- 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]
与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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