HDU 5621 KK's Point (组合数学）

KK's Point

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1142    Accepted Submission(s): 374

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

234

 

Sample Output

35

 

Source

BestCoder Round #71 (div.2)

 

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题意：在圆上有n个点，问最多有多少个交点（包括圆上的点），

思路：每四个点会有1个交点，所以也就转换为了组合数学中的知识，c(n,4),但要注意的时，数据太大，用__int64  也会超，要用到unsigned (虽然知道有这个数据类型，但一直没用过）。。。。

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;unsigned __int64 k,i,j,t,n;int main(){scanf("%I64u",&t);while(t--){scanf("%I64u",&n);k=n;if(n>=4)k=k+n*(n-1)/2*(n-2)/3*(n-3)/4;printf("%I64u\n",k);}return 0;}