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Clarify the problem constraints (e.g., single transaction, cannot sell before buying) and then present an O(n) one-pass solution that tracks the minimum price seen so far and the maximum profit. Walk through a small example to validate the logic and discuss edge cases like decreasing prices.
Pro tip: Explicitly state that you're optimizing for time and space complexity (O(n) time, O(1) space) and mention that this is a classic problem often used to assess algorithmic thinking. Also, relate it to real-world scenarios like trading or feature engineering in ML pipelines to show domain awareness.
Confirm that only one buy and one sell are allowed, and that the sell must occur after the buy. Ask about edge cases such as empty array or single element.
Mention the O(n^2) brute force approach of checking all pairs, then explain how to optimize to O(n) by tracking the minimum price and maximum profit in one pass.
Initialize min_price to infinity and max_profit to 0. Iterate through prices, update min_price if current price is lower, else update max_profit if current price - min_price is greater.
Use a sample array 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.
State that time complexity is O(n) and space is O(1). Discuss edge cases: empty array returns 0, decreasing prices yield 0 profit, and large arrays are handled efficiently.
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