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


考察二叉树的种类，卡特兰数的例子。这里要注意的是空树也属于二叉搜索树。代码如下：

public class Solution {
    public int numTrees(int n) {
        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = 1;
        for(int i = 2; i <= n; i++) {
            for(int j = 0; j < i; j++) {
                dp[i] += dp[j] * dp[i - j - 1];
            }
        }
        return dp[n];
    }
}