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How Many Trees?

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2828    Accepted Submission(s): 1657

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

123

 

Sample Output

125

第一次用Java写大数，感觉超简单~~~

代码：

import java.math.*;import java.util.*;public class Main {    public static void main(String[] args) {      // TODO Auto-generated method stub        Integer n,N=102,i;        BigInteger []f=new BigInteger[N];        f[1]=BigInteger.valueOf(1);        for(i=2;i<N;i++)            f[i]=f[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));        Scanner cin=new Scanner(System.in);        while(cin.hasNext())        {          n=cin.nextInt();          System.out.println(f[n]);        }               cin.close();    }}