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POFinding a good match of two lists of numbers
 

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  1. POFinding a good match of two lists of numbers
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    <p>I got two sets of numbers, with <strong>SET2</strong> having more items in it usually. It's guaranteed that the count of <strong>SET2</strong> is equal or greater than the count of <strong>SET1</strong>. Acutally, since the order matters the input are rather lists than sets.</p> <p>My goal is to combine (sum up) / reorder the numbers from <strong>SET2</strong> to make it as similar to <strong>SET1</strong> as possible. I define the similarity as the sum of the deviations at every position. See <a href="https://stackoverflow.com/questions/14480336/more-efficient-way-to-build-sum-than-for-loop/14480404#14480404">this post</a> for the way I calculate the similarity. The smaller the sum, the better. </p> <p>My first approach was to try all combinations and pick the best one. This only works for quite small sets (esp. the second one). See <a href="https://stackoverflow.com/questions/14438404/pool-numbers-in-a-set-of-numbers-to-match-the-size-of-another-set/14440778#14440778">this post</a> and the answer from Rawling. Is there a smarter way to get a good combination? I definitely don't need the best one. A good one would be fine as a result. Obviously a sets with empty subsets are nonsense. Extremly unbalanced sets don't seem to be very promising to me. SET1 tends to have about 8 but can have up to 18 entries. SET2 has often a count of more than 10 (up to 35). The sum of the numbers in the two sets is equal (except for rounding errors). </p> <p>Here is an example with good and bad results (not all possible ones):</p> <pre><code>SET1 = { 272370, 194560, 233430 }; SET2 = { 53407.13, 100000, 365634.03, 181319.07 } 272370 | 194560 | 233430 --------------------------------------------------------------------- 365634.03 | 100000 + 53407.13 | 181319.07 (best match) 365634.03 | 181319.07 | 100000 + 53407.13 (good) 365634.03 | 100000 |181319.07 + 53407.13 (ok) 53407.13 |365634.03 + 100000 | 181319.07 (bad) 53407.13 |365634.03 + 181319.07 | 100000 (bad) . |365634.03 + 181319.07 | 53407.13 + 100000 (invalid) 53407.13 + 100000 |365634.03 + 181319.07 | (invalid) </code></pre> <p>Please let me know if I forgot to describe a premiss or my description is unclear or even faulty. I'm also happy to provide another example. </p> <p>Thanks in advance!</p>
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    1. COAre you looking for optimal answer or for fast heuristic?
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    2. COA fast heuristic would be perfect. Especially since an exhaustive calculation is not possible. Thanks for the comment @Ari.
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