Iteratively calculate the power set of a set or vector - c++

Question

While there are plenty of examples on how to generate the actual power set of a set, I can't find anything about iteratively (as in std::iterator) generating the power set. The reason why I would appreciate such an algorithm is the size of my base set. As the power set of a n-element set has 2^n elements, I would quickly run out of memory when actually computing the set. So, is there any way to create an iterator for the power set of a given set? Is it even possible?
If it would be easier, an iterator that creates sets of ints would be fine - I could use them as indices for the actual set/vector.
As I actually work on a std::vector, random access would be possible if neccessary

Answer 1

Using for_each_combination from Combinations and Permutations one can easily iterate through all members of the power set of a std::vector<AnyType>. For example:
#include <vector>
#include <iostream>
#include "../combinations/combinations"
int
main()
{
std::vector<int> v{1, 2, 3, 4, 5};
std::size_t num_visits = 0;
for (std::size_t k = 0; k <= v.size(); ++k)
for_each_combination(v.begin(), v.begin()+k, v.end(),
[&](auto first, auto last)
{
std::cout << '{';
if (first != last)
{
std::cout << *first;
for (++first; first != last; ++first)
std::cout << ", " << *first;
}
std::cout << "}\n";
++num_visits;
return false;
});
std::cout << "num_visits = " << num_visits << '\n';
}
This visits each power set member of this vector, and executes the functor, which simply counts the number of visits and prints out the current power set:
{}
{1}
{2}
{3}
{4}
{5}
{1, 2}
{1, 3}
{1, 4}
{1, 5}
{2, 3}
{2, 4}
{2, 5}
{3, 4}
{3, 5}
{4, 5}
{1, 2, 3}
{1, 2, 4}
{1, 2, 5}
{1, 3, 4}
{1, 3, 5}
{1, 4, 5}
{2, 3, 4}
{2, 3, 5}
{2, 4, 5}
{3, 4, 5}
{1, 2, 3, 4}
{1, 2, 3, 5}
{1, 2, 4, 5}
{1, 3, 4, 5}
{2, 3, 4, 5}
{1, 2, 3, 4, 5}
num_visits = 32
The syntax I've used above is C++14. If you have C++11, you will need to change:
[&](auto first, auto last)
to:
[&](std::vector<int>::const_iterator first, std::vector<int>::const_iterator last)
And if you are in C++98/03, you will have to write a functor or function to replace the lambda.
The for_each_combination function allocates no extra storage. This is all done by swapping members of the vector into the range [v.begin(), v.begin()+k). At the end of each call to for_each_combination the vector is left in its original state.
If for some reason you want to "exit" the for_each_combination early, simply return true instead of false.