find if two arrays contain the same set of integers without extra space and faster than NlogN

Question

I came across this post, which reports the following interview question:

Given two arrays of numbers, find if each of the two arrays have the same s

Answer 1

A special, not harder case is when one array holds 1,2,..,n. This was discussed many times:

• How to tell if an array is a permutation in O(n)?
• Algorithm to determine if array contains n...n+m?
• mathoverflow

and despite many tries no deterministic solutions using O(1) space and O(n) time were shown. Either you can cheat the requirements in some way (reuse input space, assume integers are bounded) or use probabilistic test.

Probably this is an open problem.