hdoj1023——卡特兰数

hdoj1023——卡特兰数

Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 6418    Accepted Submission(s): 3494

Problem Description

As we all know the Train Problem I, the boss of the Ignatius Train Station want to know if all the trains come in strict-increasing order, how many orders that all the trains can get out of the railway.

 

 

Input

The input contains several test cases. Each test cases consists of a number N(1<=N<=100). The input is terminated by the end of file.

 

 

Output

For each test case, you should output how many ways that all the trains can get out of the railway.

 

 

Sample Input

1 2 3 10

 

 

Sample Output

1 2 5 16796

Hint

The result will be very large, so you may not process it by 32-bit integers.

 

虽然是火车入栈，但和括号匹配是同一个道理，标准的卡特兰数，数比较大，学了java真是方便。。

import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
    public static BigInteger fac(BigInteger n){
        BigInteger a=new BigInteger("1");
        BigInteger zero=new BigInteger("0");
        if(n.equals(a)||n.equals(zero)) return a;
        return n.multiply(fac(n.subtract(a)));
    }
    public static BigInteger C(BigInteger n,BigInteger k){
        return fac(n).divide(fac(k).multiply(fac(n.subtract(k))));
    }
    public static BigInteger Catlan(BigInteger n){
        BigInteger a=new BigInteger("1");
        return C(n.add(n),n).divide(n.add(a));
    }
    public static void main(String[] args){
        Scanner in=new Scanner(System.in);
        BigInteger n;
        BigInteger two=new BigInteger("2");
        while(in.hasNext()){
            n=in.nextBigInteger();
            System.out.println(Catlan(n).toString());
        }
    }
}