I am trying to come up with a new way to check that whether a specific item exists in a collection.
In the current implementation, a simple hash table will do but it takes O(n) to update the table if I am changing n values at once.
I have looked up solutions related to probabilistic data structure such as bloom filter, but these have the issue of false positive, which cannot happen in the system.
I have also thought about hash functions with intentional collision so that the result can be stored to verify the only the items with collision, however, there exists none of such at this moment.
Is there any other data structure/algorithms related to this problem?