Unique Binary Search Trees II

Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.

For example,
Given n = 3, your program should return all 5 unique BST's shown below.

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

confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

Solution:
If it asks us to list all possibilities, use DFS in most cases.
DFS in the code is tricky. 

 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; left = null; right = null; }
 * }
 */
public class Solution {
    public ArrayList<treenode> generateTrees(int n) {
        return helper(1,n);
    }
    public ArrayList<treenode> helper(int begin, int end){
        ArrayList<treenode> ret = new ArrayList<treenode>();
        if(begin > end){
            ret.add(null);
            return ret;
        }
        for(int i = begin; i <= end; i++){                 // for all roots
            ArrayList<treenode> left = helper(begin, i-1); //generate left subtree
            ArrayList<treenode> right = helper(i+1, end);  //generate right subtree
            for(TreeNode l : left){
                for(TreeNode r : right){
                   TreeNode tmp = new TreeNode(i);
                   tmp.left = l;
                   tmp.right = r;
                   ret.add(tmp);
                }
            }
        }
        return ret;
    }
}