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POInstance of subset sum problem
 

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  1. POInstance of subset sum problem
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    <p>I have a problem which is a pretty clear instance of the subset sum problem:</p> <p>"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."</p> <p>What I wanted to ask is more of an explanation than a solution.</p> <p>This was an instance-specific solution I came up before thinking about the complexity of the problem.</p> <ul> <li>Sort the array A[] and, during sort, sum each element to a counter 'extSum' (O(NLogN))</li> <li>Define to pointers low = A[0] and high = A[n-1]</li> <li>Here is the deciding code:</li> <li><pre><code>while(A[low]&lt;0){ sum = extSum; if(extSum&gt;0){ while(sum - A[high] &lt; sum){ tmp = sum - A[high]; if(tmp==0) return true; else if(tmp &gt; 0){ sum = tmp; high--; } else{ high--; } } extSum -= A[low]; low++; high = n - 1; } else{ /* Symmetric code: switch low, high and the operation &gt; and &lt; */ } } return false; </code></pre></li> </ul> <p>First of all, is this solution correct? I made some tests, but I am not sure...it looks too easy...<br> Isn't the time complexity of this code O(n^2)?</p> <p>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....</p> <p>Thank you for the clarifications</p> <p><strong>EDIT:</strong> 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.</p>
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      1. USLuchian Grigore
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    1. COIf I understand your code properly, aren't you assuming the subset will be contiguous? This isn't necessarily the case
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      1. USIsmail Badawi
    2. CO@isbadawi: well, I just assume it's gonna be sorted, and this is because I sort it as a first step.
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    3. COI mean e.g. what if your input is [-4, 1, 4]. A solution is {-4, 4}, but you won't find it
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      1. USIsmail Badawi
 

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