ZOJ 3822 Domination(概率DP)
来源:互联网 发布:windows安装器安装win7 编辑:程序博客网 时间:2024/06/05 15:38
思路:一道比较简单的概率DP,转移方程见代码
#include<iostream>#include<cstdio>#include<cmath>using namespace std;int T;double dp[55][55][2550];int main(){scanf("%d",&T);while(T--){ int n,m;scanf("%d%d",&n,&m);int sum = n*m;for(int k = 1;k<=sum;k++)for(int i = 1;i<=n;i++)for(int j = 1;j<=m;j++)dp[i][j][k]=0.0;dp[0][0][0]=1.0;for (int k = 1;k<=sum;k++)for(int i = 1;i<=n;i++)for(int j = 1;j<=m;j++){dp[i][j][k]+=(dp[i][j][k-1]*(i*j-k+1)*1.0 / (sum-k+1)); dp[i][j][k]+=(dp[i-1][j][k-1]*(n-i+1)*j*1.0 / (sum-k+1));dp[i][j][k]+=(dp[i][j-1][k-1]*(m-j+1)*i*1.0 / (sum-k+1));dp[i][j][k]+=(dp[i-1][j-1][k-1]*(n-i+1)*(m-j+1)*1.0 / (sum-k+1));}double ans = 0.0;for(int k = 1;k<=sum;k++)ans+=(dp[n][m][k]-dp[n][m][k-1])*k;printf("%.12lf\n",ans);}}
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