How to tell if an array is a permutation in O(n)?

Question

Input: A read-only array of N elements containing integer values from 1 to N (some integer values can appear more than once!). And a memory zone of a fixed<

Answer 1

Depending on how much space you have, relative to N, you might try using hashing and buckets.

That is, iterate over the entire list, hash each element, and store it in a bucket. You'll need to find a way to reduce bucket collisions from the hashes, but that is a solved problem.

If an element tries to go into a bucket with an item identical to it, it is a permutation.

This type of solution would be O(N) as you touch each element only once.

However, the problem with this is whether space M is larger than N or not. If M > N, this solution will be fine, but if M < N, then you will not be able to solve the problem with 100% accuracy.