SCL-- AC 自动机
2015-05-21 23:53:19
总结：来小结一下 AC 自动机的模板以及算法细节。
1 const int RA = 26; 2 const int MAXN = 500010; 3 4 struct AC_auto{ 5 int next[MAXN][RA],f[MAXN],cnt[MAXN],last[MAXN]; 6 int root,tot; 7 void new_node(int p){ //初始化新节点 8 for(int i = 0; i < RA; ++i) next[p][i] = 0; //以0表示无后继 9 f[p] = cnt[p] = last[p] = 0; //失配、结尾、后缀链接数组清零 10 } 11 void init(){ //ac自动机初始化函数 12 root = tot = 0; //初始化root和节点计数器 13 new_node(root); //初始化根 14 } 15 void insert(char *str){ //插入函数，类似字典数 16 int len = strlen(str); 17 int p = root; 18 for(int i = 0; i < len; ++i){ 19 int id = str[i] - 'a'; 20 if(next[p][id] == 0){ //发现没后继节点 21 next[p][id] = ++tot; 22 new_node(tot); 23 } 24 p = next[p][id]; //走边 25 } 26 cnt[p]++; //给单词结尾标记+1 27 } 28 void getfail(){ 29 queue<int> Q; //BFS 30 f[root]= root; //初始化根的失配指向自己 31 for(int i = 0; i < RA; ++i){ //初始化队列 32 int u = next[root][i]; 33 if(u) Q.push(u); 34 } 35 while(!Q.empty()){ 36 int x = Q.front(); Q.pop(); 37 for(int i = 0; i < RA; ++i){ 38 int u = next[x][i]; 39 if(u == 0){ 40 next[x][i] = next[f[x]][i]; //事实上是把失配提前计算出来 41 continue; 42 } 43 Q.push(u); 44 int v = f[x]; //寻找失配节点 45 while(v && next[v][i] == 0) v = f[v]; 46 f[u] = next[v][i]; //找到失配后继点 / 返回根节点 47 last[u] = cnt[f[u]] ? f[u] : last[f[u]]; //后缀链接 48 } 49 } 50 } 51 int find(){ //查询函数 52 int len = strlen(S); 53 int p = root,res = 0; //从根出发，res是匹配计数器 54 for(int i = 0; i < len; ++i){ 55 int id = S[i] - 'a'; 56 p = next[p][id]; 57 int cur = p; 58 while(cur != root){ //顺着失配走，遍历每个匹配模板串 59 res += cnt[cur]; 60 cnt[cur] = 0; //匹配完要清空 61 cur = last[cur]; //顺着后缀链接走（用fail也行，但效率低） 62 } 63 } 64 return res; 65 } 66 }ac;
相关的几个模板题：
（1）hdu 2222，纯模板辣。
如果不采用 last 数组优化将会跑出 700+ MS，加了 last 优化能做到 200+ MS
#include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include <vector> #include <map> #include <set> #include <stack> #include <queue> #include <string> #include <iostream> #include <algorithm> using namespace std; #define getmid(l,r) ((l) + ((r) - (l)) / 2) #define MP(a,b) make_pair(a,b) #define PB(a) push_back(a) typedef long long ll; typedef pair<int,int> pii; const double eps = 1e-8; const int INF = (1 << 30) - 1; const int RA = 26; const int MAXN = 500010; char S[1000010]; int T,N; struct AC_auto{ int next[MAXN][RA],f[MAXN],cnt[MAXN],last[MAXN]; int root,tot; void new_node(int p){ //初始化新节点 for(int i = 0; i < RA; ++i) next[p][i] = 0; //以0表示无后继 f[p] = cnt[p] = last[p] = 0; //失配、结尾、后缀链接数组清零 } void init(){ //ac自动机初始化函数 root = tot = 0; //初始化root和节点计数器 new_node(root); //初始化根 } void insert(char *str){ //插入函数，类似字典数 int len = strlen(str); int p = root; for(int i = 0; i < len; ++i){ int id = str[i] - 'a'; if(next[p][id] == 0){ //发现没后继节点 next[p][id] = ++tot; new_node(tot); } p = next[p][id]; //走边 } cnt[p]++; //给单词结尾标记+1 } void getfail(){ queue<int> Q; //BFS f[root]= root; //初始化根的失配指向自己 for(int i = 0; i < RA; ++i){ //初始化队列 int u = next[root][i]; if(u) Q.push(u); } while(!Q.empty()){ int x = Q.front(); Q.pop(); for(int i = 0; i < RA; ++i){ int u = next[x][i]; if(u == 0){ next[x][i] = next[f[x]][i]; //事实上是把失配提前计算出来 continue; } Q.push(u); int v = f[x]; //寻找失配节点 while(v && next[v][i] == 0) v = f[v]; f[u] = next[v][i]; //找到失配后继点 / 返回根节点 last[u] = cnt[f[u]] ? f[u] : last[f[u]]; //后缀链接 } } } int find(){ //查询函数 int len = strlen(S); int p = root,res = 0; //从根出发，res是匹配计数器 for(int i = 0; i < len; ++i){ int id = S[i] - 'a'; p = next[p][id]; int cur = p; while(cur != root){ //顺着失配走，遍历每个匹配模板串 res += cnt[cur]; cnt[cur] = 0; //匹配完要清空 cur = last[cur]; //顺着后缀链接走（用fail也行，但效率低） } } return res; } }ac; int main(){ scanf("%d",&T); while(T--){ ac.init(); scanf("%d",&N); for(int i = 1; i <= N; ++i){ scanf("%s",S); ac.insert(S); } ac.getfail(); scanf("%s",S); printf("%d\n",ac.find()); } return 0; }
（2）hdu 2896，依旧模板，只是要给每个单词结尾一个编号。
