Unique Binary Search Trees II

Problem

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.

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

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {

    public List<TreeNode> generateTrees(int n) {
        if (n <= 0) return new ArrayList<>();
        return helper(1, n);
    }

    private List<TreeNode> helper(int start, int end) {
        List<TreeNode> res = new ArrayList<>();
        if (start > end) {
            res.add(null);  //Must add null here
            return res;
        }
        for (int i = start; i <= end; i++) {
            List<TreeNode> leftSubtrees = helper(start, i - 1);
            List<TreeNode> rightSubtrees = helper(i + 1, end);
            for (TreeNode left : leftSubtrees) {
                for (TreeNode right : rightSubtrees) {
                    TreeNode root = new TreeNode(i);
                    root.left = left;
                    root.right = right;
                    res.add(root);
                }
            }
        }
        return res;
    }
}

Analysis

The idea of this solution is about Divide and Conquer
It use the similar algorithm in Problem 94 to come up with all the unique BSTs
We have a loop in recursive helper() function to construct all the unique BSTs and add them to the result
Notice that, for invalid number like start > end, we must add null to our result list