cf666E. Forensic Examination(广义后缀自动机 线段树合并)

题意

题目链接

sol

神仙题orz

后缀自动机 + 线段树合并

首先对所有的\(t_i\)建个广义后缀自动机，这样可以得到所有子串信息。

考虑把询问离线，然后把\(s\)拿到自动机上跑，同时维护一下最长能匹配的位置，对于每个以\(i\)位置为右端点的询问我们需要找到\(len\)最小的状态满足\(len[sta] >= pr - pl + 1\)(这部分把每个以\(i\)为端点的询问排序后暴力跳即可，复杂度\(o(n \sqrt{n})\))。那么现在的问题就是对于每个状态，如何知道他在每个\(t_i\)中的出现次数。

直接线段树合并一下就好啦

总复杂度：\(o(大常数的nlogn + 小常数的n\sqrt{n})\)

疯狂wa的原因居然是pair<int, int>不支持自定义小于号

#include<bits/stdc++.h>
using namespace std;
const int maxn = 2e6 + 10;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int n, m, q;
struct pair {
    int fi, se;
};
bool operator < (const pair &a, const pair &b) {
    return (a.fi < b.fi) || (a.fi == b.fi && a.se > b.se);
}
pair operator + (const pair &a, const pair &b) {
    return {a.fi + b.fi, a.se};
}
pair ans[maxn];
char s[maxn];
string t[maxn];
struct query {
    int pl, l, r, id;
    bool operator < (const query &rhs) const {
        return pl < rhs.pl;
    }
};
vector<query> qry[maxn];
namespace seg {
int root[maxn], ls[maxn], rs[maxn], cnt;
pair mx[maxn];

void update(int k) {
    mx[k] = max(mx[ls[k]], mx[rs[k]]);
}
void intadd(int &k, int l, int r, int p, int v) {
    if(!k) k = ++cnt;
    if(l == r) {mx[k].fi++; mx[k].se = l; return ;}
    int mid = l + r >> 1;
    if(p <= mid) intadd(ls[k], l, mid, p, v);
    else intadd(rs[k], mid + 1, r, p, v);
    update(k);
}
int merge(int x, int y) {
    if(!x || !y) return x ^ y;
    int nw = ++cnt; mx[nw] = mx[x];
    if(!ls[x] && !rs[x]) {mx[nw].fi += mx[y].fi; return nw;}
    ls[nw] = merge(ls[x], ls[y]);
    rs[nw] = merge(rs[x], rs[y]);
    update(nw);
    return nw;
}
pair query(int k, int l, int r, int ql, int qr) {
    if(!k) return {0, 0};
    if(ql <= l && r <= qr) return mx[k];
    int mid = l + r >> 1;
    if(ql > mid) return query(rs[k], mid + 1, r, ql, qr);
    else if(qr <= mid) return query(ls[k], l, mid, ql, qr);
    else {
        pair al = query(ls[k], l, mid, ql, qr);
        pair ar = query(rs[k], mid + 1, r, ql, qr);
        if((al.fi > ar.fi) || (al.fi == ar.fi && al.se < ar.se)) return al;
        else return ar;
    }
}
}
namespace sam {
    
int fa[maxn], ch[maxn][26], len[maxn], root = 1, las = 1, tot = 1;
vector<int> par[maxn];
void insert(int x, int id) {
    int now = ++tot, pre = las; las = now; len[now] = len[pre] + 1;
    if(id) seg::intadd(seg::root[now], 1, m, id, 1);
    for(; pre && !ch[pre][x]; pre = fa[pre]) ch[pre][x] = now;
    if(!pre) fa[now] = root;
    else {
        int q = ch[pre][x];
        if(len[pre] + 1 == len[q]) fa[now] = q;
        else {
            int nq = ++tot; fa[nq] = fa[q]; len[nq] = len[pre] + 1;
            memcpy(ch[nq], ch[q], sizeof(ch[q]));
            for(; pre && ch[pre][x] == q; pre = fa[pre]) ch[pre][x] = nq;
            fa[q] = fa[now] = nq;
        }
    }
    
}
void build() {
    for(int i = 1; i <= tot; i++) par[fa[i]].push_back(i);
}
void dfs(int x) {
    for(auto &to : par[x]) {
        dfs(to);
        seg::root[x] = seg::merge(seg::root[x], seg::root[to]); 
    }
}
void work() {
    int now = root, dl = 0;
    for(int i = 1; i <= n; i++) {
        int nxt = s[i] - 'a';
        while(!ch[now][nxt] && now) now = fa[now], dl = len[now];
        if(!now) {
            now = 1; dl = 0; 
            for(auto &q : qry[i]) ans[q.id].se = q.l;
            continue;
        }
        now = ch[now][nxt]; dl++;
        int t = now;
        for(auto &q : qry[i]) {
            if(dl < i - q.pl + 1) {ans[q.id].se = q.l; continue;}
            while(len[fa[t]] >= i - q.pl + 1) t = fa[t];
            ans[q.id] = seg::query(seg::root[t], 1, m, q.l, q.r);
            if(!ans[q.id].fi) ans[q.id].se = q.l;
        }
    }
}

}
int main() {
//  freopen("a.in", "r", stdin);
    scanf("%s", s + 1);
    n = strlen(s + 1);
    cin >> m;
    for(int i = 1; i <= m; i++) {
        cin >> t[i];
        string &ns = t[i];
        for(int j = 0; j < ns.length(); j++) sam::insert(ns[j] - 'a', i);
        sam::las = 1;
    } 
    sam::build();
    sam::dfs(1);
//  for(int i = 1; i <= seg::cnt; i++) printf("%d ", seg::mx[i]);
    cin >> q;
    for(int i = 1; i <= q; i++) {
        int l = read(), r = read(), pl = read(), pr = read();
        qry[pr].push_back({pl, l, r, i});
    }
    for(int i = 1; i <= n; i++) stable_sort(qry[i].begin(), qry[i].end());
    sam::work();
    for(int i = 1; i <= q; i++) {
        printf("%d %d\n", ans[i].se, ans[i].fi);
    }
    return 0;
}