[COCI2015]Divljak【AC自动机+fail树+LCA】

题目链接 P5840


给一组比较强的样例(我刚好是过了这个才过的):

3
aa
ba
cc
2
1 aabacc
2 2
ans:1

然后,讲一下思维的过程:

  刚看到这个问题的时候,卡在了怎样去处理“访问到仅能算一次”,而不是“访问到几次就算几次”。大白话的意思就是“aaaaaa”里有6个“a”,但是我们只能对“a”算一次,所以,返回到fail树上去。

  现在看到fail树,我们想要去重的操作,那么还是先打一下dfs序出来,然后在一条链上,我们知道dfs序更大的,一定是更深的。所以,如果说我们要去给某个点算一次的话,我们可以对它的子树中最深的算,当然,如果他的两个子树都会产生贡献的话,我们还要用LCA的差分来减一下,保证每条链上最多是“+1”。

  处理这个问题,当然有可能遇到一个点被重复出现,就譬如说“aabaa”中“a”可以出现4次,我们不能一直对着这个“a”反复操作,所以(虽然不影响——因为在同一条链上不会再产生贡献),但是为了时间上的少许优化,我们仍然可以去unique去重一下(手动最好啦!),又有dfs序更大的往往是在一条链的下面的,所以呢我们按照将序来排,先处理下面的,然后再处理上面的。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 2e6 + 7;
int N, M, tot = 0, head[maxN] = {-1}, cnt = 0, ith[100005];
char s[maxN];
struct node
{
    int nex[26], fail;
}a[maxN];
inline void Insert(int id)
{
    int len = (int)strlen(s), root = 0;
    for(int i=0, ch; i<len; i++)
    {
        ch = s[i] - 'a';
        if(!a[root].nex[ch]) { a[root].nex[ch] = ++tot; head[tot] = -1; }
        root = a[root].nex[ch];
    }
    ith[id] = root;
}
struct Eddge
{
    int nex, to;
    Eddge(int a=-1, int b=0):nex(a), to(b) {}
}edge[maxN];
inline void addEddge(int u, int v)
{
    edge[cnt] = Eddge(head[u], v);
    head[u] = cnt++;
}
inline void build_fail()
{
    queue<int> Q; Q.push(0);
    int tmp, p, son;
    while(!Q.empty())
    {
        tmp = Q.front(); Q.pop();
        for(int i=0; i<26; i++)
        {
            son = a[tmp].nex[i];
            if(son)
            {
                if(!tmp) a[son].fail = 0;
                else
                {
                    p = a[tmp].fail;
                    while(p && !a[p].nex[i]) p = a[p].fail;
                    a[son].fail = a[p].nex[i];
                }
                Q.push(son);
                addEddge(a[son].fail, son);
            }
        }
    }
}
int dfn[maxN], _Index = 0, siz[maxN], fa[maxN][21] = {0}, deep[maxN] = {0};
void dfs(int u, int father)
{
    dfn[u] = ++_Index; siz[dfn[u]] = 1;
    if(~father)
    {
        fa[dfn[u]][0] = dfn[father]; deep[dfn[u]] = deep[dfn[father]] + 1;
        for(int i=0; i < 20; i++) { fa[dfn[u]][i + 1] = fa[fa[dfn[u]][i]][i]; }
    }
    for(int i=head[u], v; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        dfs(v, u);
        siz[dfn[u]] += siz[dfn[v]];
    }
}
bool live_the_same = true;
inline int _LCA(int u, int v)
{
    if(deep[u] < deep[v]) swap(u, v);
    int det = deep[u] - deep[v];
    if(det) for(int i=log2(det); ~i; i--) if((det >> i) & 1) u = fa[u][i];
    if(u == v) return u;
    live_the_same = false;
    for(int i=20; i>=0; i--)
    {
        if(fa[u][i] ^ fa[v][i])
        {
            u = fa[u][i];
            v = fa[v][i];
        }
    }
    return fa[u][0];
}
int vt[maxN], iter;
inline bool cmp(int e1, int e2) { return e1 > e2; }
int trie[maxN] = {0};
inline void update(int x, int val) { while(x < maxN) { trie[x] += val; x += lowbit(x); } }
inline int query(int x) { int ss = 0; while(x) { ss += trie[x]; x -= lowbit(x); } return ss; }
inline int Range_Query(int l, int r) { return query(r) - query(l - 1); }
inline void _Fid()
{
    int len = (int)strlen(s), root = 0;
    iter = 0;
    for(int i=0, ch; i<len; i++)
    {
        ch = s[i] - 'a';
        if(a[root].nex[ch])
        {
            root = a[root].nex[ch];
            vt[++iter] = dfn[root];
        }
        else
        {
            root = a[root].fail;
            while(root && !a[root].nex[ch]) root = a[root].fail;
            if(a[root].nex[ch])
            {
                root = a[root].nex[ch];
                vt[++iter] = dfn[root];
            }
        }
    }
    sort(vt + 1, vt + iter + 1, cmp);
    len = 0;
    if(iter)
    {
        vt[++len] = vt[1];
        for(int i=2; i<=iter; i++)
        {
            if(vt[i] ^ vt[len]) vt[++len] = vt[i];
        }
    }
    int u, v;
    if(len == 1)
    {
        u = vt[1];
        update(u, 1);
    }
    else
    {
        u = vt[1];
        update(u, 1);
        for(int i=2, _lca; i<=len; i++)
        {
            live_the_same = true;
            v = vt[i]; _lca = _LCA(u, v);
            if(!live_the_same)
            {
                update(v, 1); update(_lca, -1);
            }
            u = v;
        }
    }
}
int main()
{
    scanf("%d", &N);
    for(int i=1; i<=N; i++)
    {
        scanf("%s", s);
        Insert(i);
    }
    build_fail();
    dfs(0, -1);
    scanf("%d", &M);
    int op, x;
    while(M--)
    {
        scanf("%d", &op);
        if(op == 1)
        {
            scanf("%s", s);
            _Fid();
        }
        else
        {
            scanf("%d", &x);
            printf("%d\n", Range_Query(dfn[ith[x]], dfn[ith[x]] + siz[dfn[ith[x]]] - 1));
        }
    }
    return 0;
}
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