_pointer = C[c] - 1;
            for (; pos + 1 > bkt_s[c]; --pos)
            {
                while (pos < offset)
                {
                    // Load buffered values
                    offset -= partsize;
                    for (size_t i = 0, cur_part = offset / partsize; i < cached_array[cur_part].size();)
                    {
                        size_t src = cached_array[cur_part][i++];
                        size_t val = cached_array[cur_part][i++];
                        assert((src - offset) < array.size());
                        array[src - offset] = val;
                    }
                    assert((offset / partsize) < parts - 1);
                    cached_array[offset / partsize].reset();
                }

                assert((pos - offset) < array.size());
                size_t idx = array[pos - offset];
                if (idx == 0) { idx = n; }
                --idx;
                assert((idx) < text.size());
                size_t symbol = text[idx];
                if (symbol <= c)
                {
                    if (idx == n - 1) { cached_sa[sa_pointer--] = 0; }
                    else
                    {
                        cached_sa[sa_pointer--] = idx + 1;
                    }
                    assert((symbol) < bkt_s.size());
                    bkt_s[symbol] = bkt_s[symbol] - 1;
                    size_t val = idx;
                    size_t src = bkt_s[symbol];
                    if (src >= offset)
                    {
                        assert((src - offset) < array.size());
                        array[src - offset] = val;
                    }
                    else
                    {
                        size_t part = src / partsize;
                        assert(part < parts - 1);
                        cached_array[part].push_back(src);
                        cached_array[part].push_back(val);
                    }
                }
                else
                {
                    if (idx == n - 1) { cached_sa[sa_pointer--] = 0; }
                    else
                    {
                        cached_sa[sa_pointer--] = idx + 1;
                    }
                }
            }
            // continue with stack
            while (right_pointer < number_of_lms_strings and text[right[right_pointer]] == c)
            {
                size_t idx = right[right_pointer--];
                if (idx == 0) { idx = n; }
                --idx;
                size_t symbol = text[idx];
                assert((symbol) < bkt_s.size());
                bkt_s[symbol] = bkt_s[symbol] - 1;

                size_t val = idx;
                size_t src = bkt_s[symbol];
                if (src >= offset)
                {
                    assert((src - offset) < array.size());
                    array[src - offset] = val;
                }
                else
                {
                    size_t part = src / partsize;
                    assert((part) < parts - 1);
                    cached_array[part].push_back(src);
                    cached_array[part].push_back(val);
                }
            }
        }
        for (size_t i = 0; i < cached_array.size(); ++i) { cached_array[i].close(true); }
    }
    right.close(true);
    cached_sa.close();

    return;
}

} // namespace sdsl

#endif
