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PORearranging a sequence to maximize difference in order, ruby
 

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  1. PORearranging a sequence to maximize difference in order, ruby
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    <p>I have an ordered sequence in the form of an array. e.g.</p> <pre><code>original_order = [1,2,3,4,5,6,7,8,9,10] </code></pre> <p>I want to know how to re-order the sequence, with the maximum difference in order, with regard to the original order. Specifically, I want to know what order would give the Maximum "score", when running the code below:</p> <p>Put simply, the below calculates the distance that each value from the sequence has "moved" in the rearranged sequence (array called rearranged), when compared to its position in the original_order sequence. It then sums the differences (distances moved) for each value, to give an overall score of "difference in order" for the rearrangement. Someone told me that this "score" I am calculating can be defined as the ordinal similarity between the two sequences (original order and rearranged).</p> <p>I think the max score can be obtained by running the code with the rearranged order as the <strong>reversed</strong> original order. I have not found a method of rearrangement that has a higher score than this, though If anyone thinks I am wrong please let me know (for the example original_order above this would be max_score = 50). I think that no other rearrangement of the sequence order can give a higher score (although there are other orders that give the same score).</p> <pre><code>position = original_order.map{|x| rearranged.index(x)} #works out the index of original_order values in rearranged index_values = Array(0..(original_order.length - 1)) # array of index values for original_order both = [] both &lt;&lt; position both &lt;&lt; index_values difference = both.transpose.map {|x| x.reduce(:-)} # taking away old position from new position, to find the distance that the value has "moved" when re-ordered difference_abs = [] difference.each do |i| difference_abs &lt;&lt; i.abs end score = difference_abs.inject(:+) </code></pre> <p>What I would like to know is:</p> <ol> <li><p>if my hypothesis that the reversed order will always give the highest possible score, regardless of the length of the sequence array, is correct</p></li> <li><p>a mathematical explanation of what my code does, and why simply reversing the original order gives the highest possible score</p></li> <li><p>if ordinal similarity is an accurate way of defining my score metric, and if not, what is?</p></li> </ol> <p>Also, any tips on simplifying my code are welcome.</p>
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    1. USAbhishek Bansal
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    1. COI think you are misusing the word "disorder". It means something else. Use another word, like "rearrangement", "replacement", etc. Also, do not show a chunk of code before explaining what it is. Don't expect people to read through your messy code. You should explain the idea of maximum score before showing the code.
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      1. USsawa
    2. CO@sawa Thanks for the input, I have made the changes you suggested.
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    3. COIt looks better.
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