Gnome sort

Gnome sort
Visualisation of Gnome sort.
Class Sorting algorithm
Data structure Array
Worst-case performance
Best-case performance
Average performance
Worst-case space complexity auxiliary

Gnome sort (dubbed Stupid sort) is a sorting algorithm originally proposed by an Iranian computer scientist Hamid Sarbazi-Azad (Professor of Computer Engineering at Sharif University of Technology) in 2000 and called "stupid sort"[1] (not to be confused with bogosort), and then later on described by Dick Grune and named "gnome sort".[2]

It 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 average, or expected, running time is O(n2), but tends towards O(n) if the list is initially almost sorted.[3][note 1]

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 next to 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 previous to the swapped elements.

Description

Dick Grune described the sorting method with the following story:[2]

Gnome Sort is based on the technique used by the standard Dutch Garden Gnome (Du.: tuinkabouter).
Here is how a garden gnome sorts a line of flower pots.
Basically, he looks at the flower pot next to him and the previous one; if they are in the right order he steps one pot forward, otherwise, he swaps them and steps one pot backward.
Boundary conditions: if there is no previous pot, he steps forwards; if there is no pot next to him, he is done.

— "Gnome Sort - The Simplest Sort Algorithm". Dickgrune.com

Code

C#

An implementation in C#:

	public static void gnomeSort(int[] anArray)
	{
		int first = 1;

		while (first < anArray.Length)
		{
			if (anArray[first - 1] <= anArray[first]) 
			{
				first ++;
			} 
			else
			{
				int tmp = anArray[first - 1];
				anArray[first - 1] = anArray[first];
				anArray[first] = tmp;
				if (-- first == 0)
				{
					first = 1;
				}
			}

		}
	}

Here is pseudocode for the gnome sort using a zero-based array:

procedure gnomeSort(a[]):
    pos := 0
    while pos < length(a):
        if (pos == 0 or a[pos] >= a[pos-1]):
            pos := pos + 1
        else:
            swap a[pos] and a[pos-1]
            pos := pos - 1

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 pos Condition in effect Action to take
[5, 3, 2, 4]0pos == 0increment pos
[5, 3, 2, 4]1a[pos] < a[pos-1]swap, decrement pos
[3, 5, 2, 4]0pos == 0increment pos
[3, 5, 2, 4]1a[pos] ≥ a[pos-1]increment pos
[3, 5, 2, 4]2a[pos] < a[pos-1]swap, decrement pos
[3, 2, 5, 4]1a[pos] < a[pos-1]swap, decrement pos
[2, 3, 5, 4]0pos == 0increment pos
[2, 3, 5, 4]1a[pos] ≥ a[pos-1]increment pos
[2, 3, 5, 4]2a[pos] ≥ a[pos-1]increment pos:
[2, 3, 5, 4]3a[pos] < a[pos-1]swap, decrement pos
[2, 3, 4, 5]2a[pos] ≥ a[pos-1]increment pos
[2, 3, 4, 5]3a[pos] ≥ a[pos-1]increment pos
[2, 3, 4, 5]4pos == length(a)finished

Optimization

The gnome sort may be optimized by introducing a variable to store the position before traversing back toward the beginning of the list. With this optimization, the gnome sort would become a variant of the insertion sort.

Here is pseudocode for an optimized gnome sort using a zero-based array:

1 procedure optimizedGnomeSort(a[]):
2     for pos in 1 to length(a):
3         gnomeSort(a, pos)
4 
5 procedure gnomeSort(a[], upperBound):
6     pos := upperBound
7     while pos > 0 and a[pos-1] > a[pos]:
8         swap a[pos-1] and a[pos]
9         pos := pos - 1

Notes

  1. ↑ ‘Almost sorted’ means here each item in the list is not farther than some small constant distance from its proper position.

References

  1. ↑ Sarbazi-Azad, Hamid (2 October 2000). "Stupid Sort: A new sorting algorithm" (PDF). Newsletter. Computing Science Department, Univ. of Glasgow (599): 4. Retrieved 25 November 2014.
  2. 1 2 "Gnome Sort - The Simplest Sort Algorithm". Dickgrune.com. 2000-10-02. Retrieved 2017-07-20.
  3. ↑ Paul E. Black. "gnome sort". Dictionary of Algorithms and Data Structures. U.S. National Institute of Standards and Technology. Retrieved 2011-08-20.
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