UVA - 11526 H(n) (数学)

【题目链接】：click here~~

【题目大意】

What is the value this simple C++ function will return?

long long H(int n){

long long res = 0;

for( int i = 1; i <= n; i=i+1 ){

res = (res + n/i);

}

return res;

}

Input

The first line of input is an integer T (T ≤ 1000) that indicates the number of test cases. Each of thenext T line will contain a single signed 32 bit integer n.

Output

For each test case, output will be a single line containing H(n).

Sample Input

2

5

10

Sample Output

10

27

就是求n/1...n/n的值

【解题思路】我们改变一下循环里面的长度，很容易想到只要循环到sqrt(n),最后结果乘以2再减去sqrt（n）平方回来的结果就是答案了。

代码：

//uva 11526
#include <bits/stdc++.h>
using namespace std;
long long t,n;
long long solve(int n)//超时
{
    long long res=0;
    for(int i=2; i<n; i++)
    {
        res+=n/i;
    }
    return res;
}
long long W(long long n)
{
    int t=sqrt(n+0.5);
    long long  res = 0;
    for(int i=1;i<=t;i++) res+=n/i;
    return (res<<1)-t*t;
}
long long  H(long long  n)//或者合并结果相同的项，答案是一样的
{
    long long  res = 0;
    long long  L=1,R=0;
    while(L<=n)
    {
        long long  p=n/L;
        R=n/p;
        res+=p*(R-L+1);
        L=R+1;
    }
    return res;
}
int main()
{
    scanf("%d",&t);
    while(t--)
    {
        scanf("%lld",&n);
        //printf("%lld\n",solve(n)+n+1);
       // printf("%lld\n",H(n));
        printf("%lld\n",W(n));
    }
    return 0;
}