BZOJ3569 DZY Loves Chinese II（随机化+树上差分+线性基）

　　上一题的强制在线版。对图跑出一个dfs树，给非树边赋上随机权值，树边的权值为覆盖他的非树边权值的异或。这样如果某条树边和覆盖他的非树边都被割掉（即图不连通），他们的异或值就为0。每次对询问看有没有子集异或值为0即可，可以简单地用线性基搞定。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
#define N 100010
#define M 500010
int n,m,k,p[N],t=1,lastans=0;
bool flag[N];
unsigned long long v[M],f[N],base[64];
struct data{int to,nxt;
}edge[M<<1];
void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}
void dfs(int k,int from)
{
    flag[k]=1;
    for (int i=p[k];i;i=edge[i].nxt)
    if (edge[i].to!=from)
    {
        if (!flag[edge[i].to]) dfs(edge[i].to,k);
        else v[i>>1]=rand()+1,v[i>>1]*=rand()+1,v[i>>1]*=rand()+1,v[i>>1]*=rand()+1;
    }
}
void getvalue(int k)
{
    flag[k]=1;
    for (int i=p[k];i;i=edge[i].nxt)
    if (!flag[edge[i].to])
    {
        getvalue(edge[i].to);
        v[i>>1]=f[edge[i].to];
        f[k]^=f[edge[i].to];
    }
}
int main()
{
    freopen("bzoj3569.in","r",stdin);
    freopen("bzoj3569.out","w",stdout);
    n=read(),m=read();
    srand(20020509*(m/n));
    for (int i=1;i<=m;i++)
    {
        int x=read(),y=read();
        addedge(x,y),addedge(y,x);
    }
    dfs(1,1);
    for (int i=2;i<=m*2+1;i++) 
    if (i&1) f[edge[i].to]^=v[i>>1],f[edge[i^1].to]^=v[i>>1];
    memset(flag,0,sizeof(flag));
    getvalue(1);
    k=read();
    for (int i=1;i<=k;i++)
    {
        int s=read();
        memset(base,0,sizeof(base));
        bool flag=1;
        for (int j=1;j<=s;j++)
        {
            int x=read()^lastans;
            unsigned long long w=v[x];
            for (int l=63;~l;l--)
            if (w&(1ll<<l))
            {
                if (!base[l]) {base[l]=w;break;}
                else w^=base[l];
            }
            if (!w) flag=0;
        }
        if (flag) lastans++,printf("Connected\n");
        else printf("Disconnected\n");
    }
    fclose(stdin);fclose(stdout);
    return 0;
}