CF1156F Card Bag

Posted 2021-03-13

鏍囩锛?a href='http://www.mamicode.com/so/1/href' title='href'>href   sort   turn   const   math   card   a*   i+1   

Link
鏄剧劧璧㈠綋涓斾粎褰撳彇鐗岀殑搴忓垪鏋勬垚浜嗕竴涓崟璋冧笂鍗囩殑搴忓垪骞朵笖鏈€鍚庝袱涓暟鐩哥瓑銆?br /> 鍏堟妸(a)鎺掑簭锛岀劧鍚庤€冭檻dp锛岃(f_{i,j})琛ㄧず鍙栦簡(i)寮犵墝锛岀(i)寮犵墝鏄?span class="math inline">(j)涓旀父鎴忓皻鏈粨鏉熺殑姒傜巼銆?br /> 涓轰簡鏂逛究鎴戜滑瑙勫畾鍚屾牱澶у皬鐨勭墝蹇呴』鍏堝彇灏忕殑銆?br /> 鍥犳鎴戜滑鏈夛細
(egin{cases}f_{i,j}=frac{(sumlimits_{k=1}^{j-1}f_{i-1,k})cnt_j}{n-i+1}&a_j e a_{j-1}\ans+=frac{f_{i-1,j-1}(cnt_j-1)}{n-i+1}end{cases})
鍏朵腑(cnt)鏄《銆?/p>

#include<cstdio>
#include<algorithm>
const int N=5007,P=998244353;
int read(){int x;scanf("%d",&x);return x;}
void mod(int&x){x-=P,x+=x>>31&P;}
int mul(int a,int b){return 1ll*a*b%P;}
int pow(int a,int k){int r=1;for(;k;k>>=1,a=mul(a,a))if(k&1)r=mul(a,r);return r;}
int a[N],cnt[N],f[N][N],sum[N][N],inv[N];
int main()
{
    int n=read(),ans=0;inv[0]=inv[1]=1;
    for(int i=2;i<=n;++i) inv[i]=mul(inv[P%i],P-P/i);
    for(int i=1;i<=n;++i) ++cnt[a[i]=read()];
    std::sort(a+1,a+n+1),std::fill(sum[0],sum[0]+n+1,1),f[0][0]=1;
    for(int i=1;i<=n;++i)
    {
        for(int j=1;j<=n;j++) a[j]==a[j-1]? (mod(ans+=mul(mul(f[i-1][j-1],inv[n-i+1]),cnt[a[j]]-1)),0):f[i][j]=mul(mul(sum[i-1][j-1],inv[n-i+1]),cnt[a[j]]);
        for(int j=1;j<=n;++j) mod(sum[i][j]=sum[i][j-1]+f[i][j]);
    }
    printf("%d",ans);
}