Knew this one cold but still fumbled the explanation a bit.
Start by clarifying the problem constraints and edge cases, then propose an efficient one-pass solution that tracks the minimum price seen so far and computes the maximum profit at each step. Explain the time and space complexity, and discuss why this approach is optimal.
Pro tip: At Citadel, interviewers value not just correct solutions but also the ability to reason about edge cases and optimize for performance. Explicitly mention that you're aiming for O(n) time and O(1) space, and briefly discuss how you'd handle large datasets or streaming input.
Ask questions to confirm assumptions: Can you buy and sell on the same day? Are prices integers? What should be returned if no profit is possible? This shows attention to detail.
Mention that a brute force approach would check all pairs of buy and sell days, resulting in O(n^2) time. This is inefficient for large inputs and sets the stage for optimization.
Explain that you can iterate through the array once, keeping track of the minimum price seen so far and the maximum profit. At each day, calculate the profit if sold today and update the maximum profit.
State that the algorithm runs in O(n) time and O(1) space. Discuss edge cases: empty array, single element, strictly decreasing prices (profit 0), and strictly increasing prices.
Walk through a small example, such as [7,1,5,3,6,4], to demonstrate how the algorithm works and verify the output (5).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.