The first three parts were manageable since there are existing writeups floating around.
Model the grid as a cellular automaton with per-cell state that includes infection status and timers for recovery or death. Use simultaneous updates each day, computing next states based on current neighbor counts and timers, and handle competing transitions by prioritizing death over recovery when thresholds are met.
Pro tip: Clearly separate the conditions for death and recovery, and ensure that once a cell enters a recovery countdown, it cannot be killed unless the infected neighbor count later meets or exceeds K. This avoids ambiguity in overlapping thresholds.
Each cell can be healthy, infected, recovering (with a countdown), or dead. Track days since infection for infected cells and days remaining in recovery for recovering cells.
For each cell, count the number of infected neighbors (including those in recovery countdown? Typically only actively infected). Use 8-directional or 4-directional adjacency as specified.
For each non-dead cell, if infected neighbors >= K, it dies immediately (or after D days? Clarify: 'dies after D days if it has at least K infected neighbors at any moment' suggests a delay). If T <= infected neighbors < K, it enters recovery countdown (if not already) and recovers after D days. If already in recovery, decrement timer; if timer reaches 0, it becomes healthy.
If a cell is in recovery countdown and later its infected neighbors reach K, it should switch to death (possibly resetting a death timer). Prioritize death over recovery when conditions overlap.
Use synchronous updates: compute all next states based on current states, then apply. Repeat for the desired number of days or until no changes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I went greedy first, picking whichever row or column had the most infected plants each day.
Model the problem as an optimization over a sequence of row/column burns, where each burn eliminates all remaining plants in that row/column. Recognize that the order of burns matters and that the optimal strategy often involves burning lines with the fewest remaining plants first, akin to a greedy heuristic for minimizing cumulative removals. Discuss potential dynamic programming or integer programming formulations for exact solutions, and analyze trade-offs between optimality and computational feasibility.
Pro tip: Connect the problem to real-world ML scenarios like feature selection or data pruning, where greedy heuristics often provide efficient approximations. Emphasize that while greedy may not always be optimal, it's often practical and can be complemented with bounds or local search.
Clarify that we have an m x n grid of plants, and each day we burn one full row or column, killing all remaining plants in that line. The goal is to minimize total dead plants over the simulation, which is equivalent to minimizing the sum of remaining plants at each burn.
Recognize that the total dead plants equals the sum over burns of the number of alive plants in the chosen line. This depends on the order of burns, as burning a row first may reduce the count in a column later.
Suggest burning the line (row or column) with the fewest remaining alive plants each day. Discuss that this greedy approach is intuitive but may not be globally optimal; provide a counterexample if possible.
Mention that the problem can be formulated as a dynamic program over subsets of rows and columns, or as an integer linear program. Note that the state space is exponential, so exact solutions are feasible only for small grids.
Compare greedy vs. exact methods in terms of time complexity and solution quality. Suggest that for large grids, heuristics like greedy or local search are preferable, while for small grids, exact methods can be used.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.