QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#382284 | #8568. Expected Diameter | Crysfly | AC ✓ | 3974ms | 56964kb | C++17 | 7.1kb | 2024-04-08 10:55:36 | 2024-04-08 10:55:37 |
Judging History
answer
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ull unsigned long long
using namespace std;
inline int read()
{
char c=getchar();int x=0;bool f=0;
for(;!isdigit(c);c=getchar())f^=!(c^45);
for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
if(f)x=-x;return x;
}
#define mod 998244353
struct modint{
int x;
modint(int o=0){x=o;}
modint &operator = (int o){return x=o,*this;}
modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
modint &operator ^=(int b){
modint a=*this,c=1;
for(;b;b>>=1,a*=a)if(b&1)c*=a;
return x=c.x,*this;
}
modint &operator /=(modint o){return *this *=o^=mod-2;}
friend modint operator +(modint a,modint b){return a+=b;}
friend modint operator -(modint a,modint b){return a-=b;}
friend modint operator *(modint a,modint b){return a*=b;}
friend modint operator /(modint a,modint b){return a/=b;}
friend modint operator ^(modint a,int b){return a^=b;}
friend bool operator ==(modint a,modint b){return a.x==b.x;}
friend bool operator !=(modint a,modint b){return a.x!=b.x;}
bool operator ! () {return !x;}
modint operator - () {return x?mod-x:0;}
bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}
vector<modint> fac,ifac,iv;
inline void initC(int n)
{
if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
int m=iv.size(); ++n;
if(m>=n)return;
iv.resize(n),fac.resize(n),ifac.resize(n);
For(i,m,n-1){
iv[i]=iv[mod%i]*(mod-mod/i);
fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
}
}
inline modint C(int n,int m){
if(m<0||n<m)return 0;
return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}
#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;
#define poly vector<modint>
const modint G=3,Ginv=modint(1)/3;
inline poly one(){poly a;a.push_back(1);return a;}
vector<int>rev;
int rts[2100000];
inline int ext(int n){
int k=0;
while((1<<k)<n)++k;return k;
}
inline void init(int k){
int n=1<<k;
rts[0]=1,rts[1<<k]=qpow(31,1<<(21-k)).x;
Rep(i,k,1)rts[1<<(i-1)]=1ull*rts[1<<i]*rts[1<<i]%mod;
For(i,1,n-1)rts[i]=1ull*rts[i&(i-1)]*rts[i&-i]%mod;
}
void ntt(poly&a,int k,int typ){
int n=1<<k;
static ull tmp[2100000];
for(int i=0;i<n;++i)tmp[i]=a[i].x;
if(typ==1){
for(int l=n>>1;l>=1;l>>=1){
ull*k=tmp;
for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
for(ull*x=k;x<k+l;++x){
int o=x[l]%mod*(*g)%mod;
x[l]=*x+mod-o,*x+=o;
}
}
}
for(int i=0;i<n;++i)a[i].x=tmp[i]%mod;
}else{
for(int l=1;l<n;l<<=1){
ull*k=tmp;
for(int*g=rts;k<tmp+n;k+=(l<<1),++g){
for(ull*x=k;x<k+l;++x){
int o=x[l]%mod;
x[l]=(*x+mod-o)*(*g)%mod,*x+=o;
}
}
}
int iv=qpow(n,mod-2).x;
for(int i=0;i<n;++i)a[i].x=tmp[i]%mod*iv%mod;
reverse(a.begin()+1,a.end());
}
}
poly operator +(poly a,poly b){
int n=max(a.size(),b.size());a.resize(n),b.resize(n);
For(i,0,n-1)a[i]+=b[i];return a;
}
poly operator -(poly a,poly b){
