How Many Pieces of Land? Euler's Theorem

How Many Pieces of Land? Euler's Theorem

Euler's theorem V-E + F = C + 1

Problem G
How Many Pieces of Land?
Input:Standard Input
Output:Standard Output
Time Limit:3 seconds

You are given an elliptical shaped land and you are asked to chooseNArbitrary points on its boundary. Then you connect all these points with one another with straight lines (that'sN * (n-1)/2ConnectionsNPoints). What is the maximum number of pieces of land you will get by choosing the points on the boundary carefully?

Fig: When the value of n is 6.

Input

The first line of the input file contains one integerS (0 <S <3500), Which indicates how many sets of input are there. The nextSLines containSSets of input. Each input contains one integerN (0 <= N <2 ^ 31) <喎?http: www.bkjia.com kf ware vc " target="_blank" class="keylink"> Signature + signature + CjQ8YnI + CjE8YnI + CjI8YnI + CjM8YnI + CjQ8YnI + signature + IDwvcD4KPHA + Signature = "2" width = "100% ""align =" center ">

Shahriar Manzoor

/** * Created by ckboss on 15-2-1. */import java.math.BigInteger;import java.util.*;public class Main {    BigInteger pfh(BigInteger n){        return n.multiply((n.add(BigInteger.ONE))).multiply((n.multiply(BigInteger.valueOf(2))).add(BigInteger.ONE)).divide(BigInteger.valueOf(6));    }    BigInteger getV(BigInteger n){        BigInteger A = n.subtract(BigInteger.valueOf(2));        BigInteger B = n.subtract(BigInteger.valueOf(3));        BigInteger temp = A.multiply(B).divide(BigInteger.valueOf(2)).multiply(A).subtract(pfh(B));        temp = temp.multiply(n).divide(BigInteger.valueOf(4));        return temp.add(n);    }    BigInteger getE(BigInteger n){        BigInteger A = n.subtract(BigInteger.valueOf(2));        BigInteger B = n.subtract(BigInteger.valueOf(3));        BigInteger temp = A.multiply(B).divide(BigInteger.valueOf(2)).multiply(A).subtract(pfh(B)).add(n).subtract(BigInteger.ONE);        temp = temp.multiply(n).divide(BigInteger.valueOf(2));        return temp.add(n);    }    Main(){        Scanner in = new Scanner(System.in);        int T_T = in.nextInt();        while(T_T-->0) {            BigInteger n = in.nextBigInteger();            BigInteger V = getV(n);            BigInteger E = getE(n);            BigInteger F = BigInteger.ONE.subtract(V).add(E);            System.out.println(F);        }    }    public static void main(String[] args){        new Main();    }}