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    <p>Since the size of the array is just 14, so i won't work upon optimization. Your problem can be solved by finding all <strong>combinations using <code>bitwise operations</code></strong>. </p> <p>The idea is: Generate all the subsets of a given array (set), this set is known as a power set .For each of the subset(Combination), check whether the summations of the element(s) of the subset equals 40 or not.</p> <p>Refer the following tutorials, to learn, <strong><em>how can you find all combinations using Bit Wise Operations</em></strong>. <a href="http://www.codechef.com/wiki/tutorial-bitwise-operations" rel="nofollow">http://www.codechef.com/wiki/tutorial-bitwise-operations</a></p> <p>The C++ implementation: </p> <pre><code>int main() { int A[] = { 1, 7, 7, 4, 6, 5, 5, 2, 4, 7, 10, 3, 9, 6 }; int n = sizeof(A) / sizeof(A[0]); int desiredsum = 40; int total_soln=0; for (int i = 0; i &lt;= (1 &lt;&lt; n); ++i) { vector &lt; int &gt;v;/*The vector contains element of a subset*/ for (int j = 0; j &lt;= n; ++j) { if (i &amp; 1 &lt;&lt; j) v.push_back(A[j]); } if (v.size() == 8)/*Check whether the size of the current subset is 8 or not*/ { //if size is 8, check whether the sum of the elements of the current // subset equals to desired sum or not int sum = 0; for (int j = 0; j &lt; v.size(); ++j) { sum += v[j]; } if (sum == desiredsum) { for (int j = 0; j &lt; v.size(); ++j) { (j == v.size() - 1) ? cout &lt;&lt; v[j] &lt;&lt; "=" : cout &lt;&lt; v[j] &lt;&lt; "+"; } total_soln++; cout &lt;&lt; desiredsum &lt;&lt; " " &lt;&lt; endl; } } } cout&lt;&lt;"Total Solutions: "&lt;&lt;total_soln&lt;&lt;endl; return 0; } </code></pre> <p>IDEONE LINK: <a href="http://ideone.com/31jh6c" rel="nofollow">http://ideone.com/31jh6c</a></p>
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