How does the gnome sort algorithm function?

The Gnome Sort algorithm functions by comparing adjacent elements and swapping them if they are in the wrong order.

Gnome Sort, also known as Stupid Sort, is a simple, yet effective sorting algorithm that works in a similar way to the Bubble Sort. It is called Gnome Sort because it mimics the way a garden gnome would sort a line of flower pots. The gnome starts at the beginning of the line and compares the current pot with the next one. If they are in the right order, the gnome steps forward. If they are in the wrong order, the gnome swaps them and steps back to compare the swapped pot with the previous one. This process continues until the gnome reaches the end of the line, at which point all the pots are sorted.

The algorithm begins at the first element of an array. It compares the current element with the next one. If the current element is smaller than the next one (meaning they are in the correct order), it moves to the next element. If the current element is larger (meaning they are in the wrong order), it swaps the two elements and then moves back one element to compare the swapped element with the previous one. This is because the swapped element could still be larger than the previous one, so it needs to be checked again.

This process continues, with the algorithm moving forward when elements are in the right order and moving back when they are in the wrong order, until it reaches the end of the array. At this point, all the elements have been sorted into their correct order.

Gnome Sort is not the most efficient sorting algorithm, with a worst-case time complexity of O(n^2), but it is easy to understand and implement. It is also an example of a stable sort, meaning that it maintains the relative order of equal sort items. This can be important in certain applications where the original order of equal elements needs to be preserved.