Summary of comparison-based sorting algorithms

Here is a summary of the algorithms we have considered:

	strategy	objects	worst case	average case
algorithm	employed	manipulated	complexity	complexity
Selection Sort	Selection	arrays	$O(n^2)$	$O(n^2)$
Insertion Sort	Insertion	arrays/lists	$O(n^2)$	$O(n^2)$
Bubblesort	Exchange	arrays	$O(n^2)$	$O(n^2)$
Heapsort	Selection	arrays	$O(n \log n)$	$O(n \log n)$
Quicksort	D & C	arrays	$O(n^2)$	$O(n \log n)$
Mergesort	D & C	lists/arrays	$O(n \log n)$	$O(n \log n)$
Treesort	Insertion	lists	$O(n^2)$	$O(n \log n)$

But what does it all mean in practice? Here is a table comparing the performance of those of the above algorithms that operate on arrays. It should again be pointed out that these numbers are only of restricted significance, since they can vary somewhat from machine (and language implementation) to machine. Quicksort2 and mergesort2 are algorithms where the recursive procedure is abandoned in favour of Selection Sort once the size of the array falls to 16 and below.

algorithm/size	128	256	512	1024	O1024	R1024	2048
Selection Sort	12	45	164	634	643	833	2497
Insertion Sort	15	69	276	1137	6	2200	4536
Bubblesort	54	221	881	3621	1285	5627	14497
Heapsort	21	45	103	236	215	249	527
Quicksort	12	27	55	112	1131	1200	230
Quicksort2	6	12	24	57	1115	1191	134
Mergesort	18	36	88	188	166	170	409
Mergesort2	6	22	48	112	94	93	254

What has to be stressed is that there is no `best sorting algorithm'. There usually is a best sorting algorithm for particular circumstances and it is up to the program designer to make sure the appropriate one is picked.