Classic multi-source BFS and I knew it immediately.
Model the grid as a graph and perform a multi-source BFS starting from all initially infected cells simultaneously. Track the time each healthy cell becomes infected, and after BFS, check if any healthy cell remains uninfected; if so, return -1, otherwise return the maximum time.
Pro tip: Clarify the problem constraints and edge cases upfront (e.g., empty grid, no healthy cells, disconnected components) to demonstrate thoroughness. Mention that BFS is optimal because it explores level by level, ensuring the minimum time is found.
Restate the problem: we need the minimum minutes until all healthy cells are infected via 4-directional spread, or -1 if impossible. Discuss edge cases: no healthy cells (return 0), no infected cells (return -1 if healthy exist), empty grid.
Recognize this as a multi-source BFS problem on a grid. Explain why BFS is suitable: it simulates simultaneous spread and guarantees minimum time.
Initialize a queue with all infected cells and set their time to 0. While the queue is not empty, pop a cell, explore its 4 neighbors; if a neighbor is healthy, infect it, set its time to current time + 1, and enqueue it.
After BFS, scan the grid to see if any healthy cell remains. If yes, return -1; otherwise, return the maximum time recorded.
State time complexity O(m*n) and space O(m*n) for the queue. Mention that in-place modification of the grid can save space, but be mindful of side effects.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the grid as a graph where initially infected cells are sources, and infection spreads to adjacent healthy cells over time. Then, count healthy cells that are not reachable from any source via a path through healthy cells (i.e., in components without an infected cell).
Pro tip: Clarify whether infection spreads only to orthogonally adjacent cells or also diagonally, as this changes the connectivity and the count of unreachable cells. Also, consider if the grid is static or if cells can become immune, but typically it's a static spread.
Confirm the spread mechanism: 4-directional or 8-directional? Does infection spread to all adjacent healthy cells simultaneously each time step? Are there any barriers or immune cells?
Treat each healthy cell as a node, with edges to adjacent healthy cells. Infected cells are sources. The infection will eventually reach all healthy cells in the same connected component as any infected cell.
Find all connected components of healthy cells that do not contain any initially infected cell. These components are completely isolated from infection.
Sum the sizes of all such components to get the total number of healthy units that can never be infected, regardless of time.
Check edge cases: no infected cells (all healthy cells unreachable), all cells infected (0 unreachable), and components separated by infected cells or boundaries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the infection spread as a multi-source BFS where each infected cell has a timestamp, and track the earliest infection time for each cell. After x minutes, any cell not yet infected becomes permanently immune; then continue the simulation only through cells infected before x, and count the remaining healthy cells at steady state.
Pro tip: Clarify whether immunity is granted at exactly x minutes or after x minutes, and whether the initial infected cells count toward the time limit; these edge cases often determine correctness.
Ask about grid size, initial infected positions, definition of 'exactly x minutes', and whether immunity applies to cells that would be infected at time x. Confirm if steady state means no more infections can occur.
Use multi-source BFS from all initially infected cells, storing the infection time for each cell. This efficiently computes the earliest infection time for all cells in O(rows*cols) time.
After BFS, mark all cells with infection time > x (or uninfected) as immune. Then, re-run BFS only through cells with infection time <= x to propagate infection to cells that were not infected by time x but are adjacent to infected cells.
Continue BFS from the frontier of cells infected at time <= x, but do not infect immune cells. Stop when no new infections occur; the number of healthy cells is the count of cells never infected.
Count all cells that remain healthy (never infected) after the simulation. This includes cells that were immune from the start and those that became immune at time x.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.