Binary Tree Maximum Path Sum

Description

A path in a binary tree is defined as:

A sequence of nodes such that each pair of adjacent nodes must have an edge connecting them. A node can only be included in a path at most once. Moreover, including the root in the path is not compulsory.

The path sum can be calculated by adding up all nodes’ values in the path. To solve this problem, we will 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.