I started with a hash set of (x, y) coordinates for live cells, which felt right.
Use a hash set to store live cell coordinates, compute the next generation by tallying neighbor counts for each live cell and its neighbors, and only keep cells that survive or are born. For snapshotting, persist the set of live cells at each generation or use a persistent data structure. For efficiency over thousands of generations, optimize neighbor counting with bitwise operations or parallelize using a grid partitioning scheme.
Pro tip: Mention that the number of live cells can grow exponentially in some patterns, so the algorithm's time per generation is O(N) where N is the number of live cells, but N itself may grow; discuss trade-offs with memory and potential optimizations like using a quadtree or hashing with spatial locality.
Choose a hash set (e.g., Python set of tuples) to store live cells, ensuring O(1) membership checks and O(N) space proportional to live cells. Discuss alternatives like a hash map with neighbor counts or a quadtree for spatial partitioning.
For each live cell, increment neighbor counts for its 8 neighbors in a temporary hash map. Then, for each cell in the map, apply Game of Life rules: survive if count is 2 or 3, born if count is 3. Build the new set of live cells.
To support snapshots, store each generation's live cell set in a list or use a persistent data structure like a persistent hash set. For querying, check membership in the current set or retrieve a past snapshot by index.
Optimize by using bitwise operations for neighbor counting, parallelizing across partitions, or employing a quadtree to skip empty regions. Consider incremental updates and caching to avoid redundant computations.
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