Domination

题目链接

复制代码

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
inline ll read(){
    int x = 0, f = 1; char ch = getchar();
    while(ch > '9' || ch < '0'){if (ch == '-') f = -1; ch = getchar();}
    while(ch >= '0' && ch <= '9'){ x = x*10+ch-'0'; ch = getchar();}
    return x*f;
}

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

const int maxn = 50;
int n, m;
double dp[maxn*maxn*2][maxn][maxn];

int main(){
    int t; 
    t = read();
    while(t--){
        n = read(); m = read();
        memset(dp, 0, sizeof(dp));
        dp[1][1][1] = 1;
        for(int i = 1;i <= n*m;i++){
            for(int j = 1;j <= n;j++){
                for(int k = 1;k <= m;k++){
                    if(dp[i][j][k]){
                        dp[i+1][j+1][k] += dp[i][j][k] * (n-j)*k/(1.0*(n*m-i));
                        dp[i+1][j][k+1] += dp[i][j][k] * (m-k)*j/(1.0*(n*m-i));
                        dp[i+1][j+1][k+1] += dp[i][j][k] * (n-j)*(m-k)/(1.0*(n*m-i));
                        if(j < n || k < m)
                            dp[i+1][j][k] += dp[i][j][k] * (j*k-i)/(1.0*(n*m-i));
                    } 
                }
            }
        }
        double ans = 0.0;
        for(int i = 1;i <= n*m;i++){
            ans += dp[i][n][m]*i;
        }
        printf("%.12lf\n", ans);
    }
    return 0;
}