Implementing an iterator over combinations of many vectors - c++

Question

I am working on a problem that requires iterating over all combinations of elements of K vectors taken one at a time. So for example for K=2 vectors v1 = [0 1] and v2 = [3 4], I would iterate over (0,3), (0,4), (1,3), (1,4).
Since K is determined at run-time, I cannot use explicit for loops. My current approach is based on this solution that implements an "odometer" incrementing an index for each vector.
#include <vector>
#include <iostream>
int main(int argc, char * argv[])
{
std::vector<int> v1( {1, 2, 3} );
std::vector<int> v2( {-2, 5} );
std::vector<int> v3( {0, 1, 2} );
std::vector<std::vector<int> > vv( {v1, v2 ,v3} );
// Iterate combinations of elems in v1, v2, v3, one at a time
std::vector<std::vector<int>::iterator> vit;
for (auto& v : vv)
vit.push_back(v.begin());
int K = vv.size();
while (vit[0] != vv[0].end())
{
std::cout << "Processing combination: [";
for (auto& i : vit)
std::cout << *i << " ";
std::cout << "]\n";
// increment "odometer" by 1
++vit[K-1];
for (int i = K-1; (i > 0) && (vit[i] == vv[i].end()); --i)
{
vit[i] = vv[i].begin();
++vit[i-1];
}
}
return 0;
}
Output:
Processing combination: [1 -2 0 ]
Processing combination: [1 -2 1 ]
Processing combination: [1 -2 2 ]
Processing combination: [1 5 0 ]
Processing combination: [1 5 1 ]
Processing combination: [1 5 2 ]
Processing combination: [2 -2 0 ]
Processing combination: [2 -2 1 ]
Processing combination: [2 -2 2 ]
Processing combination: [2 5 0 ]
Processing combination: [2 5 1 ]
Processing combination: [2 5 2 ]
Processing combination: [3 -2 0 ]
Processing combination: [3 -2 1 ]
Processing combination: [3 -2 2 ]
Processing combination: [3 5 0 ]
Processing combination: [3 5 1 ]
Processing combination: [3 5 2 ]
However, this is somewhat messy and requires a lot of boilerplate code that I'd rather move elsewhere for clarity. Ideally I would like to have a custom iterator class, say my_combination_iterator, that would allow me to do things much cleaner, e.g.:
for (my_combination_iterator it = vv.begin(); it != vv.end(); ++it)
// process combination
So far, I have looked at Boost iterator_facade. But my case seems more complicated than the one in the tutorial since I would need an iterator over a vector of Values as opposed to a single value type to define the required operators for the custom iterator.
How could such an iterator be implemented?

Answer 1

Why would you like to use custom iterators?
One could instead implement a very simple class that will iterate through all combinations:
class Combinator
{
public:
Combinator(std::vector<std::vector<int> >& vectors)
: m_vectors(vectors)
{
m_combination.reserve(m_vectors.size());
for(auto& v : m_vectors)
m_combination.push_back(v.begin());
}
bool next()
{
// iterate through vectors in reverse order
for(long long i = m_vectors.size() - 1; i >= 0; --i)
{
std::vector<int>& v = m_vectors[i];
std::vector<int>::iterator& it = m_combination[i];
if(++it != v.end())
return true;
it = v.begin();
}
return false;
}
std::vector<std::vector<int>::iterator> combination() const
{
return m_combination;
}
private:
std::vector<std::vector<int> >& m_vectors; // reference to data
std::vector<std::vector<int>::iterator> m_combination;
};
Live Demo
UPDATE:
If you would still like to use iterators, I suggest iterating over combinations. One can put all the combinations from Combinator into a container and then work with container's own iterators. In my opinion it's a cleaner solution. The only drawback is the extra-memory needed to store all combinations explicitly.