Scheduling tasks under cooling constraints is a common challenge in operating systems, rate-limited APIs, and real-time pipelines. The “Task Scheduler with Cooling Interval” problem exercises frequency counting, greedy scheduling, and heap-based prioritization to minimize idle time.

Finding the nearest neighbors to a reference point is fundamental in recommendation engines, spatial queries, and clustering. The “K Closest Points to Origin” problem is a classic warm-up for Top-K selection using heaps or sorting optimizations.

Computing running medians on a stream of numbers pops up in real-time analytics, financial tickers, and sensor dashboards. You need to support two operations—adding a number and retrieving the current median—both in sublinear time.

Combining multiple sorted streams into one sorted output is a classic challenge faced in database merge operations, log file aggregation, and external sorting. The “merge K sorted lists” problem tests your ability to coordinate multiple pointers, leverage priority data structures, and keep everything running in optimal time.