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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#431914 | #8721. 括号序列 | A_zjzj | AC ✓ | 1517ms | 24456kb | C++14 | 4.9kb | 2024-06-06 11:55:18 | 2024-06-06 11:55:20 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
using ll=long long;
#define all(a) (a).begin(),(a).end()
#ifdef DEBUG
template<class T>
ostream& operator << (ostream &out,vector<T> a){
out<<'[';
for(T x:a)out<<x<<',';
return out<<']';
}
template<class T>
vector<T> ary(T *a,int l,int r){
return vector<T>{a+l,a+1+r};
}
template<class T>
void debug(T x){
cerr<<x<<endl;
}
template<class T,class...S>
void debug(T x,S...y){
cerr<<x<<' ',debug(y...);
}
#else
#define debug(...) void()
#endif
const int N=2.5e5+10,mod=998244353;
ll qpow(ll x,ll y=mod-2,ll ans=1){
for(;y;(x*=x)%=mod,y>>=1)if(y&1)(ans*=x)%=mod;
return ans;
}
namespace Poly{
const int N=1<<19,g=3;
int lim,rev[N],pw[N];
void Init(){
int base=qpow(g,(mod-1)/N);
pw[N/2]=1;
for(int i=N/2+1;i<N;i++)pw[i]=1ll*pw[i-1]*base%mod;
for(int i=N/2-1;i>=1;i--)pw[i]=pw[i<<1];
}
void init(int n){
for(lim=1;lim<n;lim<<=1);
for(int i=1;i<lim;i++)rev[i]=rev[i>>1]>>1|(i&1?lim>>1:0);
}
void NTT(int *a,int op){
for(int i=0;i<lim;i++)if(rev[i]<i)swap(a[rev[i]],a[i]);
for(int len=1;len<lim;len<<=1){
for(int i=0;i<lim;i+=len<<1){
for(int j=0;j<len;j++){
int x=1ll*a[i|j|len]*pw[len|j]%mod;
a[i|j|len]=(a[i|j]+mod-x)%mod;
a[i|j]=(a[i|j]+x)%mod;
}
}
}
if(op<0){
reverse(a+1,a+lim);
int x=qpow(lim);
for(int i=0;i<lim;i++)a[i]=1ll*a[i]*x%mod;
}
}
namespace Public{
using poly=vector<int>;
poly operator * (const poly &a,const poly &b){
static int A[N],B[N];
int n=a.size(),m=b.size();
init(n+m-1);
copy(all(a),A),fill(A+n,A+lim,0);
copy(all(b),B),fill(B+m,B+lim,0);
NTT(A,1),NTT(B,1);
for(int i=0;i<lim;i++)A[i]=1ll*A[i]*B[i]%mod;
NTT(A,-1);
return poly{A,A+n+m-1};
}
poly operator % (const poly &a,const int &n){
poly b(a);
if(n<b.size())b.resize(n);
return b;
}
poly operator * (const poly &a,const int &k){
poly b(a);
for(int &x:b)x=1ll*x*k%mod;
return b;
}
poly operator + (const poly &a,const poly &b){
poly c(max(a.size(),b.size()),0);
for(int i=0;i<a.size();i++)c[i]=a[i];
for(int i=0;i<b.size();i++)(c[i]+=b[i])%=mod;
return c;
}
poly operator - (const poly &a,const poly &b){
poly c(max(a.size(),b.size()),0);
for(int i=0;i<a.size();i++)c[i]=a[i];
for(int i=0;i<b.size();i++)(c[i]+=mod-b[i])%=mod;
return c;
}
poly inv(const poly &a,int k=-1){
if(!~k)k=a.size();
poly f(1,qpow(a[0]));
for(int len=2;;len<<=1){
int n=min(len,k);
f=(f*2-a%n*f%n*f%n)%n;
if(n>=k)break;
}
return f;
}
poly jifen(const poly &a){
if(a.empty())return poly();
poly b(a.size()+1,0);
b[1]=1;
for(int i=2;i<b.size();i++)b[i]=1ll*b[mod%i]*(mod-mod/i)%mod;
for(int i=1;i<b.size();i++)b[i]=1ll*b[i]*a[i-1]%mod;
return b;
}
poly qiudao(const poly &a){
if(a.empty())return poly();
poly b(a.size()-1,0);
for(int i=1;i<a.size();i++)b[i-1]=1ll*a[i]*i%mod;
return b;
}
poly ln(const poly &a,int k=-1){
if(!~k)k=a.size();
return jifen(inv(a)*qiudao(a)%k)%k;
}
poly exp(const poly &a,int k=-1){
if(!~k)k=a.size();
poly f(1,1);
for(int len=2;;len<<=1){
int n=min(len,k);
f=(poly({1})-ln(f,n)+a%n)*f%n;
if(n>=k)break;
}
return f;
}
poly pow(const poly &a,ll y,int k=-1){
if(a.empty())return poly();
poly f(a);
assert(f[0]);
int iv=qpow(f[0]),his=qpow(a[0],y);
for(int &x:f)x=1ll*x*iv%mod;
f=ln(f,k);
for(int &x:f)x=y%mod*x%mod;
f=exp(f,k);
for(int &x:f)x=1ll*x*his%mod;
return f;
}
poly sqrt(const poly &a,int k=-1){
if(a.empty())return poly();
if(!~k)k=a.size();
poly f(1,::sqrt(a[0]));
for(int len=2,i2=(mod+1)/2;;len<<=1){
int n=min(len,k);
f=(f+a%n*inv(f,n)%n)*i2;
if(n>=k)break;
}
return f;
}
void div(const poly &a,const poly &b,poly &p,poly &q){
