Classic problem but I still fumbled the edge case where prices only go down.
Start by clarifying the problem constraints (e.g., single transaction, cannot sell before buying) and then propose an efficient O(n) time, O(1) space solution that tracks the minimum price seen so far and the maximum profit. Walk through the algorithm with a small example to demonstrate correctness and edge cases.
Pro tip: Mention that you would first confirm whether multiple transactions are allowed or if there are any constraints like transaction fees; this shows you think about real-world scenarios and avoid assumptions.
Ask questions to confirm the problem: single buy and sell, cannot sell before buying, and whether you can choose not to transact (profit 0).
Acknowledge that a brute force approach would check all pairs of buy and sell days, resulting in O(n^2) time, which is inefficient for large inputs.
Explain the one-pass algorithm: iterate through prices, keep track of the minimum price seen so far, and compute the profit if sold at the current price, updating the maximum profit.
Use a small array like [7,1,5,3,6,4] to illustrate how the algorithm works step by step, showing the min price and max profit updates.
State that time complexity is O(n) and space is O(1). Discuss edge cases: empty array, decreasing prices (profit 0), and single element.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.