← Snowflake Interview Insights
I got the LCA idea pretty fast but fumbled on actually reconstructing the path.
Use a recursive DFS to find the lowest common ancestor (LCA) of u and v, while simultaneously checking for their existence. Then, collect the path from u to LCA and from LCA to v, and concatenate them appropriately.
Pro tip: Emphasize that the O(h) space comes from the recursion stack, and that the algorithm handles the case where one node is an ancestor of the other naturally by returning the path from the ancestor to the descendant.
Confirm that the tree is not a BST, so no ordering assumptions can be made. Plan to use a single DFS traversal to find LCA and check existence.
Implement a recursive function that returns the LCA if both nodes are found in the subtree, or one of the nodes if only one is found, or null if neither. Use a flag or return value to indicate missing nodes.
From the LCA, perform two separate DFS traversals to find the paths to u and v. Store the paths in lists, or use a single traversal that records the path from root to each node and then extract the segments.
Reverse the path from u to LCA (excluding LCA) and append the path from LCA to v (including LCA). This gives the shortest path from u to v.
If either u or v is missing, return an empty list. Also handle the case where u equals v, returning a list with that single value.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem (e.g., graph traversal, grid pathfinding) and choose a concrete algorithm like DFS for recursion and BFS/DFS with an explicit stack/queue for iteration. Implement both versions cleanly, then analyze time and space complexity for each, highlighting trade-offs such as recursion depth limits and iterative overhead.
Pro tip: Mention that recursion can cause stack overflow for deep graphs, so iterative solutions are often preferred in production systems; also note that BFS guarantees shortest path in unweighted graphs while DFS does not.
Ask if the graph is directed/undirected, weighted/unweighted, and whether we need any path or shortest path. Confirm the representation (adjacency list, matrix, grid).
For recursion, use DFS with backtracking; for iteration, use BFS with a queue or DFS with an explicit stack. Explain why you chose each.
Write clean recursive code, handling base cases (found target, visited, out of bounds) and marking visited nodes to avoid cycles.
Write iterative code using a stack (DFS) or queue (BFS), managing visited set and parent pointers if path reconstruction is needed.
For both, state O(V+E) time for graph traversal. Space: recursion uses O(V) call stack; iterative uses O(V) for visited and queue/stack. Discuss worst-case and average-case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the types of path queries (e.g., LCA, distance, k-th ancestor) and the expected query volume. Then present each preprocessing strategy (parent pointers, Euler tour + RMQ, binary lifting) with its preprocessing time, per-query time, and memory usage, and compare trade-offs. Finally, recommend a strategy based on the query mix and constraints.
Pro tip: Mention that binary lifting and Euler tour + RMQ can be combined: use binary lifting for k-th ancestor queries and Euler tour + RMQ for LCA, achieving O(1) LCA and O(log n) k-th ancestor with O(n log n) preprocessing. This shows you understand hybrid approaches.
Ask what kinds of path queries are needed (LCA, distance, k-th ancestor, path sum, etc.) and the expected number of queries and tree size. This determines which preprocessing is optimal.
Describe storing parent pointers for each node, enabling O(depth) traversal for LCA or ancestor queries. Preprocessing is O(n), but per-query can be O(n) in worst case (skewed tree).
Explain that an Euler tour of the tree (recording nodes on entry/exit) combined with a RMQ data structure (e.g., sparse table) allows O(1) LCA queries after O(n log n) preprocessing. Memory is O(n log n).
Describe precomputing up[k][v] = 2^k-th ancestor for each node, enabling O(log n) LCA and k-th ancestor queries. Preprocessing is O(n log n) time and memory.
Contrast preprocessing time/memory vs. query time: parent pointers (O(n) prep, O(n) query), Euler+RMQ (O(n log n) prep, O(1) query), binary lifting (O(n log n) prep, O(log n) query). Recommend based on query volume and type.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Duplicate values caught me off guard more than the others.
Systematically address each edge case by explaining how your solution detects and handles it, emphasizing correctness and robustness. Then discuss trade-offs, particularly for deep skewed trees, and propose iterative alternatives to recursion to avoid stack overflow. Conclude by highlighting testing strategies to ensure all edge cases are covered.
Pro tip: Mention that you would explicitly test these edge cases with unit tests and consider iterative solutions for production systems to avoid stack overflow, showing you think beyond just passing the interview.
Restate the problem and confirm assumptions about the tree structure (e.g., binary tree, BST) and the definition of 'solution' (e.g., finding LCA, path sum). This ensures you address the correct edge cases.
For each edge case (node not exist, u==v, ancestor relationship, duplicates, deep skewed trees), explain how your algorithm handles it, including any necessary checks or modifications.
For deep skewed trees, compare recursive vs iterative approaches, mentioning stack overflow risks and how to mitigate them (e.g., using explicit stack, Morris traversal).
Describe how you would test these edge cases, such as writing unit tests with specific inputs and using property-based testing for duplicates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.