Went with DFS immediately, which was fine, but they pushed back and asked if I could do it with union-find instead.
Clarify the problem constraints (grid size, connectivity definition) and discuss trade-offs between BFS, DFS, and Union-Find. Then implement a solution that traverses the grid, marking visited land cells and incrementing the island count for each unvisited land cell encountered.
Pro tip: Mention that you can optimize space by mutating the input grid (e.g., changing '1' to '0') if allowed, but always ask the interviewer first. Also, be prepared to discuss how to handle very large grids that don't fit in memory, showing awareness of scalability.
Ask about grid dimensions, whether the grid can be modified, and if diagonal connections count. Confirm the definition of an island and expected output.
Decide between BFS, DFS, or Union-Find based on constraints. Discuss time and space complexity trade-offs for each.
Explain how you will iterate through the grid, and for each unvisited land cell, perform a traversal to mark all connected land cells as visited, incrementing the island count.
Write clean code for the chosen algorithm, handling edge cases like empty grid or all water. Use a visited set or modify the grid in-place.
Walk through a small example, test edge cases, and state the time and space complexity (e.g., O(m*n) time, O(m*n) space for visited set or O(1) if modifying grid).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Acknowledge the memory constraint and pivot to external memory algorithms or streaming approaches. Discuss trade-offs between time, space, and complexity, and propose a concrete solution like chunked processing or distributed computing.
Pro tip: Mention that you would first clarify the exact constraints (e.g., grid size, available memory, time limits) before committing to a solution—this shows you think before coding.
Ask about the grid dimensions, available memory, time limits, and whether the grid is static or dynamic. This ensures you tailor the solution to the specific scenario.
Decide between processing the grid in chunks (e.g., row-by-row or block-by-block) or using streaming algorithms if only a single pass is needed. Consider disk-based storage or memory-mapped files.
Outline how to process each chunk, maintain state (e.g., using a sliding window or boundary conditions), and combine results. For graph problems, consider partitioning the grid and handling cross-partition edges.
Discuss I/O overhead, potential for parallelization, and whether a distributed approach (e.g., MapReduce, Spark) is warranted. Compare time and space complexity with the in-memory version.
Propose testing with smaller datasets and scaling up, and mention monitoring memory usage. Be open to refining the approach based on feedback.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is LC 305 territory and I knew it existed but hadn't drilled it.
Model the grid as a dynamic set of land cells and use Union-Find (Disjoint Set Union) to track connected components. For each addLand, increment the island count, then union the new cell with any adjacent land cells, decrementing the count for each successful union. This yields O(1) amortized time per operation with path compression and union by rank.
Pro tip: Discuss how to handle duplicate addLand calls (idempotency) and the trade-off between using a hash set versus a 2D array for sparse grids, showing awareness of memory constraints in a streaming context.
Ask about grid size, number of operations, whether duplicate adds are possible, and if the grid is sparse. This determines the data structures and optimizations.
Use a hash map to map each land cell (row, col) to a unique parent index, and maintain a separate parent array for Union-Find. This handles sparse grids efficiently.
If the cell is already land, return the current count. Otherwise, mark it as land, increment the island count, and for each of the four neighbors that are land, attempt to union; if union succeeds, decrement the count.
Use path compression in find and union by rank/size to achieve near-constant time per operation. Ensure the parent array is dynamically extended as new cells are added.
State that each operation is O(α(N)) amortized, where α is the inverse Ackermann function. Discuss edge cases like duplicate adds, out-of-bounds coordinates, and large sparse grids.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the problem as a dynamic connectivity problem where each addLand operation can merge up to four neighboring islands. Use Union-Find (Disjoint Set Union) with union by rank and path compression to efficiently merge components, and maintain a running maximum island size by updating it after each union. For each addLand, check the four adjacent cells, union with existing land, and return the current max size.
Pro tip: Emphasize that the max size only increases or stays the same after each addLand, so you can update it incrementally rather than recomputing from scratch. Also, mention that using a 2D grid to track land is essential for O(1) neighbor checks.
Confirm that addLand operations are given as a stream and that after each operation we must return the size of the largest island. Discuss edge cases like duplicate land additions, out-of-bounds coordinates, and grid size limits.
Use a 2D boolean grid to track land cells and a Union-Find structure to manage connected components. Each land cell maps to a unique parent index, and we maintain a size array for each root.
For each addLand, if the cell is already land, return the current max size. Otherwise, mark it as land, initialize its Union-Find entry with size 1, and check its four neighbors. For each neighbor that is land, union the current cell with that neighbor, updating the size of the new root.
Keep a variable maxSize that is updated after each union to be the maximum of its current value and the new component size. After processing all neighbors, return maxSize.
Explain that with path compression and union by rank, each operation is nearly O(1) amortized, leading to O(k α(n)) total time for k operations. Space is O(m*n) for the grid and Union-Find arrays. Discuss alternatives like DFS/BFS per operation, which would be less efficient.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.