Trading profit with a two-day cooldown

Question

Given daily prices, you may complete unlimited round trips (holding at most one share), but after each sell you must observe a two-day cooldown before buying again.

prices = [1, 4, 0, 0, 0, 5]
-> 8           # buy@1 sell@4, cooldown two days, buy@0 sell@5

Return the maximum profit. Aim for $O(n)$ time, $O(1)$ space.

Accepted Answer

The one-day version had three end-of-day states (hold, sold, rest). Two days of cooldown just insert one extra waiting state between selling and being free again: - hold, you own the share: kept it, or bought today (only from rest). - sold, you sold today. - cool, the single forced idle day right after sold. - rest, flat and free to buy: stayed resting, or your last cooldown day (cool) just ended. Transitions per day at price p: 	ext{hold}' = \max(	ext{hold},\ 	ext{rest} - p), \quad 	ext{sold}' = 	ext{hold} + p, 	ext{cool}' = 	ext{sold}, \quad 	ext{rest}' = \max(	ext{rest},\ 	ext{co…

Trading profit with a two-day cooldown

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