int n=a.size(),m=b.size();
poly c(a),d(b);
reverse(all(c)),reverse(all(d));
p=c%(n-m+1)*inv(d%(n-m+1),n-m+1)%(n-m+1);
reverse(all(p));
q=(a-p*b)%(m-1);
}
}
}
using namespace Poly::Public;
int n,f[N];
void divide(int l,int r){
if(l==r){
f[l]=(f[l]+f[l-1]*(l-1ll))%mod*qpow(l)%mod;
return;
}
int mid=(l+r)>>1;
divide(l,mid);
poly f1(r-l+1),f2{f+l,f+1+mid};
for(int i=0;i<=r-l;i++)f1[i]=1ll*i*f[i]%mod;
f1=f1*f2;
for(int i=mid+1;i<=r;i++)(f[i]+=f1[i-l])%=mod;
f1=poly{f,f+r-l+1},f2.assign(mid-l+1,0);
for(int i=l;i<=mid;i++)f2[i-l]=1ll*i*f[i]%mod;
f1=f1*f2;
for(int i=mid+1;i<=r;i++)(f[i]+=f1[i-l])%=mod;
divide(mid+1,r);
}
void solve(int n){
if(n==1)return;
int m=n>>1;
solve(m);
poly f1{f,f+1+m},f2(m+1);
for(int i=0;i<=m;i++)f2[i]=1ll*i*f[i]%mod;
f1=f1*f2;
for(int i=m+1;i<=n;i++)(f[i]+=f1[i])%=mod;
divide(m+1,n);
}
int main(){
Poly::Init();
cin>>n,f[1]=1;
solve(n);
auto res=inv(poly({1})-poly{f,f+1+n});
int ans=res[n];
for(int i=1;i<=n;i++)ans=1ll*ans*i%mod;
cout<<ans<<endl;
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
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Test #1:
score: 100
Accepted
time: 3ms
memory: 11876kb
input:
3
output:
28
result:
ok 1 number(s): "28"
Test #2:
score: 0
Accepted
time: 0ms
memory: 11876kb
input:
1
output:
1
result:
ok 1 number(s): "1"
Test #3:
score: 0
Accepted
time: 0ms
memory: 11752kb
input:
2
output:
4
result:
ok 1 number(s): "4"
Test #4:
score: 0
Accepted
time: 0ms
memory: 11800kb
input:
4
output:
282
result:
ok 1 number(s): "282"
Test #5:
score: 0
Accepted
time: 3ms
memory: 10532kb
input:
5
output:
3718
result:
ok 1 number(s): "3718"
Test #6:
score: 0
Accepted
time: 2ms
memory: 9772kb
input:
6
output:
60694
result:
ok 1 number(s): "60694"
Test #7:
score: 0
Accepted
time: 0ms
memory: 11804kb
input:
7
output:
1182522
result:
ok 1 number(s): "1182522"
Test #8:
score: 0
Accepted
time: 3ms
memory: 11752kb
input:
8
output:
26791738
result:
ok 1 number(s): "26791738"
Test #9:
score: 0
Accepted
time: 0ms
memory: 11752kb
input:
9
output:
692310518
result:
ok 1 number(s): "692310518"
Test #10:
score: 0
Accepted
time: 3ms
memory: 9556kb
input:
10
output:
135061370
result:
ok 1 number(s): "135061370"
Test #11:
score: 0
Accepted
time: 0ms
memory: 10288kb
input:
100
output:
423669705
result:
ok 1 number(s): "423669705"
Test #12:
score: 0
Accepted
time: 6ms
memory: 9976kb
input:
1234
output:
878522960
result:
ok 1 number(s): "878522960"
Test #13:
score: 0
Accepted
time: 296ms
memory: 14176kb
input:
54321
output:
827950477
result:
ok 1 number(s): "827950477"
Test #14:
score: 0
Accepted
time: 349ms
memory: 14072kb
input:
65536
output:
380835743
result:
ok 1 number(s): "380835743"
Test #15:
score: 0
Accepted
time: 756ms
memory: 19900kb
input:
131072
output:
842796122
result:
ok 1 number(s): "842796122"
Test #16:
score: 0
Accepted
time: 668ms
memory: 18224kb
input:
131071
output:
981021531
result:
ok 1 number(s): "981021531"
Test #17:
score: 0
Accepted
time: 695ms
memory: 18004kb
input:
131070
output:
480197639
result:
ok 1 number(s): "480197639"
Test #18:
score: 0
Accepted
time: 835ms
memory: 19976kb
input:
131074
output:
383000585
result:
ok 1 number(s): "383000585"
Test #19:
score: 0
Accepted
time: 847ms
memory: 19988kb
input:
131073
output:
316664839
result:
ok 1 number(s): "316664839"
Test #20:
score: 0
Accepted
time: 1517ms
memory: 24436kb
input:
250000
output:
119658643
result:
ok 1 number(s): "119658643"
Test #21:
score: 0
Accepted
time: 1480ms
memory: 24360kb
input:
249999
output:
78110138
result:
ok 1 number(s): "78110138"
Test #22:
score: 0
Accepted
time: 1456ms
memory: 24456kb
input:
249998
output:
297253469
result:
ok 1 number(s): "297253469"
Extra Test:
score: 0
Extra Test Passed