MergeSort in scala?

Suppose you split your list into three pieces: the item you are considering, those on the left, and those on the right. Suppose further that those on the left are in a sorted set. Now you just need to walk through the list, moving items from "right" to "considered" and from "considered" to "left"; at each point, you look at the size of the subset of the sorted set that is greater than your item.

In general, the size lookup can be done in O(log(N)) as can the add-element (with a Red-Black or AVL tree, for instance). So you have O(N log N) performance.

Here is my try, I don't use MergeSort but it seems to solve the problem.

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