Codeforces 674C Levels and Regions - Problem Statement

You have $n$ game levels to split into $k$ regions of consecutive levels. Each region has an expected completion time based on level difficulties. find the smallest total expected time.

The exact formula involves replay probabilities, but the structure is: you're partitioning an array into exactly $k$ segments, reducing a cost function that's convex in $k$. This is the classic setup for Aliens Trick: partition into exactly $k$ parts with convex cost.