Harmonic Number
https://vjudge.net/contest/288520#problem/I
In mathematics, the nth 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 Hn.
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 nth 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
欧拉常数：
const double oula=0.57721566490153286060651209;
近似公式：ln(n)+C+1/(2*n) C++中log即为ln
在n小的时候不精确，需要暴力求解
1 #include<bits/stdc++.h> 2 using namespace std; 3 #define lson l,mid,rt<<1 4 #define rson mid+1,r,rt<<1|1 5 #define sqr(x) ((x)*(x)) 6 #define pb push_back 7 #define eb emplace_back 8 #define maxn 10000005 9 #define eps 1e-8 10 #define pi acos(-1.0) 11 #define rep(k,i,j) for(int k=i;k<j;k++) 12 typedef long long ll; 13 typedef pair<int,int> pii; 14 typedef pair<long long,int>pli; 15 typedef pair<int,char> pic; 16 typedef pair<pair<int,string>,pii> ppp; 17 typedef unsigned long long ull; 18 const long long mod=1e9+7; 19 const double oula=0.57721566490153286060651209; 20 using namespace std; 21 22 int t; 23 24 int main(){ 25 // std::ios::sync_with_stdio(false); 26 int t; 27 cin>>t; 28 ///log(n)+C+1/(2*n) 29 for(int _=1;_<=t;_++){ 30 int n; 31 cin>>n; 32 double ans=0; 33 if(n<=100000) 34 for(int i=1;i<=n;i++){ 35 ans=ans+1.0/i; 36 } 37 else{ 38 ans=log(n)+oula+1.0/2/n; 39 } 40 printf("Case %d: %.8f ",_,ans); 41 42 } 43 }