LeetCode – Unique Binary Search Trees II (Java)

Category: Algorithms >> Interview   May 19, 2014

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;
}

Related posts:

  1. LeetCode – Find Leaves of Binary Tree (Java)
  2. LeetCode – Unique Binary Search Trees (Java)
  3. LeetCode – Validate Binary Search Tree (Java)
  4. LeetCode – Binary Search Tree Iterator (Java)
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);