HNOI2018 毒瘤

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出题人的官方题解

我只说几个实现细节吧。

删度为1的点时显然可以用队列维护。然后取出来的时候如果度已经为0了就不管也不要删掉这个点(树的情况)

删度为2的点时,有可能出现重边,然后就会删出自环,对于自环就不要动了(基环树?)

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/*
Author: CNYALI_LK
LANG: C++
PROG: 4426.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %lld\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %lld\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>ll chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>ll chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>ll dcmp(T a,T b){return a>b;}
template<ll *a>ll cmp_a(ll x,ll y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
const ll SIZE = (1 << 21) + 1;
char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; ll f, qr;
// getchar
#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
// prll the remaining part
inline void flush () {
fwrite (obuf, 1, oS - obuf, stdout);
oS = obuf;
}
// putchar
inline void putc (char x) {
*oS ++ = x;
if (oS == oT) flush ();
}
// input a signed lleger
inline void read (signed &x) {
for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
}

inline void read (long long &x) {
for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
}
inline void read (char &x) {
x=gc();
}
inline void read(char *x){
while((*x=gc())=='\n' || *x==' '||*x=='\r');
while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
}
template<typename A,typename ...B>
inline void read(A &x,B &...y){
read(x);read(y...);
}
// prll a signed lleger
inline void write (signed x) {
if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
while (x) qu[++ qr] = x % 10 + '0', x /= 10;
while (qr) putc (qu[qr --]);
}

inline void write (long long x) {
if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
while (x) qu[++ qr] = x % 10 + '0', x /= 10;
while (qr) putc (qu[qr --]);
}
inline void write (char x) {
putc(x);
}
inline void write(const char *x){
while(*x){putc(*x);++x;}
}
inline void write(char *x){
while(*x){putc(*x);++x;}
}
template<typename A,typename ...B>
inline void write(A x,B ...y){
write(x);write(y...);
}
//no need to call flush at the end manually!
struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
const ll p=998244353;
ll n,m,to[400055],lst[400055],beg[100005],e,a[200005][2][2],c[100005],d[100005],del[200005],delpoll[100005];
void add(ll u,ll v){to[++e]=v;lst[e]=beg[u];beg[u]=e;}
ll deg[100005];
ll q[100005],*l=q+1,*r=q;
ll poll[100005],w[200005][2][2],u[100005],v[100005];
int main(){
#ifdef cnyali_lk
freopen("4426.in","r",stdin);
freopen("4426.out","w",stdout);
#endif
read(n,m);
e=1;
for(ll i=1;i<=n;++i)c[i]=d[i]=1;
for(ll i=1;i<=m;++i){
read(*u,*v);
add(*u,*v);
add(*v,*u);
a[i][1][0]=a[i][0][1]=a[i][0][0]=1;
++deg[*u];++deg[*v];
}
for(ll i=1;i<=n;++i){
if(deg[i]==1)*(++r)=i;
}
while(l<=r){
if(!deg[*l])break;
ll x=0;

for(ll i=beg[*l];i;i=lst[i])if(!del[i>>1]){
++x;
del[i>>1]=1;
if((--deg[to[i]])==1)*(++r)=to[i];
if(i&1){
c[to[i]]*=(c[*l]*a[i>>1][1][1]+d[*l]*a[i>>1][0][1])%p;
d[to[i]]*=(c[*l]*a[i>>1][1][0]+d[*l]*a[i>>1][0][0])%p;
}
else{
c[to[i]]*=(c[*l]*a[i>>1][1][1]+d[*l]*a[i>>1][1][0])%p;
d[to[i]]*=(c[*l]*a[i>>1][0][1]+d[*l]*a[i>>1][0][0])%p;
}
c[to[i]]%=p;
d[to[i]]%=p;
}
delpoll[*l]=1;
++l;
}
for(ll i=1;i<=n;++i)if(deg[i]==2){
ll t=0;

for(ll j=beg[i];j;j=lst[j]){
if(!del[j>>1]){
poll[t]=to[j];
w[t][0][0]=a[j>>1][0][0];
w[t][1][1]=a[j>>1][1][1];
w[t][1][0]=a[j>>1][1][0];
w[t][0][1]=a[j>>1][0][1];
if(!(j&1))swap(w[t][0][1],w[t][1][0]);
++t;
}
}
if(poll[0]==i || poll[1]==i)break;
for(ll j=beg[i];j;j=lst[j]){
if(!del[j>>1]){
del[j>>1]=1;
--deg[i];
--deg[to[j]];
}
}
add(poll[1],poll[0]);
add(poll[0],poll[1]);
++deg[poll[0]];
++deg[poll[1]];
a[e>>1][0][0]=(c[i]*w[0][1][0]%p*w[1][1][0]+d[i]*w[0][0][0]%p*w[1][0][0])%p;
a[e>>1][0][1]=(c[i]*w[0][1][0]%p*w[1][1][1]+d[i]*w[0][0][0]%p*w[1][0][1])%p;
a[e>>1][1][0]=(c[i]*w[0][1][1]%p*w[1][1][0]+d[i]*w[0][0][1]%p*w[1][0][0])%p;
a[e>>1][1][1]=(c[i]*w[0][1][1]%p*w[1][1][1]+d[i]*w[0][0][1]%p*w[1][0][1])%p;
delpoll[i]=1;
}
ll t=0;
for(ll i=1;i<=n;++i)if(!delpoll[i]){poll[delpoll[i]=t]=i;++t;}
m=e>>1;e=0;
for(ll i=1;i<=m;++i)if(!del[i]){
++e;
u[e]=delpoll[to[i<<1]];
v[e]=delpoll[to[i<<1|1]];
w[e][0][0]=a[i][0][0];
w[e][0][1]=a[i][0][1];
w[e][1][0]=a[i][1][0];
w[e][1][1]=a[i][1][1];
}
ll ans=0,s;
for(ll i=0;i<1<<t;++i){
s=1;
for(ll j=0;j<t;++j){
s=s*((i&(1<<j))?c[poll[j]]:d[poll[j]])%p;

}
for(ll j=1;j<=e;++j)s=s*w[j][!!(i&(1<<u[j]))][!!(i&(1<<v[j]))]%p;
ans=(ans+s)%p;
}

printf("%lld\n",ans);
return 0;
}

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