← Microsoft Interview Insights
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 test with examples including no-profit scenarios.
Pro tip: Mention that this is a classic 'best time to buy and sell stock' problem and that the optimal solution runs in O(n) time with O(1) space, which is optimal since you must examine each price at least once. Also, proactively discuss how you would handle edge cases like an empty array or decreasing prices.
Ask clarifying questions: Is the array guaranteed non-empty? Can prices be zero or negative? Should we return 0 if no profit? Confirm that only one transaction is allowed.
Briefly mention that a naive solution would check all pairs of buy and sell days, resulting in O(n^2) time, to establish a baseline and show you understand the problem.
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, update the minimum and compute the profit if sold today, updating the maximum profit.
State that the algorithm runs in O(n) time and O(1) space, and argue its correctness by noting that the maximum profit is achieved by buying at the lowest price before the selling day.
Walk through a few test cases: a profitable scenario, a decreasing array (profit 0), and an empty or single-element array. Verify the output matches expectations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.