Best Time to Buy and Sell Stock with Cooldown.

In Simple Words: State machine DP with three states:

• holding: either keep holding or buy after resting (rest - price).
• sold: sell stock held today (holding + price).
• rest: either rest again or rest after selling yesterday (max(rest, sold)).
• Time: $O(N)$ | Space: $O(1)$

def maxProfit(prices: list[int]) -> int:
    sold, rest, hold = 0, 0, float('-inf')
    for p in prices:
        prev_sold = sold
        sold = hold + p
        hold = max(hold, rest - p)
        rest = max(rest, prev_sold)
    return max(sold, rest)