[SDOI2018]战略游戏【广义圆方树+虚树】

题目链接 P4606

---

  很容易发现一点，题目要我们求的实际上就是我们的新构的树中的，圆点的个数，所以呢，在这里我们可以直接通过先利用广义圆方树来再求一个虚树，我们直接查询虚树就可以完成这个要求了。

#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 = 2e5 + 7;
int N, M, Q, LOG2[maxN];
struct Graph
{
    int head[maxN], cnt;
    struct Eddge
    {
        int nex, to, val;
        Eddge(int a=-1, int b=0, int c=0):nex(a), to(b), val(c) {}
    } edge[maxN << 2];
    inline void addEddge(int u, int v, int w)
    {
        edge[cnt] = Eddge(head[u], v, w);
        head[u] = cnt++;
    }
    inline void _add(int u, int v, int w) { addEddge(u, v, w); addEddge(v, u, w); }
    inline void init()
    {
        cnt = 0;
        for(int i=1; i<=N; i++) head[i] = -1;
    }
} Old, Now;
struct Tarjan_Struct
{
    int dfn[maxN], tot, low[maxN], Bcnt, Stap[maxN], Stop;
    void Tarjan(int u, int fa)
    {
        dfn[u] = low[u] = ++tot;
        Stap[++Stop] = u;
        for(int i=Old.head[u], v, p; ~i; i=Old.edge[i].nex)
        {
            v = Old.edge[i].to;
            if(v == fa) continue;
            if(!dfn[v])
            {
                Tarjan(v, u);
                if(low[v] >= dfn[u])
                {
                    Bcnt++; Now.head[N + Bcnt] = -1;
                    do
                    {
                        p = Stap[Stop--];
                        Now._add(p, Bcnt + N, 0);
                    } while(v ^ p);
                    Now._add(u, Bcnt + N, 0);
                }
                low[u] = min(low[u], low[v]);
            }
            else low[u] = min(low[u], dfn[v]);
        }
    }
    inline void clear() { tot = Stop = Bcnt = 0; for(int i=1; i<=N; i++) dfn[i] = 0; }
} tj;
struct pre_Build_Graph
{
    int dfn[maxN], tot, deep[maxN], root[maxN][20], have_id[maxN];
    void pre_dfs(int u, int fa)
    {
        dfn[u] = ++tot; deep[u] = deep[fa] + 1; root[u][0] = fa; have_id[u] = have_id[fa] + (u > N ? 0 : 1);
        for(int i=0; i <= LOG2[N]; i++) root[u][i + 1] = root[root[u][i]][i];
        for(int i=Now.head[u], v; ~i; i=Now.edge[i].nex)
        {
            v = Now.edge[i].to;
            if(v == fa) continue;
            pre_dfs(v, u);
        }
    }
    void clear() { tot = 0; root[0][0] = 0; have_id[0] = 0; deep[0] = 0; }
} pbg;
inline int _LCA(int u, int v)
{
    if(pbg.deep[u] < pbg.deep[v]) swap(u, v);
    int det = pbg.deep[u] - pbg.deep[v];
    for(int i=LOG2[det]; i>=0; i--)
    {
        if((det >> i) & 1) u = pbg.root[u][i];
    }
    if(u == v) return u;
    for(int i=LOG2[N]; i>=0; i--)
    {
        if(pbg.root[u][i] ^ pbg.root[v][i])
        {
            u = pbg.root[u][i];
            v = pbg.root[v][i];
        }
    }
    return pbg.root[u][0];
}
inline bool cmp(int e1, int e2) { return pbg.dfn[e1] < pbg.dfn[e2]; }
int ans_sum, qid[maxN], Stk[maxN], Stp;
bool used[maxN] = {false};
inline void Insert(int u)
{
    if(!Stp) { Stk[++Stp] = u; return; }
    int lca = _LCA(u, Stk[Stp]);
    if(lca == Stk[Stp]) { Stk[++Stp] = u; return; }
    while(Stp > 1 && pbg.dfn[lca] <= pbg.dfn[Stk[Stp - 1]])
    {
        ans_sum += pbg.have_id[Stk[Stp]] - pbg.have_id[Stk[Stp - 1]] - (used[Stk[Stp]] ? 1 : 0);
        Stp--;
    }
    if(lca ^ Stk[Stp])
    {
        ans_sum += pbg.have_id[Stk[Stp]] - pbg.have_id[lca] - (used[Stk[Stp]] ? 1 : 0);
        Stk[Stp] = lca;
    }
    Stk[++Stp] = u;
}
inline void init()
{
    tj.clear(); pbg.clear();
    Old.init(); Now.init();
}
int main()
{
    for(int i = 1, j = 2, k = 0; i < maxN; i++)
    {
        if(i == j) { k++; j <<= 1; }
        LOG2[i] = k;
    }
    int T; scanf("%d", &T);
    while(T--)
    {
        scanf("%d%d", &N, &M);
        init();
        for(int i=1, u, v; i<=M; i++)
        {
            scanf("%d%d", &u, &v);
            Old._add(u, v, 0);
        }
        tj.Tarjan(1, 0);
        pbg.pre_dfs(1, 0);
        scanf("%d", &Q);
        int sz;
        while(Q--)
        {
            scanf("%d", &sz);
            for(int i=1; i<=sz; i++) { scanf("%d", &qid[i]); used[qid[i]] = true; }
            sort(qid + 1, qid + sz + 1, cmp);
            Stp = 0; ans_sum = 0;
            for(int i=1; i<=sz; i++) Insert(qid[i]);
            while(Stp > 1)
            {
                ans_sum += pbg.have_id[Stk[Stp]] - pbg.have_id[Stk[Stp - 1]] - (used[Stk[Stp]] ? 1 : 0);
                Stp--;
            }
            if(!used[Stk[Stp]] && Stk[Stp] <= N) ans_sum++;
            for(int i=1; i<=sz; i++) used[qid[i]] = false;
            printf("%d\n", ans_sum);
        }
    }
    return 0;
}