How does the 'did you mean' feature works in git?

/*
 * This function implements the Damerau-Levenshtein algorithm to
 * calculate a distance between strings.
 *
 * Basically, it says how many letters need to be swapped, substituted,
 * deleted from, or added to string1, at least, to get string2.
 *
 * The idea is to build a distance matrix for the substrings of both
 * strings.  To avoid a large space complexity, only the last three rows
 * are kept in memory (if swaps had the same or higher cost as one deletion
 * plus one insertion, only two rows would be needed).
 *
 * At any stage, "i + 1" denotes the length of the current substring of
 * string1 that the distance is calculated for.
 *
 * row2 holds the current row, row1 the previous row (i.e. for the substring
 * of string1 of length "i"), and row0 the row before that.
 *
 * In other words, at the start of the big loop, row2[j + 1] contains the
 * Damerau-Levenshtein distance between the substring of string1 of length
 * "i" and the substring of string2 of length "j + 1".
 *
 * All the big loop does is determine the partial minimum-cost paths.
 *
 * It does so by calculating the costs of the path ending in characters
 * i (in string1) and j (in string2), respectively, given that the last
 * operation is a substitution, a swap, a deletion, or an insertion.
 *
 * This implementation allows the costs to be weighted:
 *
 * - w (as in "sWap")
 * - s (as in "Substitution")
 * - a (for insertion, AKA "Add")
 * - d (as in "Deletion")
 *
 * Note that this algorithm calculates a distance _iff_ d == a.
 */
int levenshtein(const char *string1, const char *string2,
                int w, int s, int a, int d)
{
        int len1 = strlen(string1), len2 = strlen(string2);
        int *row0, *row1, *row2;
        int i, j;

        ALLOC_ARRAY(row0, len2 + 1);
        ALLOC_ARRAY(row1, len2 + 1);
        ALLOC_ARRAY(row2, len2 + 1);

        for (j = 0; j <= len2; j++)
                row1[j] = j * a;
        for (i = 0; i < len1; i++) {
                int *dummy;

                row2[0] = (i + 1) * d;
                for (j = 0; j < len2; j++) {
                        /* substitution */
                        row2[j + 1] = row1[j] + s * (string1[i] != string2[j]);
                        /* swap */
                        if (i > 0 && j > 0 && string1[i - 1] == string2[j] &&
                                        string1[i] == string2[j - 1] &&
                                        row2[j + 1] > row0[j - 1] + w)
                                row2[j + 1] = row0[j - 1] + w;
                        /* deletion */
                        if (row2[j + 1] > row1[j + 1] + d)
                                row2[j + 1] = row1[j + 1] + d;
                        /* insertion */
                        if (row2[j + 1] > row2[j] + a)
                                row2[j + 1] = row2[j] + a;
                }

                dummy = row0;
                row0 = row1;
                row1 = row2;
                row2 = dummy;
        }


        i = row1[len2];
        free(row0);
        free(row1);
        free(row2);

        return i;
}

load_command_list("git-", &main_cmds, &other_cmds);

add_cmd_list(&main_cmds, &cfg.aliases);
add_cmd_list(&main_cmds, &other_cmds);
QSORT(main_cmds.names, main_cmds.cnt, cmdname_compare);
uniq(&main_cmds);

extract_cmds(&common_cmds, common_mask);

/* This abuses cmdname->len for levenshtein distance */
for (i = 0, n = 0; i < main_cmds.cnt; i++) {
        int cmp = 0; /* avoid compiler stupidity */
        const char *candidate = main_cmds.names[i]->name;

        /*
         * An exact match means we have the command, but
         * for some reason exec'ing it gave us ENOENT; probably
         * it's a bad interpreter in the #! line.
         */
        if (!strcmp(candidate, cmd))
                die(_(bad_interpreter_advice), cmd, cmd);

        /* Does the candidate appear in common_cmds list? */
        while (common_cmds[n].name &&
               (cmp = strcmp(common_cmds[n].name, candidate)) < 0)
                n++;
        if (common_cmds[n].name && !cmp) {
                /* Yes, this is one of the common commands */
                n++; /* use the entry from common_cmds[] */
                if (starts_with(candidate, cmd)) {
                        /* Give prefix match a very good score */
                        main_cmds.names[i]->len = 0;
                        continue;
                }
        }

        main_cmds.names[i]->len =
                levenshtein(cmd, candidate, 0, 2, 1, 3) + 1;
}
FREE_AND_NULL(common_cmds);

QSORT(main_cmds.names, main_cmds.cnt, levenshtein_compare);

/* skip and count prefix matches */
for (n = 0; n < main_cmds.cnt && !main_cmds.names[n]->len; n++)
        ; /* still counting */

if (main_cmds.cnt <= n) {
        /* prefix matches with everything? that is too ambiguous */
        best_similarity = SIMILARITY_FLOOR + 1;
} else {
        /* count all the most similar ones */
        for (best_similarity = main_cmds.names[n++]->len;
             (n < main_cmds.cnt &&
              best_similarity == main_cmds.names[n]->len);
             n++)
                ; /* still counting */
}

/* ... other code ... */

fprintf_ln(stderr, _("git: '%s' is not a git command. See 'git --help'."), cmd);  

if (SIMILAR_ENOUGH(best_similarity)) {
        fprintf_ln(stderr,
                   Q_("\nThe most similar command is",
                      "\nThe most similar commands are",
                   n));

        for (i = 0; i < n; i++)
                fprintf(stderr, "\t%s\n", main_cmds.names[i]->name);
}