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POHow to divide a line of numbers into N groups such that the sums of each group are closest to their mean?
 

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  1. POHow to divide a line of numbers into N groups such that the sums of each group are closest to their mean?
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    <p>I have the following problem: I have M numbers arranged into a line. I need to divide the line into N groups such that the sums of the numbers of each group are closest to the mean of these sums by some metric. The actual metric is not important: we can choose to minimize sum of absolute differences, or variance, etc., depending on which leads to the simplest solution.</p> <p>A similar problem is partitioning of sets, which is NP Hard. However, here we have additional constraint: groups must pack successive numbers, so there might be a solution that doesn't involve brute-force search. The numbers are large.</p> <p><strong>EDIT</strong></p> <p>Example:</p> <p>Numbers: 1 2 3 4 5 6 7 8 9 10, need to divide into 3 groups</p> <p>Let's say we want to minimize sum of absolute differences (SAD).</p> <p>Groups: (1) 1 2 3 4 5 6 (sum = 21); (2) 7 8 (sum = 15); (3) 9 10 (sum = 19)</p> <p>Mean = (21+15+19)/3 = 18.33, SAD = 21-18.33 + 18.33-15 + 19-18.33 = 6.67 &lt;- That's what we want to minimize.</p>
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      1. POHow to divide a line of numbers into N groups such that the sums of each group are closest to their mean?
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    1. COCan you give some examples of input and expected output?
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      1. POHow to divide a line of numbers into N groups such that the sums of each group are closest to their mean?
      1. USPaul
    2. COI am not sure this problem statement makes sense and I cannot understand it. You say "the sums of each group are closest to the mean of these sums": do you mean that you want to minimize the dispersion of the sums of the groups ? If this is the case, I expect that the groups will be highly imbalanced.
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      1. POHow to divide a line of numbers into N groups such that the sums of each group are closest to their mean?
      1. USYves Daoust
 

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