LeetCode 124 Binary Tree Maximum Path Sum - Problem Statement

Find the maximum sum path in a binary tree. A path can start and end at any nodes, but must follow edges. observation: at each node, the path either passes through it (joining left and right subtrees) or is entirely in one subtree.

Return two values: $maxDown$ = max sum path starting at this node and going down, $maxPath$ = max path in subtree. At node $v$: $maxDown = \max(v.val, v.val + \max(left.maxDown, right.maxDown))$. $maxPath = \max(left.maxPath, right.maxPath, v.val + left.maxDown + right.maxDown)$.