That's not what big O notation is about. It represents the growth rate. In a the case of a hash table, the size of the thing you are hashing is not affected by the number of items present in the hash table. Putting a trillion bit integer into a hash table of other integers is still O(1); it's a constant.
>In a the case of a hash table, the size of the thing you are hashing is not affected by the number of items present in the hash table.
But it is, and that's precisely the reason why hash tables are not O(1) but rather O(log(n)). By the pigeon hole principle, it is impossible to store N items in a hash table using a key whose representation is less than log(N) bits without a collision. This means that there is a relationship between the the size of the key being hashed and the number of elements being inserted in the hash map, specifically the relationship is an element of O(log(n)).
> But it is, and that's precisely the reason why hash tables are not O(1) but rather O(log(n))
I'm sorry, but as a reader it is quite amusing that various posters are claiming (all without citing any sources) hashtables are O(1), O(n) and O(log(n))
