if you are able to use anything and everything, I believe you can do this by simply defining a sort criteria function that says if its less than zero then its less than all positive values (and zero), then use the stablesort on it with your custom function and it should be successful.
However I am not sure this is the least number of operations required. You may need to sit down and figure out if there is a better mousetrap. I suspect there is, as you need like 1 iteration of a sort, not the full blown thing, such that it 'pivots' on zero, stable. The subsequent iterations with other pivots would not be required. That gives you just N operations. But, the question is, how many operations does it do if you use your custom criteria, since that would be one and done after a single pass too, I believe. It may execute a bunch of donothing passes, which eat time and energy, though... you don't want that.

regardless, a normal sort will not solve the problem, it MUST be a stable sort, and it MUST only sort off (greater than) or (less than or equal) to zero.
here is 10 cents worth of effort. I fixed it for you, they now go left with the reverse of the condition I had.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

#include <iostream>
#include <sstream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <array>
using namespace std;
bool negleft(int a, int b)
{
return(b >= 0 && a<0);
}
int main()
{
vector<int> v {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,15,15,0,0};
stable_sort(v.begin(), v.end(),negleft);
for(int &i:v)
cout << i << endl;
}
 
output:
1 2 3 5 7 11 13 0 4 6 8 9 10 12 14 15 15 15 15 0 0
I think its right, but its still on you to verify it for all the edge cases and ensure the condition is 100% correct. It still shows the idea, at least. Some of this is experience... its not clear what a stable sort is nor that it even exists in most textbooks, so while its a 2 line problem if you know the trick, the trick isn't well advertised to most beginners. So this is a little mercy for you because of that  in the future, you need to show a better understanding of the problem and how to solve it and a solid try at it.