File: str-kmp.h

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/* Substring search in a NUL terminated string of UNIT elements,
   using the Knuth-Morris-Pratt algorithm.
   Copyright (C) 2005-2018 Free Software Foundation, Inc.
   Written by Bruno Haible <bruno@clisp.org>, 2005.

   This program is free software: you can redistribute it and/or
   modify it under the terms of either:

     * the GNU Lesser General Public License as published by the Free
       Software Foundation; either version 3 of the License, or (at your
       option) any later version.

   or

     * the GNU General Public License as published by the Free
       Software Foundation; either version 2 of the License, or (at your
       option) any later version.

   or both in parallel, as here.
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, see <https://www.gnu.org/licenses/>.  */

/* Before including this file, you need to define:
     UNIT                    The element type of the needle and haystack.
     CANON_ELEMENT(c)        A macro that canonicalizes an element right after
                             it has been fetched from needle or haystack.
                             The argument is of type UNIT; the result must be
                             of type UNIT as well.  */

/* Knuth-Morris-Pratt algorithm.
   See https://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
   HAYSTACK is the NUL terminated string in which to search for.
   NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
   units.
   Return a boolean indicating success:
   Return true and set *RESULTP if the search was completed.
   Return false if it was aborted because not enough memory was available.  */
static bool
knuth_morris_pratt (const UNIT *haystack,
                    const UNIT *needle, size_t needle_len,
                    const UNIT **resultp)
{
  size_t m = needle_len;

  /* Allocate the table.  */
  size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
  if (table == NULL)
    return false;
  /* Fill the table.
     For 0 < i < m:
       0 < table[i] <= i is defined such that
       forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
       and table[i] is as large as possible with this property.
     This implies:
     1) For 0 < i < m:
          If table[i] < i,
          needle[table[i]..i-1] = needle[0..i-1-table[i]].
     2) For 0 < i < m:
          rhaystack[0..i-1] == needle[0..i-1]
          and exists h, i <= h < m: rhaystack[h] != needle[h]
          implies
          forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
     table[0] remains uninitialized.  */
  {
    size_t i, j;

    /* i = 1: Nothing to verify for x = 0.  */
    table[1] = 1;
    j = 0;

    for (i = 2; i < m; i++)
      {
        /* Here: j = i-1 - table[i-1].
           The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
           for x < table[i-1], by induction.
           Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
        UNIT b = CANON_ELEMENT (needle[i - 1]);

        for (;;)
          {
            /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
               is known to hold for x < i-1-j.
               Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
            if (b == CANON_ELEMENT (needle[j]))
              {
                /* Set table[i] := i-1-j.  */
                table[i] = i - ++j;
                break;
              }
            /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
               for x = i-1-j, because
                 needle[i-1] != needle[j] = needle[i-1-x].  */
            if (j == 0)
              {
                /* The inequality holds for all possible x.  */
                table[i] = i;
                break;
              }
            /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
               for i-1-j < x < i-1-j+table[j], because for these x:
                 needle[x..i-2]
                 = needle[x-(i-1-j)..j-1]
                 != needle[0..j-1-(x-(i-1-j))]  (by definition of table[j])
                    = needle[0..i-2-x],
               hence needle[x..i-1] != needle[0..i-1-x].
               Furthermore
                 needle[i-1-j+table[j]..i-2]
                 = needle[table[j]..j-1]
                 = needle[0..j-1-table[j]]  (by definition of table[j]).  */
            j = j - table[j];
          }
        /* Here: j = i - table[i].  */
      }
  }

  /* Search, using the table to accelerate the processing.  */
  {
    size_t j;
    const UNIT *rhaystack;
    const UNIT *phaystack;

    *resultp = NULL;
    j = 0;
    rhaystack = haystack;
    phaystack = haystack;
    /* Invariant: phaystack = rhaystack + j.  */
    while (*phaystack != 0)
      if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
        {
          j++;
          phaystack++;
          if (j == m)
            {
              /* The entire needle has been found.  */
              *resultp = rhaystack;
              break;
            }
        }
      else if (j > 0)
        {
          /* Found a match of needle[0..j-1], mismatch at needle[j].  */
          rhaystack += table[j];
          j -= table[j];
        }
      else
        {
          /* Found a mismatch at needle[0] already.  */
          rhaystack++;
          phaystack++;
        }
  }

  freea (table);
  return true;
}

#undef CANON_ELEMENT