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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#416642 | #8721. 括号序列 | Afterlife | AC ✓ | 1751ms | 46904kb | C++20 | 5.3kb | 2024-05-22 01:20:44 | 2024-05-22 01:20:44 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod=998244353;
inline int inc(int x,int y){return x+y>=mod?x+y-mod:x+y;}
inline int dec(int x,int y){return x-y<0?x-y+mod:x-y;}
inline int mul(int x,int y){return (ll)x*y%mod;}
inline int qpow(int x,int y){
int res=1;
for(;y;y>>=1)res=y&1?mul(res,x):res,x=mul(x,x);
return res;
}
inline int inv(int x){return qpow(x,mod-2);}
const int N=1<<20;
namespace NTT{
int re[N],w[2][N];
inline int getre(int n){
int len=1,bit=0;
while(len<n)len<<=1,++bit;
for(int i=1;i<len;++i)re[i]=(re[i>>1]>>1)|((i&1)<<(bit-1));
w[0][0]=w[1][0]=1,w[0][1]=qpow(3,(mod-1)/len),w[1][1]=inv(w[0][1]);
for(int o=0;o<2;++o)for(int i=2;i<len;++i)
w[o][i]=mul(w[o][i-1],w[o][1]);
return len;
}
inline void NTT(int* a,int n,int o=0){
for(int i=1;i<n;++i)if(i<re[i])swap(a[i],a[re[i]]);
int R;
for(int k=1;k<n;k<<=1)
for(int i=0,t=k<<1,st=n/t;i<n;i+=t)
for(int j=0,nw=0;j<k;++j,nw+=st)
R=mul(a[i+j+k],w[o][nw]),a[i+j+k]=dec(a[i+j],R),a[i+j]=inc(a[i+j],R);
if(o){
R=inv(n);
for(int i=0;i<n;++i)a[i]=mul(a[i],R);
}
}
int t0[N],t1[N],t2[N];
inline void multi(const int* a,const int* b,int* c,int n,int m){
if(n+m<=32){
memset(c,0,sizeof(int)*(n+m+1));
for(int i=0;i<=n;++i)
for(int j=0;j<=m;++j)
c[i+j]=inc(c[i+j],mul(a[i],b[j]));
return;
}
int len=getre(n+m+1);
memset(t0,0,sizeof(int)*len),memcpy(t0,a,sizeof(int)*(n+1));
memset(t1,0,sizeof(int)*len),memcpy(t1,b,sizeof(int)*(m+1));
NTT(t0,len),NTT(t1,len);
for(int i=0;i<len;++i)t0[i]=mul(t0[i],t1[i]);
NTT(t0,len,1);
memcpy(c,t0,sizeof(int)*(n+m+1));
}
inline void inver(const int* a,int* b,int n){
int len=1;
while(len<=n)len<<=1;
memset(t0,0,sizeof(int)*len),memcpy(t0,a,sizeof(int)*(n+1));
memset(t1,0,sizeof(int)*(len<<1));
memset(t2,0,sizeof(int)*(len<<1));
t2[0]=inv(t0[0]);
for(int k=1;k<=len;k<<=1){
memcpy(t1,t0,sizeof(int)*k);
getre(k<<1);
NTT(t1,k<<1),NTT(t2,k<<1);
for(int i=0;i<(k<<1);++i)t2[i]=mul(t2[i],dec(2,mul(t1[i],t2[i])));
NTT(t2,k<<1,1);
for(int i=k;i<(k<<1);++i)t2[i]=0;
}
memcpy(b,t2,sizeof(int)*(n+1));
}
} //namespace NTT
struct poly:public vector<int>{
inline int time()const{return size()-1;}
inline poly(int tim=0,int c=0){
resize(tim+1);
if(tim>=0)at(0)=c;
}
inline poly operator%(const int& n)const{
poly r(*this);
r.resize(n);
return r;
}
inline poly operator%=(const int& n){
resize(n);
return *this;
}
inline poly operator+(const poly& p)const{
int n=time(),m=p.time();
poly r(*this);
if(n<m)r.resize(m+1);
for(int i=0;i<=m;++i)r[i]=inc(r[i],p[i]);
return r;
}
inline poly operator-(const poly& p)const{
int n=time(),m=p.time();
poly r(*this);
if(n<m)r.resize(m+1);
for(int i=0;i<=m;++i)r[i]=dec(r[i],p[i]);
return r;
}
inline poly operator*(const poly& p)const{
poly r(time()+p.time());
NTT::multi(&((*this)[0]),&p[0],&r[0],time(),p.time());
return r;
}
inline poly operator*(const int& k)const{
poly r(*this);
int n=time();
for(int i=0;i<=n;++i)r[i]=mul(r[i],k);
return r;
}
inline poly operator~()const{
poly r(*this);
reverse(r.begin(),r.end());
return r;
}
};
inline poly inv(const poly& a){
poly r(a.time());
NTT::inver(&a[0],&r[0],a.time());
return r;
}
inline poly der(const poly& a){
int n=a.time();
poly r(n-1);
for(int i=1;i<=n;++i)r[i-1]=mul(a[i],i);
return r;
}
int _[N];
inline poly itr(const poly& a){
int n=a.time();
poly r(n+1);
_[1]=1;
for(int i=2;i<=n+1;++i)_[i]=mul(_[mod%i],mod-mod/i);
for(int i=0;i<=n;++i)r[i+1]=mul(a[i],_[i+1]);
return r;
}
inline poly ln(const poly& a){
return itr(der(a)*inv(a)%a.time());
}
inline poly exp(const poly& a){
poly r(0,1);
int n=a.time(),k=1;
while(r.time()<n)
r%=k,r=r*(a%k-ln(r)+poly(0,1))%k,k<<=1;
return r%(n+1);
}
inline poly qpow(const poly& a,int k){
return exp(ln(a)*k);
}
