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POgiven a set of n integers, return all subsets of k elements that sum to 0
 

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  1. POgiven a set of n integers, return all subsets of k elements that sum to 0
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    <p>given a unsorted set of <code>n</code> integers, return all subsets of size k (i.e. each set has k unique elements) that sum to 0.</p> <p>So I gave the interviewer the following solution ( which I studied on <a href="http://geekviewpoint.com/Numbers_functions_in_java/" rel="noreferrer">GeekViewpoint</a>). No extra space used, everything is done in place, etc. But of course the cost is a high time complexity of O(n^k) where <code>k=tuple</code> in the solution.</p> <pre><code>public void zeroSumTripplets(int[] A, int tuple, int sum) { int[] index = new int[tuple]; for (int i = 0; i &lt; tuple; i++) index[i] = i; int total = combinationSize(A.length, tuple); for (int i = 0; i &lt; total; i++) { if (0 != i) nextCombination(index, A.length, tuple); printMatch(A, Arrays.copyOf(index, tuple), sum); }// for }// zeroSumTripplets(int[], int, int) private void printMatch(int[] A, int[] ndx, int sum) { int calc = 0; for (int i = 0; i &lt; ndx.length; i++) calc += A[ndx[i]]; if (calc == sum) { Integer[] t = new Integer[ndx.length]; for (int i = 0; i &lt; ndx.length; i++) t[i] = A[ndx[i]]; System.out.println(Arrays.toString(t)); }// if }// printMatch(int[], int[], int) </code></pre> <p>But then she imposed the following requirements: </p> <ul> <li>must use hashmap in answer so to reduce time complexity</li> <li>Must absolutely -- ABSOLUTELY -- provide time complexity for general case</li> <li>hint when k=6, O(n^3)</li> </ul> <p>She was more interested in time-complexity more than anything else.</p> <p>Does anyone know a solution that would satisfy the new constraints?</p> <hr> <p>EDIT:</p> <p>Supposedly, in the correct solution, the map is to store the elements of the input and the map is then to be used as a look up table just as in the case for <code>k=2</code>. </p> <p>When the size of the subset is 2 (i.e. <code>k=2</code>), the answer is trivial: loop through and load all the elements into a map. Then loop through the inputs again this time searching the map for <code>sum - input[i] where i is the index from 0 to n-1</code>, which would then be the answers. Supposedly this trivial case can be extended to where <code>k</code> is anything.</p>
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    1. COThere is no question here. Interesting as it is, there is no question. Are you looking for a solution taking into account the added constraints?
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    2. COQ: And your question is?
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    3. COedit to add last line: `Does anyone know a solution that would satisfy the new constraints?`
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