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AC自动机及多模式匹配

AC自动机及多模式匹配

作者: 胡哈哈哈 | 来源:发表于2016-05-20 00:40 被阅读804次
    • 在接触AC自动机之前,只仅仅掌握单模式匹配的算法:比如KMP、BMH等算法;经过优化后,KMP和BMH都具有线性时间复杂度,而实际情况下,一般的匹配问题BMH具有亚线性的表现。而昨天接触的AC自动机则是一种结合了字典树和KMP的一种算法,使得在多模式匹配下,时间复杂度达到O(Σmi + n),其中n为原串长度,mi为第i个模式串的长度;
    • 匹配过程中类似于KMP,原串不走回头路,利用之前已经匹配过的结果来构造特殊的字典树从而形成AC自动机;
    • 创建自动机的过程中,最为重要的是fail指针的构造;我是从这篇文章中学会的,AC自动机算法详解;fail指针的作用类似于KMP中的next数组;
    • 我的这个模板中并没有考虑对自动机的优化, 比如ptr->fail->next[i]ptr->next[i]若同时不存在, 则ptr->fail其实是可以直接指向ptr->fail->fail的原因很简单, 因为ptr->next[i]发生失配时, ptr = ptr->fail, 此时肯定仍然失配, 需要继续ptr->fail,当然优化的代价是增加对存储空间的占用, fail需要变为vector<trieTreeNode*> fail,每个字母都应对应一个fail指针。
    ////////////////////////////////////////////////////////////////////////////////
    /*
    1 const vector<string> &patterns: several pattern strings;
    2 const string &s: original strings;
    3 vector<string> &answer: the patterns which are matched in the original strings;
    4 return the number of patterns which are matched.
    */
    ////////////////////////////////////////////////////////////////////////////////
    #include <iostream>
    #include <vector>
    #include <queue>
    #include <string>
    #include <unordered_set>
    #define ALPH_NUM 26
    using namespace std;
    
    struct trieTreeNode {
        vector<trieTreeNode*> next;
        bool mark;
        trieTreeNode *fail;
        trieTreeNode(): next(26, nullptr), mark(false), fail(nullptr) {}
    };
    
    trieTreeNode *createAcAutomation(const vector<string> &patterns);
    int findPatterns(vector<string> &answer, trieTreeNode *root, const string &s);
    void makeFoundPatterns(vector<string> &answer, unordered_set<trieTreeNode*> &save, trieTreeNode *root, string pattern);
    inline char turn_char(int index);
    int multiPatternsMatchingByAcAutomation(const vector<string> &patterns, const string &s, vector<string> &answer);
    
    trieTreeNode *createAcAutomation(const vector<string> &patterns) {
        trieTreeNode *root = new trieTreeNode(), *ptr, *cur;
        for (int i = 0; i != patterns.size(); ++i) {
            cur = root;
            for (int k = 0; k != patterns[i].size(); ++k) {
                int index = patterns[i][k] - 'a';
                if (!cur->next[index])
                    cur->next[index] = new trieTreeNode();
                cur = cur->next[index];
            }
            cur->mark = true;
        }
        queue<trieTreeNode*> makeFail;
        makeFail.push(root);
        while (!makeFail.empty()) {
            cur = makeFail.front(); makeFail.pop();
            for (int i = 0; i != ALPH_NUM; ++i) {
                if (cur->next[i]) {
                    for (ptr = cur->fail; ptr && !ptr->next[i]; ptr = ptr->fail);
                    cur->next[i]->fail = ptr ? ptr->next[i] : root;
                    makeFail.push(cur->next[i]);
                }
            }
        }
        return root;
    }
    
    int findPatterns(vector<string> &answer, trieTreeNode *root, const string &s) {
        int count = 0;
        string pattern;
        unordered_set<trieTreeNode*> save;
        trieTreeNode *cur = root;
        for (int i = 0; i != s.size(); ) {
            int index = s[i] - 'a';
            if (!cur) {
                cur = root; ++i;
            }
            else if (cur->next[index]) {
                cur = cur->next[index];
                if (cur->mark) {
                    ++count;
                    save.insert(cur);
                }
                ++i;
            }
            else {
                cur = cur->fail;
                if (cur && cur->mark) {
                    ++count;
                    save.insert(cur);
                }
            }
        }
        makeFoundPatterns(answer, save, root, pattern);
        return count;
    }
    
    void makeFoundPatterns(vector<string> &answer, unordered_set<trieTreeNode*> &save,
        trieTreeNode *root, string pattern) {
        unordered_set<trieTreeNode*>::iterator it = save.find(root);
        if (it != save.end())
            answer.push_back(pattern);
        for (int i = 0; i != ALPH_NUM; ++i) {
            if (root->next[i]) {
                string t(pattern);
                t.push_back(turn_char(i));
                makeFoundPatterns(answer, save, root->next[i], t);
            }
        }
    }
    
    inline char turn_char(int index) {
        return 'a' + index;
    }
    
    int multiPatternsMatchingByAcAutomation(const vector<string> &patterns, const string &s, vector<string> &answer) {
        trieTreeNode *root = createAcAutomation(patterns);
        return findPatterns(answer, root, s);
    }
    
    

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