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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#619664#8635. 圆qijianci100 ✓71ms101556kbC++14930b2024-10-07 14:57:082024-10-07 14:57:09

Judging History

你现在查看的是最新测评结果

  • [2024-10-07 14:57:09]
  • 评测
  • 测评结果:100
  • 用时:71ms
  • 内存:101556kb
  • [2024-10-07 14:57:08]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
const int N=5005,M=998244353;
int f[N][N],n,fac[N],inv[N],ans;
int qpow(int x,int y,int res=1){
    while(y){
        if(y&1)res=1ll*res*x%M;
        x=1ll*x*x%M,y>>=1;
    } return res;
}
int md(int x){if(x>=M)x-=M;return x;}
int C(int x,int y){
    return 1ll*fac[x]*inv[y]%M*inv[x-y]%M;
}
signed main(){
    ios::sync_with_stdio(false);
    // freopen("color.in","r",stdin);
    // freopen("color.out","w",stdout);
    int i,j,k,l,r,x,y,z;
    cin>>n,f[1][1]=1,fac[0]=inv[0]=1;
    for(i=2;i<=n;++i)for(j=min(i-1,n-3);j>=i-3&&j>0;--j)
        for(k=1;k<=n;++k)f[i][k+1]=md(f[i][k+1]+f[j][k]);
    for(i=1;i<=n;++i)fac[i]=1ll*fac[i-1]*i%M;
    inv[n]=qpow(fac[n],M-2);
    for(i=n-1;i;--i)inv[i]=inv[i+1]*(i+1ll)%M;
    for(i=n-2;i<=n;++i)for(j=1;j<=n;++j)
        ans=(ans+1ll*f[i][j]*qpow(C(n-1,j-1),M-2)%M*j)%M;
    printf("%d\n",ans);
    return 0;
}

Details

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Pretests


Final Tests

Test #1:

score: 10
Accepted
time: 0ms
memory: 3856kb

input:

3

output:

1

result:

ok 1 number(s): "1"

Test #2:

score: 10
Accepted
time: 0ms
memory: 3860kb

input:

4

output:

2

result:

ok 1 number(s): "2"

Test #3:

score: 10
Accepted
time: 0ms
memory: 3872kb

input:

6

output:

299473309

result:

ok 1 number(s): "299473309"

Test #4:

score: 10
Accepted
time: 0ms
memory: 3896kb

input:

10

output:

487238321

result:

ok 1 number(s): "487238321"

Test #5:

score: 10
Accepted
time: 1ms
memory: 4228kb

input:

100

output:

41620761

result:

ok 1 number(s): "41620761"

Test #6:

score: 10
Accepted
time: 1ms
memory: 4804kb

input:

200

output:

208771764

result:

ok 1 number(s): "208771764"

Test #7:

score: 10
Accepted
time: 0ms
memory: 6824kb

input:

500

output:

888621375

result:

ok 1 number(s): "888621375"

Test #8:

score: 10
Accepted
time: 71ms
memory: 97656kb

input:

4798

output:

319137015

result:

ok 1 number(s): "319137015"

Test #9:

score: 10
Accepted
time: 62ms
memory: 101532kb

input:

4999

output:

818467659

result:

ok 1 number(s): "818467659"

Test #10:

score: 10
Accepted
time: 61ms
memory: 101556kb

input:

5000

output:

142907477

result:

ok 1 number(s): "142907477"