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    <p>The problem you are facing is a well known and studied one, and is called <strong><a href="http://en.wikipedia.org/wiki/Subset_sum_problem" rel="nofollow">The Subset Sum Problem</a></strong>.</p> <p>Unfortunately, the problem is <a href="http://en.wikipedia.org/wiki/NP-complete" rel="nofollow">NP-Complet</a>e, so <strong>there is no known polynomial solution for it</strong><sup>1</sup>. <br>In fact, there is no known polynomial solution to even determine if such a subset (even a single one) exists, let alone find it.</p> <p>However, if your input consists of relatively small (absolute value) integers, there is a pretty efficient (pseudo polynomial) <a href="http://en.wikipedia.org/wiki/Subset_sum_problem#Pseudo-polynomial_time_dynamic_programming_solution" rel="nofollow"><strong>dynamic programming solution</strong></a> that can be utilized to solve the problem.</p> <p>If this is not the case some <strong>other alternatives</strong> are:</p> <ol> <li>Using exponential solution like <a href="http://en.wikipedia.org/wiki/Brute-force_search" rel="nofollow">brute force</a> (you might be able to optimize it using <a href="http://en.wikipedia.org/wiki/Branch_and_bound" rel="nofollow">branch and bound</a> technique)</li> <li>Heuristical solutions, such as <a href="https://en.wikipedia.org/wiki/Hill_climbing" rel="nofollow">Steepest Ascent Hill Climbing</a> or <a href="http://en.wikipedia.org/wiki/Genetic_algorithm" rel="nofollow">Genethic Algorithm</a>s.</li> <li><a href="http://en.wikipedia.org/wiki/Subset_sum_problem#Polynomial_time_approximate_algorithm" rel="nofollow">Approximation algorithm</a>s</li> </ol> <hr> <p>(1) And most computer science researchers believe one does not exist, this is basically the <a href="https://en.wikipedia.org/wiki/P_versus_NP_problem" rel="nofollow">P VS NP Problem</a>.</p>
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    1. COThanks, I was afraid of this. I'm going to research the articles you suggested!
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