Stooge sort

Stooge sort is a recursive sorting algorithm with a time complexity of O(n^{log 3 / log 1.5} ) = O(n^2.7095...). The running time of the algorithm is thus slower compared to efficient sorting algorithms, such as Merge sort, and is even slower than Bubble sort, a canonical example of a fairly inefficient and simple sort.

The algorithm is defined as follows:

• If the value at the end is smaller than the value at the start, 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
• else: exit the procedure

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. However, if the code is written to end on a base case of size 1, rather than terminating on either size 1 or size 2, rounding the 2/3 of 2 upwards gives an infinite number of calls.

The algorithm gets its name from slapstick routines of The Three Stooges, in which each stooge hits the other two.

Implementation

 function stoogesort(array L, i = 0, j = length(L)-1)
     if L[j] < L[i] then
         L[i] ↔ L[j]
     if (j - i + 1) > 2 then
         t = (j - i + 1) / 3
         stoogesort(L, i  , j-t)
         stoogesort(L, i+t, j  )
         stoogesort(L, i  , j-t)
     return L

References

• Black, Paul E. "stooge sort". Dictionary of Algorithms and Data Structures. National Institute of Standards and Technology. Retrieved 2011-06-18. 
• 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. 

External links

• Everything2.com – Stooge sort
• Sorting Algorithms (including Stooge sort)
• Stooge sort – implementation and comparison