LightOJ - 1245 - Harmonic Number (II)（数学）

链接：

https://vjudge.net/problem/LightOJ-1245

题意:

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.

思路：

考虑对整数n/i的上下限，下限为最大值为n/(n/i))。不断循环，相等的值直接跳过去就不会超时了。

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<math.h>
#include<vector>
#include<map>

using namespace std;
typedef long long LL;
const int INF = 1e9;

const int MAXN = 1e7+10;
const int MOD = 1e9+7;

LL n;

int main()
{
    int t, cnt = 0;
    scanf("%d", &t);
    while(t--)
    {
        printf("Case %d:", ++cnt);
        scanf("%lld", &n);
        LL p = 1;
        LL sum = 0;
        while(p <= n)
        {
            LL tmp = n/p;
            LL next = n/(n/p);
            sum += 1LL*tmp*(next-p+1);
            p = next+1;
        }
        printf(" %lld\n", sum);
    }
    
    return 0;
}