1 介绍

本博客用来记录AC自动机相关题目。

AC自动机是以Trie的结构为基础，结合KMP的思想建立的自动机，用于解决多模式匹配等任务。

2 训练

题目1：1282搜索关键词

C++代码如下，

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;const int N = 10010, S = 55, M = 1000010;int n;
int tr[N*S][26], cnt[N*S], idx;
char str[M];
int q[N*S], ne[N*S];void insert() {int p = 0;for (int i = 0; str[i]; ++i) {int t = str[i] - 'a';if (!tr[p][t]) tr[p][t] = ++idx;p = tr[p][t];}cnt[p]++;
}void build() {int hh = 0, tt = -1;for (int i = 0; i < 26; ++i) {if (tr[0][i]) {q[++tt] = tr[0][i];}}while (hh <= tt) {int t = q[hh++];for (int i = 0; i < 26; ++i) {int p = tr[t][i];if (!p) tr[t][i] = tr[ne[t]][i];else {ne[p] = tr[ne[t]][i];q[++tt] = p; }}}
}int main() {int T;scanf("%d", &T);while (T--) {memset(tr, 0, sizeof tr);memset(cnt, 0, sizeof cnt);memset(ne, 0, sizeof ne);idx = 0;scanf("%d", &n);for (int i = 0; i < n; ++i) {scanf("%s", str);insert();}build();scanf("%s", str);int res = 0;for (int i = 0, j = 0; str[i]; ++i) {int t = str[i] - 'a';j = tr[j][t];int p = j;while (p) {res += cnt[p];cnt[p] = 0;p = ne[p];}}printf("%d\n", res);}return 0;
}

用string类型的find()函数的暴力写法，通过了 12/13个数据，

#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>using namespace std;int main() {int T;cin >> T;while (T--) {int n;cin >> n;vector<string> words(n);for (int i = 0; i < n; ++i) cin >> words[i];string article;cin >> article;int res = 0;for (auto word : words) {if (article.find(word) != string::npos) res++;}cout << res << endl;}return 0;
}

题目2：1285单词

C++代码如下，

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;const int N = 1000010;int n;
int tr[N][26], f[N], idx;
int q[N], ne[N];
char str[N];
int id[210];void insert(int x) {int p = 0;for (int i = 0; str[i]; i++) {int t = str[i] - 'a';if (!tr[p][t]) tr[p][t] = ++idx;p = tr[p][t];f[p]++;}id[x] = p;
}void build() {int hh = 0, tt = -1;for (int i = 0; i < 26; ++i) {if (tr[0][i]) {q[++tt] = tr[0][i];}}while (hh <= tt) {int t = q[hh++];for (int i = 0; i < 26; ++i) {int &p = tr[t][i];if (!p) p = tr[ne[t]][i];else {ne[p] = tr[ne[t]][i];q[++tt] = p;}}}
}int main() {scanf("%d", &n);for (int i = 0; i < n; ++i) {scanf("%s", str);insert(i);}build();for (int i = idx - 1; i >= 0; --i) f[ne[q[i]]] += f[q[i]];for (int i = 0; i < n; ++i) printf("%d\n", f[id[i]]);return 0;
}

使用kmp来做，超时了，通过了 9/11个数据

#include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <string>using namespace std;void kmp(string &pattern_str, string &match_str) {//cout << "pattern_str = " << pattern_str << ", match_str = " << match_str << endl;int n = pattern_str.size();int m = match_str.size();pattern_str = '#' + pattern_str;match_str = '$' + match_str;//求取next数组nevector<int> ne(n + 10, 0);for (int i = 2, j = 0; i <= n; ++i) {while (j && pattern_str[i] != pattern_str[j+1]) j = ne[j];if (pattern_str[i] == pattern_str[j+1]) j++;ne[i] = j;}//返回匹配的下标位置vector<int> idxs; //匹配串match_str中的下标位置，表示从改下标起，与模式串pattern_str匹配for (int i = 1, j = 0; i <= m; ++i) {while (j && match_str[i] != pattern_str[j+1]) j = ne[j];if (match_str[i] == pattern_str[j+1]) j++;if (j == n) {//cout << i - n << " ";idxs.emplace_back(i-n);j = ne[j];}}// for (int idx : idxs) {//     cout << idx << " ";// }// cout << endl;cout << idxs.size() << endl;pattern_str = pattern_str.substr(1);match_str = match_str.substr(1);return;
}int main() {int n;cin >> n;vector<string> words(n);for (int i = 0; i < n; ++i) cin >> words[i];string article;for (auto word : words) article += word + "?";for (auto word : words) {kmp(word, article);}return 0;
}

题目3：1053修复DNA

C++代码如下，

#include <iostream>
#include <cstring>
#include <iostream>
#include <algorithm>using namespace std;const int N = 1010;int n, m;
int tr[N][4], dar[N], idx;
int q[N], ne[N];
char str[N];int f[N][N];int get(char c) {if (c == 'A') return 0;if (c == 'T') return 1;if (c == 'G') return 2;return 3;
}void insert() {int p = 0;for (int i = 0; str[i]; ++i) {int t = get(str[i]);if (tr[p][t] == 0) tr[p][t] = ++idx;p = tr[p][t];}dar[p] = 1;
}void build() {int hh = 0, tt = -1;for (int i = 0; i < 4; ++i) {if (tr[0][i]) {q[++tt] = tr[0][i];}}while (hh <= tt) {int t = q[hh++];for (int i = 0; i < 4; ++i) {int p = tr[t][i];if (!p) tr[t][i] = tr[ne[t]][i];else {ne[p] = tr[ne[t]][i];q[++tt] = p;dar[p] |= dar[ne[p]];}}}
}int main() {int T = 1;while (scanf("%d", &n), n) {memset(tr, 0, sizeof tr);memset(dar, 0, sizeof dar);memset(ne, 0, sizeof ne);idx = 0;for (int i = 0; i < n; ++i) {scanf("%s", str);insert();}build();scanf("%s", str + 1);m = strlen(str + 1);memset(f, 0x3f, sizeof f);f[0][0] = 0;for (int i = 0; i < m; ++i) {for (int j = 0; j <= idx; ++j) {for (int k = 0; k < 4; ++k) {int t = get(str[i+1]) != k;int p = tr[j][k];if (!dar[p]) f[i+1][p] = min(f[i+1][p], f[i][j] + t);}}}int res = 0x3f3f3f3f;for (int i = 0; i <= idx; ++i) res = min(res, f[m][i]);if (res == 0x3f3f3f3f) res = -1;printf("Case %d: %d\n", T++, res);}return 0;
}

3 参考

AC自动机-OI Wiki