Question

I was curious to know how to select a sorting algorithm based on the input, so that I can get the best efficiency.

Should it be on the size of the input or how the input is arranged(Asc/Desc) or the data structure used etc … ?

Answer 1

The importance of algorithms generally, and in sorting algorithms as well is as following:

(*) Correctness – This is the most important thing. It worth nothing if your algorithm is super fast and efficient, but is wrong. In sorting, even if you have 2 candidates that are sorting correctly, but you need a stable sort – you will chose the stable sort algorithm, even if it is less efficient – because it is correct for your purpose, and the other is not.

Next are basically trade offs between running time, needed space and implementation time (If you will need to implement something from scratch rather then use a library, for a minor performance enhancement – it probably doesn’t worth it)

Some things to take into consideration when thinking about the trade off mentioned above:

1. Size of the input (for example: for small inputs, insertion sort is empirically faster then more advanced algorithms, though it takes O(n^2)).
2. Location of the input (sorting algorithms on disk are different from algorithms on RAM, because disk reads are much less efficient when not sequential. The algorithm which is usually used to sort on disk is a variation of merge-sort).
3. How is the data distributed? If the data is likely to be “almost sorted” – maybe a usually terrible bubble-sort can sort it in just 2-3 iterations and be super fast comparing to other algorithms.
4. What libraries do you have already implemented? How much work will it take to implement something new? Will it worth it?
5. Type (and range) of the input – for enumerable data (integers for example) – an integer designed algorithm (like radix sort) might be more efficient then a general case algorithm.
6. Latency requirement – if you are designing a missile head, and the result must return within specific amount of time, quicksort which might decay to quadric running time on worst case – might not be a good choice, and you might want to use a different algorithm which have a strict O(nlogn) worst case instead.
7. Your hardware – if for example you are using a huge cluster and a huge data – a distributed sorting algorithm will probably be better then trying to do all the work on one machine.