String_Search.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_Search.H
 *  @brief Classical pattern searching algorithms over strings.
 *
 *  This header provides single-pattern matching algorithms commonly used in
 *  competitive programming and production text processing:
 *  - Knuth-Morris-Pratt (KMP)
 *  - Z-algorithm
 *  - Boyer-Moore-Horspool
 *  - Rabin-Karp (rolling hash with exact verification)
 *
 *  All APIs return all match positions (0-based), including overlaps.
 *
 *  @example kmp_example.cc
 *  @example z_algorithm_example.cc
 *  @example horspool_example.cc
 *  @example rabin_karp_example.cc
 *
 *  @ingroup Algorithms
 *  @author Leandro Rabindranath Leon
 */

# ifndef STRING_SEARCH_H
# define STRING_SEARCH_H

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

# include <tpl_array.H>

namespace Aleph
{
  namespace string_search_detail
  {
    /** @brief Generate an array of all positions from 0 to text_size.
     *  @param[in] text_size The size of the text.
     *  @return Array of positions.
     */
    inline Array<size_t> all_match_positions(const size_t text_size)
    {
      Array<size_t> matches;
      matches.reserve(text_size + 1);
      for (size_t i = 0; i <= text_size; ++i)
        matches.append(i);
      return matches;
    }


    /** @brief Find a character not present in either string.
     *  @param[in] a First string.
     *  @param[in] b Second string.
     *  @param[out] delimiter The unused character found.
     *  @return true if an unused character was found, false otherwise.
     */
    inline bool find_unused_delimiter(const std::string_view a,
                                      const std::string_view b,
                                      char & delimiter)
    {
      std::array<bool, 256> used{};
      used.fill(false);
      for (const unsigned char c : a)
        used[c] = true;

      for (const unsigned char c : b)
        used[c] = true;

      for (size_t i = 0; i < 256; ++i)
        if (not used[i])
          {
            delimiter = static_cast<char>(i);
            return true;
          }

      return false;
    }


    /** @brief Check if pattern matches text at given position.
     *  @param[in] text The text to search in.
     *  @param[in] pattern The pattern to match.
     *  @param[in] pos The position in text to check.
     *  @return true if matches, false otherwise.
     */
    inline bool equals_at(const std::string_view text,
                          const std::string_view pattern,
                          const size_t pos)
    {
      for (size_t i = 0; i < pattern.size(); ++i)
        if (text[pos + i] != pattern[i])
          return false;
      return true;
    }
  } // namespace string_search_detail


  /** @brief Prefix-function used by KMP.
   *
   *  For each index `i`, returns the length of the longest proper prefix of
   *  `pattern[0..i]` which is also a suffix of `pattern[0..i]`.
   *
   *  @param[in] pattern Pattern to preprocess.
   *  @return Prefix-function array with size `pattern.size()`.
   *  @throws None.
   *
   *  @par Complexity
   *  O(m) time and O(m) space, where `m = pattern.size()`.
   */
  inline Array<size_t> kmp_prefix_function(const std::string_view pattern)
  {
    Array<size_t> pi;
    if (pattern.empty())
      return pi;

    pi = Array<size_t>::create(pattern.size());
    pi[0] = 0;

    size_t j = 0;
    for (size_t i = 1; i < pattern.size(); ++i)
      {
        while (j > 0 and pattern[i] != pattern[j])
          j = pi[j - 1];

        if (pattern[i] == pattern[j])
          ++j;

        pi[i] = j;
      }

    return pi;
  }


  /** @brief Find all occurrences of a pattern using KMP.
   *
   *  @param[in] text Text where matches are searched.
   *  @param[in] pattern Pattern to find.
   *  @return Array with all match start indices (0-based).
   *  @throws None.
   *
   *  @note If `pattern` is empty, returns all positions in `[0, text.size()]`.
   *
   *  @par Complexity
   *  O(n + m) time and O(m) extra space.
   */
  inline Array<size_t> kmp_search(const std::string_view text,
                                  const std::string_view pattern)
  {
    if (pattern.empty())
      return string_search_detail::all_match_positions(text.size());

    Array<size_t> matches;
    if (text.size() < pattern.size())
      return matches;

    const Array<size_t> pi = kmp_prefix_function(pattern);

    size_t j = 0;
    for (size_t i = 0; i < text.size(); ++i)
      {
        while (j > 0 and text[i] != pattern[j])
          j = pi[j - 1];

        if (text[i] == pattern[j])
          ++j;

        if (j == pattern.size())
          {
            matches.append(i + 1 - pattern.size());
            j = pi[j - 1];
          }
      }

    return matches;
  }


  /** @brief Compute Z-array for a string.
   *
   *  `z[i]` equals the longest length `L` such that
   *  `s[0..L-1] == s[i..i+L-1]`.
   *
   *  @param[in] s Input string.
   *  @return Z-array with size `s.size()`. When non-empty, `z[0] = s.size()`.
   *  @throws None.
   *
   *  @par Complexity
   *  O(n) time and O(n) space.
   */
  inline Array<size_t> z_algorithm(const std::string_view s)
  {
    Array<size_t> z;
    if (s.empty())
      return z;

    z = Array<size_t>::create(s.size());
    z[0] = s.size();

    size_t l = 0;
    size_t r = 0;

    for (size_t i = 1; i < s.size(); ++i)
      {
        if (i <= r)
          z[i] = std::min(r - i + 1, z[i - l]);
        else
          z[i] = 0;

