虚树+dp
直接看zlttttt的强大题解 zlttttt的题解看这里
#include<bits/stdc++.h>
#define ui unsigned int
#define ll long long
#define db double
#define ld long double
#define ull unsigned long long
const int MAXN=100000+10,MAXM=100010+10,Mod=998244353;
int n,m,e,to[MAXM<<1],nex[MAXM<<1],beg[MAXN],w[MAXM<<1],Jie[MAXN][20],dfn,dfsrk[MAXN],st[MAXN],ed[MAXN],dep[MAXN],cnt,Idfn,Icnt,Istack[MAXN],Ist[MAXN],Idfsrk[MAXN],slt[MAXN],Ipoint[MAXN],In,Ie,Ibeg[MAXN],Inex[MAXM<<1],Ito[MAXM<<1],f[MAXN][2],lmt[MAXN],g[MAXN][2];
std::pair<int,int> stack[MAXM];
struct data{
int k0,k1;
data(int a=0,int b=0){
k0=a,k1=b;
}
inline data operator + (const data &A) const {
return data(k0+A.k0,k1+A.k1);
};
inline data operator * (const int a) const {
return data(1ll*k0*a%Mod,1ll*k1*a%Mod);
};
inline int value(int a,int b){
return (1ll*a*k0%Mod+1ll*b*k1%Mod)%Mod;
};
};
data coeffi[MAXN][2];
template<typename T> inline void read(T &x)
{
T data=0,w=1;
char ch=0;
while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
if(ch=='-')w=-1,ch=getchar();
while(ch>='0'&&ch<='9')data=((T)data<<3)+((T)data<<1)+(ch^'0'),ch=getchar();
x=data*w;
}
template<typename T> inline void write(T x,char ch='\0')
{
if(x<0)putchar('-'),x=-x;
if(x>9)write(x/10);
putchar(x%10+'0');
if(ch!='\0')putchar(ch);
}
template<typename T> inline void chkmin(T &x,T y){x=(y<x?y:x);}
template<typename T> inline void chkmax(T &x,T y){x=(y>x?y:x);}
template<typename T> inline T min(T x,T y){return x<y?x:y;}
template<typename T> inline T max(T x,T y){return x>y?x:y;}
inline void insert(int x,int y)
{
to[++e]=y;
nex[e]=beg[x];
beg[x]=e;
w[e]=1;
}
inline void dfs1(int x,int f)
{
dep[x]=dep[f]+1;Jie[x][0]=f;
dfsrk[st[x]=++dfn]=x;
for(register int i=beg[x];i;i=nex[i])
if(to[i]==f)w[i]=0;
else
{
if(!dep[to[i]])dfs1(to[i],x);
else w[i]=0,stack[++cnt]=std::pair<int,int>(min(x,to[i]),max(x,to[i]));
}
ed[x]=dfn;
}
inline bool cmp(int a,int b)
{
return st[a]<st[b];
}
inline int LCA(int u,int v)
{
if(dep[u]<dep[v])std::swap(u,v);
if(dep[u]>dep[v])
for(register int i=19;i>=0;--i)
if(dep[Jie[u][i]]>=dep[v])u=Jie[u][i];
if(u==v)return u;
for(register int i=19;i>=0;--i)
if(Jie[u][i]!=Jie[v][i])u=Jie[u][i],v=Jie[v][i];
return Jie[u][0];
}
inline void Iinsert(int x,int y)
{
Ito[++Ie]=y;
Inex[Ie]=Ibeg[x];
Ibeg[x]=Ie;
}
inline void dfs3(int x,int tp)
{
f[x][0]=f[x][1]=1;
for(register int i=beg[x];i;i=nex[i])
if(to[i]!=Jie[x][0]&&to[i]!=tp&&!slt[to[i]])
{
dfs3(to[i],tp);
f[x][0]=1ll*f[x][0]*((f[to[i]][0]+f[to[i]][1])%Mod)%Mod;
