The Amazon branding around 'distribution centers' threw me off for longer than I'd like to admit.
Model the problem as tracking the direction of demand changes and assigning hub numbers accordingly, ensuring that each change in direction requires a new hub. Use a greedy strategy: start with hub 0, increment hub number on an increase, decrement on a decrease, and keep the same on flat demand. The minimum number of unique hubs is the number of distinct hub numbers visited.
Pro tip: Clarify with the interviewer whether the hub numbers can go negative or if they are bounded; this affects whether you need to offset the numbers to start from 1. Also, consider if the sequence can be empty or have a single element, and handle those edge cases.
Restate the problem to ensure you understand the rule: hub number changes based on demand direction. Ask about edge cases: empty sequence, single element, and whether hub numbers can be negative.
Initialize current hub to 0 and a set to track unique hubs. Iterate through the demand sequence, comparing each element with the previous one. Update the hub number: +1 for increase, -1 for decrease, no change for flat. Add each new hub number to the set.
Choose a small example, e.g., [1,2,2,1,3], and simulate the algorithm step by step to demonstrate correctness. Show how the set of unique hubs grows and why it's minimal.
State that the time complexity is O(n) and space complexity is O(n) in the worst case (if all hubs are unique). Discuss edge cases: empty sequence returns 0, single element returns 1, and all flat returns 1.
Mention that the set could be replaced by tracking min and max hub numbers if only the count is needed, but the set is straightforward. Also, note that the problem is essentially counting the number of distinct values in a walk.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.