class Solution {
    // O(n^2) O(n^2)
    public List<TreeNode> generateTrees(int n) {
        if (n == 0) return new ArrayList<TreeNode>();
        return genTree(1, n);
    }

    private List<TreeNode> genTree(int start, int end) {
        List<TreeNode> list = new ArrayList<>();

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

        // this part can be ignored
        if ( start == end ) {
            list.add(new TreeNode(start));
            return list;
        }

        List<TreeNode> left, right;
        for (int i=start; i<=end; i++) {
            left = genTree(start, i-1);
            right = genTree(i+1, end);

            for (TreeNode lnode : left) {
                for (TreeNode rnode : right) {
                    TreeNode root = new TreeNode(i);
                    root.left = lnode;
                    root.right = rnode;

                    list.add(root);
                }
            }
        }

        return list;
    }
}