Algorithm to tell if two arrays have identical members

Question

What\'s the best algorithm for comparing two arrays to see if they have the same members?

Assume there are no duplicates, the members can be in any order, and that n

Answer 1

Assuming you don't want to disturb the original arrays and space is a consideration, another O(n.log(n)) solution that uses less space than sorting both arrays is:

1. Return FALSE if arrays differ in size
2. Sort the first array -- O(n.log(n)) time, extra space required is the size of one array
3. For each element in the 2nd array, check if it's in the sorted copy of the first array using a binary search -- O(n.log(n)) time

If you use this approach, please use a library routine to do the binary search. Binary search is surprisingly error-prone to hand-code.

[Added after reviewing solutions suggesting dictionary/set/hash lookups:]

In practice I'd use a hash. Several people have asserted O(1) behaviour for hashes, leading them to conclude a hash-based solution is O(N). Typical inserts/lookups may be close to O(1), and some hashing schemes guarantee worst-case O(1) lookup, but worst-case insertion -- in constructing the hash -- isn't O(1). Given any particular hashing data structure, there would be some set of inputs which would produce pathological behaviour. I suspect there exist hashing data structures with the combined worst-case to [insert-N-elements then lookup-N-elements] of O(N.log(N)) time and O(N) space.