Each element adds O(1) breakpoints (sometimes 2). Total breakpoints: O(n). Each heap operation (insert, pop) is O(logn).
Each element does O(1) operations. Total time: O(nlogn). Space: O(n) for the heaps. Compare to naive: O(n⋅range) where range is the value domain. Slope Trick ignores the range. The observation: each element adds at most two breakpoints. Total breakpoints stay O(n) throughout.