Step by Step solution about How to resolve the algorithm Order disjoint list items step by step in the Mathematica/Wolfram Language programming language

This Wolfram programming language source code defines a function order that takes two arguments: a list m and a list of elements n to be ordered. It rearranges the elements in m according to the order specified in n while keeping the remaining elements in their original positions. The output is a string representation of the reordered list.

Here's a breakdown of the code:

1. order[m_, n_] :=: This line defines the order function with two parameters: m (the original list) and n (the list of elements to be ordered).

2. ReplacePart[m, ...]: This line uses the ReplacePart function to modify the original list m.

3. MapThread[Rule, ...]: This part generates rules that specify how the elements in m should be reordered. It uses the MapThread function to apply the Rule function to each pair of corresponding positions and elements from m and n.

   • Position[m, Alternatives @@ n][[;; Length[n]]]: This part identifies the positions of the elements in m that match any of the elements in n (using the Alternatives @@ n expression). It then takes the first Length[n] positions, ensuring that only the necessary elements are reordered.
   • {Position[m, Alternatives @@ n][[;; Length[n]]], n}: This part creates a list of rules where each rule assigns an element from n to the corresponding position in m.

4. Print[StringRiffle[...]: This line prints the string representation of the reordered list using the StringRiffle function, which concatenates the elements with an empty string as a separator.

5. order[{"the", "cat", "sat", "on", "the", "mat"}, {"mat", "cat"}]]: This line reorders the list {"the", "cat", "sat", "on", "the", "mat"} according to the order specified in {"mat", "cat"} and prints the resulting list.

6. The following lines similarly reorder and print other lists, demonstrating the functionality of the order function with different input lists:

   • {"the", "cat", "sat", "on", "the", "mat"} reordered by {"cat", "mat"}
   • {"A", "B", "C", "A", "B", "C", "A", "B", "C"} reordered by {"C", "A", "C", "A"}
   • {"A", "B", "C", "A", "B", "D", "A", "B", "E"} reordered by {"E", "A", "D", "A"}
   • {"A", "B"} reordered by {"B"}
   • {"A", "B"} reordered by {"B", "A"}
   • {"A", "B", "B", "A"} reordered by {"B", "A"}

order[m_, n_] := 
  ReplacePart[m, 
   MapThread[
    Rule, {Position[m, Alternatives @@ n][[;; Length[n]]], n}]];
Print[StringRiffle[
   order[{"the", "cat", "sat", "on", "the", "mat"}, {"mat", 
     "cat"}]]];
Print[StringRiffle[
   order[{"the", "cat", "sat", "on", "the", "mat"}, {"cat", 
     "mat"}]]];
Print[StringRiffle[
   order[{"A", "B", "C", "A", "B", "C", "A", "B", "C"}, {"C", "A", 
     "C", "A"}]]];
Print[StringRiffle[
   order[{"A", "B", "C", "A", "B", "D", "A", "B", "E"}, {"E", "A", 
     "D", "A"}]]];
Print[StringRiffle[order[{"A", "B"}, {"B"}]]];
Print[StringRiffle[order[{"A", "B"}, {"B", "A"}]]];
Print[StringRiffle[order[{"A", "B", "B", "A"}, {"B", "A"}]]];