How to obtain the index permutation after the sorting

Create an array of indexes, fill it with numbers 0..N-1, and sort it using a custom comparator. The comparator should compare items from the original array at indexes lhs and rhs. Sorting the array of indexes this way reorders them as a permutation:

vector<int> data = {5, 16, 4, 7};   
vector<int> index(data.size(), 0);
for (int i = 0 ; i != index.size() ; i++) {
    index[i] = i;
}
sort(index.begin(), index.end(),
    [&](const int& a, const int& b) {
        return (data[a] < data[b]);
    }
);
for (int i = 0 ; i != index.size() ; i++) {
    cout << index[i] << endl;
}

This prints 2, 0, 3, 1

Here is a demo on ideone.

Note: you can use index to retrieve the data in sorted order:

for (int i = 0 ; i != index.size() ; i++) {
    cout << data[index[i]] << endl;
}