| 记录编号 |
611351 |
评测结果 |
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
|
| 题目名称 |
[THUPC 2025 Final] 对脑电波 |
最终得分 |
100 |
| 用户昵称 |
 LikableP |
是否通过 |
通过 |
| 代码语言 |
C++ |
运行时间 |
205.473 s |
| 提交时间 |
2026-01-28 13:07:28 |
内存使用 |
526.65 MiB |
显示代码纯文本
#include <bits/stdc++.h>
using namespace std;
inline int read()
{
int s=0,f=1;
char c=getchar();
while(c<'0'||c>'9')
{
if(c=='-')
f=-1;
c=getchar();
}
while(c>='0'&&c<='9')
{
s=s*10+c-'0';
c=getchar();
}
return s*f;
}
int N,K,M,S;
int a[5007];
long long ans=0;
const int mod=998244353;
int dp0[5007][5007],dp[5007][5007],dp2[5003][5003],g3[5003][5003];
long long jc[5003],ny[5003];
long long cf[5007][5007];
long long CC[5007][5007];
inline long long qpow(long long x,long long y)
{
long long anss=1;
while(y)
{
if(y&1)
anss=anss*x%mod;
x=x*x%mod;
y>>=1;
}
return anss;
}
inline long long C(int n,int m)
{
if(n<0||m<0||n<m)
return 0;
return CC[n][m];
}
struct INIT{
inline void init()
{
for(int i=0;i<=5001;++i)
{
if(i==0)
jc[i]=ny[i]=1;
else
jc[i]=jc[i-1]*i%mod,ny[i]=qpow(jc[i],mod-2);
for(int j=0;j<=5001;++j)
{
cf[i][j]=qpow(i,j);
if(j<=i)
{
if(j==0)
CC[i][j]=1;
else
CC[i][j]=(CC[i-1][j-1]+CC[i-1][j])%mod;
}
}
}
dp0[0][0]=dp0[1][1]=1;
dp[1][1]=1;
for(int i=2;i<=N;++i)
{
for(int j=1;j<=i;++j)
{
dp0[i][j]=((long long)dp0[i-1][j-1]+(long long)dp0[i-1][j]*(i-1))%mod;
dp[i][j]=dp0[i-1][j-1];
}
}
for(int i=1;i<=N;++i)
for(int j=2;j<=i;++j)
dp2[i][j]=(dp2[i][j]+(long long)dp[i-1][j-1]*(i-1))%mod;
for(int i=1;i<=N;++i)
{
for(int j=1;j<=i;++j)
{
g3[i][j]=(g3[i][j]+(long long)dp0[i-1][j-1]*(i-1))%mod;
}
}
}
}Init;
struct CASE1{
long long ans=0;
int b[5007];
long long f[5007][5007];
inline long long Solve()
{
int c1=S+1,c2=S+1;
for(int i=2;i<=S;++i)
{
if(a[i-1]<a[i])
c1=min(c1,i);
if(a[i-1]>a[i])
c2=min(c2,i);
}
if(c2>c1)
{
for(int i=1;i<=S;++i)
a[i]=M-a[i]+1;
swap(c1,c2);
}
int n=N-(S-c1+1),m=n,k=K-(S-c1+1);
for(int i=1;i<c1;++i)
{
b[i]=a[i];
for(int j=c1;j<=S;++j)
{
if(a[i]>a[j])
--b[i];
}
}
for(int i=1;i<=n;++i)
f[c1-1][i]=C(b[c1-1]-1,i-1)*jc[i-1]%mod*i%mod;
for(int j=c1-2;j>=1;--j)
for(int i=1;i<=n;++i)
{
f[j][i]=f[j+1][i-1];
if(b[j]-i+1>=0)
f[j][i]=(f[j][i]+f[j][i-1]*(b[j]-i+1))%mod;
}
int i1=m-b[1]+1,j1=k-(c1-2);
for(int nj2=c1-2;nj2<=k-1;++nj2)
{
int j2=k-nj2-1,i2=n-nj2-i1;
long long anss=(long long)dp[i1][j1]*dp[i2+1][j2+1]%mod*C(i1-1+i2,i2)%mod;
ans=(ans+anss*f[2][nj2])%mod;
}
for(int i=1;i<3;++i)
{
b[i]=a[i];
for(int j=3;j<=S;++j)
{
if(a[i]>a[j])
--b[i];
}
}
n=N-(S-2);
for(int nj1=1;nj1+S<=K;++nj1)
