Train Problem II

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 11174    Accepted Submission(s): 5923

 

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.

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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.

Author

Ignatius.L

卡特兰数应用  （板子）   直接用java大整数了   不知道python可不可以。。。

公式：

递推式： h(n)=h(n-1)*(4*n-2)/(n+1);

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

public class Main {
	
	public static void main(String[] args){
		
		Scanner sc = new Scanner(System.in);
		
		BigInteger s[] = new BigInteger[105];
		
		s[1] = BigInteger.ONE;
		
		for(int i = 2;i < 105;i ++){
			
			s[i] = s[i-1].multiply(BigInteger.valueOf(4 * i - 2)).divide(BigInteger.valueOf(i + 1));
				
		}
		while(sc.hasNext()){
			
			int n =  sc.nextInt();
			System.out.println(s[n]);
		}
	}
}