HDU 5621 KK's Point（数学+规律题）

KK's Point

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1327    Accepted Submission(s): 439

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)

 

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题意：圆上有n个点，任意两点相连，任意三条线不交于1点，问构成的图上有多少点。

思路：一开始画了5个点，6个点，7个点的情况，然后在画图的过程中发现每个四边形都会贡献一个交点，所以就直接Cn4看n个点的图能有多少四边形即可。注意要用unsigned long long不然会爆，且n<4的时候直接输出n即可。

include 
#include 
#include 
#include 
#include 
using namespace std;

int main(){
    
    int t;
    scanf("%d",&t);
    while(t--){
        unsigned long long n;
        scanf("%llu",&n);
        unsigned long long sum=0;
        if(n>=4)
            sum=n*(n-1)/2*(n-2)/3*(n-3)/4+n;
        else
            sum=n;
        printf("%llu\n",sum);
    } 
    return 0;
}