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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#259682 | #7761. 物理实验 | grass8cow | 10 | 634ms | 23620kb | C++17 | 4.3kb | 2023-11-21 10:59:16 | 2023-11-21 10:59:17 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
#define vi vector<int>
#define pb push_back
const int mod=998244353,G=3,GI=(mod+1)/3,inv2=(mod+1)/2;
int qpow(int a,int b){
int c=1;for(;b;b>>=1){
if(b&1)c=1ll*a*c%mod;
a=1ll*a*a%mod;
}
return c;
}
int L,lb[1<<20];
void init(int n){
L=1;while(L<=n)L<<=1;
for(int i=0;i<L;i++)lb[i]=(lb[i>>1]>>1)|((i&1)?(L>>1):0);
}
void NTT(vi &a,int fl){
for(int i=0;i<L;i++)if(i>lb[i])swap(a[i],a[lb[i]]);
for(int o=1;o<L;o<<=1){
int Wn=qpow(fl?G:GI,(mod-1)/(o<<1));
for(int i=0;i<L;i+=(o<<1))for(int j=0,w=1;j<o;j++,w=1ll*w*Wn%mod){
int x=a[i+j],y=1ll*w*a[i+j+o]%mod;
a[i+j]=(x+y)%mod,a[i+j+o]=(x-y)%mod;
}
}
if(!fl){
int I=qpow(L,mod-2);
for(int i=0;i<L;i++)a[i]=1ll*a[i]*I%mod;
}
}
vi operator * (vi a,vi b){
if(a.empty()||b.empty())return {};
vi c;int n=a.size()+b.size()-1;init(n);
a.resize(L),b.resize(L),NTT(a,1),NTT(b,1);
for(int i=0;i<L;i++)a[i]=1ll*a[i]*b[i]%mod;
NTT(a,0);
while((int)a.size()>n)a.pop_back();
return a;
}
vi operator + (vi a,vi b){
if(a.empty())return b;if(b.empty())return a;
if(a.size()<b.size())swap(a,b);int sz=b.size();
for(int i=0;i<sz;i++)(a[i]+=b[i])%=mod;return a;
}
vi mulT(vi a,vi b){
//注意:第二个是常量!c_j=sum a_{i-j}b_j a_i=sum c_{i+j}b_{m-1-j}
int n=a.size(),m=b.size();reverse(b.begin(),b.end());
b=a*b;
for(int i=0;i<n;i++)a[i]=b[i+m-1];
return a;
}
vi az[401000];
void cs(int p,int l,int r,vi &x){
if(l==r){
az[p].resize(2);
az[p][0]=1,az[p][1]=-x[l];
return;
}
int mid=(l+r)>>1;cs(p<<1,l,mid,x),cs(p<<1|1,mid+1,r,x);
az[p]=az[p<<1]*az[p<<1|1];
}
void cs2(int p,int l,int r,vi &x){
if(l==r){
az[p].resize(2);
az[p][0]=-x[l],az[p][1]=1;
return;
}
int mid=(l+r)>>1;cs2(p<<1,l,mid,x),cs2(p<<1|1,mid+1,r,x);
az[p]=az[p<<1]*az[p<<1|1];
}
vi WT;
vi Inv(vi &a,int n){
if(n==1)return vi(1,qpow(a[0],mod-2));
vi b=Inv(a,(n+1)>>1);
init(2*n);b.resize(L),WT.resize(L);
for(int i=0;i<n;i++)WT[i]=a[i];
for(int i=n;i<L;i++)WT[i]=0;
NTT(WT,1),NTT(b,1);
for(int i=0;i<L;i++)b[i]=1ll*b[i]*(2-1ll*b[i]*WT[i]%mod)%mod;
NTT(b,0);b.resize(n);return b;
}
void Sol(int p,int l,int r,vi x,vi &y){
x.resize(r-l+1);
if(l==r){y[l]=x[0];return;}
int mid=(l+r)>>1;
Sol(p<<1,l,mid,mulT(x,az[p<<1|1]),y);
Sol(p<<1|1,mid+1,r,mulT(x,az[p<<1]),y);
}
vi Qz(vi a,vi b,int n){
a.resize(n+1),b.resize(n);
vi c;cs(1,0,n-1,b);
c.resize(n);
Sol(1,0,n-1,mulT(a,Inv(az[1],n+1)),c);
return c;
}
struct mat{vi a[2][2];};
mat operator * (const mat &a,const mat &b){
mat c;for(int k=0;k<2;k++)for(int i=0;i<2;i++)for(int j=0;j<2;j++){
vi xp=a.a[i][k]*b.a[k][j];
c.a[i][j]=c.a[i][j]+xp;
}
return c;
}
vi sol(vi p,vi q,int l,int r){
if(l>r)return {};
if(l==r&&r==0)return {(int)(1ll*p[0]*qpow(q[0],mod-2)%mod)};
vi q_;
for(int i=0;i<(int)q.size();i++)q_.pb((i&1)?(-q[i]):q[i]);
vi P=p*q_,Q=q*q_,A,B,q2;
for(int i=0;i*2<(int)Q.size();i++)q2.pb(Q[i*2]);
for(int i=0;i*2<(int)P.size();i++)A.pb(P[i*2]);
for(int i=0;i*2+1<(int)P.size();i++)B.pb(P[i*2+1]);
vi o1=sol(A,q2,(l+1)/2,r/2),o2=sol(B,q2,l/2,(r-1)/2),o3;
for(int i=l,x=0,y=0;i<=r;i++){
