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

the number of unique binary search tree can be interpreted as given an index i from [1,...,n],

numTrees(1...i)*numTrees(i+1...n).

So here is the dp solutions.

public int numTrees(int n) {
        if (n<=1) {
            return n;
        }

        int[] results = new int[n+1];
        results[0] = 1;
        results[1] = 1;

        for (int i=2; i<=n; i++) {
            for (int j=0; j<i; j++) {
                results[i] += results[j] * results[i-j-1];
            }
        }      
        return results[n];
    }