经典算法题每日演练――第八题 AC自动机 - 一线码农 - 博客园


  上一篇我们说了单模式匹配算法KMP,现在我们有需求了,我要检查一篇文章中是否有某些敏感词,这其实就是多模式匹配的问题。

当然你也可以用KMP算法求出,那么它的时间复杂度为O(c*(m+n)),c:为模式串的个数。m:为模式串的长度,n:为正文的长度,那

么这个复杂度就不再是线性了,我们学算法就是希望能把要解决的问题优化到极致,这不,AC自动机就派上用场了。

   其实AC自动机就是Trie树的一个活用,活用点就是灌输了kmp的思想,从而再次把时间复杂度优化到线性的O(N),刚好我前面的文

章已经说过了Trie树和KMP,这里还是默认大家都懂。

一:构建AC自动机

  同样我也用网上的经典例子,现有say she shr he her 这样5个模式串,主串为yasherhs,我要做的就是哪些模式串在主串中出现过?

1: 构建trie树

    如果看过我前面的文章,构建trie树还是很容易的。

2:失败指针

    构建失败指针是AC自动机的核心所在,玩转了它也就玩转了AC自动机,失败指针非常类似于KMP中的next数组,也就是说,

 当我的主串在trie树中进行匹配的时候,如果当前节点不能再继续进行匹配,那么我们就会走到当前节点的failNode节点继续进行

匹配,构建failnode节点也是很流程化的。

①:root节点的子节点的failnode都是指向root。

②:当走到在"she"中的"h"节点时,我们给它的failnode设置什么呢?此时就要走该节点(h)的父节点(s)的失败指针,一直回溯直

     到找到某个节点的孩子节点也是当初节点同样的字符(h),没有找到的话,其失败指针就指向root。

     比如:h节点的父节点为s,s的failnode节点为root,走到root后继续寻找子节点为h的节点,恰好我们找到了,(假如还是没

             有找到,则继续走该节点的failnode,嘿嘿,是不是很像一种回溯查找),此时就将 "she"中的"h"节点的fainode"指向

            "her"中的"h"节点,好,原理其实就是这样。(看看你的想法是不是跟图一样)


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