Friday, 28 February 2014

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
Data structure
 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

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