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

Example:

Input: 3Output: 5Explanation: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

难度：medium

题目：给定整数n，计算有多少种BST结构。

class Solution {    public int numTrees(int n) {        long c = 1;        // Catalan number        // Catalan (n+1) = (4n+2) / (n+2) Catalan n        for(int i = 1; i < n; i++){            c = c * 2 * (2 * i + 1) / (i + 2);        }                return (int) c;    }}