The minimum workers part I got pretty quickly, standard interval scheduling with a min-heap on end times.
Parse each CSV line into start and end times (start + duration), then sort all events by time. Use a sweep-line algorithm with a min-heap to track active jobs and assign workers, ensuring no overlap. Finally, output the minimum number of workers and the assignment log.
Pro tip: Clarify edge cases upfront, such as jobs with zero duration or overlapping boundaries, and mention that the greedy assignment is optimal because it reuses workers as soon as they are free.
Read the stream line by line, split each line into start time and duration, and compute the end time. Convert times to a comparable format (e.g., minutes since midnight) for easy sorting.
Create a list of events (start and end) and sort them by time. For simultaneous events, process end events before start events to allow immediate worker reuse.
Iterate through sorted events, maintaining a min-heap of available workers (by their free time). For each start event, assign the earliest available worker or create a new one if none are free. For each end event, mark the worker as free.
Keep a log of assignments (worker ID, job details) and the maximum number of workers used. After processing, print the minimum worker count and the full assignment log.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where the problem diverges from the textbook version.
Start by clarifying the assignment policy: if the goal is to balance load, assign to the least-loaded worker; if to minimize wait, assign to the longest-idle worker. Then explain that a min-heap keyed by the chosen metric (e.g., current load or idle time) efficiently retrieves the best worker in O(log n) time, with updates when workers become free or busy.
Pro tip: Mention that in a real system like Lyft, you'd also consider factors like worker location, job priority, and fairness, and that the heap can be augmented with lazy deletion or indexed for efficient updates.
Ask whether the goal is load balancing, minimizing wait time, or another metric. This determines the key for the data structure.
Select a min-heap (priority queue) keyed by the chosen metric (e.g., current load, idle time) to efficiently find the best worker.
Describe how to extract the best worker in O(log n) and update the heap when a worker becomes free or busy, also O(log n).
Compare with other structures like balanced BSTs or sorted lists, and mention real-world considerations like concurrency and fairness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Said O(n log n) time and O(n) space, which they seemed fine with.
Walk through your solution step by step, identifying the dominant operations and how they scale with input size. State the time and space complexity clearly, then briefly justify each with reference to your code or algorithm. If applicable, mention trade-offs and optimizations you considered.
Pro tip: Always relate complexity to the actual constraints (e.g., input size limits) and discuss whether your solution meets them; this shows you think about practical performance, not just theoretical Big-O.
Define what n, m, etc. represent in your problem (e.g., array length, string length, number of nodes). This sets the context for complexity analysis.
Break down your algorithm into loops, recursion, or operations. Determine how many times each operation executes relative to input size, and sum them to get the overall time complexity.
Consider all extra space used: data structures, recursion stack, temporary variables. Express it in terms of input size, ignoring constant factors.
Explain why the complexity is what it is, and simplify to Big-O notation by dropping constants and lower-order terms.
Mention if you could trade time for space or vice versa, and whether your solution is optimal or if there's room for improvement.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.