if(i&1)o3.push_back(o2[y]),y++;
else o3.push_back(o1[x]),x++;
}
return o3;
}
int n,m,P,lp,rp,a[101000],b[100100];
int od[10010],od2[10010];
int main(){
scanf("%d%d%d%d%d",&n,&m,&P,&lp,&rp);
P=1ll*P*(1-P)%mod;
vi a1,a2;
for(int i=0;i<m;i++)a1.pb(0),a2.pb(0);
for(int i=0,x;i<n;i++)scanf("%d",&x),a1[x]++,a2[(m-x)%m]++;
a1=a1*a2;
for(int i=0;i<(int)a1.size();i++){int e=i%m;e=min(e,m-e);(a[e]+=a1[i])%=mod;}
for(int i=1;i<m;i++)a[i]=1ll*a[i]*inv2%mod,b[i]=min(i,m-i);m--;
mat A,B;A.a[0][0]={(2*P-1)%mod,1},A.a[0][1]={1};
B.a[0][0]={(2*P-1)%mod,1},B.a[0][1]={1},B.a[1][0]={-(int)(1ll*P*P%mod)};
for(int o=m;o;o>>=1){if(o&1)A=A*B;B=B*B;}
vi q=A.a[0][1];
reverse(q.begin(),q.end());
for(int i=1;i<=m;i++)od[i]=a[i];
vi f;
for(int i=0;i<m;i++){
memset(od2,0,sizeof(od2));
f.push_back(0);
for(int j=1;j<=m;j++)(f[i]+=1ll*od[j]*b[j]%mod)%=mod;
for(int j=1;j<=m;j++){
(od2[j+1]+=1ll*od[j]*P%mod)%=mod;
(od2[j-1]+=1ll*od[j]*P%mod)%=mod;
(od2[j]+=1ll*od[j]*(1-P*2)%mod)%=mod;
}
for(int j=1;j<=m;j++)od[j]=od2[j];
}
f=f*q;while((int)f.size()>m)f.pop_back();
vi ans=sol(f,q,lp,rp);
for(int i=0;i<=rp-lp;i++)printf("%d ",(ans[i]+mod)%mod);
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Subtask #1:
score: 0
Time Limit Exceeded
Test #1:
score: 0
Time Limit Exceeded
input:
7500 7500 96132844 1 7500 1791 817 5559 4742 5272 3988 6672 1355 2783 5552 6885 5321 5996 6495 3072 2241 5527 856 6250 2741 4223 1560 6529 5330 3517 2637 6577 244 1739 5147 2648 6466 1479 7340 7355 176 183 1417 2943 5134 3879 3574 734 4880 7451 3778 1466 5237 2015 1334 6105 4859 1331 5805 3175 4795 ...
output:
result:
Subtask #2:
score: 0
Skipped
Dependency #1:
0%
Subtask #3:
score: 10
Accepted
Test #5:
score: 10
Accepted
time: 632ms
memory: 23620kb
input:
100000 7500 500440646 935892941 935892941 3280 7218 1216 489 4036 7029 5538 4805 2544 568 4303 816 739 2284 1294 6062 808 3029 3565 4344 7124 3917 705 3637 6076 2019 4233 2032 7327 5672 2872 2593 22 1534 2071 5782 3228 5460 1217 5138 7285 3679 2751 213 2242 2673 2746 7041 7001 860 2591 7347 3330 213...
output:
768801558
result:
ok 1 number(s): "768801558"
Test #6:
score: 0
Accepted
time: 634ms
memory: 23592kb
input:
100000 7499 356847081 883948227 883948227 549 2423 3380 3811 4666 3645 5857 7184 7137 861 2619 519 409 1607 2298 7164 2216 2856 6790 6857 405 1928 5391 2949 6345 4839 2372 2974 4699 2688 6768 684 2012 3642 6225 6948 5313 6936 876 38 3004 7440 4671 208 4906 4714 7067 3424 3163 6165 115 4974 2178 4613...
output:
701047464
result:
ok 1 number(s): "701047464"
Subtask #4:
score: 0
Skipped
Dependency #2:
0%
Subtask #5:
score: 0
Time Limit Exceeded
Test #9:
score: 0
Time Limit Exceeded
input:
100000 50000 559705157 50000 50000 27437 48841 4744 41269 30017 24703 22660 38617 9707 42083 31500 14053 45335 20769 16455 30887 31847 6833 44822 14557 15400 18868 15093 47184 35490 48961 45686 45613 297 31598 7021 9194 30432 14570 44495 39114 21800 16034 12668 49738 20083 31717 22713 34958 46363 35...
output:
result:
Subtask #6:
score: 0
Skipped
Dependency #2:
0%
Subtask #7:
score: 0
Skipped
Dependency #3:
100%
Accepted
Dependency #5:
0%
Subtask #8:
score: 0
Skipped
Dependency #7:
0%
Subtask #9:
score: 0
Skipped
Dependency #6:
0%
Subtask #10:
score: 0
Skipped
Dependency #4:
0%