95. Unique Binary Search Trees II

Given an integer 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.

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

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public ArrayList<TreeNode> generateTrees(int n) {
        if(n < 1)
            return new ArrayList<TreeNode>();
        return generate(1, n);
    }

    private ArrayList<TreeNode> generate(int start, int end){
        ArrayList<TreeNode> rst = new ArrayList<TreeNode>();   

        if(start > end){
            rst.add(null);
            return rst;
        }

        for(int i=start; i<=end; i++){
            ArrayList<TreeNode> left = generate(start, i-1);
            ArrayList<TreeNode> right = generate(i+1, end);
            for(TreeNode l: left){
                for(TreeNode r: right){
                    // should new a root here because it need to 
                    // be different for each tree
                    TreeNode root = new TreeNode(i);  
                    root.left = l;
                    root.right = r;
                    rst.add(root);
                }
            }
        }
        return