Unique Binary Search Trees II

Problem

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

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

Code - Java

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *   public int val;
 *   public TreeNode left, right;
 *   public TreeNode(int val) {
 *     this.val = val;
 *     this.left = this.right = null;
 *   }
 * }
 */
public class Solution {
    /**
     * @paramn n: An integer
     * @return: A list of root
     */
    public List<TreeNode> generateTrees(int n) {

        List<List<TreeNode>> dp = new ArrayList<>();

        List<TreeNode> empty = new ArrayList<>();
        empty.add(null);
        if (n == 0) return empty;

        List<TreeNode> list = new ArrayList<>();
        dp.add(empty);
        dp.add(list);
        dp.get(1).add(new TreeNode(1));

        for (int i = 2; i <= n; i++) {
            List<TreeNode> newList = new ArrayList<>();
            dp.add(newList);
            for (int leftCnt = 0; leftCnt <= i - 1; leftCnt++) {
                int rightCnt = i - 1 - leftCnt;

                List<TreeNode> leftList = dp.get(leftCnt);
                List<TreeNode> rightList = dp.get(rightCnt);
                for (TreeNode left : leftList) {
                    for (TreeNode right : rightList) {
                        TreeNode root = new TreeNode(leftCnt + 1);
                        root.left = copy(left);
                        root.right = copy(right);
                        updateValue(root.right, leftCnt + 1);
                        dp.get(i).add(root);
                    }
                }
            }
        }
        return dp.get(n);
    }

    private TreeNode copy(TreeNode node) {
        if (node == null) return null;
        TreeNode newNode = new TreeNode(node.val);
        newNode.left = copy(node.left);
        newNode.right = copy(node.right);
        return newNode;
    }

    private void updateValue(TreeNode node, int plus) {
        if (node == null) return;
        node.val += plus;
        updateValue(node.left, plus);
        updateValue(node.right, plus);
    }
}