Leetcode 3279. Maximum Total Area Occupied by Pistons

Given a set of pistons (with sizes/extension limits and positions), choose how far each can extend or where to place them so their occupied regions do not overlap and the sum of their areas is maximized. This is a hard geometric/optimization problem combining continuous placement and combinatorial non‑overlap constraints, requiring careful sorting, interval reasoning and advanced DP/optimization to handle interactions between neighboring pistons.