How to obtain the index permutation after the sorting

Question

Given an array arr = {5, 16, 4, 7}, we can sort it through sort(arr, arr+sizeof(arr)/sizeof(arr[0])). so now the array arr = {4, 5, 7, 16}

Answer 1

Why not put some satellite data? Instead of sorting the numbers, just sort pairs of numbers and their indices. Since the sorting is first done on the first element of the pair, this shouldn't disrupt a stable sorting algorithm.

For unstable algorithms, this will change it to a stable one.

But note that if you try sorting this way it generates the index while sorting, not after.

Also, since knowing the permutation index would lead to a O(n) sorting algorithm, so you cannot do it faster than O(nlogn).