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) 2005-2024 Free Software Foundation, Inc.
   4    Written by Bruno Haible <bruno@clisp.org>, 2005.
   5
   6    This file is free software.
   7    It is dual-licensed under "the GNU LGPLv3+ or the GNU GPLv2+".
   8    You can redistribute it and/or modify it under either
   9      - the terms of the GNU Lesser General Public License as published
  10        by the Free Software Foundation, either version 3, or (at your
  11        option) any later version, or
  12      - the terms of the GNU General Public License as published by the
  13        Free Software Foundation; either version 2, or (at your option)
  14        any later version, or
  15      - the same dual license "the GNU LGPLv3+ or the GNU GPLv2+".
  16
  17    This file is distributed in the hope that it will be useful,
  18    but WITHOUT ANY WARRANTY; without even the implied warranty of
  19    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  20    Lesser General Public License and the GNU General Public License
  21    for more details.
  22
  23    You should have received a copy of the GNU Lesser General Public
  24    License and of the GNU General Public License along with this
  25    program.  If not, see <https://www.gnu.org/licenses/>.  */
  26
  27 /* Before including this file, you need to define:
  28      UNIT                    The element type of the needle and haystack.
  29      CANON_ELEMENT(c)        A macro that canonicalizes an element right after
  30                              it has been fetched from needle or haystack.
  31                              The argument is of type UNIT; the result must be
  32                              of type UNIT as well.  */
  33
  34 /* Knuth-Morris-Pratt algorithm.
  35    See https://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
  36    HAYSTACK is the NUL terminated string in which to search for.
  37    NEEDLE is the string to search for in HAYSTACK, consisting of NEEDLE_LEN
  38    units.
  39    Return a boolean indicating success:
  40    Return true and set *RESULTP if the search was completed.
  41    Return false if it was aborted because not enough memory was available.  */
  42 static bool
  43 knuth_morris_pratt (const UNIT *haystack,
  44                     const UNIT *needle, size_t needle_len,
  45                     const UNIT **resultp)
  46 {
  47   size_t m = needle_len;
  48
  49   /* Allocate the table.  */
  50   size_t *table = (size_t *) nmalloca (m, sizeof (size_t));
  51   if (table == NULL)
  52     return false;
  53   /* Fill the table.
  54      For 0 < i < m:
  55        0 < table[i] <= i is defined such that
  56        forall 0 < x < table[i]: needle[x..i-1] != needle[0..i-1-x],
  57        and table[i] is as large as possible with this property.
  58      This implies:
  59      1) For 0 < i < m:
  60           If table[i] < i,
  61           needle[table[i]..i-1] = needle[0..i-1-table[i]].
  62      2) For 0 < i < m:
  63           rhaystack[0..i-1] == needle[0..i-1]
  64           and exists h, i <= h < m: rhaystack[h] != needle[h]
  65           implies
  66           forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1].
  67      table[0] remains uninitialized.  */
  68   {
  69     size_t i, j;
  70
  71     /* i = 1: Nothing to verify for x = 0.  */
  72     table[1] = 1;
  73     j = 0;
  74
  75     for (i = 2; i < m; i++)
  76       {
  77         /* Here: j = i-1 - table[i-1].
  78            The inequality needle[x..i-1] != needle[0..i-1-x] is known to hold
  79            for x < table[i-1], by induction.
  80            Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
  81         UNIT b = CANON_ELEMENT (needle[i - 1]);
  82
  83         for (;;)
  84           {
  85             /* Invariants: The inequality needle[x..i-1] != needle[0..i-1-x]
  86                is known to hold for x < i-1-j.
  87                Furthermore, if j>0: needle[i-1-j..i-2] = needle[0..j-1].  */
  88             if (b == CANON_ELEMENT (needle[j]))
  89               {
  90                 /* Set table[i] := i-1-j.  */
  91                 table[i] = i - ++j;
  92                 break;
  93               }
  94             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
  95                for x = i-1-j, because
  96                  needle[i-1] != needle[j] = needle[i-1-x].  */
  97             if (j == 0)
  98               {
  99                 /* The inequality holds for all possible x.  */
 100                 table[i] = i;
 101                 break;
 102               }
 103             /* The inequality needle[x..i-1] != needle[0..i-1-x] also holds
 104                for i-1-j < x < i-1-j+table[j], because for these x:
 105                  needle[x..i-2]
 106                  = needle[x-(i-1-j)..j-1]
 107                  != needle[0..j-1-(x-(i-1-j))]  (by definition of table[j])
 108                     = needle[0..i-2-x],
 109                hence needle[x..i-1] != needle[0..i-1-x].
 110                Furthermore
 111                  needle[i-1-j+table[j]..i-2]
 112                  = needle[table[j]..j-1]
 113                  = needle[0..j-1-table[j]]  (by definition of table[j]).  */
 114             j = j - table[j];
 115           }
 116         /* Here: j = i - table[i].  */
 117       }
 118   }
 119
 120   /* Search, using the table to accelerate the processing.  */
 121   {
 122     size_t j;
 123     const UNIT *rhaystack;
 124     const UNIT *phaystack;
 125
 126     *resultp = NULL;
 127     j = 0;
 128     rhaystack = haystack;
 129     phaystack = haystack;
 130     /* Invariant: phaystack = rhaystack + j.  */
 131     while (*phaystack != 0)
 132       if (CANON_ELEMENT (needle[j]) == CANON_ELEMENT (*phaystack))
 133         {
 134           j++;
 135           phaystack++;
 136           if (j == m)
 137             {
 138               /* The entire needle has been found.  */
 139               *resultp = rhaystack;
 140               break;
 141             }
 142         }
 143       else if (j > 0)
 144         {
 145           /* Found a match of needle[0..j-1], mismatch at needle[j].  */
 146           rhaystack += table[j];
 147           j -= table[j];
 148         }
 149       else
 150         {
 151           /* Found a mismatch at needle[0] already.  */
 152           rhaystack++;
 153           phaystack++;
 154         }
 155   }
 156
 157   freea (table);
 158   return true;
 159 }
 160
 161 #undef CANON_ELEMENT