Iterate through different subset of size k

Question

I have an array of n integers (not necessarily distinct!) and I would like to iterate over all subsets of size k. However I\'d like to exclude all duplicate subsets.

Answer 1

I like bit-twiddling for this problem. Sure, it limits you to only 32 elements in your vector, but it's still cool.

First, given a bit mask, determine the next bitmask permutation (source):

uint32_t next(uint32_t v) {
    uint32_t t = v | (v - 1);
    return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1));  
}

Next, given a vector and a bitmask, give a new vector based on that mask:

std::vector filter(const std::vector& v, uint32_t mask) {
    std::vector res;
    while (mask) {
        res.push_back(v[__builtin_ctz(mask)]);
        mask &= mask - 1;
    }   
    return res;
}

And with that, we just need a loop:

std::set> get_subsets(const std::vector& arr, uint32_t k) {   
    std::set> s;
    uint32_t max = (1 << arr.size());
    for (uint32_t v = (1 << k) - 1; v < max; v = next(v)) {
        s.insert(filter(arr, v));
    }
    return s;
}

int main()
{
    auto s = get_subsets({1, 2, 2, 3, 3, 3, 3}, 2);
    std::cout << s.size() << std::endl; // prints 5
}