「NOI 2011」阿狸的打字机 「AC 自动机」「数据结构」

首先你需要明白，你不能把每个串都一遍遍插入，复杂度不对。

但是显然，trie树的规模很小。所以我们可以直接边在trie上dfs边插入，代码比较可读：

void construct(char* s) {
    int u = 0; 
    for (int i = 1; s[i]; ++i) {
        if (s[i] >= 'a' && s[i] <= 'z') {
            if (!tr[u][s[i] - 'a']) tr[u][s[i] - 'a'] = ++tot, ff[tr[u][s[i] - 'a']] = u;
            u = tr[u][s[i] - 'a'];
        } 
        else if (s[i] == 'B') u = ff[u]; // 撤销一个字符，也就是往父亲跳一格
        else if (s[i] == 'P') end_pos[++sz] = u; // 存储每个串的结尾位置
    }
}

然后把AC自动机建出来这题就很显然了。

也就是说，X在Y内出现了多少次，等价于在fail树上X的子树内有多少个Y经过的节点。

这个Y经过的节点也可以按dfs的顺序来，进来的时候+1，出去的时候-1，这样就可以离线存询问然后用树状数组维护dfs序就行了。

代码很好理解，只是一开始getfail写错了自闭了半天...

#include <bits/stdc++.h>

#define test(...) fprintf(stderr, __VA_ARGS__)
#define dbg(x) cerr << #x << " = " << x << '\n'

using namespace std;

typedef long long ll;
typedef pair <int, int> pii;
typedef vector <int> vi;
typedef unsigned int ui;
typedef vector <pair <int, int> > edges;
const int N = 100000 + 10; 
int n, m;
char s[N];
int tr[N][26], ff[N], fail[N], tot, end_pos[N], sz, answer[N];
vi g[N];
vector <pii> queries[N];
void construct(char* s) {
    int u = 0; 
    for (int i = 1; s[i]; ++i) {
        if (s[i] >= 'a' && s[i] <= 'z') {
            if (!tr[u][s[i] - 'a']) tr[u][s[i] - 'a'] = ++tot, ff[tr[u][s[i] - 'a']] = u;
            u = tr[u][s[i] - 'a'];
        } 
        else if (s[i] == 'B') u = ff[u];
        else if (s[i] == 'P') end_pos[++sz] = u;
    }
}
void get_fail() {
    queue <int> q;
    for (int i = 0; i < 26; ++i)
        if (tr[0][i]) q.push(tr[0][i]);
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        for (int i = 0; i < 26; ++i) {
            if (tr[u][i]) fail[tr[u][i]] = tr[fail[u]][i], q.push(tr[u][i]);
            else tr[u][i] = tr[fail[u]][i];
        }
    }
    for (int i = 1; i <= tot; ++i) {
        g[fail[i]].push_back(i), g[i].push_back(fail[i]);
    }
}
int c[N], L[N], R[N], cc;
void upd(int x, int val) {
    for(; x <= cc; x += (x & -x)) c[x] += val;
}
int range(int l, int r) {
    int ans = 0;
    for (; r; r -= (r & -r)) ans += c[r];
    --l; 
    for (; l; l -= (l & -l)) ans -= c[l];
    return ans;
}
void dfs(int u, int pre) {
    L[u] = ++cc;
    for (int i = 0; i < (int)g[u].size(); i++) if (g[u][i] != pre) dfs(g[u][i], u);
    R[u] = cc; 
}
void get_ans(char* s) {
    int nowsz = 0, u = 0;
    for (int i = 1; s[i]; ++i) {
        if (s[i] >= 'a' && s[i] <= 'z')
            upd(L[tr[u][s[i] - 'a']], 1), u = tr[u][s[i] - 'a'];
        else if (s[i] == 'B') {
            upd(L[u], -1);
            u = ff[u];
        } else if (s[i] == 'P') {
            ++nowsz;
            for (int i = 0; i < (int)queries[nowsz].size(); ++i) {
                int u = queries[nowsz][i].first, id = queries[nowsz][i].second;
                answer[id] = range(L[end_pos[u]], R[end_pos[u]]);
            }
        }
    }
}
void solve() {
    scanf ("%s", s + 1);
    construct(s);
    get_fail();
    scanf ("%d", &m);
    for (int i = 1; i <= m; ++i) {
        int x, y;
        scanf ("%d%d", &x, &y);
        queries[y].push_back({x, i});
    }
    dfs(0, 0);
//  dbg(cc); dbg(tot);
    get_ans(s);
    for (int i = 1; i <= m; ++i) 
        printf("%d\n", answer[i]); 
}

int main() {
#ifdef LOCAL
    freopen("sample.in", "r", stdin);
    freopen("test.out", "w", stdout);
#endif
  int tests = 1;
  while (tests--) solve();
  return 0;
}