int n=max(a.size(),b.size());a.resize(n),b.resize(n);
For(i,0,n-1)a[i]-=b[i];return a;
}
poly operator *(poly a,modint b){
int n=a.size();
For(i,0,n-1)a[i]*=b;return a;
}
poly operator *(poly a,poly b){
if(!a.size()||!b.size())return {};
if((int)a.size()<=32 || (int)b.size()<=32){
poly c(a.size()+b.size()-1,0);
for(int i=0;i<a.size();++i)for(int j=0;j<b.size();++j)c[i+j]+=a[i]*b[j];
return c;
}
int n=(int)a.size()+(int)b.size()-1,k=ext(n);
a.resize(1<<k),b.resize(1<<k);
ntt(a,k,1),ntt(b,k,1);
For(i,0,(1<<k)-1)a[i]*=b[i];
ntt(a,k,-1),a.resize(n);return a;
}
poly Tmp;
poly pmul(poly a,poly b,int n,bool ok=0)
{
int k=ext(n);
a.resize(1<<k),ntt(a,k,1);
if(!ok) b.resize(1<<k),ntt(b,k,1),Tmp=b;
For(i,0,(1<<k)-1)a[i]*=Tmp[i];
ntt(a,k,-1),a.resize(n);
return a;
}
poly inv(poly a,int n)
{
a.resize(n);
if(n==1){
poly f(1,1/a[0]);
return f;
}
poly f0=inv(a,(n+1)>>1),f=f0;
poly now=pmul(a,f0,n,0);
for(int i=0;i<f0.size();++i)now[i]=0;
now=pmul(now,poly(0),n,1);
f.resize(n);
for(int i=f0.size();i<n;++i)f[i]=-now[i];
return f;
}
poly inv(poly a){return inv(a,a.size());}
poly deriv(poly a){
int n=(int)a.size()-1;
For(i,0,n-1)a[i]=a[i+1]*(i+1);
a.resize(n);return a;
}
poly inter(poly a){
int n=a.size()+1;a.resize(n); initC(n);
Rep(i,n-1,1)a[i]=a[i-1]*iv[i];
a[0]=0;return a;
}
poly ln(poly a){
int n=a.size();
a=deriv(a)*inv(a),a.resize(n-1);return inter(a);
}
poly exp(poly a,int k){
int n=1<<k;a.resize(n);
if(n==1)return one();
poly f0=exp(a,k-1);f0.resize(n);
return f0*(one()+a-ln(f0));
}
poly exp(poly a){
int n=a.size();
a=exp(a,ext(n));a.resize(n);return a;
}
poly div(poly a,poly b){
int n=a.size(),m=b.size(),k=ext(n-m+1);
reverse(a.begin(),a.end()),reverse(b.begin(),b.end());
a.resize(n-m+1),b.resize(n-m+1);
a=a*inv(b),a.resize(n-m+1),reverse(a.begin(),a.end()); return a;
}
poly modulo(poly a,poly b){
if(b.size()>a.size())return a;
int n=b.size()-1;
a=a-div(a,b)*b;a.resize(n);return a;
}
#define maxn 200005
#define inf 0x3f3f3f3f
int n;
modint p1,p2;
poly g[2005],h[2005],h2[2005];
signed main()
{
n=read(); initC(n+5);
modint X=read(),Y=read();
p1=X/Y,p2=1-p1;
if(n==1){
puts("0");
exit(0);
}
init(19);
g[0].resize(n+1),g[0][1]=1;
h[0]=g[0];
For(i,1,n){
if(i==1) g[i]=exp(g[i-1]*p1);
else g[i]=exp(g[i-1]*p1+g[i-2]*p2);
g[i].insert(g[i].begin(),0);
g[i].resize(n+1);
h[i]=g[i]-g[i-1];
// For(j,0,n) cout<<(g[i][j]*fac[j]).x<<" "; cout<<" g\n";
// For(j,0,n) cout<<(h[i][j]*fac[j]).x<<" "; cout<<" h\n";
}
// exit(0);
modint res=0;
// on edge
For(i,0,n){
// poly ans=h[i]*h[i];
// modint add=ans[n]*((mod+1)/2);
// cout<<"ans: "<<i*2+1<<" "<<add.x<<"\n";
modint add=0;
For(j,0,n) add+=h[i][j]*h[i][n-j];
add*=((mod+1)/2);
// cout<<"ans_2 "<<i<<" "<<add.x<<"\n";
add*=(i*2+(p1+p2*2));
res+=add;
if(i){
// (i-1) - 2 - i
add=0;
For(j,0,n) add+=h[i][j]*h[i-1][n-j];
add*=(i*2+1)*p2;
res+=add;
}
}
// cout<<"res "<<(res*fac[n]).x<<"\n";
// puts("QAQ");
// on point
For(i,1,n){
poly hh=h[i-1]*p1;
if(i>=2) hh=hh+h[i-2]*p2;
// poly tmp=(exp(hh)-one()-hh);
