LIS.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef LIS_H
# define LIS_H
 
# include <algorithm>
# include <cstddef>
# include <limits>
# include <utility>
 
# include <ahFunction.H>
# include <tpl_array.H>
 
namespace Aleph
{
  template <typename T>
  struct LIS_Result
  {
    size_t length = 0;        
    Array<T> subsequence;     
  };
 
  namespace lis_detail
  {
    template <typename T, class Compare>
    [[nodiscard]] inline size_t
    lower_bound_pos(const Array<T> & tails, const T & value, Compare cmp)
    {
      size_t lo = 0, hi = tails.size();
      while (lo < hi)
        {
          const size_t mid = lo + (hi - lo) / 2;
          if (cmp(tails[mid], value))
            lo = mid + 1;
          else
            hi = mid;
        }
      return lo;
    }
 
    template <typename T, class Compare>
    [[nodiscard]] inline size_t
    upper_bound_pos(const Array<T> & tails, const T & value, Compare cmp)
    {
      size_t lo = 0, hi = tails.size();
      while (lo < hi)
        {
          const size_t mid = lo + (hi - lo) / 2;
          if (cmp(value, tails[mid]))
            hi = mid;
          else
            lo = mid + 1;
        }
      return lo;
    }
  } // namespace lis_detail
 
 
  template <typename T, class Compare = Aleph::less<T>>
  [[nodiscard]] LIS_Result<T>
  longest_increasing_subsequence(const Array<T> & seq,
                                 Compare cmp = Compare())
  {
    const size_t n = seq.size();
    if (n == 0)
      return LIS_Result<T>{0, Array<T>()};
 
    // tails[i] = smallest tail element for IS of length i+1
    Array<T> tails;
    tails.reserve(n);
 
    // parent[i] = index of predecessor of seq[i] in best IS ending at seq[i]
    Array<size_t> parent = Array<size_t>::create(n);
    // pos[i] = index in seq of the element at tails[i]
    Array<size_t> tail_idx;
    tail_idx.reserve(n);
 
    for (size_t i = 0; i < n; ++i)
      {
        const size_t lo = lis_detail::lower_bound_pos(tails, seq[i], cmp);
 
        if (lo == tails.size())
          {
            tails.append(seq[i]);
            tail_idx.append(i);
          }
        else
          {
            tails[lo] = seq[i];
            tail_idx[lo] = i;
          }
 
        parent(i) = lo > 0 ? tail_idx[lo - 1]
                            : std::numeric_limits<size_t>::max();
      }
 
    // reconstruct
    const size_t lis_len = tails.size();
    Array<T> result = Array<T>::create(lis_len);
    size_t idx = tail_idx[lis_len - 1];
    for (size_t k = lis_len; k > 0; --k)
      {
        result(k - 1) = seq[idx];
        idx = parent(idx);
      }
 
    return LIS_Result<T>{lis_len, std::move(result)};
  }
 
 
  template <typename T, class Compare = Aleph::less<T>>
  [[nodiscard]] size_t
  lis_length(const Array<T> & seq, Compare cmp = Compare())
  {
    const size_t n = seq.size();
    if (n == 0)
      return 0;
 
    Array<T> tails;
    tails.reserve(n);
 
    for (size_t i = 0; i < n; ++i)
      {
        const size_t lo = lis_detail::lower_bound_pos(tails, seq[i], cmp);
 
        if (lo == tails.size())
          tails.append(seq[i]);
        else
          tails[lo] = seq[i];
      }
 
    return tails.size();
  }
 
 
  template <typename T, class Compare = Aleph::less<T>>
  [[nodiscard]] LIS_Result<T>
  longest_nondecreasing_subsequence(const Array<T> & seq,
                                    Compare cmp = Compare())
  {
    const size_t n = seq.size();
    if (n == 0)
      return LIS_Result<T>{0, Array<T>()};
 
    Array<T> tails;
    tails.reserve(n);
 
    Array<size_t> parent = Array<size_t>::create(n);
    Array<size_t> tail_idx;
    tail_idx.reserve(n);
 
    for (size_t i = 0; i < n; ++i)
      {
        const size_t pos = lis_detail::upper_bound_pos(tails, seq[i], cmp);
 
        if (pos == tails.size())
          {
            tails.append(seq[i]);
            tail_idx.append(i);
          }
        else
          {
            tails[pos] = seq[i];
            tail_idx[pos] = i;
          }
 
        parent(i) = pos > 0 ? tail_idx[pos - 1]
                            : std::numeric_limits<size_t>::max();
      }
 
    const size_t len = tails.size();
    Array<T> result = Array<T>::create(len);
    size_t idx = tail_idx[len - 1];
    for (size_t k = len; k > 0; --k)
      {
        result(k - 1) = seq[idx];
        idx = parent(idx);
      }
 
    return LIS_Result<T>{len, std::move(result)};
  }
} // namespace Aleph
 
# endif // LIS_H