Model the grid as a graph and use multi-source BFS to compute the minimum time to infect all healthy cells, tracking the maximum distance reached. For part (b), either simulate step-by-step up to minute t or use the BFS distances to determine each cell's state at time t.
Pro tip: Clarify edge cases upfront: if there are no healthy cells, the answer is 0; if there are healthy cells but no infected cells, it's impossible (-1). Also, mention that obstacles block spread, and consider using a queue for BFS to achieve O(m*n) time.
Identify the four cell states (empty, healthy, infected, obstacle) and the spread rule: infected cells infect orthogonally adjacent healthy cells each minute. Clarify that empty and obstacle cells never become infected.
Initialize a queue with all initially infected cells and set their distance to 0. Perform BFS, and for each infected cell, attempt to infect its four neighbors if they are healthy, marking them infected and enqueueing with distance+1.
Track the maximum distance assigned during BFS. After BFS, if any healthy cell remains uninfected, return -1; otherwise, the maximum distance is the minimum minutes to infect the entire grid.
If t is less than the maximum distance, simulate the spread for t minutes (or use BFS distances to determine which cells are infected by time t). Return the grid with infected cells updated accordingly.
Discuss time and space complexity (O(m*n) for BFS). Handle edge cases: no healthy cells, no infected cells, obstacles blocking all paths, and t larger than the maximum distance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I said each test case is independent so just re-run BFS per case.
Start by restating the original problem and its current complexity, then outline how to generalize it to multiple test cases and larger grids. Discuss algorithmic optimizations (e.g., precomputation, caching, or more efficient data structures) and analyze the expected time and space complexity. Conclude by comparing trade-offs and mentioning potential bottlenecks.
Pro tip: Quantify the performance impact of your optimizations with Big-O notation and discuss how constant factors matter at scale. Also, mention any practical constraints like memory limits or I/O overhead that could affect real-world performance.
Restate the original problem and ask clarifying questions about the number of test cases, grid size limits, and time/memory constraints. This shows you understand the scope and can tailor your solution accordingly.
Analyze the time and space complexity of your initial solution. Determine which parts would scale poorly with more test cases or larger grids, such as repeated computations or inefficient data access.
Suggest techniques like precomputing results, memoization, or using batch processing to handle multiple test cases efficiently. For example, if the problem involves queries on a grid, consider preprocessing the grid to answer queries in O(1) or O(log n) time.
Discuss algorithmic improvements for larger grids, such as using more efficient data structures (e.g., sparse matrices, segment trees) or parallelization. Also consider memory optimization techniques like compression or streaming if the grid is too large to fit in memory.
Provide the new time and space complexity after optimizations, and compare with the original. Discuss trade-offs between time and space, and mention any assumptions or limitations of your approach.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.