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

The provided Wolfram code defines a function called shellSort that implements the Shell sort algorithm for sorting a list of elements. Here's a step-by-step explanation of how the code works:

1. The function takes a single argument, lst, which is the list to be sorted.

2. It initializes a new list called list as a copy of the input list lst.

3. It initializes a variable called incr with the value Round[Length[list]/2]. This variable represents the initial increment to be used in the Shell sort algorithm.

4. The code enters a While loop that continues as long as incr is greater than 0.

5. Inside the loop, there is a For loop that iterates from i = incr + 1 to i <= Length[list], with an increment of 1. This loop processes each element in the list.

6. For each element at index i, it temporarily stores the value in a variable called temp and initializes j to i.

7. It enters a nested While loop that continues as long as j is greater than or equal to (incr + 1) and the element at index j - incr in the list is greater than temp. This loop finds the correct position for the element temp in the already sorted part of the list.

8. Inside the nested loop, it shifts the element at index j - incr one position to the right (i.e., list[[j]] = list[[j - incr]]). It also decrements j by incr.

9. After finding the correct position, it assigns the value of temp to the element at index j in the list (list[[j]] = temp). This effectively inserts the element temp into its sorted position.

10. After sorting all elements in the current increment, it checks if incr is equal to 2. If it is, it sets incr to 1. Otherwise, it sets incr to Round[incr/2.2], which calculates the next increment to be used in the next iteration.

11. The main While loop continues until incr becomes 0, at which point the list is fully sorted.

12. Finally, the function returns the sorted list list.

The Shell sort algorithm uses multiple increments to sort the list, improving the efficiency compared to simple insertion sort. In each increment, it sorts the elements that are incr positions apart, gradually reducing the increment until the list is completely sorted.

shellSort[ lst_ ] := Module[ {list = lst, incr, temp, i, j},
 incr = Round[Length[list]/2];
 While[incr > 0,

  For[i = incr + 1, i <= Length[list], i++,

   temp = list[[i]]; j = i;

   While[(j >= (incr + 1)) && (list[[j - incr]] > temp) ,
    list[[j]] = list[[j - incr]];  j = j-incr;
   ];

   list[[j]] = temp;];
   If[incr == 2, incr = 1, incr = Round[incr/2.2]]
];  list
]