Multi-source BFS, start by seeding all the infected cells into the queue at once.
Model the spread as a multi-source BFS starting from all initially infected cells simultaneously. Process the grid level by level, incrementing the minute count each level, and after BFS check if any healthy cells remain uninfected. If so, return -1; otherwise return the total minutes elapsed.
Pro tip: Explicitly discuss edge cases like an empty grid, no healthy cells, or no infected cells, and mention that you can optimize space by modifying the grid in-place or using a queue of coordinates.
Clarify that infection spreads in 4 directions each minute, and we need the minimum time until all healthy cells are infected or determine impossibility. Confirm grid dimensions and cell values.
Scan the grid to enqueue all initially infected cells (value 2) and count the number of healthy cells (value 1). If there are no healthy cells, return 0 immediately.
While the queue is not empty, process all nodes at the current level (representing one minute), infecting adjacent healthy cells, marking them as infected, decrementing the healthy count, and enqueueing them for the next level. Increment the minute counter after each level.
After BFS completes, if the healthy count is greater than 0, return -1 because some cells are unreachable. Otherwise, return the total minutes elapsed (which is the number of levels processed minus one, or the minute counter after the last infection).
State that time complexity is O(m*n) since each cell is processed at most once, and space complexity is O(m*n) for the queue in the worst case. Mention edge cases like all cells infected initially, no infected cells, or disconnected components.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They asked this verbally while I was still cleaning up the 4-directional code.
First, clarify that the only change is expanding the neighbor offsets from 4 to 8 directions, which affects the BFS/DFS traversal. Then, re-run the algorithm on the same example input, showing the step-by-step spread and the final infected grid or time.
Pro tip: Mention that while the code change is trivial, the time complexity remains O(m*n) but the constant factor increases; also note that diagonal spread can cause faster infection, so the answer may differ significantly.
State that the infection now spreads to all 8 neighboring cells (horizontal, vertical, and diagonal) instead of 4.
Modify the direction arrays to include the four diagonal offsets: (-1,-1), (-1,1), (1,-1), (1,1).
Apply the updated BFS/DFS to the same example input, tracking the infection spread step by step.
Determine the new final state or time to full infection, and compare with the original 4-direction result.
Explain any changes in complexity, edge cases (e.g., diagonal blocking), and potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.