String_DP.H

/*
                          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

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*/


/** @file String_DP.H
 *  @brief Dynamic-programming algorithms for string similarity and alignment.
 *
 *  Includes:
 *  - Levenshtein edit distance
 *  - Damerau-Levenshtein edit distance (full transposition model)
 *  - LCS (Longest Common Subsequence)
 *  - Longest Common Substring
 *
 *  @example edit_distance_example.cc
 *  @example damerau_levenshtein_example.cc
 *  @example lcs_longest_common_substring_example.cc
 *
 *  @ingroup Algorithms
 *  @author Leandro Rabindranath Leon
 */

# ifndef STRING_DP_H
# define STRING_DP_H

# include <algorithm>
# include <string>
# include <string_view>
# include <array>

# include <tpl_array.H>

namespace Aleph
{
  namespace string_dp_detail
  {
    inline Array<size_t> make_zero_row(const size_t cols)
    {
      Array<size_t> row = Array<size_t>::create(cols);
      for (size_t j = 0; j < cols; ++j)
        row[j] = 0;
      return row;
    }


    inline Array<Array<size_t>> make_zero_matrix(const size_t rows,
                                                 const size_t cols)
    {
      Array<Array<size_t>> mat;
      mat.reserve(rows);
      for (size_t i = 0; i < rows; ++i)
        mat.append(make_zero_row(cols));
      return mat;
    }
  } // namespace string_dp_detail


  /** @brief Levenshtein distance (insert/delete/substitute each cost 1).
   *
   *  @param[in] a First string.
   *  @param[in] b Second string.
   *  @return Edit distance.
   *  @throws None.
   *
   *  @par Complexity
   *  O(nm) time and O(min(n,m)) space.
   */
  inline size_t levenshtein_distance(const std::string_view a,
                                     const std::string_view b)
  {
    if (a.empty())
      return b.size();
    if (b.empty())
      return a.size();

    std::string_view s1 = a;
    std::string_view s2 = b;
    if (s1.size() > s2.size())
      std::swap(s1, s2);

    Array<size_t> prev = Array<size_t>::create(s1.size() + 1);
    Array<size_t> curr = Array<size_t>::create(s1.size() + 1);

    for (size_t j = 0; j <= s1.size(); ++j)
      {
        prev[j] = 0;
        curr[j] = 0;
      }

    for (size_t j = 0; j <= s1.size(); ++j)
      prev[j] = j;

    for (size_t i = 1; i <= s2.size(); ++i)
      {
        curr[0] = i;

        for (size_t j = 1; j <= s1.size(); ++j)
          {
            const size_t cost = s2[i - 1] == s1[j - 1] ? 0 : 1;
            curr[j] = std::min({
                                 prev[j] + 1,
                                 curr[j - 1] + 1,
                                 prev[j - 1] + cost
                               });
          }

        prev.swap(curr);
      }

    return prev[s1.size()];
  }


  /** @brief Alias for Levenshtein distance.
   *
   *  @param[in] a First string.
   *  @param[in] b Second string.
   *  @return Edit distance.
   *  @throws None.
   */
  inline size_t edit_distance(const std::string_view a,
                              const std::string_view b)
  {
    return levenshtein_distance(a, b);
  }


  /** @brief Damerau-Levenshtein distance with adjacent transpositions.
   *
   *  This implementation follows the "full" dynamic-programming model using
   *  last-seen positions and supports multiple transpositions.
   *
   *  @param[in] a First string.
   *  @param[in] b Second string.
   *  @return Damerau-Levenshtein distance.
   *  @throws None.
   *
   *  @par Complexity
   *  O(nm) time and O(nm) space.
   */
  inline size_t damerau_levenshtein_distance(const std::string_view a,
                                             const std::string_view b)
  {
    const size_t n = a.size();
    const size_t m = b.size();

    const size_t inf = n + m;
    Array<Array<size_t>> d =
        string_dp_detail::make_zero_matrix(n + 2, m + 2);

    d[0][0] = inf;
    for (size_t i = 0; i <= n; ++i)
      {
        d[i + 1][1] = i;
        d[i + 1][0] = inf;
      }

    for (size_t j = 0; j <= m; ++j)
      {
        d[1][j + 1] = j;
        d[0][j + 1] = inf;
      }

    std::array<size_t, 256> last_row = {0};

    for (size_t i = 1; i <= n; ++i)
      {
        size_t last_match_col = 0;

