A friend asked me why insertion sort was faster than merge sort for small arrays. I Wikipedia'd it, and it looks like there is simply higher overhead for the merge sort, and n hasn't gotten large enough for the time complexity to overcome this. They also talk about how big you have to get before the merge sort overcomes this. Their conclusion was 8 to 20 elements.
I decided I wanted to compare the run times of the sort algorithms, so I coded an insertion sort and merge sort, then set them up to be timed against each other. My results are a lot higher, needing around 96-101 elements before it starts to be faster to merge sort (data used to determine this). I don't know if that is because of inefficiencies in how I wrote my sort, or if it is because gcc has done fancy optimizations and changed the code in ways that I'm not aware of.
Still, it was fun. Here is a graph showing the results
To remove the generated files
$ rake clobber
To build either sort
$ rake merge.out $ rake insertion.out
To run either sort
$ rake merge $ rake insertion
To run them both
$ rake time
To run them both with a range of times
$ rake time-many
There are three variables you can change:
arysize defaults to 5, and is the size of the arrays to be sorted
$ rake time arysize=150
times defaults to 1,000,000 and is the number of arrays to sort (number of times to repeat the sort)
$ rake insertion times=100
testsize defaults to 10 and is the upper bound on the range tested when running time-many
$ rake time-many testsize=350
This code is unmaintained.
If you do something interesting with it, let me know so I can be happy.
Copyright (c) 2010 Joshua Cheek
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