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Description

Problem G
Triangle Counting

Input: Standard Input

Output: Standard Output

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

Input

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

Output

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

Sample Input Output for Sample Input

5
8

0

3
22

Problemsetter: Mohammad Mahmudur Rahman

f[i] 是以i为最大边的三角形的个数。
代码：

#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <string>  
#include <queue>  
#include <stack>

using namespace std;

int n;
long long f[1000010];

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;

    while (scanf("%d", &n) != EOF)
    {
        if (n < 3) break;
        printf("%lld\n",f[n]);
    }
    return 0;
}