【HDOJ】1134 Game of Connections

Catlan数。

/* 1134 */
import java.util.Scanner;
import java.math.BigInteger;

/*
    Catalan:
    (1) h(n) = h(n-1) * (4*n-2) / (n+1)
    (2) h(n) = C(2n, n) / (n+1)
    (3) h(n) = C(2n, n) - C(2n, n+1)
*/

public class Main {
    public static void main(String args[]) {
        Scanner cin = new Scanner(System.in);
        BigInteger[] bi = new BigInteger[MAXN];
        bi[1] = BigInteger.ONE;
        bi[2] = BigInteger.valueOf(2);
        for (int i=3; i<MAXN; ++i) {
            BigInteger x = BigInteger.valueOf(4*i-2);
            BigInteger y = BigInteger.valueOf(i+1);
            bi[i] = bi[i-1].multiply(x).divide(y);
        }
        int n;
        while (cin.hasNext()) {
            n = cin.nextInt();
            if (n == -1)
                break;
            System.out.println(bi[n]);
        }
    }
    
    public static final int MAXN = 101;
}