The question itself is pretty standard but I fumbled around with a brute force explanation first before they nudged me toward the linear approach.
Use a single pass through the array, tracking the minimum price seen so far and the maximum profit achievable at each step. This greedy approach ensures O(n) time and O(1) space by updating the minimum and profit in constant time per element.
Pro tip: Explicitly state the time and space complexity and why the greedy approach is optimal, as interviewers often look for candidates who can justify their solution's efficiency. Also, mention edge cases like empty array or decreasing prices to show thoroughness.
Confirm that you need to find the maximum profit from one buy and one sell, with buy before sell, and return 0 if no profit. Ask about input constraints (e.g., array size, price range) to ensure your solution handles all cases.
Explain that you will iterate through the array once, keeping track of the minimum price seen so far and the maximum profit. At each price, update the minimum and then compute the potential profit if sold at the current price, updating the maximum profit if larger.
Use a small example like [7,1,5,3,6,4] to demonstrate how the algorithm works step by step, showing the updates to min_price and max_profit. This helps the interviewer follow your logic.
State that the algorithm runs in O(n) time because it makes a single pass, and O(1) space because it only uses a few variables. Emphasize that this meets the problem's requirements.
Mention that if the array is empty or has only one element, the profit is 0. Also, if prices are strictly decreasing, the algorithm correctly returns 0.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.