How can I represent a set in ampl into a vector in c++? - c++

Question

I have two sets in ampl to be implemented in c++, set NS and set S.
But I'm not understanding the set S very well.
set N ordered := {1..n};
set NS ordered := 1..(2**n-1);
set S {s in NS} := {i in N: (s div 2**(ord(i)-1)) mod 2 = 1};
If n = 4, I will have:
set N := 1 2 3 4
set NS := 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15;
set S[1] := 1;
set S[2] := 2;
set S[3] := 1 2;
set S[4] := 3;
set S[5] := 1 3;
set S[6] := 2 3;
set S[7] := 1 2 3;
set S[8] := 4;
set S[9] := 1 4;
set S[10] := 2 4;
set S[11] := 1 2 4;
set S[12] := 3 4;
set S[13] := 1 3 4;
set S[14] := 2 3 4;
set S[15] := 1 2 3 4;
The first set can be easily created.
vector <int> NS;
int auxMax = pow(2,n)-1;
for (int i = 0; i < auxMax; i++) {
NS.push_back(i);
}
Although I know how the operators div (returns the truncated quotient when its left operand is divided by its right operand), mod (computes the remainder) and ord(returns the numerical position of [i] within the set N) work, I'm not able to make a struct of "for" to fed set S.
Can anyone help me understanding the generation of set S and transforming it to a vector in c++?
Thank you!

Answer 1

Im not familiar with ampl, but I'll give it a go:
Assuming I understood that {} translates to some form of vector type.
Result is the following:
int main()
{
const int n = 4;
int NS = pow(2, n) - 1;
std::vector< std::vector<int> > S;
for (int s = 1; s <= NS; s++) // {s in NS}
{
std::vector<int> iN;
for (int ord_i = 1; ord_i <= n; ord_i++) // {i in N}
{
if ((s / (int)pow(2, ord_i - 1)) % 2 == 1)
iN.push_back(ord_i);
}
S.push_back(iN);
}
}