inline poly operator/(const poly& f,const poly& g){
int n=f.time()-g.time()+1;
return ~((~f)*inv((~g)%n)%n);
}
inline poly operator%(const poly& f,const poly& g){
if(f.time()<g.time())return f;
return (f-g*(f/g)%g.time())%g.time();
}
int t[250005];
int main() {
int n ; cin >> n; n++ ;
t[0] =1 ;
for(int i = 1;i <= n + 2;i++) t[i] = 1LL * t[i - 1] * i % mod;
int l = 1 ;
poly f(1) ; f[0] = 0;
poly x2(2) ; x2[0] = 2 ; x2[1] = 1;
poly s1(1) ; s1[0] = 1;
while(l <= n) {
/// p(F) = 2*exp(f) - (x + 2)
l <<= 1;
f.resize(l);
// poly g =(exp(f) * 2 - x2) * inv(exp(f) * 2);
f = f - (exp(f) * 2 - x2 - f) * inv(exp(f) * 2 - s1) ;
f.resize(l) ;
}
f.resize(n + 1);
// for(int i = 0;i <= n;i++) cout << f[i] <<' ' ; cout << '\n';
poly g(n + 1) ;
for(int i = 1;i <= n;i++) {
if(i % 2 == 0) f[i] = (mod - f[i] ) % mod;
// cout << 1LL*f[i]*t[i] % mod << ' ';
g[i - 1] = (1LL * f[i] * t[i] % mod * qpow(t[i - 1] , mod - 2)) % mod;
}
// cout << '\n';
g = itr(g);
// cout << g[0] << '\n';
for(int i = 1;i <= n;i++) g[i] = (mod - g[i]) % mod;
g[0] = 1;
g = inv(g) ;
// for(int i = 0;i <= n;i++) cout << 1LL * g[i] * t[i] % mod << ' ' ; cout << '\n';
cout << 1LL * g[n - 1] * t[n - 1] % mod << '\n';
}
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Details
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Test #1:
score: 100
Accepted
time: 2ms
memory: 13884kb
input:
3
output:
28
result:
ok 1 number(s): "28"
Test #2:
score: 0
Accepted
time: 0ms
memory: 16156kb
input:
1
output:
1
result:
ok 1 number(s): "1"
Test #3:
score: 0
Accepted
time: 2ms
memory: 15924kb
input:
2
output:
4
result:
ok 1 number(s): "4"
Test #4:
score: 0
Accepted
time: 0ms
memory: 15936kb
input:
4
output:
282
result:
ok 1 number(s): "282"
Test #5:
score: 0
Accepted
time: 2ms
memory: 14148kb
input:
5
output:
3718
result:
ok 1 number(s): "3718"
Test #6:
score: 0
Accepted
time: 0ms
memory: 13772kb
input:
6
output:
60694
result:
ok 1 number(s): "60694"
Test #7:
score: 0
Accepted
time: 0ms
memory: 15992kb
input:
7
output:
1182522
result:
ok 1 number(s): "1182522"
Test #8:
score: 0
Accepted
time: 0ms
memory: 13860kb
input:
8
output:
26791738
result:
ok 1 number(s): "26791738"
Test #9:
score: 0
Accepted
time: 0ms
memory: 15924kb
input:
9
output:
692310518
result:
ok 1 number(s): "692310518"
Test #10:
score: 0
Accepted
time: 0ms
memory: 15868kb
input:
10
output:
135061370
result:
ok 1 number(s): "135061370"
Test #11:
score: 0
Accepted
time: 0ms
memory: 13908kb
input:
100
output:
423669705
result:
ok 1 number(s): "423669705"
Test #12:
score: 0
Accepted
time: 7ms
memory: 14124kb
input:
1234
output:
878522960
result:
ok 1 number(s): "878522960"
Test #13:
score: 0
Accepted
time: 364ms
memory: 18496kb
input:
54321
output:
827950477
result:
ok 1 number(s): "827950477"
Test #14:
score: 0
Accepted
time: 779ms
memory: 35844kb
input:
65536
output:
380835743
result:
ok 1 number(s): "380835743"
Test #15:
score: 0
Accepted
time: 1732ms
memory: 45728kb
input:
131072
output:
842796122
result:
ok 1 number(s): "842796122"
Test #16:
score: 0
Accepted
time: 1729ms
memory: 46240kb
input:
131071
output:
981021531
result:
ok 1 number(s): "981021531"
Test #17:
score: 0
Accepted
time: 841ms
memory: 36596kb
input:
131070
output:
480197639
result:
ok 1 number(s): "480197639"
Test #18:
score: 0
Accepted
time: 1733ms
memory: 46128kb
input:
131074
output:
383000585
result:
ok 1 number(s): "383000585"
Test #19:
score: 0
Accepted
time: 1725ms
memory: 45900kb
input:
131073
output:
316664839
result:
ok 1 number(s): "316664839"
Test #20:
score: 0
Accepted
time: 1751ms
memory: 46904kb
input:
250000
output:
119658643
result:
ok 1 number(s): "119658643"
Test #21:
score: 0
Accepted
time: 1750ms
memory: 45712kb
input:
249999
output:
78110138
result:
ok 1 number(s): "78110138"
Test #22:
score: 0
Accepted
time: 1749ms
memory: 46428kb
input:
249998
output:
297253469
result:
ok 1 number(s): "297253469"
Extra Test:
score: 0
Extra Test Passed