HDU6143 Killer Names

HDU6143 Killer Names

思路：

简单组合数学

\[Ans=\sum_{i=1}^{m-1}\sum_{j=1}^{m-i}C[m][i]C[m-i][j]S[n][i]S[n][j]i!j!\\ 意思为枚举在名和姓中的字母，\\然后把n个\mathbb{不同}空位分给i/j个\mathbb{不同}字母\\ 显然不重不漏 \]

\(\mathfrak{Talk\ is\ cheap,show\ you\ the\ code.}\)

#include<map>
#include<cmath>
#include<stack>
#include<deque>
#include<queue>
#include<cstdio>
#include<vector>
#include<climits>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
# define Type template<typename T>
# define ll long long
# define read read1<ll>()
Type T read1(){
    T t=0;char k;
    bool v=0;
    do (k=getchar())=='-'&&(v=1);while('0'>k||k>'9');
    while('0'<=k&&k<='9')t=(t<<3)+(t<<1)+(k^'0'),k=getchar();
    return v?-t:t;
}
ll qkpow(ll n,ll x,ll mo){
    if(!x)return 1;
    ll t=qkpow(n,x>>1,mo);
    t=t*t%mo;
    if(x&1)t=t*n%mo;
    return t;
}
# define mod 1000000007ll
# define N 2000
int S[N|3][N|1],fac[N|3],C[N|3][N|3];
int main(){
    fac[0]=S[0][0]=1;
    for(int i=1;i<=N;++i)S[i][i]=1,fac[i]=1ll*fac[i-1]*i%mod;
    for(int i=0;i<=N;++i){
        C[i][i]=C[i][0]=1;
        for(int j=1;j<i;++j)
            C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
    }
    for(int i=1;i<=N;++i)
        for(int j=1;j<=i;++j)
            S[i][j]=(S[i-1][j-1]+1ll*S[i-1][j]*j)%mod;
    for(int T=read;T--;){
        int n=read,m=read,ans=0;
        for(int i=1;i<m;++i)
            for(int j=1;i+j<=m;++j)
                ans=(ans+1ll*C[m][i]*C[m-i][j]%mod*S[n][i]%mod*S[n][j]%mod*fac[i]%mod*fac[j])%mod;
        printf("%lld\n",ans);            
    }
    return 0;
}