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;
}