Clarify the problem constraints (grid size, memory limits) and edge cases (start or end blocked). Then propose a graph traversal (BFS or DFS) treating each passable cell as a node, and discuss trade-offs between BFS (shortest path) and DFS (simpler, but may hit recursion limits). Finally, analyze time and space complexity and consider optimizations like in-place marking or bidirectional search.
Pro tip: Mention that you can avoid extra space by marking visited cells in-place (e.g., set to 1), but note that this mutates the input; if mutation is not allowed, use a separate visited set. Also, for very large grids, consider iterative DFS to avoid stack overflow.
Ask about grid dimensions, whether the start or end can be blocked, and if modifying the grid is allowed. Confirm movement is only up/down/left/right.
Select BFS for shortest path or DFS for simplicity. Explain that both work for reachability, but BFS is often preferred for pathfinding.
Use a queue (BFS) or stack (DFS) to explore neighbors, marking cells as visited to avoid cycles. Check boundaries and passability (0).
State O(m*n) time and space. Discuss in-place marking, bidirectional BFS, or early termination when target is reached.
Walk through examples: empty grid, start blocked, end blocked, single row/column, and a grid with no path.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I jumped to a full sort by frequency which works but is O(n log n).
Start by clarifying the problem constraints (e.g., input size, value range, expected time/space complexity) and then propose a solution using a hash map to count frequencies followed by a heap or bucket sort to extract the top k. Discuss trade-offs between different approaches and analyze time/space complexity.
Pro tip: Mention that if the input is very large and k is small, a min-heap of size k is more space-efficient than sorting all unique elements. Also, if the value range is known and small, bucket sort can achieve O(n) time.
Ask about input size, value range, whether k is always valid, and if the output order matters. This shows attention to detail and helps choose the optimal approach.
Use a hash map to count the occurrence of each number. This takes O(n) time and O(n) space.
Use a min-heap of size k to keep the k most frequent elements, or use bucket sort if the frequency range is bounded. Discuss trade-offs.
State the time and space complexity of your approach. Consider edge cases like k=0, k larger than unique elements, or empty input.
Walk through a small example to verify correctness and explain how ties are handled arbitrarily.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.