Codeforces 865D Buy Low Sell High - Why It Works

Think of profit as a function of the last action. Each buy/sell pair contributes to the piecewise linear profit function. The heap tracks slope-change points. Pushing $p_i$ twice after a sell lets you retroactively change the decision. If a higher price appears later, the second $p_i$ can be popped as a "buy" price.

This is Slope Trick in disguise: you're maintaining a convex function of decisions without storing all states. The heap gives you $O(\log n)$ updates.