Started with the 2D table approach which felt natural and got it working, but then they asked if I could do better on space.
Start by clearly defining the problem and deriving the 2D DP recurrence, then explain how to optimize space by observing that each state only depends on a limited set of previous states. Finally, implement the 1D DP solution, ensuring correctness and discussing trade-offs.
Pro tip: Always verify that the space optimization doesn't compromise the ability to reconstruct the solution if needed; sometimes you need to keep additional state or use a different approach. Also, mention that you'd test with edge cases like empty input or single row/column.
Clarify the problem statement, identify the input/output, and determine what the DP state represents. Discuss any constraints that might affect the approach.
Formulate the recurrence relation for the 2D DP table, explaining how each cell depends on previous cells. Analyze the time and space complexity of this naive approach.
Observe that each row (or column) only depends on the previous row (or column), so you can reduce the 2D table to a 1D array. Explain how to update the 1D array in-place to avoid overwriting needed values.
Write clean code for the optimized solution, handling initialization and iteration order carefully. Walk through a small example to demonstrate correctness.
State the new space complexity (e.g., O(n) instead of O(m*n)) and confirm time complexity remains the same. Discuss any limitations, such as inability to reconstruct the path without extra storage.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Went with BFS since it felt more intuitive to me in the moment.
Clarify the problem to determine if it's about connectivity, grouping, or cycle detection, then choose Union-Find for dynamic connectivity or BFS/DFS for static graph traversal. Explain the algorithm step-by-step, analyze time and space complexity, and discuss trade-offs between the two approaches.
Pro tip: Mention that Union-Find with path compression and union by rank achieves near O(1) amortized time per operation, making it ideal for incremental connectivity, while BFS/DFS is better for finding actual paths or when the graph is static.
Ask clarifying questions to determine if the graph is static or dynamic, if you need to find connected components, detect cycles, or check connectivity between specific nodes.
Decide between Union-Find and BFS/DFS based on problem requirements: Union-Find for dynamic connectivity and grouping, BFS/DFS for pathfinding or when the graph is represented explicitly.
Describe the steps of your chosen approach, including data structures (e.g., parent array for Union-Find, queue/stack for BFS/DFS) and how you'll handle edge cases.
State the time and space complexity, explaining how optimizations like path compression and union by rank affect performance.
Compare the chosen approach with the alternative, highlighting scenarios where one is preferable over the other, and mention any potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.