My first instinct was to just find the global min and max and call it done.
Clarify the problem constraints first, especially whether you can hold at most one share at a time and whether short selling is allowed. Then explain that the optimal strategy is to capture every upward price movement by buying before each increase and selling before each decrease, which can be implemented with a simple greedy algorithm in O(n) time.
Pro tip: Mention that this greedy approach is optimal because any profitable trade can be decomposed into a series of consecutive day trades, so summing all positive daily differences yields the maximum profit. Also, briefly discuss edge cases like decreasing prices or single-day input to show thoroughness.
Ask whether you can hold at most one share at a time, whether you can buy and sell on the same day, and whether short selling is allowed. Confirm that the goal is to maximize total profit over the n days.
Explain that the maximum profit is achieved by buying before every price increase and selling before every price decrease. This is equivalent to summing all positive differences between consecutive days.
Iterate through the price array from day 2 to day n, and for each day, if the price is higher than the previous day, add the difference to the total profit. This greedy approach runs in O(n) time and O(1) space.
Prove that any optimal solution can be transformed into this greedy strategy without reducing profit, because each upward movement can be captured independently. State the time and space complexity.
Handle cases like strictly decreasing prices (profit 0), single day (profit 0), and mention extensions such as allowing multiple shares or transaction fees if relevant.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.