I knew the basic buy-low-sell-high problem cold, so I started heading down that path and had to stop myself.
Clarify the problem constraints and edge cases, then propose a dynamic programming solution that tracks two states: holding a stock and not holding a stock, with a cooldown period after selling. Optimize to O(n) time and O(1) space by maintaining variables for the maximum profit in each state.
Pro tip: Mention that the cooldown can be handled by using a 'cooldown' state or by adjusting the transition from selling to buying with a one-day delay, and emphasize that this approach generalizes to similar problems like 'Best Time to Buy and Sell Stock with Cooldown'.
Restate the problem in your own words, confirm that you can make unlimited transactions, and that after selling you must wait one day before buying again. Ask clarifying questions about edge cases (e.g., empty array, single day).
Define two states: 'hold' (holding a stock) and 'sold' (not holding a stock, and not in cooldown). Also consider a 'cooldown' state. Derive the recurrence relations for each state.
Initialize variables for the maximum profit in each state at day 0. Iterate through the prices, updating the states based on the transitions. Return the maximum profit from the 'sold' or 'cooldown' state at the end.
Walk through a small example (e.g., [1,2,3,0,2]) to verify the DP transitions and ensure the cooldown is respected. Check edge cases like increasing prices, decreasing prices, and empty array.
State that the time complexity is O(n) and space complexity is O(1). Mention that the solution can be further simplified by using two variables instead of three, and discuss potential variations.
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