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Solution: Binary Tree Maximum Path Sum

Explore how to compute the maximum path sum in a binary tree by implementing a recursive function that evaluates each node’s contribution. Understand how to decide when to continue or start new paths to optimize the total sum. Learn the time and space complexity implications of this approach within tree depth-first search.

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Statement

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

A path in a binary tree is defined as follows:

  • A sequence of nodes in which each pair of adjacent nodes must have an edge connecting them.
    • A node can only be included in a path once at most.
    • Including the root in the path is not compulsory.

You can calculate the path sum by adding up all node values in the path. To solve this problem, calculate the maximum path sum given the root of a binary tree so that there won’t be any greater path than it in the tree.

Constraints:

  • 1≤1\leq Number of nodes in the tree ≤500\leq500.
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