Is Find Duplicate Subtrees easy or hard?

Find Duplicate Subtrees is generally considered a medium-level problem. The challenge lies in recognizing that subtree structures must be uniquely represented and compared efficiently, typically using DFS traversal combined with hashing.

Find Duplicate Subtrees Python/Java solution

Python and Java implementations typically perform a postorder DFS and store subtree representations in a hash map. The optimized version assigns unique IDs to subtree structures, ensuring O(n) time complexity while keeping memory usage linear.

How to solve Find Duplicate Subtrees in O(n)?

Traverse the tree using postorder DFS and assign a unique ID to each distinct subtree structure. Store tuples (value, leftID, rightID) in a hash map that maps structures to IDs. Maintain a frequency map for each ID and record the subtree root when its count reaches two.

What is the best approach for Find Duplicate Subtrees?

The most efficient approach uses DFS with unique subtree identifiers stored in a hash map. Each subtree is represented by a tuple of (node value, left subtree ID, right subtree ID), which is mapped to a unique integer. This avoids expensive string comparisons and runs in O(n) time with O(n) space.

Is Find Duplicate Subtrees asked at Google/Amazon/Meta?

Find Duplicate Subtrees is a common binary tree hashing problem that has appeared in interviews at companies like Google, Amazon, and Meta. It tests understanding of DFS traversal, subtree representation, and efficient hashing techniques for structural comparison.

What data structure is used in Find Duplicate Subtrees?

The solution relies on hash maps to store serialized subtree representations or subtree identifiers and their frequencies. Depth-first search recursion processes the binary tree, while the hash table allows constant-time lookup to detect duplicate subtree structures.

What is the time complexity of Find Duplicate Subtrees?

The optimized solution runs in O(n) time because each node in the binary tree is processed once during DFS. Hash map lookups and ID assignments are constant time on average. A simpler serialization approach may degrade to O(n^2) time due to repeated string concatenation.

652. Find Duplicate Subtrees - Practice Online

Given the root of a binary tree, return all duplicate subtrees.

For each kind of duplicate subtrees, you only need to return the root node of any one of them.

Two trees are duplicate if they have the same structure with the same node values.

Example 1:

Input: root = [1,2,3,4,null,2,4,null,null,4]
Output: [[2,4],[4]]

Example 2:

Input: root = [2,1,1]
Output: [[1]]

Example 3:

Input: root = [2,2,2,3,null,3,null]
Output: [[2,3],[3]]

Constraints:

The number of the nodes in the tree will be in the range [1, 5000]
-200 <= Node.val <= 200