求解概率的坑题

D - Problem D

Time Limit:1000MS     Memory Limit:131072KB     64bit IO Format:%lld & %llu

Submit Status

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

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

绝对是被坑了，一直都没有想到通过递推的的方式来求解，结果计算越来越复杂，后来就不能忍了，受不了，以后坚决不能犯这样的低级错误……