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 stable-sort 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 do-nothing passes, which eat time and energy, though... you don't want that. 
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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.