Fastest data structure for inserting/sorting

Question

I need a data structure that can insert elements and sort itself as quickly as possible. I will be inserting a lot more than sorting. Deleting is not much of a concern and nethier is space. My specific implementation will additionally store nodes in an array, so lookup will be O(1), i.e. you don't have to worry about it.

Answer 1

If you're inserting a lot more than sorting, then it may be best to use an unsorted list/vector, and quicksort it when you need it sorted. This keeps inserts very fast. The one¹ drawback is that sorting is a comparatively lengthy operation, since it's not amortized over the many inserts. If you depend on relatively constant time, this can be bad.

_{¹ Come to think of it, there's a second drawback. If you underestimate your sort frequency, this could quickly end up being overall slower than a tree or a sorted list. If you sort after every insert, for instance, then the insert+quicksort cycle would be a bad idea.}