SPOJ.1026.Favorite Dice（概率 dp + 数学期望）

FAVDICE - Favorite Dice

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BuggyD loves to carry his favorite die around. Perhaps you wonder why it's his favorite? Well, his die is magical and can be transformed into an N-sided unbiased die with the push of a button. Now BuggyD wants to learn more about his die, so he raises a question:

What is the expected number of throws of his die while it has N sides so that each number is rolled at least once?

Input

The first line of the input contains an integer t, the number of test cases. t test cases follow.

Each test case consists of a single line containing a single integer N (1 <= N <= 1000) - the number of sides on BuggyD's die.

Output

For each test case, print one line containing the expected number of times BuggyD needs to throw his N-sided die so that each number appears at least once. The expected number must be accurate to 2 decimal digits.

Example

Input:
2
1
12

Output:
1.00
37.24

解决方案：

N 个面的骰子显示 i 个面需要丢掷次数的期望为 dp [i-1] + N / ( N - i ) （一共有 N 个面，还剩下 N - i 个面）.

参考代码：

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int t;
    cin>>t;
    double n;
    while(t--&&cin>>n)
    {
        double dp[1010]={0.00,1.00};
        for(int i=2;i<=n;i++)
        {
            dp[i]=dp[i-1]+n/(n+1-i);
        }
        printf("%.2lf\n",dp[(int)n]);
    }
    return 0;
}