LightOJ - 1234 LightOJ - 1245 Harmonic Number（欧拉系数+调和级数）

Harmonic Number

 

In mathematics, the n^th harmonic number is the sum of the reciprocals of the first n natural numbers:

 

 

In this problem, you are given n, you have to find H_n.

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10⁸).

Output

For each case, print the case number and the n^th harmonic number. Errors less than 10^-8 will be ignored.

Sample Input

12

1

2

3

4

5

6

7

8

9

90000000

99999999

100000000

Sample Output

Case 1: 1

Case 2: 1.5

Case 3: 1.8333333333

Case 4: 2.0833333333

Case 5: 2.2833333333

Case 6: 2.450

Case 7: 2.5928571429

Case 8: 2.7178571429

Case 9: 2.8289682540

Case 10: 18.8925358988

Case 11: 18.9978964039

Case 12: 18.9978964139

 

求1+1/2+1/3+...+1/n

 

#include<bits/stdc++.h>
#define e 0.57721566490153286060651209
using namespace std;
typedef long long ll;

double a[10005];
int main()
{
    int tt=0,t,n,i;
    a[1]=1;
    for(i=2;i<=10000;i++){
        a[i]=a[i-1]+1.0/i;
    }
    scanf("%d",&t);
    while(t--){
        scanf("%d",&n);
        if(n<=10000){
            printf("Case %d: %.10lf\n",++tt,a[n]);
        }
        else{
            double ans=log(n)+e+1.0/(2*n);
            printf("Case %d: %.10lf\n",++tt,ans);
        }
    }
    return 0;
}

LightOJ - 1234