How to distribute a value into vector

[tiliavirga]

I didn't use the zero combination because i need this code run faster
But since #post 10 i realized its still take lost of time on big value
So redesign my algorithm now i don't want zero combination and dual character in one array like .10, 11, 12 .. so on
For example
Slots = 3
Sum = 17

Have you noticed my post #11?

Say we have V=3 (slots) and D= 17 (sum).

Just use V=3 and D=D-V = 17-3 = 14. Then run Gosper's hack with those values and add 1 to each number in every output combination, like,

void test() {
	int V = 3; // vector size
	int D = 17-V; // modified sum

	const BitSet ONE = BitSet(1);
	BitSet your_start = (ONE << (V + D - 1)) | ((ONE << (V - 1)) - ONE);

//	std::cout << "Expected number of combinations: " << bs_binominal(V+D-1, V-1) << std::endl;

	long long int c = 0; // counter
	for (BitSet x = your_start; x < gosper_limit<BitSet>(V + D); x = gosper_next<BitSet>(x)) {
		VecSet v = bs_0vector(x);
		for (auto& n : v) ++n; // add on 1 to each number in VecSet
		std::cout << bs_0string(v) << std::endl;
		++c;
	}
	std::cout << "Actual number of combinations = " << c << std::endl;
}

I generates exactly the 120 combinations you are looking for, nothing more nothing less.

So Gosper's hack now can be used to very efficiently produce the result you wanted. The D+V <= 62 limit is still there of course but since I too am interested in an unlimited algorithm for this I'll post my own replacement for Gosper's hack anytime soon.