C++ sorting and keeping track of indexes

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?

Solution 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.

Solution 2:

You could sort std::pair instead of just ints - first int is original data, second int is original index. Then supply a comparator that only sorts on the first int. Example:

Your problem instance: v = [5 7 8]
New problem instance: v_prime = [<5,0>, <8,1>, <7,2>]

Sort the new problem instance using a comparator like:

typedef std::pair<int,int> mypair;
bool comparator ( const mypair& l, const mypair& r)
   { return l.first < r.first; }
// forgetting the syntax here but intent is clear enough

The result of std::sort on v_prime, using that comparator, should be:

v_prime = [<5,0>, <7,2>, <8,1>]

You can peel out the indices by walking the vector, grabbing .second from each std::pair.

Solution 3:

Suppose Given vector is

A=[2,4,3]

Create a new vector

V=[0,1,2] // indicating positions

Sort V and while sorting instead of comparing elements of V , compare corresponding elements of A

 //Assume A is a given vector with N elements
 vector<int> V(N);
 std::iota(V.begin(),V.end(),0); //Initializing
 sort( V.begin(),V.end(), [&](int i,int j){return A[i]<A[j];} );

Solution 4:

vector<pair<int,int> >a;

for (i = 0 ;i < n ; i++) {
    // filling the original array
    cin >> k;
    a.push_back (make_pair (k,i)); // k = value, i = original index
}

sort (a.begin(),a.end());

for (i = 0 ; i < n ; i++){
    cout << a[i].first << " " << a[i].second << "\n";
}

Now a contains both both our values and their respective indices in the sorted.

a[i].first = value at i'th.

a[i].second = idx in initial array.

Solution 5:

I wrote generic version of index sort.

template <class RAIter, class Compare>
void argsort(RAIter iterBegin, RAIter iterEnd, Compare comp, 
    std::vector<size_t>& indexes) {

    std::vector< std::pair<size_t,RAIter> > pv ;
    pv.reserve(iterEnd - iterBegin) ;

    RAIter iter ;
    size_t k ;
    for (iter = iterBegin, k = 0 ; iter != iterEnd ; iter++, k++) {
        pv.push_back( std::pair<int,RAIter>(k,iter) ) ;
    }

    std::sort(pv.begin(), pv.end(), 
        [&comp](const std::pair<size_t,RAIter>& a, const std::pair<size_t,RAIter>& b) -> bool 
        { return comp(*a.second, *b.second) ; }) ;

    indexes.resize(pv.size()) ;
    std::transform(pv.begin(), pv.end(), indexes.begin(), 
        [](const std::pair<size_t,RAIter>& a) -> size_t { return a.first ; }) ;
}

Usage is the same as that of std::sort except for an index container to receive sorted indexes. testing:

int a[] = { 3, 1, 0, 4 } ;
std::vector<size_t> indexes ;
argsort(a, a + sizeof(a) / sizeof(a[0]), std::less<int>(), indexes) ;
for (size_t i : indexes) printf("%d\n", int(i)) ;

you should get 2 1 0 3. for the compilers without c++0x support, replace the lamba expression as a class template:

template <class RAIter, class Compare> 
class PairComp {
public:
  Compare comp ;
  PairComp(Compare comp_) : comp(comp_) {}
  bool operator() (const std::pair<size_t,RAIter>& a, 
    const std::pair<size_t,RAIter>& b) const { return comp(*a.second, *b.second) ; }        
} ;

and rewrite std::sort as

std::sort(pv.begin(), pv.end(), PairComp(comp)()) ;