Question

I’m trying to make a hash function so I can tell if too lists with same sizes contain the same elements.

For exemple this is what I want:
f((1 2 3))=f((1 3 2))=f((2 1 3))=f((2 3 1))=f((3 1 2))=f((3 2 1)).

Any ideea how can I approch this problem ? I’ve tried doing the sum of squares of all elements but it turned out that there are collisions,for exemple f((2 2 5))=33=f((1 4 4)) which is wrong as the lists are not the same.

I’m looking for a simple approach if there is any.

Answer 1

You’re probably out of luck if you really want no collisions. There are N choose k sets of size k with elements in 1..N (and worse, if you allow repeats). So imagine you have N=256, k=8, then N choose k is ~4 x 10^14. You’d need a very large integer to distinctly hash all of these sets.

Possibly you have N, k such that you could still make this work. Good luck.

If you allow occasional collisions, you have lots of options. From simple things like your suggestion (add squares of elements) and computing xor the elements, to complicated things like sort them, print them to a string, and compute MD5 on them. But since collisions are still possible, you have to verify any hash match by comparing the original lists (if you keep them sorted, this is easy).