1245 - Harmonic Number (II)

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Time Limit: 3 second(s)	Memory Limit: 32 MB

I was trying to solve problem ‘1234 - Harmonic Number’ , I wrote the
following code

long long H ( int n ) {
long long res = 0 ;
for ( int i = 1 ; i <= n ; i ++ )
res = res + n / i ;
return res ;
}

Yes, my error was that I was using the integer divisions only. However, you
are given n , you have to find H(n) as in my code.

Input

Input starts with an integer T (≤ 1000) , denoting the number of test
cases.

Each case starts with a line containing an integer n (1 ≤ n < 2 31 ) .

Output

For each case, print the case number and H(n) calculated by the code.

Sample Input

Output for Sample Input

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2147483647

Case 1: 1

Case 2: 3

Case 3: 5

Case 4: 8

Case 5: 10

Case 6: 14

Case 7: 16

Case 8: 20

Case 9: 23

Case 10: 27

Case 11: 46475828386

运算到sqrt（n）

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <ctype.h>
#include <time.h>
#include <queue>
#include <iterator>

using namespace std;

int t,cases = 1;
int n;
long long ans;

long long solve(long long  n)
{
    long long res = 0;
    for (int i = 1; i <= sqrt(n); i++)
    {
        res += n / i;
        if (n / i > n / (i + 1))
            res += (n / i - n / (i + 1))*i;
    }
    if ((long long)sqrt(n) == n/(long long)sqrt(n))
        res -= (int)sqrt(n);
    return res;
}

int main()
{
    scanf("%d",&t);
    while (t--)
    {
        scanf("%d",&n);
        ans = solve(n);
        printf("Case %d: %lld\n",cases++,ans);
    }
    return 0;
}