Start by clarifying the problem and edge cases, then propose an O(n) single-pass solution that tracks the minimum departure cost seen so far and computes the best total for each possible return day. After deriving the algorithm, analyze its time and space complexity, prove correctness, and discuss handling of ties and small n.
Pro tip: Explicitly mention that the problem can be solved in one pass by maintaining the minimum D[i] for i < j, which is a common pattern in optimization problems. Also, proactively discuss how to handle ties (e.g., return the earliest pair) and edge cases like n < 2, showing thoroughness.
Ask about input constraints, expected output format (e.g., return indices or just cost), and how to handle ties or n < 2. Confirm that i and j are 0-indexed or 1-indexed.
Propose a single-pass O(n) solution: iterate j from 1 to n-1, keep track of the minimum D[i] for i < j, and compute D[i] + R[j] to update the minimum total and best pair.
State that time complexity is O(n) and space is O(1). Prove correctness by induction: after processing j, the stored minimum D is correct for all i < j, and the best total is updated correctly.
If n < 2, return an error or indicate no valid pair. For ties, decide on a rule (e.g., smallest i, then smallest j) and implement accordingly.
Walk through a small example (e.g., D=[3,1,4], R=[2,5,1]) to verify the algorithm and edge cases. Mention potential pitfalls like integer overflow if costs are large.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
BFS was the obvious move and I called it immediately.
Start by clarifying the problem and edge cases, then explain a BFS approach since it finds the shortest path in an unweighted grid. Detail how to reconstruct the path using a parent map or by storing paths in the queue, and analyze time and space complexity.
Pro tip: Mention that BFS is preferred over DFS because it guarantees the shortest path and avoids deep recursion, but note that DFS uses less memory in some cases. Also, discuss how to handle large grids by using a visited set or modifying the grid in-place.
Confirm movement directions, start/end cells, and what to return if no path exists. Check if start or end is blocked, or if grid is empty.
Select BFS for shortest path in unweighted grid. Explain why BFS is suitable and mention DFS as an alternative with trade-offs.
Describe how to track the path: either store the path in the queue or maintain a parent map/dictionary to backtrack from the end cell.
State time complexity O(m*n) since each cell is visited at most once, and space complexity O(m*n) for the queue and visited set/parent map.
Walk through a small example, consider optimizations like early exit when reaching the end, and discuss memory improvements (e.g., in-place marking).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.