Knew this one cold so I jumped straight to the linear scan approach, tracking the running minimum and updating max profit as I go.
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 algorithm clearly, analyze its time and space complexity, and discuss potential pitfalls or alternative approaches.
Pro tip: Mention that this is a classic 'buy low, sell high' problem and that the optimal solution runs in O(n) time with O(1) space, which is crucial for handling large datasets typical at Uber. Also, proactively discuss how you would handle edge cases like empty arrays or decreasing prices.
Ask about input size, whether prices can be negative, and if multiple transactions are allowed (though the problem states one). Confirm that buying and selling must be on different days and that no profit means return 0.
Briefly mention that a naive solution would check all pairs of buy and sell days, resulting in O(n^2) time, which is inefficient for large inputs.
Explain that you can iterate through the array once, keeping track of the minimum price seen so far and the maximum profit that can be achieved by selling at the current price.
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 (profit = last - first).
Walk through a small example, such as [7,1,5,3,6,4], to demonstrate how the algorithm works and verify the output (5 in this case).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.