C++ sorting and keeping track of indexes

Question

Using C++, and hopefully the standard library, I want to sort a sequence of samples in ascending order, but I also want to remember the original indexes of the new samples.

For example, I have a set, or vector, or matrix of samples A : [5, 2, 1, 4, 3]. I want to sort these to be B : [1,2,3,4,5], but I also want to remember the original indexes of the values, so I can get another set which would be: C : [2, 1, 4, 3, 0 ] - which corresponds to the index of each element in 'B', in the original 'A'.

For example, in Matlab you can do:

 [a,b]=sort([5, 8, 7])
 a = 5 7 8
 b = 1 3 2

Can anyone see a good way to do this?

Answer 1

Using C++ 11 lambdas:

#include <iostream>
#include <vector>
#include <numeric>      // std::iota
#include <algorithm>    // std::sort, std::stable_sort

using namespace std;

template <typename T>
vector<size_t> sort_indexes(const vector<T> &v) {

  // initialize original index locations
  vector<size_t> idx(v.size());
  iota(idx.begin(), idx.end(), 0);

  // sort indexes based on comparing values in v
  // using std::stable_sort instead of std::sort
  // to avoid unnecessary index re-orderings
  // when v contains elements of equal values 
  stable_sort(idx.begin(), idx.end(),
       [&v](size_t i1, size_t i2) {return v[i1] < v[i2];});

  return idx;
}

Now you can use the returned index vector in iterations such as

for (auto i: sort_indexes(v)) {
  cout << v[i] << endl;
}

You can also choose to supply your original index vector, sort function, comparator, or automatically reorder v in the sort_indexes function using an extra vector.