        while (i + z[i] < s.size() and s[z[i]] == s[i + z[i]])
          ++z[i];

        if (const size_t reach = i + z[i]; reach > r + 1)
          {
            l = i;
            r = reach - 1;
          }
      }

    return z;
  }


  /** @brief Find all occurrences of a pattern using the Z-algorithm.
   *
   *  @param[in] text Text where matches are searched.
   *  @param[in] pattern Pattern to find.
   *  @return Array with all match start indices (0-based).
   *  @throws None.
   *
   *  @note If no delimiter byte is available between `pattern` and `text`,
   *        this function falls back to `kmp_search`.
   *  @note If `pattern` is empty, returns all positions in `[0, text.size()]`.
   *
   *  @par Complexity
   *  O(n + m) time and O(n + m) space.
   */
  inline Array<size_t> z_search(const std::string_view text,
                                const std::string_view pattern)
  {
    if (pattern.empty())
      return string_search_detail::all_match_positions(text.size());

    if (text.size() < pattern.size())
      return {};

    char delimiter = 0;
    if (not string_search_detail::find_unused_delimiter(pattern, text, delimiter))
      return kmp_search(text, pattern);

    std::string combined;
    combined.reserve(pattern.size() + text.size() + 1);
    combined += pattern;
    combined += delimiter;
    combined += text;

    const Array<size_t> z = z_algorithm(combined);

    Array<size_t> matches;
    const size_t offset = pattern.size() + 1;
    for (size_t i = offset; i < combined.size(); ++i)
      if (z[i] >= pattern.size())
        matches.append(i - offset);

    return matches;
  }


  /** @brief Find all occurrences using Boyer-Moore-Horspool.
   *
   *  @param[in] text Text where matches are searched.
   *  @param[in] pattern Pattern to find.
   *  @return Array with all match start indices (0-based).
   *  @throws None.
   *
   *  @note If `pattern` is empty, returns all positions in `[0, text.size()]`.
   *
   *  @par Complexity
   *  Average-case sublinear. Worst-case O(nm). Extra space O(1)
   *  (fixed 256-byte alphabet table).
   */
  inline Array<size_t> boyer_moore_horspool_search(const std::string_view text,
                                                   const std::string_view pattern)
  {
    if (pattern.empty())
      return string_search_detail::all_match_positions(text.size());

    Array<size_t> matches;
    const size_t n = text.size();
    const size_t m = pattern.size();

    if (n < m)
      return matches;

    Array<size_t> shift = Array<size_t>::create(256);
    for (size_t i = 0; i < 256; ++i)
      shift[i] = m;

    for (size_t i = 0; i + 1 < m; ++i)
      shift[static_cast<unsigned char>(pattern[i])] = m - 1 - i;

    size_t i = 0;
    while (i + m <= n)
      {
        size_t j = m;
        while (j > 0 and pattern[j - 1] == text[i + j - 1])
          --j;

        if (j == 0)
          matches.append(i);

        const auto c = static_cast<unsigned char>(text[i + m - 1]);
        const size_t step = shift[c] == 0 ? 1 : shift[c];
        i += step;
      }

    return matches;
  }


  /** @brief Find all occurrences using Rabin-Karp with rolling hash.
   *
   *  Hash collisions are filtered by exact character-by-character verification,
   *  so returned matches are exact.
   *
   *  @param[in] text Text where matches are searched.
   *  @param[in] pattern Pattern to find.
   *  @param[in] base Rolling-hash base.
   *  @return Array with all match start indices (0-based).
   *  @throws None.
   *
   *  @note If `pattern` is empty, returns all positions in `[0, text.size()]`.
   *  @note The rolling hash uses implicit modulo via `uint64_t` overflow
   *        (no explicit prime modulus).  This is sufficient for general use
   *        but may produce more collisions on adversarial inputs.
   *
   *  @par Complexity
   *  Expected O(n + m), worst-case O(nm) due to adversarial collisions.
   */
  inline Array<size_t> rabin_karp_search(const std::string_view text,
                                         const std::string_view pattern,
                                         const uint64_t base = 911382323ull)
  {
    if (pattern.empty())
      return string_search_detail::all_match_positions(text.size());

    Array<size_t> matches;
    const size_t n = text.size();
    const size_t m = pattern.size();

    if (n < m)
      return matches;

    uint64_t power = 1;
    for (size_t i = 1; i < m; ++i)
      power *= base;

    uint64_t pattern_hash = 0;
    uint64_t window_hash = 0;

    for (size_t i = 0; i < m; ++i)
      {
        pattern_hash = pattern_hash * base
                       + static_cast<unsigned char>(pattern[i]) + 1ull;
        window_hash = window_hash * base
                      + static_cast<unsigned char>(text[i]) + 1ull;
      }

    if (window_hash == pattern_hash
        and string_search_detail::equals_at(text, pattern, 0))
      matches.append(0);

    for (size_t i = m; i < n; ++i)
      {
        const uint64_t old_c = static_cast<unsigned char>(text[i - m]) + 1ull;
        const uint64_t new_c = static_cast<unsigned char>(text[i]) + 1ull;

        window_hash = (window_hash - old_c * power) * base + new_c;

        if (const size_t pos = i + 1 - m; window_hash == pattern_hash
                                          and string_search_detail::equals_at(text, pattern, pos))
          matches.append(pos);
      }

    return matches;
  }
} // namespace Aleph

# endif // STRING_SEARCH_H