The DP formulation clicked pretty fast for me.
Clarify the problem constraints and edge cases, then present a dynamic programming solution that tracks the maximum profit with and without holding a stock, incorporating the transaction fee on each sale. Walk through the recurrence relations, provide a concrete example, and analyze time and space complexity.
Pro tip: Mention that the DP can be optimized to O(1) space by keeping only the previous day's states, and discuss how the fee affects the decision to sell versus hold. This shows you consider practical optimizations and trade-offs.
Confirm that you can buy and sell multiple times, but must sell before buying again, and that the fee is deducted from each sale. Ask about edge cases like empty array or fee larger than any profit.
Define two states: cash (max profit with no stock) and hold (max profit while holding a stock). Derive transitions: cash = max(cash, hold + price - fee) and hold = max(hold, cash - price).
Use a small array like [1,3,2,8,4,9] with fee=2 to demonstrate how the states update and yield the maximum profit.
State that the algorithm runs in O(n) time and O(1) space, as it processes each price once and only stores two variables.
Mention that a greedy approach fails due to the fee, and that the DP is optimal. Optionally, discuss how the solution changes if the fee is charged on both buy and sell.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Fee on both sides is basically just adjusting two transitions in the recurrence, not a big structural change.
First, restate the original problem and its assumptions to ensure clarity. Then, systematically analyze how each modification affects the problem's constraints and the optimal strategy, discussing algorithmic adjustments and trade-offs. Finally, summarize the impact on time/space complexity and potential edge cases.
Pro tip: Demonstrate awareness that these changes often transform the problem from a simple greedy or DP to a more complex state-based DP, and mention that you would validate with small examples before coding.
Briefly restate the original problem, including the commission fee structure (only on selling) and the constraint of holding at most one share at a time.
Explain how adding a fee on buying changes the profit calculation and may affect the decision to buy. Discuss how this impacts the DP recurrence or greedy choice, and whether the optimal strategy shifts.
Describe how allowing multiple shares changes the state space. If shares are indistinguishable, it may become a resource allocation problem; if distinguishable (e.g., different prices), it becomes more complex, possibly requiring a different DP or greedy approach.
Propose specific changes to the algorithm, such as adding a dimension to the DP state or using a priority queue. Compare time and space complexity implications and mention any new edge cases.
Recap how each change affects the solution, emphasizing the increased complexity and the need to re-evaluate assumptions. Mention that you would test with examples to ensure correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.