My first instinct was to treat it like the simpler version where the path only goes parent to child.
Use a post-order DFS that returns the longest consecutive path starting at the current node, considering both increasing and decreasing sequences. At each node, combine the best child paths that continue the sequence (value differs by 1) to update a global maximum, allowing the path to pass through the node.
Pro tip: Clarify that the path can go through a node in a child-parent-child direction, meaning you need to consider both children simultaneously to form a longer path. Also, mention that you can optimize space by using recursion and avoiding explicit memoization.
Confirm that the path can be increasing or decreasing, and that it can pass through a node connecting two children. Ensure you understand that the path length is measured in number of nodes (or edges, but typically nodes).
Design a DFS function that returns the longest consecutive path starting at the current node, considering both increasing and decreasing sequences. It should return two values: the longest increasing path and the longest decreasing path starting at this node.
For each child, recursively get its increasing and decreasing path lengths. If the child's value is current+1, it can extend the increasing path; if current-1, it can extend the decreasing path. Combine the best increasing and decreasing paths from different children to form a path through the current node, and update the global maximum.
For a null node, return (0,0). For a leaf, return (1,1). After processing children, return the longest increasing and decreasing paths starting at the current node (1 + max from children if applicable).
State that the time complexity is O(n) since each node is visited once, and space complexity is O(h) for recursion stack, where h is the tree height.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.