Is Unique Binary Search Trees II easy or hard?

Unique Binary Search Trees II is considered a Medium problem on LeetCode. The recursion concept is straightforward, but recognizing that each number can act as a root and combining all subtree permutations requires a solid understanding of recursion, BST properties, and Catalan-number growth.

Unique Binary Search Trees II Python/Java solution

In Python or Java, implement a recursive function that returns all BST roots for a range [start, end]. For each root choice i, generate all left subtrees from [start, i-1] and right subtrees from [i+1, end], then combine them. Memoization using a dictionary or map improves performance.

How to solve Unique Binary Search Trees II in O(n)?

Generating all unique BST structures cannot be done in O(n) because the output size itself is exponential (Catalan growth). The optimal approach enumerates all trees using recursion or dynamic programming, which requires O(Cn * n) time since every valid structure must be built.

What is the best approach for Unique Binary Search Trees II?

Recursive tree construction with memoization is the most practical approach. Choose each value as the root, recursively generate all left and right subtrees, and combine them. Adding memoization avoids recomputing subtree ranges and keeps the solution efficient while still generating all Catalan-number trees.

Is Unique Binary Search Trees II asked at Google/Amazon/Meta?

Tree construction and Catalan-number problems appear frequently in interviews at companies like Google, Amazon, and Meta. Variants involving BST generation, subtree combinations, or counting unique trees are common interview patterns in tree and dynamic programming categories.

What data structure is used in Unique Binary Search Trees II?

The solution primarily uses binary trees, specifically Binary Search Trees. Recursion builds tree nodes, and dynamic programming with memoization may use a hash map or 2D cache to store lists of previously computed subtree structures.

What is the time complexity of Unique Binary Search Trees II?

The time complexity is O(Cn * n), where Cn is the nth Catalan number. The algorithm must generate every valid BST structure, and the number of such trees grows roughly as 4^n / (n^(3/2)). Each generated tree also requires node connections, contributing the extra factor of n.

Description Solution Video 12:51

95. Unique Binary Search Trees II

Medium63.3% acceptance5 companies

Given an integer n, return all the structurally unique BST's (binary search trees), which has exactly n nodes of unique values from 1 to n. Return the answer in any order.

Example 1:

Input: n = 3
Output: [[1,null,2,null,3],[1,null,3,2],[2,1,3],[3,1,null,null,2],[3,2,null,1]]

Example 2:

Input: n = 1
Output: [[1]]

Constraints:

1 <= n <= 8

Asked at 5 companies

Google Amazon Microsoft Meta Bloomberg

Topics

12:51

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

95. Unique Binary Search Trees II

Asked at 5 companies

Topics

Similar problems