Spent the first few minutes just re-reading the input format because it's given as parent-child pairs rather than a typical tree structure, so you have to build the tree yourself first.
Use a post-order DFS that returns the longest strictly increasing downward path starting at each node. At each node, combine the longest increasing paths from its children to compute the longest path passing through the node, and track the global maximum. Then reconstruct the path by storing parent pointers or by recording the start and end nodes.
Pro tip: Clarify whether the path must be strictly increasing (yes) and whether it can go through a node with two children (no, because it's a downward path). Also, discuss how to reconstruct the actual path, not just its length, as the output requires node values.
Confirm that the path must be strictly increasing, can start and end at any node, and is a downward path (parent to child). Ask if the tree can be empty or have duplicate values.
Design a DFS function that returns the length of the longest strictly increasing path starting at the current node and going downward. Also, track the global maximum length and the node where the longest path starts.
At each node, recursively process left and right children. If a child's value is greater than the current node's value, consider extending the path from that child. Update the global maximum if the path through the current node is longer.
After finding the start node and maximum length, traverse down the tree following the increasing condition to collect the node values. Alternatively, store parent pointers during DFS to reconstruct the path.
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.