Binary Tree Maximum Path Sum

Asked byDoorDashAmazonFacebookMicrosoftGoogleByteDance

Problem

Given the root of a binary tree, return the maximum path sum of any non-empty path, where a path is any sequence of nodes connected by parent-child edges that does not need to pass through the root, and each node may appear at most once.

Examples

Example 1

Input:root = [1,2,3]

Output:6

Example 2

Input:root = [-10,9,20,null,null,15,7]

Output:42

The path 15 → 20 → 7 sums to 42.

Constraints

The number of nodes is in the range [1, 3 * 10^4].

Solve it in the editor. Sign in free to run your Python or JavaScript against test cases, get a verdict, and track your attempts.

Solve on FeatCode →

How to approach it: the Trees pattern

A tree is a hierarchical structure where each node has at most a fixed number of children (two, for binary trees). Almost every tree problem reduces to a traversal — decide what order you visit nodes in, and what you do at each one.

Look for this pattern when

The problem is naturally recursive: "the answer for this tree depends on the answer for its subtrees."
You need level-by-level information (BFS) versus depth-first structural information (DFS).

Read the full Trees guide →

Video walkthroughs

Original problem on LeetCode ↗