Stooge sort

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.

 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  } 

-- 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 

• Black, Paul E. "stooge sort". Dictionary of Algorithms and Data Structures. National Institute of Standards and Technology. Retrieved 18 June 2011.
• Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001) [1990]. "Problem 7-3". Introduction to Algorithms (2nd ed.). MIT Press and McGraw-Hill. pp. 161–162. ISBN 0-262-03293-7.

• Sorting Algorithms (including Stooge sort)
• Stooge sort – implementation and comparison

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