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  • Harmonic Number

    http://acm.hust.edu.cn:8080/judge/contest/view.action?cid=8086#problem/D

    D - Harmonic Number

    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 nu

    mber 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

    View Code
    #include <iostream>
    #include <stdio.h>
    #include <math.h>
    using namespace std;
    #define M  0.57721566490153286060651209
    double b[10000];
    int main()
    {
        int n,i;
        b[1]=1;
        for (i=2;i<10000;i++)
        {
            b[i]=b[i-1]+1.0/i;
        }
        cin>>n;
        for (i=1;i<=n;i++)
        {
            int m;
            cin>>m;  
            if (m<10000)
            {
                printf("Case %d: %.10lf\n",i,b[m]);        
            }
            else
            {
                double a=log(m)+M+1.0/(2*m);
                printf("Case %d: %.10lf\n",i,a);    
            }
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/wujianwei/p/2497276.html
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