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	${\displaystyle O(n)}$

Stooge sort is a recursive sorting algorithm. It is notable for its exceptionally bad time complexity of ${\displaystyle O(n^{\log 3/\log 1.5})}$ = ${\displaystyle O(n^{2.7095...})}$ 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]

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
 }

Haskell

-- Not the best but equal to above 

stoogesort :: (Ord a) => [a] -> [a]
stoogesort [] = []
stoogesort src = innerStoogesort src 0 ((length src) - 1)

innerStoogesort :: (Ord a) => [a] -> Int -> Int -> [a]
innerStoogesort src i j 
    | (j - i + 1) > 2 = src''''
    | otherwise = src'
    where 
        src'    = swap src i j -- need every call
        t = floor (fromIntegral (j - i + 1) / 3.0)
        src''   = innerStoogesort src'   i      (j - t)
        src'''  = innerStoogesort src'' (i + t)  j
        src'''' = innerStoogesort src''' i      (j - t)

swap :: (Ord a) => [a] -> Int -> Int -> [a]
swap src i j 
    | a > b     =  replaceAt (replaceAt src j a) i b
    | otherwise = src
    where 
        a = src !! i
        b = src !! j

replaceAt :: [a] -> Int -> a -> [a]
replaceAt (x:xs) index value
    | index == 0 = value : xs
    | otherwise  =  x : replaceAt xs (index - 1) value