Is Unique Binary Search Trees easy or hard?

Unique Binary Search Trees is rated Medium difficulty on LeetCode with an acceptance rate around 63%. The challenge is recognizing the recursive subtree counting pattern and converting it into a dynamic programming recurrence.

Unique Binary Search Trees Python/Java solution

In Python or Java, the typical solution builds a DP array where dp[i] stores the number of BSTs using i nodes. For each i from 2 to n, iterate root from 1..i and accumulate dp[root-1] * dp[i-root]. Both languages implement this in O(n^2) time and O(n) space.

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

Use the Catalan number formula C(n) = (1 / (n + 1)) * binomial(2n, n). Instead of computing factorials, iteratively calculate the binomial coefficient to avoid overflow. This computes the result in O(n) time and constant space.

What is the best approach for Unique Binary Search Trees?

Dynamic Programming is the most commonly used approach in interviews. Define dp[n] as the number of unique BSTs that can be formed with n nodes and compute dp[n] = sum(dp[left] * dp[right]) for all possible roots. This runs in O(n^2) time and O(n) space and clearly demonstrates the BST root partition idea.

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

Unique Binary Search Trees is a classic dynamic programming and combinatorics problem frequently asked in interviews at companies like Amazon, Google, and Meta. It tests understanding of BST properties, recursion-to-DP transitions, and recognition of Catalan number patterns.

What data structure is used in Unique Binary Search Trees?

The problem revolves around Binary Search Trees conceptually, but the implementation mainly uses a dynamic programming array to store counts of subtree combinations. The DP table captures how many BST structures can be formed for each subtree size.

What is the time complexity of Unique Binary Search Trees?

The standard dynamic programming solution runs in O(n^2) time because for each node count you iterate over all possible roots. Space complexity is O(n) for the DP array. Using the Catalan number formula reduces the computation to O(n) time with O(1) extra space.

Description Solution Video 11:20

96. Unique Binary Search Trees

Medium64.0% acceptance10 companies

Given an integer n, return the number of structurally unique BST's (binary search trees) which has exactly n nodes of unique values from 1 to n.

Example 1: