My first instinct was to BFS from each gate separately, which works but is way too slow and they pushed back on it pretty fast.
Use a multi-source BFS starting from all gates simultaneously, treating each gate as a source with distance 0. Propagate distances level by level to neighboring empty cells, updating their values until all reachable cells are filled. This ensures each cell gets the minimum distance to any gate in O(m*n) time.
Pro tip: Mention that BFS from gates is optimal because it explores cells in increasing order of distance, and discuss how to handle unreachable cells (remain INF) and walls (skipped). Also, note that you can modify the grid in-place to save space.
Clarify that gates are sources, walls are obstacles, and empty cells need the shortest distance to any gate. Confirm grid dimensions and that movement is 4-directional.
Explain why BFS is ideal: it finds shortest paths in unweighted graphs. Starting from all gates ensures we compute distances from the nearest gate efficiently.
Iterate through the grid, add all gate coordinates (value 0) to a queue. This sets up the BFS frontier.
While the queue is not empty, pop a cell, explore its 4 neighbors. If a neighbor is an empty cell (INF), update its distance to current distance + 1 and enqueue it.
State time complexity O(m*n) since each cell is processed once. Space O(m*n) for the queue. Discuss edge cases: no gates, all walls, unreachable cells remain INF.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Treat the grid as a graph and use DFS or BFS to explore each island, counting its area and tracking the maximum. Iterate through each cell; when you find a '1', traverse all connected '1's, mark them as visited, and update the max area.
Pro tip: Mention that you can mutate the grid in-place (e.g., change '1' to '0') to avoid extra space, but clarify if the input can be modified. Also, discuss handling large grids with iterative BFS to avoid recursion depth limits.
Confirm grid dimensions, connectivity (4-directional), and whether the grid can be modified. Ask about edge cases like empty grid or no islands.
Decide between DFS (recursive or iterative) and BFS. Consider trade-offs: DFS is simpler but may hit recursion limits; BFS uses a queue and is safer for large grids.
For each unvisited '1', start a traversal to count connected '1's. Mark cells as visited (e.g., set to '0' or use a visited set) to avoid revisiting.
After each traversal, compare the island's area with the current maximum and update if larger.
State time complexity O(m*n) and space complexity O(m*n) in worst case (e.g., all 1s). Discuss edge cases like single row/column, all 0s, all 1s.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.