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Solution: Binary Tree Maximum Path Sum

Explore the solution to find the maximum path sum in a binary tree by applying depth-first search and recursion. Understand how to compute maximum contributions from subtrees, decide between continuing or starting new paths, and manage edge cases for optimal results. Gain insight into time and space complexity analysis for this binary tree problem.

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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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