Given daily stock `prices`, buy and sell as many times as you like — no two positions open at once, so a share must be sold before another is bought — but every completed round trip costs a flat `fee`, charged when the position closes. Maximize total profit. Every day only asks one question: given whether a share is currently held, is acting (buying into nothing, or selling out of a position) better than leaving things exactly as they are? Two running totals capture everything needed to answer that — the best result with nothing held, and the best result already holding one share — and each day's decision only ever needs yesterday's version of those two numbers. The fee just gets folded into the moment of selling, so a trade only ever gets taken when the price gap actually covers it.