levenshtein.c

   1 #include "cache.h"
   2 #include "levenshtein.h"
   3
   4 /*
   5  * This function implements the Damerau-Levenshtein algorithm to
   6  * calculate a distance between strings.
   7  *
   8  * Basically, it says how many letters need to be swapped, substituted,
   9  * deleted from, or added to string1, at least, to get string2.
  10  *
  11  * The idea is to build a distance matrix for the substrings of both
  12  * strings.  To avoid a large space complexity, only the last three rows
  13  * are kept in memory (if swaps had the same or higher cost as one deletion
  14  * plus one insertion, only two rows would be needed).
  15  *
  16  * At any stage, "i + 1" denotes the length of the current substring of
  17  * string1 that the distance is calculated for.
  18  *
  19  * row2 holds the current row, row1 the previous row (i.e. for the substring
  20  * of string1 of length "i"), and row0 the row before that.
  21  *
  22  * In other words, at the start of the big loop, row2[j + 1] contains the
  23  * Damerau-Levenshtein distance between the substring of string1 of length
  24  * "i" and the substring of string2 of length "j + 1".
  25  *
  26  * All the big loop does is determine the partial minimum-cost paths.
  27  *
  28  * It does so by calculating the costs of the path ending in characters
  29  * i (in string1) and j (in string2), respectively, given that the last
  30  * operation is a substitution, a swap, a deletion, or an insertion.
  31  *
  32  * This implementation allows the costs to be weighted:
  33  *
  34  * - w (as in "sWap")
  35  * - s (as in "Substitution")
  36  * - a (for insertion, AKA "Add")
  37  * - d (as in "Deletion")
  38  *
  39  * Note that this algorithm calculates a distance _iff_ d == a.
  40  */
  41 int levenshtein(const char *string1, const char *string2,
  42                 int w, int s, int a, int d)
  43 {
  44         int len1 = strlen(string1), len2 = strlen(string2);
  45         int *row0 = xmalloc(sizeof(int) * (len2 + 1));
  46         int *row1 = xmalloc(sizeof(int) * (len2 + 1));
  47         int *row2 = xmalloc(sizeof(int) * (len2 + 1));
  48         int i, j;
  49
  50         for (j = 0; j <= len2; j++)
  51                 row1[j] = j * a;
  52         for (i = 0; i < len1; i++) {
  53                 int *dummy;
  54
  55                 row2[0] = (i + 1) * d;
  56                 for (j = 0; j < len2; j++) {
  57                         /* substitution */
  58                         row2[j + 1] = row1[j] + s * (string1[i] != string2[j]);
  59                         /* swap */
  60                         if (i > 0 && j > 0 && string1[i - 1] == string2[j] &&
  61                                         string1[i] == string2[j - 1] &&
  62                                         row2[j + 1] > row0[j - 1] + w)
  63                                 row2[j + 1] = row0[j - 1] + w;
  64                         /* deletion */
  65                         if (row2[j + 1] > row1[j + 1] + d)
  66                                 row2[j + 1] = row1[j + 1] + d;
  67                         /* insertion */
  68                         if (row2[j + 1] > row2[j] + a)
  69                                 row2[j + 1] = row2[j] + a;
  70                 }
  71
  72                 dummy = row0;
  73                 row0 = row1;
  74                 row1 = row2;
  75                 row2 = dummy;
  76         }
  77
  78         i = row1[len2];
  79         free(row0);
  80         free(row1);
  81         free(row2);
  82
  83         return i;
  84 }