Get indexes of unique elements in two different arrays in linear time

Question

I have two array of the same set of elements, say for exemple: $a_1 = [x_1, x_2, …, x_n]$ and $a_2 = [y_1, y_2, …, y_n]$ so that $i \neq j \Rightarrow x_i \neq x_j$

Is it possible, in linear time, to construct the array $[(x_1, k_1), (x_2, k_2), …, (x_n, k_n)]$ so that $y_{k_i} = x_i$ ?

I found that with dictionnaries, I can get $O(n)$ in average and $O(n^2)$ in worst (hashtable) or $O(n\log n)$ in average and worst (balancing trees), but can't find a way to make it $O(n)$ in worst case.

We can suppose that the $x_i$ objects are integers, since it could represent memory pointers.

I found that it is possible if the set is $[\![1, n]\!]$ (just construct the array directly).

Thanks for your help.