        for (size_t j = 1; j <= m; ++j)
          {
            const size_t i1 = last_row[static_cast<unsigned char>(b[j - 1])];
            const size_t j1 = last_match_col;

            size_t cost = 1;
            if (a[i - 1] == b[j - 1])
              {
                cost = 0;
                last_match_col = j;
              }

            d[i + 1][j + 1] = std::min({
                                         d[i][j] + cost,
                                         d[i + 1][j] + 1,
                                         d[i][j + 1] + 1,
                                         d[i1][j1] + (i - i1 - 1) + 1 + (j - j1 - 1)
                                       });
          }

        last_row[static_cast<unsigned char>(a[i - 1])] = i;
      }

    return d[n + 1][m + 1];
  }


  /** @brief Result for Longest Common Subsequence (LCS). */
  struct LCS_Result
  {
    size_t length = 0;        /**< Length of the subsequence */
    std::string subsequence; /**< The subsequence string */
  };


  /** @brief Compute Longest Common Subsequence.
   *
   *  @param[in] a First string.
   *  @param[in] b Second string.
   *  @return LCS length and one optimal subsequence.
   *  @throws None.
   *
   *  @par Complexity
   *  O(nm) time and O(nm) space.
   */
  inline LCS_Result longest_common_subsequence(const std::string_view a,
                                               const std::string_view b)
  {
    const size_t n = a.size();
    const size_t m = b.size();

    Array<Array<size_t>> dp =
        string_dp_detail::make_zero_matrix(n + 1, m + 1);

    for (size_t i = 1; i <= n; ++i)
      for (size_t j = 1; j <= m; ++j)
        if (a[i - 1] == b[j - 1])
          dp[i][j] = dp[i - 1][j - 1] + 1;
        else
          dp[i][j] = std::max(dp[i - 1][j], dp[i][j - 1]);

    std::string seq;
    seq.reserve(dp[n][m]);

    size_t i = n;
    size_t j = m;
    while (i > 0 and j > 0)
      if (a[i - 1] == b[j - 1])
        {
          seq.push_back(a[i - 1]);
          --i;
          --j;
        }
      else if (dp[i - 1][j] >= dp[i][j - 1])
        --i;
      else
        --j;

    std::reverse(seq.begin(), seq.end());

    return LCS_Result{dp[n][m], seq};
  }


  /** @brief Result for longest common substring. */
  struct Longest_Common_Substring_Result
  {
    size_t length = 0;    /**< Length of common substring */
    size_t begin_a = 0;   /**< Start index in first string */
    size_t begin_b = 0;   /**< Start index in second string */
    std::string substring; /**< The common substring */
  };


  /** @brief Compute the longest common substring (contiguous) between two strings.
   *
   *  @param[in] a First string.
   *  @param[in] b Second string.
   *  @return Length, starting indices, and substring.
   *  @throws None.
   *
   *  @par Complexity
   *  O(nm) time and O(m) space.
   */
  inline Longest_Common_Substring_Result
  longest_common_substring(const std::string_view a,
                           const std::string_view b)
  {
    const size_t n = a.size();
    const size_t m = b.size();

    Array<size_t> prev = Array<size_t>::create(m + 1);
    Array<size_t> curr = Array<size_t>::create(m + 1);

    for (size_t j = 0; j <= m; ++j)
      {
        prev[j] = 0;
        curr[j] = 0;
      }

    size_t best_len = 0;
    size_t end_a = 0;
    size_t end_b = 0;

    for (size_t i = 1; i <= n; ++i)
      {
        for (size_t j = 1; j <= m; ++j)
          if (a[i - 1] == b[j - 1])
            {
              curr[j] = prev[j - 1] + 1;
              if (curr[j] > best_len)
                {
                  best_len = curr[j];
                  end_a = i;
                  end_b = j;
                }
            }
          else
            curr[j] = 0;

        prev.swap(curr);
        for (size_t j = 0; j <= m; ++j)
          curr[j] = 0;
      }

    Longest_Common_Substring_Result result;
    result.length = best_len;

    if (best_len == 0)
      {
        result.substring = "";
        return result;
      }

    result.begin_a = end_a - best_len;
    result.begin_b = end_b - best_len;
    result.substring = std::string(a.substr(result.begin_a, best_len));

    return result;
  }
} // namespace Aleph

# endif // STRING_DP_H