← Two Sigma Interview Insights
I knew the answer pretty quickly, track the running minimum price and compare each day's price against it to update the max profit.
Clarify the problem constraints and edge cases, then explain a one-pass greedy algorithm that tracks the minimum price seen so far and computes the maximum profit at each step. Emphasize that this achieves O(n) time and O(1) space by avoiding nested loops or extra data structures.
Pro tip: Mention that this is equivalent to Kadane's algorithm on the array of daily price differences, showing deeper algorithmic insight. Also, explicitly state that you return 0 if no profit is possible, which handles decreasing prices.
Confirm the problem: at most one buy-sell transaction, return 0 if no profit, and the O(n) time and O(1) space constraints. Restate to ensure alignment with the interviewer.
Acknowledge that a brute-force O(n^2) solution exists but is inefficient. Then propose a one-pass approach that tracks the minimum price and maximum profit.
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 than max_profit.
State that the algorithm runs in O(n) time and O(1) space. Discuss edge cases: empty array, single element, strictly decreasing prices (profit 0), and strictly increasing prices.
Write clean code with meaningful variable names. Walk through a small example to verify correctness, and mention potential pitfalls like integer overflow (if prices are large).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.