Is Maximum Distinct Path Sum in a Binary Tree easy or hard?

This problem is generally classified as Medium difficulty. The traversal itself is standard DFS, but the challenge is managing path state correctly with backtracking while enforcing the distinct-value constraint. Candidates comfortable with recursion and hash sets typically solve it within typical interview time limits.

Maximum Distinct Path Sum in a Binary Tree Python/Java solution

Most implementations follow the same DFS + backtracking pattern. Maintain a global or external variable for the maximum sum, pass the current sum and a hash set into recursive calls, and remove values when returning from recursion. The logic translates directly across Python, Java, C++, Go, and TypeScript.

How to solve Maximum Distinct Path Sum in a Binary Tree in O(n)?

Run a single DFS traversal while maintaining a hash set of values on the current path and a running path sum. When visiting a node, check if its value already exists in the set. If it does, stop exploring that branch; otherwise add the value, update the sum, explore children, then remove the value during backtracking. This ensures each node contributes to the computation only once.

What is the best approach for Maximum Distinct Path Sum in a Binary Tree?

The most efficient approach uses Depth-First Search with a hash set to track values currently present in the path. During traversal, if a value already exists in the set, the branch is stopped because the path would violate the distinct constraint. With backtracking, each node is added and removed exactly once, producing an O(n) time solution with O(h) recursion space.

Is Maximum Distinct Path Sum in a Binary Tree asked at Google/Amazon/Meta?

Tree traversal problems combined with hash-based constraints appear frequently in interviews at companies like Google, Amazon, and Meta. Variations include longest unique path, path sum constraints, and tree DFS with state tracking. This problem tests recursion design, pruning logic, and efficient use of hash structures.

What data structure is used in Maximum Distinct Path Sum in a Binary Tree?

The core data structure is a hash set or hash table used to store values currently present in the DFS path. It enables constant-time duplicate detection while traversing the binary tree. The algorithm also relies on recursion or an explicit stack to perform depth-first traversal.

What is the time complexity of Maximum Distinct Path Sum in a Binary Tree?

The optimal DFS + hash table solution runs in O(n) time where n is the number of nodes in the tree. Each node is visited once, and hash set operations such as insert, lookup, and delete take O(1) on average. Space complexity is O(h) due to recursion stack and the set storing values along the current path.

3879. Maximum Distinct Path Sum in a Binary Tree - Practice Online

You are given the root of a binary tree, where each node contains an integer value.

A valid path in the tree is a sequence of connected nodes such that:

The path can start and end at any node in the tree.
The path does not need to pass through the root.
All node values along the path are distinct.

Return an integer denoting the maximum possible sum of node values among all valid paths.

Example 1:

Input: root = [2,2,1]

Output: 3

Explanation:

The path 2 → 2 is invalid because the value 2 is not distinct.
The maximum-sum valid path is 2 → 1, with a sum = 2 + 1 = 3.

Example 2:

Input: root = [1,-2,5,null,null,3,5]

Output: 9

Explanation:

The path 3 → 5 → 5 is invalid due to duplicate value 5.
The maximum-sum valid path is 1 → 5 → 3, with a sum = 1 + 5 + 3 = 9.

Example 3:

Input: root = [4,6,6,null,null,null,9]

Output: 19

Explanation:

The path 6 → 4 → 6 → 9 is invalid because the value 6 appears more than once.
The maximum-sum valid path is 4 → 6 → 9, with a sum = 4 + 6 + 9 = 19.

Constraints:

The number of nodes in the tree is in the range [1, 1000].
-1000 <= Node.val <= 1000