Classic multi-source BFS, I knew it immediately.
Model the grid as a graph and use multi-source BFS starting from all initially infected cells simultaneously. Track the time each healthy cell gets infected, and after BFS, check if any healthy cell remains uninfected; if so, return -1, otherwise return the maximum infection time.
Pro tip: Clarify that the problem is equivalent to finding the shortest path from any infected cell to each healthy cell, and mention that BFS is optimal because each minute corresponds to one layer of expansion. Also, handle edge cases like no healthy people (return 0) and no infected people (return -1 if healthy exist).
Restate the problem: each minute, infected cells spread to adjacent healthy cells in 4 directions. Determine edge cases: no healthy cells (return 0), no infected cells but healthy exist (return -1), and grid boundaries.
Scan the grid to enqueue all initially infected cells with time 0, and count the number of healthy cells. Use a queue for BFS and a variable to track the maximum time.
While the queue is not empty, pop a cell and its time, explore its 4 neighbors. If a neighbor is healthy, infect it (mark as infected), decrement the healthy count, enqueue it with time+1, and update the maximum time.
After BFS, if the healthy count is greater than 0, return -1 (impossible to infect all). Otherwise, return the maximum time recorded.
State time complexity O(m*n) since each cell is processed once, and space complexity O(m*n) for the queue. Mention that in-place modification of the grid can save space if allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Mostly the same BFS, just treat immune cells like walls.
First, clarify the original problem and the meaning of 'immune' cells. Then, adapt your algorithm to treat immune cells as blocked nodes, and determine the conditions under which the target becomes unreachable, returning -1.
Pro tip: Explicitly state that immune cells are like obstacles, and discuss how this affects the algorithm's complexity and edge cases, such as when the start or target is immune.
Restate the original problem and confirm what 'immune' means (e.g., cannot be infected, cannot be traversed). Ask if immune cells are given as input or must be inferred.
Treat immune cells as blocked nodes in the grid/graph. Update the algorithm to skip these cells during traversal or infection spread.
Modify BFS/DFS or simulation to ignore immune cells. If using a queue, do not enqueue immune cells. If using dynamic programming, set their values to unreachable.
Return -1 if the target cannot be reached due to immune cells blocking all paths, or if the start or target itself is immune (if that's disallowed).
Discuss how immune cells affect time/space complexity (usually unchanged) and mention edge cases like no immune cells, all cells immune, or disconnected components.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the model by defining each source's infection rate and probability, then choose a mathematical representation such as a multi-type branching process or a system of differential equations. Discuss solution methods like numerical simulation or matrix exponentiation, and analyze the impact of different parameters on the overall spread.
Pro tip: Emphasize the importance of validating the model with edge cases (e.g., one source with zero rate) and discussing computational trade-offs between simulation and analytical solutions. Show awareness that in practice, parameters are often estimated from data, so sensitivity analysis is crucial.
Ask clarifying questions to understand the number of sources, whether they interact, and what 'spread' means (e.g., number of infected individuals over time). State any simplifying assumptions.
Select a model that captures multiple sources with different rates/probabilities, such as a multi-type branching process, a compartmental model with multiple infectious classes, or a network diffusion model.
Write down the governing equations (e.g., ODEs for expected values) or define the stochastic simulation steps. Include parameters for each source's rate and probability.
Decide between analytical (e.g., solving ODEs, matrix exponentiation) and numerical (e.g., Monte Carlo simulation) approaches based on scale and required precision. Analyze how different parameters affect the outcome.
Compare computational complexity, accuracy, and scalability of chosen methods. Mention potential extensions like time-varying rates or source interactions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by restating the problem and clarifying the update model: are new infected cells added one at a time or in batches, and what queries need to be answered incrementally? Then propose a data structure that maintains the current answer (e.g., count of connected components or affected regions) and updates it in O(1) or O(log n) per new infection by only examining the new cell's neighbors and merging components as needed.
Pro tip: Mention that you would handle deletions or re-infections by using a union-find with rollback or a dynamic connectivity structure, but only if the interviewer asks—showing you know the limits of your approach without overcomplicating the initial solution.
Ask whether updates are single-cell insertions or batches, whether cells can be cured (deletions), and what exactly needs to be maintained (e.g., number of infected clusters, total infected area, or shortest path to a target).
Select a structure like union-find (disjoint set) for connectivity, or a grid with per-cell state and neighbor checks. Explain how it supports efficient updates and queries.
For each new infected cell, check its four neighbors. If a neighbor is infected, union their components. Update any global counters (e.g., number of components) based on the merges.
State the time per update (near O(1) amortized with union-find) and space (O(n) for the grid and parent array). Discuss trade-offs versus recomputing from scratch (O(n) per update).
Mention handling of deletions (e.g., using dynamic connectivity or rebuilding periodically), concurrency if updates are parallel, and how to answer queries like 'is cell A connected to B?' efficiently.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.