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

Yes, there is one with O(NlogN) time.Since the sorting takes O(NlogN) time anyway, this will not affect overall time complexity.
Time Complexity: O(NlogN)
Space Complexity:O(N)
where N=number of elements in input array

Algorithm:

1. Make copy of input array(P) call it Q.
2. Sort input array P.
3. For each number in Q, do binary search to find index of that element in P.