UVa 11401 Triangle Counting(递推)

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 (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

 题意:1..n构成三角形的数目

分析:先做出n的,在做n+1,递推

代码:

#include<iostream>//数学M
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
const int MAXN=1000050;
long long x[MAXN];
long long xx[MAXN];
void init()
{
    int i;
    x[3]=0;xx[3]=0;
    for(i=4;i<MAXN;i++)
    {
        x[i]=x[i-1]+i/2-1;
        xx[i]=xx[i-1]+x[i];
    }
}
int main()
{
    int n,i;
  // freopen("../../out.txt","w",stdout);
    init();
    while(scanf("%d",&n)==1)
    {
        if(n<3)break;
        printf("%I64d\n",xx[n]);
    }
    return 0;
}


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