hdu 5621

KK's Point

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 357    Accepted Submission(s): 124

Problem Description

Our lovely KK has a difficult mathematical problem:He points N(2≤N≤105) points on a circle,there are all different.Now he's going to connect the N points with each other(There are no three lines in the circle to hand over a point.).KK wants to know how many points are there in the picture(Including the dots of boundary).

 

 

Input

The first line of the input file contains an integer T(1≤T≤10) , which indicates the number of test cases.

For each test case, there are one lines,includes a integer N(2≤N≤105) ,indicating the number of dots of the polygon.

 

 

Output

For each test case, there are one lines,includes a integer,indicating the number of the dots.

 

 

Sample Input

2 3 4

 

 

Sample Output

3 5

 

 

Source

BestCoder Round #71 (div.2)

题意：n个不同的点 两点画一条线 最多两条线交于一点 问最多有多少个交点 包括边界点

 

题解

我们先撇开边界上的点不管，那么所有的点都是有两条线所构成的

手算得出N=4的时候，能形成一个点

那么，我们只要知道N个点可以构成几个四边形即可 C（4，n）​​

最后我们再把边界上的N个点加上

 

bc 结束了交了几遍wa 爆long long

改用 usigned long long

 

#include<iostream>
#include<cstring>
#include<cstdio>
#define LL unsigned long long
using namespace std;
LL t;
LL n;
int main()
{

    while(scanf("%I64d",&t)!=EOF)
    {
        for(LL i=1; i<=t; i++)
        {
            scanf("%I64d",&n);
            printf("%I64u\n",n+n*(n-1)/2*(n-2)/3*(n-3)/4);
        }
    }
    return 0;
}