How does the gnome sort algorithm work?

The gnome sort algorithm, also known as the "stupid sort," is a simple sorting algorithm that works by repeatedly comparing adjacent elements and swapping them if they are in the wrong order. It gets its name from the way it moves elements through the list, similar to how a gnome would rearrange garden gnomes.

Here is how the gnome sort algorithm works:

1. Start at the first element of the list.
2. Compare the current element with the previous element.
3. If the current element is in the correct order or if it is the first element, move to the next element.
4. If the current element is in the wrong order, swap it with the previous element and move one step back.
5. Repeat steps 2-4 until the current element is in the correct order.
6. Move to the next element and repeat steps 2-6 until the end of the list is reached.

This process is repeated until the entire list is sorted. The algorithm essentially moves elements towards their correct positions by repeatedly swapping adjacent elements until no more swaps are needed.

Gnome sort has a time complexity of O(n^2) in the worst case, making it inefficient for large lists. However, it has the advantage of being easy to understand and implement, making it suitable for small lists or as a teaching tool for understanding sorting algorithms.