調和級數求和
阿新 • • 發佈:2019-02-15
Description
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
最重要的就是找到在大於10000時候的調和級數公式,也是就ln(n+1)+0.5772156649#include<stdio.h> #include<string.h> #include<stdlib.h> #include<ctype.h> #include<math.h> #include<iostream>using namespace std; #include<algorithm> #define N 2100 double a[10010]; #define Max 0x3f3f3f3f int main() { int i, n, T, t=1; scanf("%d", &T); while(T--) { a[1]=1; for(i=2;i<10000;i++) { a[i]=a[i-1]+1.0/i; } scanf("%d", &n); printf("Case %d: ", t++); if(n<10000) { /*if(n==1) printf("1\n"); else if(n==2) printf("1.5\n"); else if(n==6) printf("2.450\n"); else*/ printf("%.10f\n", a[n]); } else { double sum; sum=log(n)+0.5772156649+1.0/(2*n); printf("%.10f\n", sum); } } return 0; }