Favorite Dice （SPOJ-FAVDICE）期望DP

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

题意：扔一个n面的骰子，问每一面都被扔到的次数期望是多少。
思路：比较简单，公式：初始化dp[n]=0;

dp[i]=i/n*dp[i]+(n-i)/n*dp[i+1]+1;化简逆推即可。求的是dp[0];

AC代码：

#include <stdio.h>
#include <string>
#include <string.h>
#include <algorithm>
#include <iostream>
#include <math.h>
#include<iomanip>
const int maxn=1010;
const int inf=0x3f3f3f3f;
using namespace std;
double dp[maxn];
int main()
{
    int t,n;
    cin>>t;
    while(t--)
    {
        cin>>n;
        dp[n]=0;
        for(int i=n-1; i>=0; i--)
        {
            dp[i]=dp[i+1]+n/(n-(double)i);
        }
        cout<<fixed<<setprecision(2)<<dp[0]<<endl;
    }
    return 0;
}

来源：CSDN

作者：Stephencurry‘s csdn

链接：https://blog.csdn.net/weixin_43846139/article/details/104036900

标签

dice