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

The provided Wolfram Mathematica code defines a function called countingSort that performs counting sort on a given list. Counting sort is a sorting algorithm that works by counting the number of occurrences of each distinct element in the input and then using these counts to determine the final sorted order of the elements.

Here's a step-by-step explanation of the code:

1. Function Input: The countingSort function takes a single argument, list, which is the input list that needs to be sorted.

2. Initialization:

   • minElem: This variable is initialized to the minimum element in the input list using the Min function.
   • maxElem: This variable is initialized to the maximum element in the input list using the Max function.
   • count: This is an array of zeros of length (maxElem - minElem + 1). It will store the count of each distinct element in the input list.

3. Counting the Occurrences:

   • The code uses a For loop to iterate through each element in the input list.
   • For each element, it increments the corresponding count in the count array.

4. Sorting:

   • The code uses another For loop to iterate through each distinct element (from the minimum to maximum).
   • Inside this loop, it uses a While loop to place the copies of the current element into the sorted output list.
   • The count of the current element is decremented after each placement, and the position in the output list is incremented.

5. Returning the Sorted List:

   • The function returns the sorted list.

To use the countingSort function, you can pass the input list as an argument and assign the result to a variable, like this:

sortedList = countingSort[list];

Counting sort is particularly efficient for sorting lists with a small number of distinct elements or when the range of values is relatively small.

countingSort[list_] := Module[{minElem, maxElem, count, z, number},
  minElem = Min[list]; maxElem = Max[list];
  count = ConstantArray[0, (maxElem - minElem + 1)];
  For[number = 1, number < Length[list], number++, 
   count[[number - minElem + 1]] = count[[number - minElem + 1]] + 1;] ;
  z = 1;
  For[i = minElem, i < maxElem, i++, 
   While[count[[i - minElem + 1]] > 0,
    list[[z]] = i; z++;
    count[[i - minElem + 1]] = count[[i - minElem + 1]] - 1;]
   ];   
  ]