Use a single pass through the array, tracking the minimum price seen so far and the maximum profit achievable by selling at the current price. Update the minimum and maximum profit as you iterate. This yields an O(n) time, O(1) space solution.
Pro tip: Emphasize that the algorithm effectively finds the maximum difference between a later element and an earlier element, which is a classic pattern. Mention that this approach is optimal because any correct algorithm must examine each price at least once.
Restate the problem: given an array of daily stock prices, find the maximum profit from at most one buy-then-sell transaction. Confirm that buying and selling must occur on different days and that no transaction is allowed if it results in a loss (profit can be 0).
Initialize min_price to the first price and max_profit to 0. Iterate through the array starting from the second element: update min_price to the minimum of min_price and the current price, and update max_profit to the maximum of max_profit and (current price - min_price).
Argue by induction or loop invariant: after processing the first i elements, min_price is the minimum price in that prefix, and max_profit is the maximum profit achievable using a buy and sell within that prefix. At each step, the new max_profit considers selling at the current price after buying at the minimum price seen so far, ensuring all possible transactions are considered.
Time complexity is O(n) because we make a single pass through the array. Space complexity is O(1) because we only use a constant number of variables (min_price and max_profit).
Mention edge cases: empty array or single element (profit 0), strictly decreasing prices (profit 0), and strictly increasing prices (profit = last - first). Also note that the algorithm handles these naturally.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem: we need to maintain the maximum profit seen so far as prices stream in, updating after each new price. Then, adapt the classic single-pass solution by tracking the minimum price seen so far and the maximum profit, updating both with each new price. Finally, discuss how this approach handles streaming constraints and potential extensions.
Pro tip: Emphasize that the streaming solution requires only O(1) space and O(1) time per update, which is optimal. Also, mention that this approach is robust to large or infinite streams, making it suitable for real-time systems.
Restate the problem to ensure understanding: given a stream of stock prices, after each new price, output the maximum profit achievable by buying and selling at some point up to the current time.
Recall the classic single-pass algorithm for maximum profit: track the minimum price seen so far and the maximum profit, updating both as you iterate through the prices.
Explain that the same algorithm works in a streaming setting because it only requires the minimum price and maximum profit seen so far, which can be updated incrementally with each new price.
State that each update takes O(1) time and O(1) space, which is optimal for streaming. Discuss that the algorithm processes each price exactly once.
Mention handling of edge cases (e.g., decreasing prices, single price) and potential extensions like multiple transactions or real-time constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.