This is a heap problem and I knew it pretty fast, but getting the edge cases right took longer than I'd like to admit.
Model the problem as a simulation using a min-heap to track available tasks by processing time, and sort tasks by enqueue time to efficiently add tasks as time progresses. Iterate through time, adding newly available tasks to the heap, then process the task with the smallest processing time (ties broken by index), updating the current time accordingly.
Pro tip: Clarify tie-breaking rules and edge cases (e.g., simultaneous enqueues, idle CPU) upfront, and discuss how the heap comparator should be defined to handle ties by index. Also, mention that the solution runs in O(n log n) time and O(n) space, which is optimal for this problem.
Restate the problem to ensure clarity: tasks have enqueue and processing times, CPU picks shortest processing time among available tasks, ties broken by index. Identify edge cases like no tasks available initially or multiple tasks with same enqueue time.
Use a min-heap (priority queue) to efficiently retrieve the available task with the shortest processing time, with a custom comparator that breaks ties by index. Sort the tasks by enqueue time to process them in order of availability.
Initialize current time to the earliest enqueue time. While there are tasks left, add all tasks with enqueue time <= current time to the heap. If heap is empty, jump current time to the next task's enqueue time. Otherwise, pop the task with smallest processing time, record its index, and increment current time by its processing time.
Ensure the heap comparator correctly orders by processing time and then by index. Handle the case where multiple tasks have the same enqueue time by adding them all before processing. Also, consider the scenario where the CPU is idle and must wait for the next task.
State that the time complexity is O(n log n) due to sorting and heap operations, and space complexity is O(n). Walk through a small example to verify correctness, and discuss potential optimizations or alternative approaches.
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