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

This Wolfram code snippet defines two functions, compress and decompress, that implement the Lempel-Ziv-Welch (LZW) compression algorithm, which is a lossless data compression algorithm that is used in many popular file formats like GIF and TIFF.

The compress function takes an uncompressed string as input and returns a compressed string. The function begins by initializing a dictionary of size 256, which maps each ASCII character to itself. The algorithm iteratively scans the input string and constructs a prefix code for every substring that it encounters. The prefix code for a substring is the code for the longest prefix of the substring that is already in the dictionary. If the substring is not in the dictionary, a new entry is added to the dictionary, and the code for the new entry is used to represent the substring. The compressed string is constructed by concatenating the codes for the substrings in the input string.

The decompress function takes a compressed string as input and returns the decompressed string. The function begins by initializing a dictionary of size 256, which maps each ASCII character to itself. The algorithm iteratively decodes the compressed string by reading a code and looking up the corresponding string in the dictionary. The decoded string is constructed by concatenating the strings that are looked up in the dictionary.

The following example illustrates how to use the compress and decompress functions:

compress["TOBEORNOTTOBEORTOBEORNOT"]
decompress[%]

The output of the above code is TOBEORNOTTOBEORTOBEORNOT.

compress[uncompressed_] :=
  Module[{dictsize, dictionary, w, result, wc},
   dictsize = 256;
   dictionary = # -> # & /@ FromCharacterCode /@ Range@dictsize;
   w = "";
   result = {};
   Do[wc = w <> c;
    If[MemberQ[dictionary[[All, 1]], wc],
     w = wc,
     AppendTo[result, w /. dictionary];
     AppendTo[dictionary, wc -> dictsize];
     dictsize++;
     w = c],
    {c, Characters[uncompressed]}];
   AppendTo[result, w /. dictionary];
   result];
decompress::bc = "Bad compressed `1`";
decompress[compressed_] :=
  Module[{dictsize, dictionary, w, result, entry},
   dictsize = 256;
   dictionary = # -> # & /@ FromCharacterCode /@ Range@dictsize;
   w = result = compressed[[1]];
   Do[Which[MemberQ[dictionary[[All, 1]], k],
     entry = k /. dictionary,
     k == dictsize,
     entry = w <> StringTake[w, 1],
     True,
     Message[decompress::bc, k]];
    result = result <> entry;
    AppendTo[dictionary, dictsize -> w <> StringTake[entry, 1]];
    dictsize++;
    w = entry,
    {k, compressed[[2 ;;]]}];
   result];
(*How to use:*)
compress["TOBEORNOTTOBEORTOBEORNOT"]
decompress[%]