Treat the grid as a graph and use DFS or BFS to explore each island, summing cell values and tracking the maximum. Iterate through all cells, and when encountering unvisited land, traverse the entire island, mark cells as visited, and update the global maximum sum.
Pro tip: Clarify edge cases upfront (e.g., all water, negative values, large grid) and discuss trade-offs between DFS (recursive, risk of stack overflow) and BFS (iterative, uses queue). Mention that modifying the grid in-place to mark visited saves space but may not be allowed if input must be preserved.
Restate the problem: find max sum of connected land cells (4-directional). Ask about grid size, value ranges (negative?), and whether input can be modified.
Decide between DFS (recursive or iterative) and BFS. Consider recursion depth for large grids; iterative DFS or BFS avoids stack overflow.
Iterate through each cell. When a non-zero unvisited cell is found, traverse all connected land cells, summing values and marking visited (e.g., set to 0 or use a visited set).
After each island traversal, compare the island's sum with the current maximum and update if larger. Handle negative sums by initializing max to negative infinity or 0 if all sums are non-negative.
State time complexity O(m*n) and space complexity O(m*n) worst-case for recursion/queue. Walk through edge cases: empty grid, all water, single island, multiple islands, negative values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the definition of an island and the constraints (e.g., grid size, value range). Then, propose an algorithm that identifies islands while filtering out any containing negative cells, and computes the maximum sum among valid islands. Discuss trade-offs between different approaches (e.g., DFS vs. BFS, union-find) and analyze time/space complexity.
Pro tip: Mention edge cases like empty grid, all negative cells, or islands with zero sum, and how your solution handles them. Also, consider if the grid can be modified in-place to save space, but discuss the trade-off of mutating input.
Restate the problem to ensure understanding: an island is a group of connected cells (likely 4-directionally). Valid islands have all non-negative values; any island with a negative cell is ignored. We need the maximum sum of all valid islands.
Select a graph traversal method (DFS or BFS) to explore islands. For each unvisited cell, start a traversal, track if any negative cell is encountered, and accumulate the sum. If no negative cells, update the maximum sum.
Consider edge cases: empty grid, single cell, all cells negative, islands with zero sum. Discuss constraints like grid dimensions and value ranges to determine if integer overflow is a concern.
Analyze time complexity: O(R*C) since each cell is visited once. Space complexity: O(R*C) for visited set or recursion stack. Discuss trade-offs: DFS recursion depth vs. BFS queue memory, and whether to modify the grid in-place to save space.
Walk through a small example to verify the approach, including an island with a negative cell that should be ignored, and another valid island with maximum sum.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Easy extension once you're already tracking components.
Use a graph traversal algorithm like DFS or BFS to explore each island, computing its sum and tracking the maximum. When a new maximum is found, record any cell from that island as the representative index.
Pro tip: Clarify whether the grid contains negative values; if so, the maximum sum island might not be the largest, and you must consider all islands. Also, mention that you can return any cell, so you can simply store the first cell encountered during traversal.
Confirm that an island is a connected component of 1s (or positive values) and that you need to return the maximum sum and a cell index. Ask about grid size, value range, and connectivity (4-directional vs 8-directional).
Select DFS (recursive or iterative) or BFS to explore each island. DFS is often simpler for grid traversal, but BFS avoids recursion depth issues.
Iterate through each cell; when an unvisited land cell is found, traverse the entire island, summing values and marking visited. Track the maximum sum and a representative cell (e.g., the starting cell).
After computing an island's sum, compare with the current maximum. If greater, update the maximum and store the representative cell's coordinates.
After processing all cells, return the maximum sum and the stored cell index. If no island exists, handle appropriately (e.g., return null or -1).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where things got genuinely annoying.
Clarify the problem: identify all islands (connected components of 1s), compute each island's sum, and track the island with the maximum sum. For ties, compare the last cell in row-major order (largest row, then largest column) and select the island with the lexicographically largest last cell. Return that cell's coordinates.
Pro tip: During traversal, maintain the last cell of each island by updating it whenever you visit a cell with a larger row-major index. This avoids a second pass and ensures you have the correct last cell for tie-breaking.
Confirm that islands are 4-directionally connected, sums are of cell values (likely 1s), and tie-breaking uses the last cell in row-major order. Ask about grid size and value ranges to choose appropriate algorithms.
Use BFS or DFS to explore each island. Iterate through the grid in row-major order to ensure that the last cell visited for an island is indeed its last cell in row-major order.
During traversal, accumulate the sum of cell values and keep track of the cell with the largest row-major index (i.e., update whenever current cell's row or column is greater).
Maintain the best island's sum and last cell. When a new island has a higher sum, update. If sums are equal, compare last cells: choose the one with larger row, or if rows equal, larger column.
After processing all islands, return the last cell (row, column) of the winning island. If no islands exist, return an appropriate default (e.g., (-1, -1) or as specified).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said O(m*n) time and O(m*n) space for the visited array and call stack, which is correct.
Start by clarifying the problem variants and constraints, then for each variant, describe the algorithm, justify design choices, and analyze time/space complexity. Compare trade-offs and mention potential optimizations.
Pro tip: Always state assumptions and edge cases before diving into algorithms; this shows thoroughness and prevents misalignment with the interviewer.
Ask questions to understand each variant's specific requirements, input sizes, and expected outputs. Confirm any assumptions about data characteristics.
For each variant, briefly describe the chosen algorithm (e.g., brute force, dynamic programming, greedy) and why it's suitable. Mention key data structures used.
Derive Big-O for time and space for each variant, explaining the dominant operations. Consider best, average, and worst cases.
Discuss trade-offs between variants and potential optimizations (e.g., caching, early termination). Relate to real-world constraints like memory or latency.
Recap the approaches and complexities, and invite feedback or further questions to ensure alignment.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.