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I am looking for a functional data structure that would work in this role.

Adding items to the struct happens often. Removing items from the struct happens as often as adding them but I have no way of knowing what order the deletion happens in. Over the long term addions will equal removal Rarely I need all items currently in the struct

I thought of using a queue but out of order removal from a queue is expensive.

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My recommendation is a straightforward hash map. If you have a good hash function for your distribution of keys, the time complexity for adding and removing (with an arbitrary key) is amortized $O(1)$.

EDIT: Hash maps can be purely functional if you want (example), they just become a whole lot less efficient. I don't think it's theoretically possible to get lower than $O(\log n)$, which is what you get from using a red-black tree as the backend. The linked HAMT implementation is also $O(\log n)$, just with a significantly smaller hidden constant.

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  • $\begingroup$ Hash maps are good but I'm looking for a functional data structure rather then an imperative one. $\endgroup$ – Q the Platypus May 17 '19 at 1:33
  • $\begingroup$ @QthePlatypus Hashmaps can be functional, they just stop being $O(1)$ (because functional-ness usually makes things less efficient). Added a note on that with an example. $\endgroup$ – Draconis May 17 '19 at 1:44

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