算法提高-AC自动机

AC自动机其实就是Trie+KMP，AC自动机还可与稍微扩展一下，扩展成Trie图的形式（每次fial的时候可以一步到位，不需要一步一步慢慢跳）
很好的一篇博客trie树和优化成trie图都说的很清楚

AcWing 1282. 搜索关键词

#include 
#include 
using namespace std;

const int N = 1e4 + 10, S = 55, M = 1e6 + 10;
int n, T;
int cnt[N * S], q[N * S], tr[N * S][26], ne[N * S], idx;
char str[M];

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()//建立trie树
{
    int hh = 0, tt = -1;
    for (int i = 0; i < 26; ++ i)
    {
        if (tr[0][i]) q[++tt] = tr[0][i];//之前没加if TLE了
    }
    
    while (hh <= tt)
    {
        int t = q[hh++];
        for (int i = 0; i < 26; ++ i)
        {
            int p = tr[t][i];
            if (p)
            {
                int j = ne[t];
                while (j && !tr[j][i]) j = ne[j];
                if (tr[j][i]) j = tr[j][i];
                ne[p] = j;
                q[++tt] = p;
            }
        }
    }
}

void match()//匹配
{
    int res = 0;
    cin >> str;
    for (int i = 0, j = 0; str[i]; ++ i)
    {
        int t = str[i] - 'a';
        while (j && !tr[j][t]) j = ne[j];
        
        if (tr[j][t]) j = tr[j][t];
        int p = j;
        while (p)
        {
            res += cnt[p];
            cnt[p] = 0;
            p = ne[p];
        }
    }
    
    cout << res << endl;
}
void solve()
{
    memset(cnt, 0, sizeof cnt); 
    memset(tr, 0, sizeof tr);
    memset(ne, 0, sizeof ne);
    idx = 0;
    cin >> n;
    for (int i = 0; i < n; ++ i)
    {
        cin >> str;
        insert();
    }
    
    build();
    match();
}
int main()
{
    cin >> T;
    while (T --) solve();
    return 0;
}
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优化成trie图

#include 
#include 
using namespace std;

const int N = 1e4 + 10, S = 55, M = 1e6 + 10;
int n, T;
int cnt[N * S], q[N * S], tr[N * S][26], ne[N * S], idx;
char str[M];

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()//建立trie树
{
    int hh = 0, tt = -1;
    for (int i = 0; i < 26; ++ i)
    {
        if (tr[0][i]) q[++tt] = tr[0][i];//之前没加if TLE了
    }
    
    while (hh <= tt)
    {
        int t = q[hh++];
        for (int i = 0; i < 26; ++ i)
        {
            int p = tr[t][i];
            //优化 相当于并查集路径压缩的思想
            if(!p) tr[t][i] = tr[ne[t]][i];//如果不存在t的子节点i
            else
            {
                ne[p] = tr[ne[t]][i];
                q[++tt] = p;
            }
        }
    }
}

void match()//匹配
{
    int res = 0;
    cin >> str;
    for (int i = 0, j = 0; str[i]; ++ i)
    {
        int t = str[i] - 'a';
        j = tr[j][t];//不用一步一步跳判断是否存在tr[j][t]了，最差的情况是直接指向根节点
        int p = j;
        while (p)
        {
            res += cnt[p];
            cnt[p] = 0;
            p = ne[p];
        }
    }
    
    cout << res << endl;
}
void solve()
{
    memset(cnt, 0, sizeof cnt); 
    memset(tr, 0, sizeof tr);
    memset(ne, 0, sizeof ne);
    idx = 0;
    cin >> n;
    for (int i = 0; i < n; ++ i)
    {
        cin >> str;
        insert();
    }
    
    build();
    match();
}
int main()
{
    cin >> T;
    while (T --) solve();
    return 0;
}
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优化到真正的线性复杂度