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POCounting the adjacent swaps required to convert one permutation into another
 

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    <blockquote> <p>We're given two sequences of lowercase latin alphabet letters. They're both the same length and have the same amount of given types of letters (the first has an equal number of t's as the second and so on). We are required to find the minimum number of swaps (<em>by "swap" we mean changing the order of two <strong>neighboring</strong></em> letters) required to transform the first sequence into the second. We can safely assume every two sequences CAN be transformed into each other. We could do this with brute-force, but the sequences are too long for that.</p> <p><strong>Input:</strong><br> The length of the sequences (at least 2, at most 999999) and then two sequences.</p> <p><strong>Output:</strong><br> An integer representing the number of swaps needed for the sequences to become the same.</p> <p><strong>Example:</strong><br> {5, aaaaa, aaaaa} should output {0},<br> {4, abcd, acdb} should output {2}.</p> </blockquote> <p>The first thing that came to my mind was bubblesort. We can simply bubblesort the sequence counting each swap. The problem is: a) it's O(n^2) worst-case b) I'm not convinced it would give me the smallest number for every case... Even the optimized bubblesort doesn't seem to be doing the trick. We could implement the cocktail sort which would solve the problem with turtles - but will it give me the best performance? Or maybe there's something simpler/faster?</p> <p>This question can also be phrased as: <strong>How can we determine the edit distance between two strings when the only operation allowed is transposition?</strong></p>
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    1. CONot really, prof gave us this today and before we got to work, the bell rang. It's not our homework but I find it interesting and would like to find out the way to solve it.
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    2. COpossible duplicate of [Minimum number of swaps needed to change Array 1 to Array 2?](http://stackoverflow.com/questions/2987605/minimum-number-of-swaps-needed-to-change-array-1-to-array-2)
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    3. CONo, it's not. There, you can swap any two cells - here, only the adjacent.
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