Sorting & Searching

A pile of four numbers split around one of them and put back together in order, then a search that opens straight to the middle of a sorted pile instead of reading it from the start.

Before you start. You need an index - a position in a list, counted from zero - and what Complexity & Big-O already gave you: that doubling the input can double the work, or square it, or barely change it, depending on the method. Everything else here - splitting a pile around one number, and opening a sorted pile at the middle - is new.