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If I define my own comparator for the generic HashSet<T> in System.Collections.Generic, and its runtime is O(1), is the lookup time of the hashset still O(1)?
I would think no just because there doesn’t appear to be a way to set the comparator.
The reason that the lookup time of a regular hashset is O(1) is because it uses open addressing to place objects into the array, so that won’t change even if you use your own comparator.