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    <p>This is an NP-hard problem. In other words, it's not possible to find an optimal solution without exploring all combinations, and the number of combinations is n^M (where M is the size of you array, and n the number of beans). It's a problem very similar to <em><a href="http://en.wikipedia.org/wiki/Cluster_analysis" rel="nofollow">clustering</a></em>, which is also NP-hard. </p> <p>If your data set is small enough to deal with, a brute force algorithm is best (explore all combinations).</p> <p>However, if your data set is big, you'll want a polynomial-time algorithm that won't get you the optimal solution, but a good approximation. In that case, I suggest you use something similar to <em><a href="http://en.wikipedia.org/wiki/K-means_clustering" rel="nofollow">K-Means</a></em>...</p> <p>Step 1. Calculate the expected sum per bin. Let <em>A</em> be your array, then the expected sum per bin is <em>SumBin = SUM(A) / n</em> (the sum of all elements in your array over the number of bins). </p> <p>Step 2. Put all elements of your array in some collection (e.g. another array) that we'll call <em>The Bag</em> (this is just a conceptual, so you understand the next steps).</p> <p>Step 3. Partition <em>The Bag</em> into <em>n</em> groups (preferably randomly, so that each element ends up in some bin <em>i</em> with probability 1/<em>n</em>). At this point, your bins have all the elements, and <em>The Bag</em> is empty.</p> <p>Step 4. Calculate the sum for each bin. If result is the same as last iteration, <strong>exit</strong>. (this is the <em>expectation</em> step of <em>K-Means</em>)</p> <p>Step 5. For each bin <em>i</em>, if its sum is greater than <em>SumBin</em>, pick the first element greater than <em>SumBin</em> and put it back in <em>The Bag</em>; if its sum is less than <em>SumBin</em>, pick the first element less than <em>SumBin</em> and put back in <em>The Bag</em>. This is the gradient descent step (aka <em>maximization</em> step) of <em>K-Means</em>.</p> <p>Step 6. Go to step 3.</p> <p>This algorithm is just an approximation, but it's fast and guaranteed to converge.</p> <p>If you are skeptical about a randomized algorithm like the above, after the first iteration when you are back to step 3, instead of assigning elements randomly, you can do so optimally by running the <em><a href="http://en.wikipedia.org/wiki/Assignment_problem" rel="nofollow">Hungarian algorithm</a></em>, but I am not sure that will guarantee better over-all results. </p>
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    1. POGrouping arbitrary arrays of data into N bins
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    1. POGrouping arbitrary arrays of data into N bins
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    1. COAssuming that `P != NP`, you should add :P
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      1. USNiklas B.
    2. COHaha. http://stackoverflow.com/questions/3461980/p-np-question
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