f[x][1]=1ll*f[x][1]*f[to[i]][0]%Mod;
}
}
inline void calc(int s,int t)
{
coeffi[s][0]=data(1,0);coeffi[s][1]=data(0,1);
data now;
for(register int i=s;Jie[i][0]!=t;i=Jie[i][0])
{
dfs3(Jie[i][0],i);
slt[Jie[i][0]]=1;
now=coeffi[s][0];
coeffi[s][0]=(coeffi[s][0]+coeffi[s][1])*f[Jie[i][0]][0];
coeffi[s][1]=now*f[Jie[i][0]][1];
}
}
inline void dfs2(int x)
{
for(register int i=Ibeg[x];i;i=Inex[i])dfs2(Ito[i]),calc(Ito[i],x);
f[x][0]=f[x][1]=1;
for(register int i=beg[x];i;i=nex[i])
if(!slt[to[i]]&&to[i]!=Jie[x][0]&&w[i]>0)
{
dfs3(to[i],0);
f[x][0]=1ll*f[x][0]*((f[to[i]][0]+f[to[i]][1])%Mod)%Mod;
f[x][1]=1ll*f[x][1]*f[to[i]][0]%Mod;
}
}
inline void dfs4(int x)
{
g[x][0]=f[x][0];
g[x][1]=f[x][1];
for(register int i=Ibeg[x],k0,k1;i;i=Inex[i])
{
dfs4(Ito[i]);
k0=coeffi[Ito[i]][0].value(g[Ito[i]][0],g[Ito[i]][1]);
k1=coeffi[Ito[i]][1].value(g[Ito[i]][0],g[Ito[i]][1]);
g[x][0]=1ll*g[x][0]*((k0+k1)%Mod)%Mod;
g[x][1]=1ll*g[x][1]*k0%Mod;
}
if(~lmt[x])g[x][lmt[x]^1]=0;
}
int main()
{
freopen("duliu.in","r",stdin);
freopen("duliu.out","w",stdout);
read(n);read(m);
for(register int i=1;i<=m;++i)
{
int u,v;
read(u);read(v);
insert(u,v);insert(v,u);
}
dep[1]=1;
dfs1(1,0);
for(register int j=1;j<20;++j)
for(register int i=1;i<=n;++i)Jie[i][j]=Jie[Jie[i][j-1]][j-1];
std::sort(stack+1,stack+cnt+1);
cnt=std::unique(stack+1,stack+cnt+1)-stack-1;
for(register int i=1;i<=cnt;++i)
{
if(!slt[stack[i].first])
{
slt[stack[i].first]=1;
Ipoint[++In]=stack[i].first;
Ist[Idfsrk[++Idfn]=stack[i].first]=Idfn;
}
if(!slt[stack[i].second])
{
slt[stack[i].second]=1;
Ipoint[++In]=stack[i].second;
Ist[Idfsrk[++Idfn]=stack[i].second]=Idfn;
}
}
std::sort(Ipoint+1,Ipoint+In+1,cmp);
for(register int i=2,limit=In;i<=limit;++i)Ipoint[++In]=LCA(Ipoint[i-1],Ipoint[i]);
Ipoint[++In]=1;
std::sort(Ipoint+1,Ipoint+In+1,cmp);
In=std::unique(Ipoint+1,Ipoint+In+1)-Ipoint-1;
Istack[++Icnt]=Ipoint[1];
for(register int i=2;i<=In;++i)
if(Icnt)
{
while(Icnt&&ed[Istack[Icnt]]<st[Ipoint[i]])Icnt--;
Iinsert(Istack[Icnt],Ipoint[i]);
Istack[++Icnt]=Ipoint[i];
}
for(register int i=1;i<=In;++i)slt[Ipoint[i]]=1;
dfs2(1);
for(register int i=1;i<=n;++i)lmt[i]=-1;
int ans=0;
for(register int i=(1<<Idfn)-1;i>=0;--i)
{
int mark=0;
for(register int j=1;j<=cnt;++j)
if((i>>(Ist[stack[j].first]-1)&1)&&(i>>(Ist[stack[j].second]-1)&1))
{
mark=1;
break;
}
if(mark)continue;
for(register int j=1;j<=Idfn;++j)lmt[Idfsrk[j]]=(i>>(j-1))&1;
dfs4(1);
(ans+=(g[1][0]+g[1][1])%Mod)%=Mod;
}
write(ans,'\n');
return 0;
}