lib/str-kmp.h

   1 /* Substring search in a NUL terminated string of UNIT elements,
   2    using the Knuth-Morris-Pratt algorithm.
   3    Copyright (C) 2005-2020 Free Software Foundation, Inc.
   4    Written by Bruno Haible <bruno@clisp.org>, 2005.
   5
   6    This program is free software; you can redistribute it and/or modify
   7    it under the terms of the GNU General Public License as published by
   8    the Free Software Foundation; either version 2, or (at your option)
   9    any later version.
  10
  11    This program is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14    GNU General Public License for more details.
  15
  16    You should have received a copy of the GNU General Public License
  17    along with this program; if not, see <https://www.gnu.org/licenses/>.  */
  18
  19 /* Before including this file, you need to define:
  20      UNIT                    The element type of the needle and haystack.
  21      CANON_ELEMENT(c)        A macro that canonicalizes an element right after
  22                              it has been fetched from needle or haystack.
  23                              The argument is of type UNIT; the result must be
  24                              of type UNIT as well.  */
  25
  26 /* Knuth-Morris-Pratt algorithm.
  27    See https://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
  28    HAYSTACK is the NUL terminated string in which to search for.
  29    NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
  30    units.
  31    Return a boolean indicating success:
  32    Return true and set *RESULTP if the search was completed.
  33    Return false if it was aborted because not enough memory was available.  */
  34 static bool
  35 knuth_morris_pratt (const UNIT *haystack,
  36                     const UNIT *needle, size_t needle_len,
  37                     const UNIT **resultp)
  38 {
  39   size_t m = needle_len;
  40
  41   /* Allocate the table.  */
  42   size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
  43   if (table == NULL)
  44     return false;
  45   /* Fill the table.
  46      For 0 < i < m:
  47        0 < table[i] <= i is defined such that
  48        forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
  49        and table[i] is as large as possible with this property.
  50      This implies:
  51      1) For 0 < i < m:
  52           If table[i] < i,
  53           needle[table[i]..i-1] = needle[0..i-1-table[i]].
  54      2) For 0 < i < m:
  55           rhaystack[0..i-1] == needle[0..i-1]
  56           and exists h, i <= h < m: rhaystack[h] != needle[h]
  57           implies
  58           forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
  59      table[0] remains uninitialized.  */
  60   {
  61     size_t i, j;
  62
  63     /* i = 1: Nothing to verify for x = 0.  */
  64     table[1] = 1;
  65     j = 0;
  66
  67     for (i = 2; i < m; i++)
  68       {
  69         /* Here: j = i-1 - table[i-1].
  70            The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
  71            for x < table[i-1], by induction.
  72            Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
  73         UNIT b = CANON_ELEMENT (needle[i - 1]);
  74
  75         for (;;)
  76           {
  77             /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
  78                is known to hold for x < i-1-j.
  79                Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
  80             if (b == CANON_ELEMENT (needle[j]))
  81               {
  82                 /* Set table[i] := i-1-j.  */
  83                 table[i] = i - ++j;
  84                 break;
  85               }
  86             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
  87                for x = i-1-j, because
  88                  needle[i-1] != needle[j] = needle[i-1-x].  */
  89             if (j == 0)
  90               {
  91                 /* The inequality holds for all possible x.  */
  92                 table[i] = i;
  93                 break;
  94               }
  95             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
  96                for i-1-j < x < i-1-j+table[j], because for these x:
  97                  needle[x..i-2]
  98                  = needle[x-(i-1-j)..j-1]
  99                  != needle[0..j-1-(x-(i-1-j))]  (by definition of table[j])
 100                     = needle[0..i-2-x],
 101                hence needle[x..i-1] != needle[0..i-1-x].
 102                Furthermore
 103                  needle[i-1-j+table[j]..i-2]
 104                  = needle[table[j]..j-1]
 105                  = needle[0..j-1-table[j]]  (by definition of table[j]).  */
 106             j = j - table[j];
 107           }
 108         /* Here: j = i - table[i].  */
 109       }
 110   }
 111
 112   /* Search, using the table to accelerate the processing.  */
 113   {
 114     size_t j;
 115     const UNIT *rhaystack;
 116     const UNIT *phaystack;
 117
 118     *resultp = NULL;
 119     j = 0;
 120     rhaystack = haystack;
 121     phaystack = haystack;
 122     /* Invariant: phaystack = rhaystack + j.  */
 123     while (*phaystack != 0)
 124       if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
 125         {
 126           j++;
 127           phaystack++;
 128           if (j == m)
 129             {
 130               /* The entire needle has been found.  */
 131               *resultp = rhaystack;
 132               break;
 133             }
 134         }
 135       else if (j > 0)
 136         {
 137           /* Found a match of needle[0..j-1], mismatch at needle[j].  */
 138           rhaystack += table[j];
 139           j -= table[j];
 140         }
 141       else
 142         {
 143           /* Found a mismatch at needle[0] already.  */
 144           rhaystack++;
 145           phaystack++;
 146         }
 147   }
 148
 149   freea (table);
 150   return true;
 151 }
 152
 153 #undef CANON_ELEMENT