Domination

题目链接

 #include <bits/stdc++.h>
 using namespace std;
 typedef long long ll;
 inline ll read(){
     int x = , f = ; char ch = getchar();
     while(ch > '' || ch < ''){if (ch == '-') f = -; ch = getchar();}
     while(ch >= '' && ch <= ''){ x = x*+ch-''; ch = getchar();}
     return x*f;
 }

 /************************************************************************/

 const int maxn = ;
 int n, m;
 double dp[maxn*maxn*][maxn][maxn];

 int main(){
     int t;
     t = read();
     while(t--){
         n = read(); m = read();
         memset(dp, , sizeof(dp));
         dp[][][] = ;
         for(int i = ;i <= n*m;i++){
             for(int j = ;j <= n;j++){
                 for(int k = ;k <= m;k++){
                     if(dp[i][j][k]){
                         dp[i+][j+][k] += dp[i][j][k] * (n-j)*k/(1.0*(n*m-i));
                         dp[i+][j][k+] += dp[i][j][k] * (m-k)*j/(1.0*(n*m-i));
                         dp[i+][j+][k+] += dp[i][j][k] * (n-j)*(m-k)/(1.0*(n*m-i));
                         if(j < n || k < m)
                             dp[i+][j][k] += dp[i][j][k] * (j*k-i)/(1.0*(n*m-i));
                     }
                 }
             }
         }
         double ans = 0.0;
         for(int i = ;i <= n*m;i++){
             ans += dp[i][n][m]*i;
         }
         printf("%.12lf\n", ans);
     }
     return ;
 }