Gnome Sort

Gnome Sort

Gnome sort (Stupid sort), originally proposed by Hamid Sarbazi-Azad in 2000 and called Stupid sort (not to be confused with Bogosort), and then later on described by Dick Grune and named "Gnome sort",^[1] is a sorting algorithm which is similar to insertion sort, except that moving an element to its proper place is accomplished by a series of swaps, as in bubble sort. It is conceptually simple, requiring no nested loops. The running time is O , but tends towards O(n) if the list is initially almost sorted.^[2] In practice the algorithm can run as fast asInsertion sort^{[citation needed]}. The average runtime is  .

The algorithm always finds the first place where two adjacent elements are in the wrong order, and swaps them. It takes advantage of the fact that performing a swap can introduce a new out-of-order adjacent pair only right before or after the two swapped elements. It does not assume that elements forward of the current position are sorted, so it only needs to check the position directly before the swapped elements.

Class	Sorting algorithm
Data structure	Array
Worst case performance
Best case performance
Average case performance
Worst case space complexity	auxiliary

Example

Given an unsorted array, a = [5, 3, 2, 4], the gnome sort would take the following steps during the while loop. The "current position" is highlighted in bold:

Current array	Action to take
[5, 3, 2, 4]	a[pos] < a[pos-1], swap:
[3, 5, 2, 4]	a[pos] >= a[pos-1], increment pos:
[3, 5, 2, 4]	a[pos] < a[pos-1], swap and pos > 1, decrement pos:
[3, 2, 5, 4]	a[pos] < a[pos-1], swap and pos <= 1, increment pos:
[2, 3, 5, 4]	a[pos] >= a[pos-1], increment pos:
[2, 3, 5, 4]	a[pos] < a[pos-1], swap and pos > 1, decrement pos:
[2, 3, 4, 5]	a[pos] >= a[pos-1], increment pos:
[2, 3, 4, 5]	a[pos] >= a[pos-1], increment pos:
[2, 3, 4, 5]	pos == length(a), finished.

Algorithm

procedure optimizedGnomeSort(a[])

    pos := 1

    last := 0

    while pos < length(a)

        if (a[pos] >= a[pos-1])

            if (last != 0)

                pos := last

                last := 0

            end if

            pos := pos + 1

        else

            swap a[pos] and a[pos-1]

            if (pos > 1)

                if (last == 0)

                    last := pos

                end if

                pos := pos - 1

            else

                pos := pos + 1

            end if

        end if

    end while

end procedure