Classic BFS from multiple sources at once.
Model the grid as a graph and use multi-source BFS to simulate the simultaneous spread of infection level by level. Track the time as the number of BFS layers, and after the BFS, check if any uninfected plants remain to return the sentinel value if so.
Pro tip: Clarify the sentinel value and edge cases upfront (e.g., empty grid, no initially infected plants) to show attention to detail. Also, discuss how you would optimize for large grids, such as using a queue and in-place marking to save space.
Ask about the grid dimensions, sentinel value, and what constitutes a plant (e.g., 0 for healthy, 1 for infected). Confirm whether diagonal spread is allowed and if all plants must be infected.
Scan the grid to find all initially infected plants and add their coordinates to a queue. Count the total number of healthy plants to track progress.
Process the queue level by level, infecting adjacent healthy plants in each iteration. Increment the time after each level and update the count of healthy plants.
After BFS, if any healthy plants remain, return the sentinel value (e.g., -1). Otherwise, return the total time elapsed.
State the time complexity O(m*n) and space complexity O(m*n) in the worst case. Mention potential optimizations like using a 2D array for visited or modifying the grid in-place.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Basically the same BFS but now you're tracking per-cell distances instead of just the max.
Model the infection spread as a multi-source BFS where all initially infected cells are enqueued at time 0, and each step infects adjacent uninfected cells. Record the time when each cell is first infected, ensuring all cells are processed. If some cells remain uninfected, mark their time as -1 or infinity.
Pro tip: Clarify with the interviewer whether infection spreads to all 4 directions or 8, and whether the grid has obstacles. Also, mention that using a queue and a visited array ensures O(m*n) time complexity, which is optimal.
Confirm the grid dimensions, initial infected cells, movement directions (4 or 8), and whether there are any blocked cells. Also, agree on the output format for unreachable cells.
Create a 2D array to store infection times, initialized to -1 (or infinity). Use a queue for BFS and enqueue all initially infected cells with time 0.
While the queue is not empty, dequeue a cell, and for each valid neighbor that is not yet infected, set its infection time to current time + 1 and enqueue it.
After BFS, any cell still with -1 remains uninfected. Return the time grid, possibly converting -1 to a specific value like -1 or infinity as required.
State that time complexity is O(m*n) since each cell is visited once, and space complexity is O(m*n) for the queue and time grid.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where things got a bit messy for me.
Clarify the existing infection model and the desired output, then propose a multi-source extension using a priority queue (or BFS with multiple starting nodes) to process infection events in chronological order. Discuss trade-offs between time-stepped simulation and event-driven simulation, and how to handle simultaneous infections and source independence.
Pro tip: Demonstrate awareness of real-world constraints: ask whether sources can be added dynamically or if all are known upfront, and mention that the same framework can be adapted for incremental updates.
Ask about the graph representation, infection propagation rules (e.g., time to infect neighbors), and whether sources are independent or can interact. Confirm the expected output (e.g., infection time per node).
Propose using a priority queue to process infection events in order of time, initializing with all sources at their start times. Alternatively, use multi-source BFS if all edges have equal weight.
Explain how to track the earliest infection time for each node, updating only if a new source reaches it earlier. Address simultaneous infections and ensure sources don't interfere.
Compare time and space complexity with the single-source case. Discuss trade-offs between event-driven and time-stepped simulation, and scalability for large graphs.
Outline test cases: sources starting at different times, overlapping infections, disconnected components, and edge cases like a source starting after others have already infected nodes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly just a BFS modification, skip cells that are obstacles during neighbor expansion.
First, clarify the problem: obstacles are cells that cannot be infected, so the infection spreads only through non-obstacle cells. Then, adapt your algorithm by treating obstacles as blocked nodes in the grid, and update your BFS/DFS or simulation to skip them. Finally, discuss how this affects time/space complexity and edge cases like unreachable regions.
Pro tip: Mention that obstacles can be modeled as walls in a graph, and that you can preprocess the grid to mark obstacles, ensuring your traversal never visits them. This shows you think about efficiency and correctness.
Confirm that obstacles are impassable cells that block infection, and that infection spreads only through adjacent non-obstacle cells. Ask if diagonal spread is allowed or if it's 4-directional.
Represent the grid as a graph where each non-obstacle cell is a node, and edges connect adjacent non-obstacle cells. Obstacles are simply nodes that are removed from the graph.
Use BFS/DFS or simulation (e.g., multi-source BFS for infection spread) but skip obstacle cells when exploring neighbors. Ensure you only enqueue or visit cells that are not obstacles.
Time and space complexity remain O(N*M) for an N x M grid, but obstacles can reduce the effective search space. Consider edge cases: no path to some cells, all cells blocked, or obstacles creating isolated regions.
Mention potential optimizations like early termination if the target is reached, or using union-find for connectivity queries if multiple queries are needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the infection model (e.g., grid, spread rules) and constraints, then propose an efficient solution such as precomputing infection times via multi-source BFS and answering each query in O(1) by comparing the precomputed time to the query day. Discuss trade-offs between preprocessing time and query time, and handle edge cases like unreachable cells.
Pro tip: Demonstrate awareness of real-world scalability by discussing how the solution would change if the grid is huge or queries are streaming, and mention that precomputation is often key to achieving low query latency.
Ask questions to understand the infection model: Is it a grid? How does infection spread? What are the constraints on grid size, number of queries, and maximum day? Are there multiple sources?
Recognize that answering each query naively by simulating up to that day is inefficient. The goal is to precompute the earliest infection time for each cell so queries become constant-time lookups.
Use multi-source BFS to compute the minimum day each cell gets infected, starting from all initially infected cells. This works because infection spreads uniformly to neighbors each day.
Discuss time and space complexity: O(N*M) preprocessing and O(1) per query. Consider alternatives like binary search on time with BFS per query, and explain why precomputation is better for many queries.
Address cases like cells never infected (set time to infinity), queries before day 0, and multiple sources. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.