Pretty clean setup, just scan every cell and check neighbors.
Clarify the problem constraints and edge cases, then propose a solution that reads the original grid and writes to a new grid to ensure simultaneous updates. Discuss time and space complexity, and consider optimizations like in-place marking if allowed.
Pro tip: Mention that you would use a separate grid or encode state changes to avoid overwriting cells before their neighbors are processed, demonstrating awareness of the simultaneity requirement.
Ask about grid dimensions, cell types, and whether in-place modification is allowed. Confirm that updates are simultaneous and that walls block infection.
Decide between using a new grid or in-place marking. For simplicity and correctness, a new grid is often preferred, but in-place can save space if carefully implemented.
Iterate through each cell, check its orthogonal neighbors for infection, and update the new grid accordingly. Ensure walls and recovered cells remain unchanged.
State that time complexity is O(rows * cols) and space complexity is O(rows * cols) for the new grid, or O(1) extra space if using in-place marking.
Walk through a small example, including edge cases like no infected cells, all walls, or infection at borders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Straightforward extension but the wall behavior is worth thinking through carefully.
Model the grid as a 2D array and simulate each step by computing the next state based on the current state, ensuring walls block spread and recovered cells are immune. Use a queue or multi-source BFS to efficiently propagate infection from all infected cells simultaneously, updating states step by step until k steps are completed.
Pro tip: Clarify the state transitions and edge cases upfront (e.g., walls, immunity, simultaneous updates) to avoid bugs, and discuss time/space complexity trade-offs between naive simulation and BFS.
Define cell states (e.g., empty, wall, infected, recovered) and confirm that infection spreads to orthogonal neighbors, walls block permanently, and recovered cells are immune. Decide on data structures to represent the grid and track changes.
For each step, compute the next state by checking each infected cell's neighbors. Ensure updates are simultaneous (use a copy or two-phase update) to avoid cascading within the same step.
Instead of scanning the entire grid each step, use a queue of infected cells to process only active frontiers. This reduces time complexity, especially for sparse infections.
Loop k times or until no new infections occur. After k steps, return the grid. Consider early termination if the infection cannot spread further.
Discuss time and space complexity (e.g., O(k * N*M) for naive, O(N*M) for BFS). Mention edge cases like k=0, no infected cells, all walls, or grid boundaries.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the rules for infection spread and recovery, then design a simulation that tracks both the infection state and the number of steps each cell has been infected. Use a separate grid or data structure to store infection timers, and update the grid in discrete steps for k iterations, ensuring recovered cells become permanently immune.
Pro tip: Discuss the trade-offs between using a single grid with encoded states versus separate grids for infection status and timers, and highlight how your choice affects time and space complexity. Also, mention edge cases like d=0 or k=0 to show thoroughness.
Ask questions to confirm the rules: how infection spreads (e.g., to orthogonal neighbors), what happens when a cell recovers (does it become susceptible again?), and the initial state of the grid. Also confirm the range of d and k.
Decide whether to use a single grid with integer values representing states (e.g., -1 for healthy, 0..d for infected steps, d+1 for recovered) or separate grids for infection status and timers. Consider memory and ease of update.
For each of the k steps, iterate through the grid to identify newly infected cells based on the previous state, update infection timers, and handle recoveries. Use a copy or buffer to avoid overwriting states mid-step.
Increment the infection timer for each infected cell each step. When a cell's timer reaches d, mark it as recovered permanently, ensuring it no longer spreads infection or becomes reinfected.
State the time complexity O(k * N * M) and space complexity O(N * M). Discuss edge cases such as d=0 (immediate recovery), k=0 (no steps), and grids with no initial infection.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The stopping condition tripped me up more than I expected.
Model the simulation as a state transition where each step simultaneously updates all cells based on the previous state. After each step, check if the grid has reached a fixed point: no infected cells and no healthy cell adjacent to an infected cell. If so, stop and return the grid and the number of steps taken; otherwise, continue until the fixed point is reached.
Pro tip: Emphasize the importance of simultaneous updates to avoid order-dependent artifacts, and discuss how early stopping can be implemented efficiently by tracking the number of infected cells and the set of healthy cells adjacent to infected ones.
Clarify that a fixed point occurs when there are no infected cells and no healthy cell is adjacent to an infected cell. This means the infection has either died out or all reachable healthy cells have been infected.
Plan a loop that continues until the fixed point is reached. In each iteration, compute the next state of the grid based on the current state, ensuring all updates are simultaneous.
For each cell, determine its next state: infected cells become healthy (or remain infected if the rule is different? Actually, based on the problem, infected cells likely become healthy after one step? But the problem says 'no infected cells remain' for fixed point, so infected cells must eventually disappear. Typically, in such simulations, infected cells become healthy after one step. So we need to clarify the rules. However, the problem statement says 'combine all previous rules', so we assume the rules are: each step, any healthy cell adjacent to an infected cell becomes infected, and infected cells become healthy? Or infected cells remain infected? The fixed point requires no infected cells, so infected cells must be removed at some point. Probably the rule is: infected cells become healthy after one step, and healthy cells adjacent to infected become infected. So we need to apply both simultaneously.)
After updating the grid, check if there are any infected cells. If none, also check if any healthy cell is adjacent to an infected cell (but since no infected cells, this is automatically false). So the condition simplifies to: no infected cells. However, the problem explicitly states both conditions, so we should check both to be safe.
Once the fixed point is reached, return the final grid and the number of steps taken (the number of iterations performed before reaching the fixed point).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.