Why is accessing an element of a dictionary by key O(1) even though the hash function may not be O(1)?

Question

I see how you can access your collection by key. However, the hash function itself has a lot of operations behind the scenes, doesn\'t it?

Assuming you have a nice h

Answer 1

Once you allow for the fact that larger and larger dictionaries take up more memory, going further down the cache hierarchy and eventually out to slow swap space on disk, it's hard to argue that it is truly O(1). The performance of the dictionary will get slower as it gets bigger, probably giving O(log N) time complexity. Don't believe me? Try it for yourself with 1, 100, 1000, 10000 and so on dictionary elements, up to say 100 billion, and measure how long it takes in practice to look up an element.

However if you make the simplifying assumption that all memory in your system is random access memory, and can be accessed in constant time, then you can claim that the dictionary is O(1). This assumption is common, even though it's not really true for any machine with disk swap space, and still pretty debatable in any case given the various levels of CPU cache.

Answer 2

It means that no matter what size your collection can be, it will still take almost the same amount of time to retrieve any of its members.

So in other words Dictionary with 5 members will let's say coud take around 0.002 ms to access one of them, as well as dictionary of 25 members should take something similar. Big O means algorithmic complexity over collection size instead of actual statements or functions executed