Why do I keep seeing different runtime complexities for these functions on a hash table?
On wiki, search and delete are O(n) (I thought the point of hash tables was to have constant lookup so what's the point if search is O(n)).
In some course notes from a while ago, I see a wide range of complexities depending on certain details including one with all O(1). Why would any other implementation be used if I can get all O(1)?
If I'm using standard hash tables in a language like C++ or Java, what can I expect the time complexity to be?
Hash tables suffer from
O(n) worst time complexity due to two reasons:
However, it is said to be
O(1) average and amortized case because:
O(n), can at most happen after
n/2ops, which are all assumed
O(1): Thus when you sum the average time per op, you get :
(n*O(1) + O(n)) / n) = O(1)
Note because of the rehashing issue - a realtime applications and applications that need low latency - should not use a hash table as their data structure.
EDIT: Annother issue with hash tables: cache
Another issue where you might see a performance loss in large hash tables is due to cache performance. Hash Tables suffer from bad cache performance, and thus for large collection - the access time might take longer, since you need to reload the relevant part of the table from the memory back into the cache.