Havel-Hakimi algorithm to determine if a graph with the given list of degree is possible.

graph-exists.cpp

bool graph_exists(std::vector<int> degrees)
{
	auto remaining = degrees.size();
	
	for (auto i = degrees.begin(), end = degrees.end(); i != end; ++i)
	{
		std::sort(i, end, std::greater<int>());

		if (*i == 0) return true;
		
		if (*i >= remaining--) return false;
	
		auto stop = i;
		std::advance(stop, *i + 1);
		
		for (auto j = std::next(i); j != stop; ++j)
		{
			if (--*j < 0) return false;
		}
	}
	
	return false;
}