Question

Given two sets A and B, what is the common algorithm used to find their union, and what is it’s running time?

My intuition:

a = set((1, 2, 3)) b = set((2, 3, 5)) union = set() for el in a:     union.add(el)  for el in b:     union.add(el) 

Add checks for a collision, which is O(1), and then adds the element, which is (??). This is done n times (where n is |a| + |b|). So this is O(n * x) where x is avg running time for the add operation.

Is this correct?

Answer 1

This is very much implementation dependent. Others have mentioned sets based on comparables (have a less-than for sorting) or hashables (have a good hash function for hashing). Another possible implementation involved ‘union-find’, which only supports a specialized subset of usual set operations but is very fast (union is amortized constant time, I think?), you can read about it here

http://en.wikipedia.org/wiki/Union_find

and see an example application here

http://lorgonblog.spaces.live.com/blog/cns!701679AD17B6D310!220.entry