Instance of subset sum problem

I have a problem which is a pretty clear instance of the subset sum开发者_StackOverflow problem:

"given a list of Integers in the range [-65000,65000], the function returns true if any subset of the list summed is equal to zero. False otherwise."

What I wanted to ask is more of an explanation than a solution.

This was an instance-specific solution I came up before thinking about the complexity of the problem.

• Sort the array A[] and, during sort, sum each element to a counter 'extSum' (O(NLogN))
• Define to pointers low = A[0] and high = A[n-1]
• Here is the deciding code:

• while(A[low]<0){
    sum = extSum;
    if(extSum>0){
      while(sum - A[high] < sum){
          tmp = sum - A[high];
          if(tmp==0) return true;
          else if(tmp > 0){
              sum = tmp;
              high--;
          }
          else{
              high--;
          }
      }
      extSum -= A[low];
      low++;
      high = n - 1;
    }
    else{
      /* Symmetric code: switch low, high and the operation > and < */
    }
  }
  return false;
  

First of all, is this solution correct? I made some tests, but I am not sure...it looks too easy...

Isn't the time complexity of this code O(n^2)?

I already read the various DP solutions and the thing I would like to understand is, for the specific instance of the problem I am facing, how much better than this naive and intuitive solution they are. I know my approach can be improved a lot but nothing that would make a big difference when it comes to the time complexity....

Thank you for the clarifications

EDIT: One obvious optimization would be that, while sorting, if a 0 is found, the function returns true immediately....but it's only for the specific case in which there are 0s in the array.

Hmm, I think {0} will beat your answer.

Because it will simply ignore while and return false.