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This part felt more open-ended than I expected.
Start by clarifying the input format and constraints, then outline the tree construction algorithm using a hash map for O(n) time. Define clear APIs for building the tree and validating input, and explain how to detect cycles and disconnected components using traversal techniques like DFS with visited states.
Pro tip: Mention that you would validate the input before construction to fail fast, and discuss how to handle edge cases like multiple roots or self-loops. Showing awareness of real-world data issues (e.g., duplicate pairs, missing managers) demonstrates maturity.
Ask about input size, whether each employee has at most one manager, and if the tree is guaranteed to be connected. Confirm the expected output (e.g., root node, adjacency list).
Define a function like buildTree(pairs) that returns the root node. Use a hash map to map each employee to their node, and another to track managers. Iterate through pairs to create nodes and link them.
Define validateInput(pairs) to check for malformed data, such as null values, duplicate employee-manager pairs, or employees with multiple managers. Return a boolean or throw an exception with details.
After building the tree, perform a DFS from the root to detect cycles (using a visited set and recursion stack) and to count visited nodes. If visited count != total nodes, there are disconnected components.
Compare iterative vs recursive DFS for cycle detection, and mention union-find as an alternative for cycle detection. Discuss time/space complexity (O(n) time, O(n) space).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Talked through parent pointers with depth tracking first since it's the most intuitive, then got into binary lifting.
Clarify the problem constraints (tree size, query frequency, k range) and then present two preprocessing strategies: binary lifting for O(log n) per query with O(n log n) preprocessing, and Euler tour + RMQ for O(1) query with O(n log n) preprocessing. Compare their trade-offs and implement one, ensuring the solution handles k >= 2 by iteratively finding the LCA of the first two nodes and then with each subsequent node.
Pro tip: Atlassian values practical trade-offs; mention that if queries are frequent, the O(1) RMQ approach is worth the extra preprocessing, but if memory is constrained, binary lifting is more space-efficient. Also, note that the iterative LCA of k nodes works because LCA is associative.
Ask about tree size, number of queries, memory limits, and whether the tree is static. This determines which preprocessing strategy is optimal.
Describe binary lifting (O(n log n) preprocessing, O(log n) per LCA) and Euler tour + RMQ (O(n log n) preprocessing, O(1) per LCA). Explain how each works and their trade-offs.
Explain that the LCA of k nodes can be found by iteratively computing LCA of the current result with the next node, leveraging associativity. Complexity becomes O(k * query_time).
For each strategy, provide overall time (preprocessing + k queries) and space. Compare and justify which is better for given constraints.
Write clean code for one approach, e.g., binary lifting, including preprocessing (DFS to compute depth and up table) and LCA function. Test with k=2 and k>2.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the part I was least prepared to articulate out loud.
Start by clarifying the LCA problem definition and assumptions (e.g., tree structure, employee IDs, whether both employees exist). Then outline a test plan covering typical cases (different subtrees, one ancestor of the other), edge cases (root as LCA, missing employee, empty tree), and verify with a mix of unit tests using a mock tree. Finally, discuss how you'd structure tests for maintainability and readability.
Pro tip: Mention that you'd write tests for both recursive and iterative implementations if applicable, and use parameterized tests to cover multiple scenarios efficiently. Also, emphasize the importance of testing with a realistic org chart to catch integration issues.
Confirm the LCA definition, input format (e.g., employee IDs, tree nodes), and assumptions like unique IDs and tree connectivity. Ask if the tree is binary or n-ary, and whether employees are guaranteed to exist.
List typical cases: employees in different subtrees, one employee is ancestor of the other, root as LCA. Edge cases: missing employee, empty tree, single node, same employee for both inputs.
Create a sample org chart (tree) with known structure, using a simple node class or mock. Ensure the tree is easy to reason about and covers all branches.
Implement unit tests using a framework like JUnit (Java) or pytest (Python). Use descriptive names, group related tests, and consider parameterized tests for multiple scenarios.
Explain how you ensure coverage of all specified cases, including negative tests. Mention any additional edge cases like null inputs or cyclic references (if applicable).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.