Stooge sort

Stooge sort is a recursive sorting algorithm. It is notable for its exceptionally poor time complexity of ${\displaystyle O(n^{\log 3/\log 1.5})}$ = ${\displaystyle O(n^{2.7095...})}$ The algorithm's running time is thus slower compared to reasonable sorting algorithms, and is slower than bubble sort, a canonical example of a fairly inefficient sort. It is, however, more efficient than Slowsort. The name comes from The Three Stooges.^[1]

Stooge sort

Visualization of Stooge sort (only shows swaps).
Class	Sorting algorithm
Data structure	Array
Worst-case performance	${\displaystyle O(n^{\log 3/\log 1.5})}$
Worst-case space complexity	${\displaystyle O(n)}$

The algorithm is defined as follows:

• If the value at the start is larger than the value at the end, swap them.
• If there are three or more elements in the list, then:
  • Stooge sort the initial 2/3 of the list
  • Stooge sort the final 2/3 of the list
  • Stooge sort the initial 2/3 of the list again

It is important to get the integer sort size used in the recursive calls by rounding the 2/3 upwards, e.g. rounding 2/3 of 5 should give 4 rather than 3, as otherwise the sort can fail on certain data.

Implementation

Pseudocode

 function stoogesort(array L, i = 0, j = length(L)-1){
     if L[i] > L[j] then       // If the leftmost element is larger than the rightmost element
         swap(L[i],L[j])       // Then swap them
     if (j - i + 1) > 2 then   // If there are at least 3 elements in the array
         t = floor((j - i + 1) / 3)
         stoogesort(L, i, j-t) // Sort the first 2/3 of the array
         stoogesort(L, i+t, j) // Sort the last 2/3 of the array
         stoogesort(L, i, j-t) // Sort the first 2/3 of the array again
     return L
 }