Stooge sort

Stooge sort is a recursive sorting algorithm. It is notable for its exceptionally bad time complexity of O(nlog 3 / log 1.5 ) = O(n2.7095...). The running time of the algorithm 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).
ClassSorting algorithm
Data structureArray
Worst-case performanceO(nlog 3/log 1.5)
Worst-case space complexityO(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 3 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

 
 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
         L[i] ↔ L[j]           // Swap the leftmost element and the rightmost element
     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
 }

References
  1. "CSE 373" (PDF). courses.cs.washington.edu. Retrieved 14 September 2020.

Sources
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