Favorite Dice,概率DP-优快云博客

本文链接：https://blog.youkuaiyun.com/xing_mo/article/details/87183306

本文详细解析了SPOJ上的FAVDICE题目，该题旨在求解一个N面骰子每面至少出现一次的期望掷骰次数。通过递推公式计算并精确到小数点后两位，提供了完整的C++代码实现。

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Favorite Dice

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

代码：

#include<bits/stdc++.h>
using namespace std;
int n,t;
double dp[1005];
int main()
{
   scanf("%d",&t);
   while(t--)
   {
       scanf("%d",&n);
       dp[n] = 0;
       for(int i = n-1;i >= 0;--i)
           dp[i] = dp[i+1] + (double)n / (n - i);
       printf("%.2f\n",dp[0]);
   }
   return 0;
}