# LeetCode – Unique Binary Search Trees II (Java)

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
```

Analysis

Check out Unique Binary Search Trees I.

This problem can be solved by recursively forming left and right subtrees. The different combinations of left and right subtrees form the set of all unique binary search trees.

Java Solution

```public List<TreeNode> generateTrees(int n) { if(n==0){ return new ArrayList<TreeNode>(); }   return helper(1, n); }   public List<TreeNode> helper(int m, int n){ List<TreeNode> result = new ArrayList<TreeNode>(); if(m>n){ result.add(null); return result; }   for(int i=m; i<=n; i++){ List<TreeNode> ls = helper(m, i-1); List<TreeNode> rs = helper(i+1, n); for(TreeNode l: ls){ for(TreeNode r: rs){ TreeNode curr = new TreeNode(i); curr.left=l; curr.right=r; result.add(curr); } } }   return result; }```
Category >> Algorithms >> Interview
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```
• Benyam Ephrem

Wow, great explanation! I love how detailed you explained your solution. I understand it 100% just by reading opaque code with single letter variables! 🙂

• gao can

Now, to pass LeetCode, you need add:
if(n == 0) return new LinkedList();

before:
return generateTrees(1, n);