#include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include <vector> #include <map> #include <set> #include <stack> #include <queue> #include <string> #include <iostream> #include <algorithm> using namespace std; #define getmid(l,r) ((l) + ((r) - (l)) / 2) #define MP(a,b) make_pair(a,b) #define PB(a) push_back(a) typedef long long ll; typedef pair<int,int> pii; const double eps = 1e-8; const int INF = (1 << 30) - 1; const int MAXN = 100010; const int RA = 128; int N,M; int vis[510]; char s[10010]; struct AC_auto{ int next[MAXN][RA],f[MAXN],num[MAXN],last[MAXN]; int root,tot; void new_node(int p){ for(int i = 0; i < RA; ++i) next[p][i] = 0; f[p] = num[p] = last[p] = 0; } void init(){ root = tot = 0; new_node(root); } void insert(int k,char *str){ int len = strlen(str); int p = root; for(int i = 0; i < len; ++i){ int id = (int)str[i]; if(next[p][id] == 0){ next[p][id] = ++tot; new_node(tot); } p = next[p][id]; } num[p] = k; } void getfail(){ queue<int> Q; f[root] = root; for(int i = 0; i < RA; ++i){ int u = next[root][i]; if(u) Q.push(u); } while(!Q.empty()){ int x = Q.front(); Q.pop(); for(int i = 0; i < RA; ++i){ int u = next[x][i]; if(u == 0){ next[x][i] = next[f[x]][i]; continue; } Q.push(u); int v = f[x]; while(v && next[v][i] == 0) v = f[v]; f[u] = next[v][i]; last[u] = num[f[u]] ? f[u] : last[f[u]]; } } } int find(char *str){ int len = strlen(str); int p = root,res = 0; for(int i = 0; i < len; ++i){ int id = (int)str[i]; //while(p && next[p][id] == 0) p = f[p]; p = next[p][id]; int cur = p; while(cur != root){ if(num[cur]) res = 1; vis[num[cur]] = 1; cur = last[cur]; } } return res; } }ac; int main(){ while(scanf("%d",&N) != EOF){ ac.init(); for(int i = 1; i <= N; ++i){ scanf("%s",s); ac.insert(i,s); } ac.getfail(); int ans = 0; scanf("%d",&M); for(int i = 1; i <= M; ++i){ scanf("%s",s); memset(vis,0,sizeof(vis)); int cur = ac.find(s); if(cur){ ans++; printf("web %d:",i); for(int j = 1; j <= N; ++j) if(vis[j]) printf(" %d",j); puts(""); } } printf("total: %d\n",ans); } return 0; }
（3）hdu 3065， 模板，计算每个模式串在文本串中的出现次数，注意读入要用 gets
#include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include <vector> #include <map> #include <set> #include <stack> #include <queue> #include <string> #include <iostream> #include <algorithm> using namespace std; #define getmid(l,r) ((l) + ((r) - (l)) / 2) #define MP(a,b) make_pair(a,b) #define PB(a) push_back(a) typedef long long ll; typedef pair<int,int> pii; const double eps = 1e-8; const int INF = (1 << 30) - 1; const int MAXN = 2000010; const int RA = 26; int N; char s[MAXN],tmp[1010][60],num[1010]; struct AC_auto{ int next[50010][RA],f[50010],cnt[50010],last[50010]; int root,tot; void new_node(int p){ for(int i = 0; i < RA; ++i) next[p][i] = 0; f[p] = cnt[p] = last[p] = 0; } void init(){ root = tot = 0; new_node(root); } void insert(int k,char *str){ int len = strlen(str); int p = root; for(int i = 0; i < len; ++i){ int id = str[i] - 'A'; if(next[p][id] == 0){ next[p][id] = ++tot; new_node(tot); } p = next[p][id]; } cnt[p] = k; } void getfail(){ queue<int> Q; f[root] = root; for(int i = 0; i < RA; ++i){ int u = next[root][i]; if(u) Q.push(u); } while(!Q.empty()){ int x = Q.front(); Q.pop(); for(int i = 0; i < RA; ++i){ int u = next[x][i]; if(u == 0){ next[x][i] = next[f[x]][i]; continue; } Q.push(u); int v = f[x]; while(v && next[v][i] == 0) v = f[v]; f[u] = next[v][i]; last[u] = cnt[f[u]] ? f[u] : last[f[u]]; } } } void find(char *str){ int len = strlen(str); int p = root; for(int i = 0; i < len; ++i){ int id = str[i] - 'A'; if(id < 0 || id >= 26){ p = root; continue; } p = next[p][id]; int cur = p; while(cur != root){ num[cnt[cur]]++; cur = last[cur]; } } } }ac; int main(){ while(scanf("%d",&N) != EOF){ memset(num,0,sizeof(num)); ac.init(); for(int i = 1; i <= N; ++i){ scanf("%s",tmp[i]); ac.insert(i,tmp[i]); } ac.getfail(); getchar(); gets(s); ac.find(s); for(int i = 1; i <= N; ++i) if(num[i]){ printf("%s: %d\n",tmp[i],num[i]); } } return 0; }
