http://acm.hdu.edu.cn/showproblem.php?pid=1023&&卡特兰数

最新推荐文章于 2015-02-01 23:29:26 发布

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本文探讨了如何通过编程解决火车调度问题，即在保证所有火车出站顺序严格递增的情况下，计算可能的出站顺序总数。提供了一个Java实现的示例代码，帮助理解并解决此类问题。

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

Sample Output

  
   1
2
5
16796

  
  
   java写的。。。。
  
  
   AC代码：
   http://blog.youkuaiyun.com/smallacmer/article/details/7770855
  
  
   import java.util.*;
import java.math.BigInteger;
public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO 自动生成方法存根
		BigInteger num[]=new BigInteger[105];
		num[1]=BigInteger.ONE;
		num[2]=BigInteger.valueOf(2);
		num[3]=BigInteger.valueOf(5);
		for(int i=4;i<105;i++)
			{
			BigInteger b=BigInteger.valueOf(4);
			b= b.multiply(BigInteger.valueOf(i)).subtract(BigInteger.valueOf(2));
            num[i]=num[i-1].multiply(b).divide(BigInteger.valueOf(i+1));
			}

		Scanner cin=new Scanner(System.in);
		int n;
		while(cin.hasNext())
		{
			n=cin.nextInt();
			System.out.println(num[n]);
		}
	}

}