I went straight to greedy nearest-neighbor and the interviewer let me run with it for a while before nudging me toward thinking about global vs local optima.
Frame the problem as a real-time optimization that balances demand prediction and driver allocation. Start by forecasting demand using historical data, then formulate a min-cost matching or assignment problem that minimizes expected pickup time, and finally discuss scalable implementation and trade-offs.
Pro tip: Emphasize that the solution must be robust to demand fluctuations and driver behavior, and propose a hybrid approach that combines predictive modeling with optimization, rather than a purely reactive one.
Use historical rider demand density to predict short-term demand across the city, incorporating temporal and spatial features. Consider models like spatio-temporal regression or deep learning for grid-based demand forecasting.
Define the objective as minimizing expected pickup time, which can be approximated by distance or travel time. Formulate as an assignment problem where idle drivers are matched to high-demand zones.
Solve the assignment problem using efficient algorithms like the Hungarian method for small-scale or min-cost flow for large-scale. For real-time, consider greedy heuristics or reinforcement learning.
Design a system that ingests live GPS data, updates demand predictions, and recomputes assignments periodically. Use streaming and distributed computing to handle scale.
Evaluate using metrics like average pickup time and driver utilization. Discuss trade-offs between optimality and computational efficiency, and how to handle uncertainty.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic interval scheduling underneath but I blanked on the clean solution for a second and started overcomplicating it with a full sort-and-graph approach.
Recognize this as the interval partitioning problem: the minimum number of drivers equals the maximum number of overlapping rides at any point in time. Sort all start and end timestamps, then sweep through them, incrementing a counter for each start and decrementing for each end, tracking the maximum. This yields an O(N log N) solution.
Pro tip: Clarify with the interviewer whether a ride ending at time t and another starting at time t are considered overlapping; typically they are not, so process ends before starts when timestamps are equal. Also mention that this greedy approach is optimal because it matches the lower bound given by the maximum overlap.
Confirm that rides cannot be assigned to the same driver if they overlap in time, and define whether endpoints touching count as overlap. Ask about input format and constraints.
Explain that the minimum number of drivers is exactly the maximum number of rides that overlap at any single moment. This is a classic interval partitioning problem.
Create two sorted lists: one of all start times and one of all end times. Use two pointers to sweep through time, incrementing a counter when a start is encountered and decrementing when an end is encountered, while tracking the maximum counter value.
State that sorting takes O(N log N) time and O(N) space. Discuss edge cases: no rides, all rides overlapping, and rides that touch at endpoints.
Walk through a small example (e.g., rides [1,3], [2,4], [3,5]) to show how the sweep works and confirm the result matches the maximum overlap.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.