{
int j1=K-nj1-(S-1),i1=(n-b[1]+1)-nj1;
int j2=K-S,i2=b[1]-2;
long long anss=(long long)dp[i1][j1]*dp[i2+1][j2+1]%mod*C(i1-1+i2,i2)%mod;
ans=(ans+anss*jc[nj1]%mod*C(n-b[1],nj1))%mod;
}
return ans;
}
}Case1;
struct CASE2{
long long ans=0;
int b[5007],n,k,c;
long long f[5007][5007];
inline long long Solve()
{
ans=0;
c=S+1;
for(int i=2;i<=S;++i)
{
if(a[i]>a[i-1])
{
c=i;
break;
}
}
for(int i=1;i<c;++i)
{
b[i]=a[i];
for(int j=c;j<=S;++j)
{
if(a[i]>a[j])
--b[i];
}
}
n=N-(S-c+1);
k=K-(S-c+1);
for(int i=0;i<=N;++i)
for(int j=0;j<=N;++j)
f[i][j]=0;
for(int i=1;i<=n;++i)
f[c-1][i]=C(b[c-1]-1,i-1)*jc[i-1]%mod*i%mod;
for(int j=c-2;j>=1;--j)
for(int i=1;i<=n;++i)
{
f[j][i]=f[j+1][i-1];
if(b[j]-i+1>=0)
f[j][i]=(f[j][i]+f[j][i-1]*(b[j]-i+1))%mod;
}
for(int i0=1;i0<=n;++i0)
{
long long anss=0;
int i1=n-b[1];
int j1=K-S;
int ai2=b[1]-i0;
for(int k2=2;k2<=ai2;++k2)
{
int i2,j2;
i2=k2-1;
j2=k-i0-1;
anss=(anss+(long long)(k2-1)*dp[i1+1][j1+1]%mod*dp[i2][j2]%mod*C(i1+i2,i2)%mod*C(i1+i2+ai2-k2,ai2-k2)%mod*jc[ai2-k2]%mod)%mod;
}
for(int k2=1;k2<=i1;++k2)
{
int i2=ai2+k2-1;
int j2=k-i0-1;
anss=(anss+(long long)ai2*dp[i2][j2]%mod*dp0[i1-k2][j1]%mod*C(i2+i1-k2-1,i2)%mod)%mod;
}
ans=(ans+anss*f[1][i0])%mod;
}
for(int i0=1;i0<=n;++i0)
{
long long anss=0;
int i1=n-b[1];
int j1=K-S;
int ai2=b[1]-i0;
for(int k2=1;k2<=i1;++k2)
{
int i2=ai2+k2;
int j2=k-i0;
anss=(anss+(long long)dp[i2][j2]*dp0[i1-k2][j1]%mod*C(i2+i1-k2-1,i2)%mod)%mod;
}
if(c==2)
ans=(ans+anss*C(b[1]-1,i0-1)%mod*jc[i0-1])%mod;
else
ans=(ans+anss*f[2][i0-1])%mod;
}
for(int i=1;i<=S;++i)
a[i]=M-a[i]+1;
return ans;
}
}Case2;
struct CASE3{
long long ans=0;
int n,k,c;
inline long long Solve()
{
n=N-S+1;
k=K-S+1;
ans=0;
c=a[1];
for(int i=1;i<=S;++i)
{
if(a[i]<a[1])
--c;
}
for(int k1=1;k1<c;++k1)
{
for(int i0=1;i0<=n;++i0)
{
int i1=n-k1-1;
int i2=n-2-i1-i0;
int j2=K-S-i0;
if(i2>=0&&j2>=0)
ans=(ans+(long long)dp[i1+1][K-S]*g3[i2+1][j2+1]%mod*C(i1+1+i2,i1+1)%mod*C(k1-1,i0-1)%mod*jc[i0-1]%mod)%mod;
}
}
for(int i=1;i<=S;++i)
a[i]=M-a[i]+1;
return ans;
}
}Case3;
bool vis[100007];
int main()
{
freopen("thupc_2025_BrainWave.in", "r", stdin);
freopen("thupc_2025_BrainWave.out", "w", stdout);
N=read(),K=read(),S=read();
M=N;
for(int i=1;i<=S;++i)
{
a[i]=read();
if(vis[a[i]])
{
puts("0");
return 0;
}
vis[a[i]]=1;
}
Init.init();
ans=(ans+Case1.Solve())%mod;
ans=(ans+Case2.Solve())%mod;
ans=(ans+Case2.Solve())%mod;
ans=(ans+Case3.Solve())%mod;
ans=(ans+Case3.Solve())%mod;
printf("%lld\n",ans);
return 0;
}