Started by thinking about brute force O(n^2) out loud which was a mistake, felt the energy shift a bit.
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 the maximum profit. Explain the algorithm clearly, analyze its time and space complexity, and discuss potential optimizations or variations.
Pro tip: Mention that this is a classic problem often solved with Kadane's algorithm variant, and emphasize that you can achieve O(n) time and O(1) space, which is optimal. Also, relate it to real-world scenarios like maximizing profit in stock trading, showing practical understanding.
Ask clarifying questions to ensure you understand the input format, constraints, and expected output. Confirm that you need to buy before selling and that you can only make one transaction.
Acknowledge that a brute force solution would be O(n^2) by checking all pairs, but then propose an O(n) one-pass solution that tracks the minimum price and maximum profit.
Walk through the algorithm: initialize min_price to infinity and max_profit to 0. Iterate through prices, update min_price if current price is lower, else calculate profit and update max_profit if higher.
State that time complexity is O(n) and space is O(1). Discuss edge cases: empty array, single element, decreasing prices (profit 0), and all increasing prices.
Run through a simple example like [7,1,5,3,6,4] to demonstrate the algorithm and verify the output (5).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.