【HDOJ】1134 Game of Connections

Catlan数。

 1 /* 1134 */
 2 import java.util.Scanner;
 3 import java.math.BigInteger;
 4
 5 /*
 6     Catalan:
 7     (1) h(n) = h(n-1) * (4*n-2) / (n+1)
 8     (2) h(n) = C(2n, n) / (n+1)
 9     (3) h(n) = C(2n, n) - C(2n, n+1)
10 */
11
12 public class Main {
13     public static void main(String args[]) {
14         Scanner cin = new Scanner(System.in);
15         BigInteger[] bi = new BigInteger[MAXN];
16         bi[1] = BigInteger.ONE;
17         bi[2] = BigInteger.valueOf(2);
18         for (int i=3; i<MAXN; ++i) {
19             BigInteger x = BigInteger.valueOf(4*i-2);
20             BigInteger y = BigInteger.valueOf(i+1);
21             bi[i] = bi[i-1].multiply(x).divide(y);
22         }
23         int n;
24         while (cin.hasNext()) {
25             n = cin.nextInt();
26             if (n == -1)
27                 break;
28             System.out.println(bi[n]);
29         }
30     }
31
32     public static final int MAXN = 101;
33 }