Is a red-black tree my ideal data structure?

Question

I have a collection of items (big rationals) that I'll be processing. In each case, processing will consist of removing the smallest item in the collection, doing some work, and then adding 0-2 new items (which will always be larger than the removed item). The collection will be initialised with one item, and work will continue until it is empty. I'm not sure what size the collection is likely to reach, but I'd expect in the range 1M-100M items. I will not need to locate any item other than the smallest.

I'm currently planning to use a red-black tree, possibly tweaked to keep a pointer to the smallest item. However I've never used one before, and I'm unsure whether my pattern of use fits its characteristics well.

1) Is there a danger the pattern of deletion from the left + random insertion will affect performance, eg by requiring a significantly higher number of rotations than random deletion would? Or will delete and insert operations still be O(log n) with this pattern of use?

2) Would some other data structure give me better performance, either because of the deletion pattern or taking advantage of the fact I only ever need to find the smallest item?

Update: glad I asked, the binary heap is clearly a better solution for this case, and as promised turned out to be very easy to implement.

Hugo

Answer 1

A binary heap is a lot better for what you want. It is easier to implement and faster since you only care about locating the smallest element and insertions. Locating the smallest element is O(1), removing it is O(log N), and an insertion is also O(log N).