Step by Step solution about How to resolve the algorithm Sorting algorithms/Gnome sort step by step in the C programming language

The provided C code implements the Gnome Sort algorithm, an in-place sorting algorithm known for its simplicity and efficiency for smaller datasets. Here's a detailed explanation of how it works:

1. Initialization:

   • The function gnome_sort takes two parameters: a, an array of integers, and n, the number of elements in the array.
   • It initializes two integer variables: i to 1 and j to 2 as indices used to track the current and next elements to compare.
   • It also defines a macro swap(i, j) that swaps the elements at indices i and j in the array a.

2. Sorting Loop:

   • The main sorting loop continues as long as i is less than n, indicating that there are still elements to sort.

   • Inside the loop:

     • It compares the current element a[i-1] with the next element a[i]. If a[i-1] is greater than a[i], this indicates that the elements are out of order.

     • In this case, it swaps a[i-1] and a[i] using the swap macro.

     • After swapping, it decrements i by 1. This ensures that it rechecks the element at a[i-1] again.

     • If i is now less than 1 (i.e., it's the first element in the array), it continues to the next iteration of the loop without decrementing i.

     • Otherwise, it sets i to j, which is incremented by 1 in each iteration, effectively moving both indices to the next two elements to be checked.

3. Loop Exit:

   • The loop continues this process until it reaches the end of the array (i.e., i becomes greater than or equal to n).

4. Finalization:

   • After the sorting is complete, the function does not need to explicitly return anything since the changes are made in-place.

5. Macro Cleanup:

   • The macro swap(i, j) is undefined at the end of the function using #undef swap. This is usually done to prevent accidental usage of the macro outside the function.

void gnome_sort(int *a, int n)
{
  int i=1, j=2, t;
# define swap(i, j) { t = a[i]; a[i] = a[j]; a[j] = t; } 
  while(i < n) {
    if (a[i - 1] > a[i]) {
      swap(i - 1, i);
      if (--i) continue;
    }
    i = j++;
  }
# undef swap
}