Step by Step solution about How to resolve the algorithm Sorting algorithms/Cocktail sort step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram programming language code implements the Cocktail Sort algorithm, which is a simple and efficient sorting algorithm that works by repeatedly comparing and swapping adjacent elements in the list until it is completely sorted.

Here's a detailed explanation of the code:

1. Initialization:

   • A variable called swapped is initialized to True. This variable is used to track whether any swaps occurred during a pass through the list. If no swaps occur, it means the list is already sorted.

2. While Loop:

   • The code enters a while loop that continues as long as the swapped variable is True. This means that at least one swap occurred during the previous pass through the list, so we need to continue sorting.

3. First Pass:

   • Inside the while loop, there's a nested For loop that iterates from i = 1 to i < Length[A] - 1. This loop processes the elements from left to right.
   • Within this loop, the code checks if the current element A[[i]] is greater than the next element A[[i+1]].
   • If A[[i]] is greater, the two elements are swapped using the built-in function A[[i;;i+1]] = A[[i+1;;i;;-1]]. This effectively swaps the elements at indices i and i+1.
   • After swapping, the swapped variable is set to True to indicate that a swap occurred during this pass.

4. Break Condition:

   • After the first pass, the code checks if the swapped variable is still False. If it is False, it means no swaps occurred during the pass, which indicates that the list is already sorted. In this case, the Break[] statement is used to exit the while loop and stop the sorting process.

5. Second Pass (Optional):

   • If the swapped variable is True after the first pass, it means the list is not fully sorted, and a second pass is needed.
   • The While loop continues with another For loop that iterates from i = Length[A] - 1 to i > 0. This loop processes the elements from right to left.
   • Similar to the first pass, this loop checks if A[[i]] is greater than A[[i+1]] and swaps them if necessary.

6. Completion:

   • The sorting process continues until either the list is completely sorted (no swaps occur in a pass) or the second pass is finished. The final sorted list is stored in the variable A.

This code provides an efficient and straightforward implementation of the Cocktail Sort algorithm, which can be useful for sorting lists of various sizes and data types in the Wolfram environment.

cocktailSort[A_List] := Module[ { swapped = True },
While[ swapped == True,
 swapped=False;
 For[ i = 1, i< Length[A]-1,i++, 
   If[ A[[i]] > A[[i+1]], A[[i;;i+1]] = A[[i+1;;i;;-1]]; swapped=True;]
 ];
If[swapped == False, Break[]];
swapped=False;
For [ i= Length[A]-1, i > 0, i--,
  If[ A[[i]] > A[[i+1]], A[[i;;i+1]] = A[[i+1;;i;;-1]]; swapped = True;]
 ]]]