I'd seen the length version before so I felt pretty good at first.
Use a depth-first search (DFS) that traverses the tree while maintaining the current increasing path. At each node, if the node's value is greater than the parent's, extend the current path; otherwise, start a new path with the current node. Track the longest path found and return its sequence of values.
Pro tip: Clarify whether the path must be strictly increasing and whether it can start at any node. Also, discuss how to handle large trees to avoid stack overflow, possibly using iterative DFS.
Confirm that the path is strictly increasing top-down, can start at any node, and that we need to return the actual sequence. Discuss edge cases like empty tree, single node, and negative values.
Decide between recursive DFS (simpler) or iterative DFS (avoids recursion limit). Explain the trade-offs and pick one based on constraints.
At each node, compare its value with the parent's. If greater, append to current path; else, start a new path with the current node. Update the longest path if the current path is longer.
Write clean code with helper functions. Test with various trees: increasing chain, decreasing chain, mixed, and single node.
Time complexity is O(n) since each node is visited once. Space complexity is O(h) for recursion stack, where h is tree height. Discuss potential optimizations if needed.
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