Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
           /     /      /       
     3     2     1      1   3      2
    /     /                        
   2     1         2                 3

 C++代码实现：

#include<iostream>
using namespace std;

class Solution {
public:
    int numTrees(int n) {
        if(n<0)
            return 0;
        if(n==1||n==0)
            return 1;
        int result=1;
        int i;
        for(i=2;i<=n;++i)
            result=(4*i-2)*result/(i+1);
        return result;
    }
};

int main()
{
    Solution s;
    cout<<s.numTrees(4)<<endl;
}

类似递推公式可以参考：http://blog.csdn.net/u011466175/article/details/38710947