I was looking at the source code of the sort() method of the java.util.ArrayList on grepcode. They seem to use insertion sort on small arrays (of size < 7) and merge sort on large arrays. I was just wondering if that makes a lot of difference given that they use insertion sort only for arrays of size < 7. The difference in running time will be hardly noticeable on modern machines.
I have read this in Cormen:
Although merge sort runs in O(n*logn) worst-case time and insertion sort runs in O(n*n) worst-case time, the constant factors in insertion sort can make it faster in practice for small problem sizes on many machines. Thus, it makes sense to coarsen the leaves of the recursion by using insertion sort within merge sort when subproblems become sufficiently small.
If I would have designed sorting algorithm for some component which I require, then I would consider using insertion-sort for greater sizes (maybe upto size < 100) before the difference in running time, as compared to merge sort, becomes evident.
My question is what is the analysis behind arriving at size < 7?
How long it takes to sort small arrays becomes very important when you realize that the overall sorting algorithm is recursive, and the small array sort is effectively the base case of that recursion.
I don’t have any inside info on how the number seven got chosen. However, I’d be very surprised if that wasn’t done as the result of benchmarking the competing algorithms on small arrays, and choosing the optimal algorithm and threshold based on that.
P.S. It is worth pointing out that Java7 uses Timsort by default.