Basic idea:
Two and only two lines can create an intersection according to the instruction.
So it is basically a permutations and combinations question: how many sets of 4 vertex does the graph have?
Since the sequence of the 4 vertex won’t affect the final result, the answer is C(n,4).
Cavets:
java only provides a 64 bits max integer, aka long. So when the n goes to 2^5, the process n * (n - 1) / 2 * (n - 2) / 3 * (n - 4) / 4 cannot work. The java.util.BigInteger will be import to solve the question.
Code:
import java.math.BigInteger;
import java.util.Scanner;
public class Main {
public static void main(String args[]) {
Scanner sc = new Scanner(System.in);BigInteger n = sc.nextBigInteger();BigInteger tmp = new BigInteger("1");BigInteger res = new BigInteger("1");for (int i = 0; i < 4; i++) {
tmp = tmp.multiply(n.subtract(BigInteger.valueOf(i)));}res = tmp.divide(BigInteger.valueOf(24));System.out.print(res);}}
Details abt BigInteger: CSDN