【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;
 }