Hash Table v/s Trees

Question

Are hashtables always faster than trees? Though Hashtables have O(1) search complexity but suppose if due to badly designed hash function lot of collisions happen and if we

Answer 1

Are hashtables always faster than trees?

No, not always. This depends on many things, such as the size of the collection, the hash function, and for some hash table implementations - also the number of delete ops.

hash-tables are O(1) per op on average - but this is not always the case. They might be O(n) in worst cases.

Some reasons I can think of at the moment to prefer trees:

1. Ordering is important. [hash-tables are not maintaining order, BST is sorted by definition]
2. Latency is an issue - and you cannot suffer the O(n) that might occur. [This might be critical for real-time systems]
3. Ther data might be "similar" related to your hash function, and many elements hashed to the same locations [collisions] is not unprobable. [this can be sometimes solved by using a different hash function]
4. For relatively small collections - many times the hidden constant between hashtable's O(1) is much higher then the tree's - and using a tree might be faster for small collections.

However - if the data is huge, latency is not an issue and collisions are unprobable - hash-tables are asymptotically better then using a tree.

Answer 2

In worst case scenario you'll have O(n) time in hast-tables. But this is a billions less probable then sun exploding write now, so when using a good hash-function you can safely assume it works in O(1) unless sun explodes.
On the other hand, performance of both Hash-Tables and Trees can vary on implementation, language, and phase of the moon, so the only good answer to this question is "Try both, think and pick better".

Answer 3

If due to badly designed hash function lot of collisions happen and if we handle collisions using chained structure (say a balanced tree) then the worst case running time for search would be O(n) (not O(log n)). Therefore you cannot conclude for big or small data sets even in case of worst case scenarios hash tables will always be faster than trees.

Answer 4

Use hashtable, and init it with the proper dimension. For example if you use only half space the collisions are very few.