Top 150 InterviewHard

Binary Tree Maximum Path Sum

Detailed guide and Python implementation for the 'Binary Tree Maximum Path Sum' problem.

Problem Statement

Hard

A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.

The path sum of a path is the sum of the node's values in the path.

Given the root of a binary tree, return the maximum path sum of any non-empty path.

The tree is represented as a level-order list. Implement a function maxPathSum(root: list) -> int.

Constraints
  • The number of nodes in the tree is in the range [1, 30000]
  • -1000 <= Node.val <= 1000

Examples

Example 1
Input
[1,2,3]
Output
6
Explanation

The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.

Example 2
Input
[-10,9,20,None,None,15,7]
Output
42
Explanation

The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.

Example 3
Input
[-3]
Output
-3
Explanation

The only path is the single node -3.

Need a Hint?
Consider using Trees-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor

Recommended Python Resources

Expand your knowledge with related interactive tutorials, cheat sheets, and code comparisons.