hdu 1130 How Many Trees?（Catalan数）

How Many Trees?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3317    Accepted Submission(s): 1922

Problem Description

A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node with label x in O(n log n) average time, where n is the size of the tree (number of vertices). 

Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree? 

 

Input

The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.

 

Output

You have to print a line in the output for each entry with the answer to the previous question.

 

Sample Input

  

   1
2
3
  

 

Sample Output

  

   1
2
5
  

 

Source

UVA

题意：

对于给定的n，求n个节点能构成多少种二叉树，左子树的值 < 根节点 < 右子树

思路：Catalan数 + 大整数

import java.math.BigInteger;
import java.util.Scanner;

public class Main {

	static BigInteger []F =  new BigInteger[105];
	public static void ini()
	{
		F[1] = BigInteger.valueOf(1);
		for(int i = 2;i < 105;i++)
		{
			F[i] = F[i-1].multiply(BigInteger.valueOf(i*4-2)).divide(BigInteger.valueOf(i+1));
		}
	}
	public static void main(String[] args) {
		// TODO 自动生成的方法存根
		ini();
		Scanner Reader = new Scanner(System.in);
		int x;
		while(Reader.hasNext())
		{
			x = Reader.nextInt();
			System.out.println(F[x]);
		}     
	}

}