CSU-ACM暑假集训基础组训练赛(5-1) B - Problem B

B - Problem B
Time Limit:2000MS Memory Limit:0KB 64bit IO Format:%lld & %llu
Submit Status Practice SPOJ
FAVDICE

Description

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.

Sample Input

Input:
2
1
12

Output:
1.00
37.24

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题目大意：

一个有n面的色子抛掷多少次能使所有面都能被抛到过，求期望值

总面数为n，当已经抛到过 i 个不同面时，我们抛出下一个不同面的概率为 (n-i)/n，那么抛的次数为 n/(n-i)，

将所有抛出下个面的次数累加起来就好了

简单的模拟题，前提是读懂题意。代码：

#include <iostream>

#include<cstdio>

#include<algorithm>

using namespace std;

int main()

{

int t,i,n;

scanf("%d",&t);

while(t--)

{

double s=0.0;

scanf("%d",&n);

for(i=0;i<n;i++)

s+=double(n)/double(n-i);

printf("%.2lf\n",s);

}

return 0;

}

总结：好好学习，天天向上。聪哥说：不会只能怪高中老师了~~~