The base version is basically a diameter-of-tree problem restricted to leaves, which I'd seen before so I got through it okay.
Clarify the problem first: the maximum distance between two alive nodes is the diameter of the minimal subtree connecting all alive nodes. For the initial case where alive nodes are leaves, compute the tree's diameter using two BFS/DFS passes; for the follow-up, use a post-order traversal that tracks the deepest alive node in each subtree and combines depths at each node to find the maximum path.
Pro tip: Explicitly state that the problem reduces to finding the diameter of the minimal subtree spanning the alive nodes, and mention that the two-pass BFS approach works only for trees (not general graphs) and only when all alive nodes are leaves; for arbitrary subsets, a single post-order traversal is more efficient and handles all cases.
Ask whether the tree is binary, whether distances are measured in edges or nodes, and confirm that 'alive' nodes are initially leaves. For the follow-up, clarify that any subset of nodes can be alive.
Explain that the maximum distance between any two alive nodes is the diameter of the minimal subtree that connects all alive nodes. This subtree is formed by the union of paths between all pairs of alive nodes.
For a tree where all leaves are alive, the diameter of the whole tree equals the maximum distance between leaves. Use two BFS/DFS passes: first from any node to find the farthest leaf, then from that leaf to find the farthest other leaf; the distance between them is the answer.
Use a post-order traversal. For each node, compute the maximum depth to an alive node in its left and right subtrees. The longest path through the node is the sum of these depths (if both exist). Track the global maximum. Return the maximum depth to an alive node in the subtree (or -infinity if none).
Time complexity is O(n) for both approaches; space is O(h) for recursion or O(n) for iterative. Handle edge cases: fewer than two alive nodes (return 0 or -1), tree with only one node, and alive nodes that are not leaves.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying requirements: operations needed (create path, set/get value), path format, concurrency, and scale. Then propose a tree-based data structure where each node represents a path component and can store a value, and discuss how to handle edge cases like nested paths and overwrites.
Pro tip: Mention that this is essentially a trie with values at nodes, and that you can optimize for common operations like prefix queries or path compression. Also, proactively discuss trade-offs between in-memory and persistent storage, and how you'd handle concurrent access.
Ask about expected operations (create, read, update, delete), path syntax (e.g., '/a/b/c'), whether values are strings or arbitrary, and concurrency/scale needs.
Propose a tree where each node has a map of child nodes and an optional value. Explain how to traverse and create nodes for each path component.
Detail algorithms for createPath (split path, traverse/create nodes, set value) and get (traverse and return value). Discuss error handling for invalid paths.
Address overwriting existing values, deleting paths, and potential optimizations like path compression or caching frequently accessed paths.
Talk about how to scale (sharding, persistent storage) and handle concurrent access (locks, transactions) if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.