Domination
Time 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 with N rows
and M columns.
Every day after work, Edward will place a chess piece on a random empty cell. A few days later, he found the chessboard was dominated by 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 of N × M dominated. Please write a program to help
him.
Input
There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:
There are only two integers N and M (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 10-8 will be accepted.
Sample Input
2 1 3 2 2
Sample Output
3.000000000000 2.666666666667
题意：RT
思路：dp[k][i][j]表示下了k个棋子，还有i行j列没有棋子的概率
转移分四种情况转移即可
只举例一种情况，可以在（i+1）*（m-j）里的格子任选一个走，总的可以选的格子数为（n*m-k+1）
所以 dp[k][i][j] + =dp[k-1][i+1][j] * (i+1)*(m-j) / (n*m-k+1)