1245 - Harmonic Number (II)



PDF (English)

Statistics

Forum


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 < 231).

Output

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

Sample Input

Output for Sample Input

11
1
2
3
4
5
6
7
8
9
10
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;
}