DominationTime Limit:8 Seconds Memory Limit:131072 KB Special Judge
Edward is the headmaster of Marjar University. He is enthusiastic about chess and often plays chess with his friends. What’s more, he bought a large decorative chessboard withNrows andMcolumns.
Every day after work, Edward will place a chess piece on a random empty cell. A few days later, he found the chessboard wasdominatedby the chess pieces. That means there is at least one chess piece in every row. Also, there is at least one chess piece in every column.
"That’s interesting!" Edward said. He wants to know the expectation number of days to make an empty chessboard ofN×Mdominated. Please write a program to help him.
Input
There are multiple test cases. The first line of input contains an integerTindicating the number of test cases. For each test case:
There are only two integersNandM(1 <=N,M<= 50).
Output
For each test case, output the expectation number of days.
Any solution with a relative or absolute error of at most 10-8will be accepted.
Sample Input21 32 2Sample Output3.0000000000002.666666666667
#include <iostream>#include <stdio.h>#include <string>#include <cstring>#include <algorithm>#include <cmath>using namespace std;double dp[55][55][2555];int n,m;int T;int main(){while(~scanf("%d",&T)){while(T–){scanf("%d %d",&n,&m);int sum=n*m;memset(dp,0,sizeof dp);dp[0][0][0]=1;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)/(sum-k+1));//行列都不增加dp[i][j][k]+=(dp[i-1][j-1][k-1]*(n-i+1)*(m-j+1)/(sum-k+1));//行列都增加dp[i][j][k]+=(dp[i-1][j][k-1]*(n-i+1)*j/(sum-k+1));//只增加行dp[i][j][k]+=(dp[i][j-1][k-1]*(m-j+1)*i/(sum-k+1));//只增加列}}}double ans=0;for(int k=1;k<=sum;k++){ans+=(dp[n][m][k]-dp[n][m][k-1])*k;//期望}printf("%.10lf\n",ans);}}return 0;}
，对人性的弱点有清醒的认识，
