Step by Step solution about How to resolve the algorithm Best shuffle step by step in the Mathematica / Wolfram Language programming language

Purpose:

The provided Wolfram language code is designed to perform the "Best Shuffle" algorithm, which aims to rearrange characters in a string such that each letter is as close as possible to its original position in the string.

Algorithm:

The Best Shuffle algorithm works as follows:

1. String Split: Convert the input string data into a list of individual characters using StringSplit.
2. Permutation Generation: Generate all possible permutations of these characters using Permutations.
3. Hamming Distance: Calculate the Hamming distance (the number of positions where two strings differ) between each permutation and the original string data.
4. Sorting: Sort the list of permutations based on the Hamming distance.
5. Result Selection: The permutation with the lowest Hamming distance is considered the "best shuffle."
6. Reconstruction: Flatten the best shuffle permutation and the original string data to obtain the shuffled string.

Usage:

The BestShuffle function is applied to an input string data to generate the best shuffle. The generated shuffle is then printed in a specific format:

<original string>, <shuffled string>, (<Hamming distance>)

Example Usage:

The code includes examples of applying the Best Shuffle algorithm to various strings:

• "abracadabra": Best shuffle: "braadcaraab", Hamming distance: 5
• "seesaw": Best shuffle: "seeasw", Hamming distance: 1
• "elk": Best shuffle: "kel", Hamming distance: 2
• "grrrrrr": Best shuffle: "rrrrrr", Hamming distance: 0
• "up": Best shuffle: "pu", Hamming distance: 1
• "a": Best shuffle: "a", Hamming distance: 0

BestShuffle[data_] := 
 Flatten[{data,First[SortBy[
     List[#, StringLength[data]-HammingDistance[#,data]] & /@ StringJoin /@ Permutations[StringSplit[data, ""]], Last]]}] 

Print[#[[1]], "," #[[2]], ",(", #[[3]], ")"] & /@  BestShuffle /@ {"abracadabra","seesaw","elk","grrrrrr","up","a"}