Buy and Sell Stock variation

This report gives no precise variation, so begin by asking whether transactions are unlimited, capped, charged a fee, or followed by a cooldown. Do not silently assume one. For the common unlimited-transactions case, maintain cash, the best profit while not holding, and hold, the best profit while holding one share. For each price, compute nextCash = max(cash, hold + price) and nextHold = max(hold, cash - price) using saved old values. A transaction cap adds a transaction index; a fee subtracts from sale; a cooldown adds a previous-cash state. Explain the invariant before coding and verify one-day, falling-price, and repeated-price cases. The basic two-state solution is O(n) time and O(1) space.