基本算法连载（10）－模式匹配之BM(Boyer-Moore)

周末两天被BM算法折磨的要死。《a fast string search algorithm》论文中提到的算法思想倒是理解的差不多，但网上（http://www-igm.univ-mlv.fr/~lecroq/string/node14.html#SECTION00140）给出的实现可就是看不懂。通过Baidu，Google一搜，可以看到很多Boyer-Moore的实现。但绝大部分实现都是简化版本，只考虑了bad-character shift，而忽略了good-suffix shift。
它思想的源泉是从右向左匹配字符串将获得更多有用的信息。The algorithm precomputes two tables to process the information it obtains in each failed verification: one table calculates how many positions ahead to start the next search based on the identity of the character that caused the match attempt to fail;the other makes a similar calculation based on how many characters were matched successfully before the match attempt failed.其中前一个称作bad-character shift，后一个称作good-suffix shift。想详细了解Boyer-Moore的思想，我极力推荐看作者发表的论文，它比网上对这个算法介绍的文章容易理解的多。
处理主串为n，模式串为m的情况，此算法的最好表现是：n/m。在这种情况下，只有模式串中的最后一个字符需要比较。不相等，马上可以跳过m个字符。从这里可以看出此算法一个违反直觉的性质：模式串越长，搜索越快。
最优的代码实现（没看懂，明天贴个我自己改的）：

void preBmBc(char *x, int m, int bmBc[]) {
 int i;

 for (i = 0; i < ASIZE; ++i)
    bmBc[i] = m;
 for (i = 0; i < m - 1; ++i)
    bmBc[x[i]] = m - i - 1;
}


void suffixes(char *x, int m, int *suff) {
 int f, g, i;

 suff[m - 1] = m;
 g = m - 1;
 for (i = m - 2; i >= 0; --i) {
    if (i > g && suff[i + m - 1 - f] < i - g)
       suff[i] = suff[i + m - 1 - f];
    else {
       if (i < g)
          g = i;
       f = i;
       while (g >= 0 && x[g] == x[g + m - 1 - f])
          --g;
       suff[i] = f - g;
    }
 }
}

void preBmGs(char *x, int m, int bmGs[]) {
 int i, j, suff[XSIZE];

 suffixes(x, m, suff);

 for (i = 0; i < m; ++i)
    bmGs[i] = m;
 j = 0;
 for (i = m - 1; i >= -1; --i)
    if (i == -1 || suff[i] == i + 1)
       for (; j < m - 1 - i; ++j)
          if (bmGs[j] == m)
             bmGs[j] = m - 1 - i;
 for (i = 0; i <= m - 2; ++i)
    bmGs[m - 1 - suff[i]] = m - 1 - i;
}


void BM(char *x, int m, char *y, int n) {
 int i, j, bmGs[XSIZE], bmBc[ASIZE];

 /* Preprocessing */
 preBmGs(x, m, bmGs);
 preBmBc(x, m, bmBc);

 /* Searching */
 j = 0;
 while (j <= n - m) {
    for (i = m - 1; i >= 0 && x[i] == y[i + j]; --i);
    if (i < 0) {
       OUTPUT(j);
       j += bmGs[0];
    }
    else
       j += MAX(bmGs[i], bmBc[y[i + j]] - m + 1 + i);
 }
}