学步园

Problem G

Triangle Counting

Input: StandardInput

Output: StandardOutput 

You are given n rods of length 1, 2…, n. You have topick any 3 of them & build a triangle. How many distinct triangles can youmake? Note that, two triangles will be considered different if they have atleast 1 pair of arms with different
length.

Input

The input for each case will haveonly a single positive integer n
(3<=n<=1000000). The end of inputwill be indicated by a case with n<3. This case should not beprocessed.

Output

For each test case, print thenumber of distinct triangles you can make.

Sample Input output                                          

 思路：列出不等式进行优化!

#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
//11401 Triangle Counting 	Accepted C++ 0.044 	2013-04-22

const int maxn = 1000010;
long long f[maxn];

int main()
{
    f[3] = 0;
    for(long long x = 4; x <= 1000000; x++) {
        f[x] = f[x-1] + (((x-1)*(x-2))/2-(x-1)/2)/2;
    }
    int n;
    while(scanf("%d",&n)==1) {
        if(n<3) break;
        cout << f[n] << endl;
    }
    return 0;
}