UVA 11401 TRIANGLE COUNTING 【加法原理】

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;}