UVA - 11401 Triangle Counting

Triangle Counting

Time Limit: 1000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

Submit Status

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

 

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Problemsetter: Mohammad Mahmudur Rahman

分析：

刘汝佳大白书里的数学水题。

ac代码：

#include <iostream>
#include<cstdio>
using namespace std;
const int maxn=1000000+10;
long long f[maxn];
int main()
{
    f[3]=0;
    for(long long x=4;x<=maxn;x++)//x用long long，因为中间计算int会溢出
    f[x]=f[x-1]+((x-1)*(x-2)/2-(x-1)/2)/2;
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        if(n<3) break;
        printf("%lld\n",f[n]);
    }
    return 0;
}