UVA

圆上有n个点，位置不确定。问这些点两两连接成的线段，最多可以把圆划分成多少块平面？

欧拉公式：V-E+F = 2，V是点数，E是边数，F是面数。

答案是F=C(n,4)+C(n,2)+1，看的别人推的。。我实在推不出来。

写这篇博客的原因是第一次用Java的BigInteger。

import java.math.BigInteger;
import java.util.*;

public class Main{
	static Scanner sc = new Scanner(System.in);
	public static void main(String args[]){
		int t = sc.nextInt();
		for (int ca = 1; ca <= t; ca++)
		{
			String s = sc.next();
			BigInteger n = new BigInteger(s);
			BigInteger ans = BigInteger.valueOf(1);
			BigInteger tmp = new BigInteger(s);
			for (int i = 1; i <= 3; i++) 
			{
				BigInteger k = BigInteger.valueOf(i);
				tmp = tmp.multiply(n.subtract(k));
			}
			for (int i = 1; i <= 4; i++)
			{
				BigInteger k = BigInteger.valueOf(i);
				tmp = tmp.divide(k);
			}
			ans = ans.add(tmp);
    	
			tmp = new BigInteger(s);
			tmp = tmp.multiply(n.subtract(BigInteger.valueOf(1)));
			tmp = tmp.divide(BigInteger.valueOf(2));
			
			ans = ans.add(tmp);
			System.out.println(ans);
		}
	}
}