poly tmp=exp(hh);
tmp=tmp-one()-hh;
// tmp=(exp(h[i-1]*p1)-one()-(h[i-1]*p1));
tmp.resize(n+1);
// For(j,0,n)cout<<(hh[j]*fac[j]).x<<" "; cout<<" hh\n";
// if(i>=2 && p2.x) {
// poly t2=(exp(h[i-2]*p2)-one()-(h[i-2]*p2));
// for(auto x:t2)cout<<x.x<<" "; cout<<"t2\n";
// tmp=tmp*t2;
// }
// tmp=tmp*g[i-1];
// cout<<"SZ "<<g[i-1].size()<<" "<<tmp.size()<<"\n";
// For(j,0,n) cout<<(tmp[j]*fac[j]).x<<" "; cout<<" tmp\n";
modint add=0;
For(j,0,n) add+=tmp[j]*g[i-1][n-j];
// cout<<"Ans "<<i*2<<" "<<add.x<<"\n";
res+=add*(i*2);
}
res*=fac[n];
// cout<<"res "<<res.x<<"\n";
res/=qpow(n,n-2);
cout<<res.x;
return 0;
}
/*
1 2 3
*/
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 2ms
memory: 8700kb
input:
2 1 3
output:
665496237
result:
ok 1 number(s): "665496237"
Test #2:
score: 0
Accepted
time: 0ms
memory: 9000kb
input:
3 2 3
output:
665496238
result:
ok 1 number(s): "665496238"
Test #3:
score: 0
Accepted
time: 3967ms
memory: 56176kb
input:
2000 1 2
output:
254870088
result:
ok 1 number(s): "254870088"
Test #4:
score: 0
Accepted
time: 3970ms
memory: 56912kb
input:
2000 1 3
output:
193693601
result:
ok 1 number(s): "193693601"
Test #5:
score: 0
Accepted
time: 3974ms
memory: 56964kb
input:
1999 188 211
output:
463395288
result:
ok 1 number(s): "463395288"
Test #6:
score: 0
Accepted
time: 3962ms
memory: 56852kb
input:
1990 470 818
output:
479264654
result:
ok 1 number(s): "479264654"
Test #7:
score: 0
Accepted
time: 948ms
memory: 21588kb
input:
1000 407 783
output:
20089106
result:
ok 1 number(s): "20089106"
Test #8:
score: 0
Accepted
time: 940ms
memory: 21456kb
input:
990 884 901
output:
94051884
result:
ok 1 number(s): "94051884"
Test #9:
score: 0
Accepted
time: 942ms
memory: 20660kb
input:
995 873 988
output:
209191626
result:
ok 1 number(s): "209191626"
Test #10:
score: 0
Accepted
time: 233ms
memory: 10908kb
input:
500 307 938
output:
603465152
result:
ok 1 number(s): "603465152"
Test #11:
score: 0
Accepted
time: 229ms
memory: 11940kb
input:
490 237 732
output:
402554558
result:
ok 1 number(s): "402554558"
Test #12:
score: 0
Accepted
time: 232ms
memory: 12028kb
input:
495 473 511
output:
833418554
result:
ok 1 number(s): "833418554"
Test #13:
score: 0
Accepted
time: 55ms
memory: 9688kb
input:
250 69 207
output:
786182422
result:
ok 1 number(s): "786182422"
Test #14:
score: 0
Accepted
time: 56ms
memory: 10128kb
input:
240 184 259
output:
473414786
result:
ok 1 number(s): "473414786"
Test #15:
score: 0
Accepted
time: 54ms
memory: 10372kb
input:
245 478 807
output:
312847415
result:
ok 1 number(s): "312847415"
Test #16:
score: 0
Accepted
time: 17ms
memory: 9972kb
input:
125 112 253
output:
31497383
result:
ok 1 number(s): "31497383"
Test #17:
score: 0
Accepted
time: 16ms
memory: 10084kb
input:
120 137 498
output:
923043504
result:
ok 1 number(s): "923043504"
Test #18:
score: 0
Accepted
time: 13ms
memory: 8116kb
input:
100 230 792
output:
203877027
result:
ok 1 number(s): "203877027"
Extra Test:
score: 0
Extra Test Passed