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

The provided code implements the gnome sort algorithm in C++. Here's a detailed explanation of how it works:

1. ** gnome_sort Function:**

   • The gnome_sort function is a generic function that takes two RandomAccessIterator arguments, begin and end, which define the range of elements to be sorted.

2. Initializations:

   • i is initialized to point to the second element (begin + 1) in the range.
   • j is initialized to point to the third element (begin + 2).

3. Sorting Loop:

   • The loop continues as long as i is not past the end of the range (i < end).

4. Comparison:

   • If the current element (*i) is less than or equal to the previous element (*(i - 1)), the algorithm swaps the two elements using std::iter_swap(i - 1, i), and decrements i to compare the previous element again.

5. Shifting:

   • If the current element is greater than the previous element (!(*i < *(i - 1))), i is incremented by 1, and j is also incremented by 1. This effectively "shifts" the comparison window forward by one element.

6. Resetting:

   • If i reaches the beginning of the range (i == begin), the comparison window is reset by setting i to j and incrementing j by 1. This prevents the algorithm from getting stuck in an infinite loop when it encounters a large number of unsorted elements at the beginning of the range.

7. Output:

   • In the main function, an array a is initialized with unsorted integers.
   • The gnome_sort function is called to sort the array in place.
   • The sorted array is then printed to the console using std::ostream_iterator.

Example: Suppose we have an unsorted array a as follows: {100, 2, 56, 200, -52, 3, 99, 33, 177, -199}.

• In the first iteration, i is 2 and j is 3. The current element a[2] (56) is greater than the previous element a[1] (2), so the comparison window shifts forward.
• In the second iteration, i is 3 and j is 4. The current element a[3] (200) is again greater than the previous element, so the window shifts forward.
• The process continues until a[8] is compared to a[7]. Since a[8] is less than a[7], the elements are swapped and i is decremented to compare a[7] again, but this time with a[8].
• This backtracking and swapping process continues until the entire range is sorted.
• Finally, the sorted array a is printed to the console: {-199, -52, 2, 3, 33, 56, 99, 100, 177, 200}.

#include <algorithm>
#include <iterator>
#include <iostream>

template<typename RandomAccessIterator>
void gnome_sort(RandomAccessIterator begin, RandomAccessIterator end) {
  auto i = begin + 1;
  auto j = begin + 2;
 
  while (i < end) {
    if (!(*i < *(i - 1))) {
      i = j;
      ++j;
    } else {
      std::iter_swap(i - 1, i);
      --i;
      if (i == begin) {
        i = j;
        ++j;
      }
    }
  }
}

int main() {
  int a[] = {100, 2, 56, 200, -52, 3, 99, 33, 177, -199};
  gnome_sort(std::begin(a), std::end(a));
  copy(std::begin(a), std::end(a), std::ostream_iterator<int>(std::cout, " "));
  std::cout << "\n";
}