Data structure Array | ||
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Worst-case performance O ( n 2 ) {\displaystyle O(n^{2})} Best-case performance Ω ( n ) {\displaystyle \Omega (n)} Average performance O ( n 2 ) {\displaystyle O(n^{2})} Worst-case space complexity O ( 1 ) {\displaystyle O(1)} auxiliary | ||
Gnome sort (or Stupid sort) is a sorting algorithm originally proposed by an Iranian computer engineer Dr. Hamid Sarbazi-Azad (Professor of Computer Engineering at Sharif University of Technology) in 2000 and called "stupid sort" (not to be confused with bogosort), and then later on described by Dick Grune and named "gnome sort". 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.
Contents
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
Here is pseudocode for the gnome sort using a zero-based array:
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:
Optimization
The gnome sort may be optimized by introducing a variable to store the position before traversing back toward the beginning of the list. This would allow the "gnome" to teleport back to his previous position after moving a flower pot. With this optimization, the gnome sort would become a variant of the insertion sort. The animation in the introduction to this topic takes advantage of this optimization.
Here is pseudocode for an optimized gnome sort using a zero-based array: