How Many Trees? 卡特兰数

How Many Trees?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4154    Accepted Submission(s): 2350

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). 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

 

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import java.util.Scanner;
import java.math.*;
public class Main {
public static void main(String args[]){
	    int n;
	   Scanner scan=new Scanner(System.in);
	   BigInteger f[]=new BigInteger[101];
	   f[0]=BigInteger.ONE;
	   f[1]=BigInteger.ONE;
	   for(int i=2;i<=100;i++)
	   {
		   f[i]=f[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));
	   }
	   while(scan.hasNext())
	   {
		   n=scan.nextInt();
		   System.out.println(f[n]);
	   }
  }
}