Longest Consecutive Path in a Binary Tree

You are given the root of a binary tree, root. Return the length of the longest path whose values are consecutive integers.

A path is a sequence of distinct nodes where each consecutive pair is directly connected as parent and child. A path can go up through a node and back down through one of its children, turning at most once, at its highest node.

Reading a path's values from one end to the other, they must increase by exactly 1 at every step. Reading the same path from the other end, they decrease by 1 at every step, so the same path can be described as either increasing or decreasing, depending on which end you start from.

The length of a path is its number of nodes. A single node is a path of length 1, so the answer is always at least 1.

Tree Encoding

Your function receives root as a TreeNode. The node type is provided for you, with val, left, and right fields.

The examples below write the tree as its level-order traversal, where null marks a missing child of a listed node and trailing nulls are omitted. That is only how the input is displayed; the decoding is done for you.