How does the gnome sort algorithm sort numbers?

The gnome sort algorithm sorts numbers by comparing each pair of adjacent numbers and swapping them if necessary.

The gnome sort algorithm, also known as the stupid sort, is a simple, yet effective sorting algorithm that is based on the technique used by the standard Dutch Garden Gnome (hence the name). This algorithm is similar to the insertion sort in its method of operation, but it is easier to implement.

The gnome sort algorithm begins at the first element (position 0) in the array. It then compares the current element with the next one. If the current element is smaller than the next one (or the next one is at the end of the array), it moves one step forward. If the current element is larger, it swaps the two elements and takes one step backward. If there is no previous element (it is at the start of the array), it moves one step forward.

The algorithm continues this process of stepping forward and comparing, swapping and stepping backward, until it reaches the end of the array. At this point, the algorithm will have sorted the array in ascending order.

The gnome sort algorithm is not the most efficient sorting algorithm, with a worst-case and average time complexity of O(n^2), but it has the advantage of being easy to understand and implement. It also does not require any additional space, making it an in-place sorting algorithm.

In summary, the gnome sort algorithm sorts numbers by continuously swapping adjacent elements that are in the wrong order, moving forward when elements are in the right order and backward when they are not, until the entire array is sorted. It's a simple yet effective method, much like the way a gnome would organise his garden!