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

You can use a signature (a commutative operation over the array members) to further optimize this in the case where the array are usually different, saving the o(n log n) or the memory allocation. A signature can be of the form of a bloom filter(s), or even a simple commutative operation like addition or xor.

A simple example (assuming a long as the signature side and gethashcode as a good object identifier; if the objects are, say, ints, then their value is a better identifier; and some signatures will be larger than long)

public bool MatchArrays(object[] array1, object[] array2)
{
   if (array1.length != array2.length)
      return false;
   long signature1 = 0;
   long signature2 = 0;
   for (i=0;i

where (using an addition operation; use a different commutative operation if desired, e.g. bloom filters)

public long CommutativeOperation(long oldValue, long newElement) {
    return oldValue + newElement;
}