CSU 1290

 

1290: Random Integers

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 72  Solved: 45
[Submit][Status][Web Board]

Description

We choose an integer K (K > 0). Then we generate N (N > 0) integers one by one randomly, each of them is in range [0, K - 1], and the appearing probabilities of each interger is the same,they are all 1/K.
Can you tell us the expectation of the number of distinct integers in that N integers?

Input

There is an integer T (1 <= T <= 200) in the first line, means there are T test cases in total.
For each test case, there are two integers K (1 <= K <= 1000), N (1 <= N <= 1000), which have the same meaning as above.

Output

For each test case, you should print the result in one line. You should keep the first 5 digits after the decimal point.

Sample Input

5
1 1
2 2
3 2
3 4
5 3

Sample Output

1.00000
1.50000
1.66667
2.40741
2.44000

HINT

 

Source

Multi-University Contest Fina

 

没看出这是DP

看出来也不一定想得到

#include <cstdio>
double dp[1005];
int main()
{
    int t;
    scanf("%d", &t);
    while (t--)
     {
        int m,n;
        scanf("%d %d", &m, &n);
        dp[1] = 1.0;
        for (int i = 2; i <= n; ++i)
            dp[i] = dp[i-1] + (m/1.0 - dp[i-1])/1.0/m;
        printf("%.5f\n", dp[n]);
    }
    return 0;
}