Common sorting strategies

One way of organizing the various sorting algorithms is by classifying the underlying idea, or `strategy'. Things you might come up with when asked for such ideas are:

selection sorting

Find the smallest item, put it in the first position, find the smallest of the remaining items, put it in the second position ...

insertion sorting

Take the items one at a time and insert them into an initially empty data structure such that at each stage, the data structure we are considering is sorted.

exchange sorting

If two items are found to be out of order, exchange them.

enumeration sorting

If we know that there are $27$ items which are smaller than the one we are currently considering then its final position will be at number $28$.

divide and conquer

This is the recursive approach: split the problem up into smaller problems. The sorting of just one item is trivial. In this case, you have to put the sorted `parts' together somehow.

All these strategies are based on comparing items and then rearranging them accordingly. We will later consider methods which make use of specific knowledge about the items that can occur which do not fall under this category. The ideas given above are also all based on the assumption that the items to be sorted all fit into the computer's internal memory, which is why we speak of internal sorting algorithms. These days, given the growing power of computers, external storing devices become less and less frequent in sorting. If not all the items can be stored in the internal memory at one time, different techniques have to be used. The underlying idea is to sort however many one can handle at a time and then carefully merge the results. We will not consider external sorting algorithms in any detail in this course. You can find some material on this topic in [Iain T. Adamson Data Structures and Algorithms: A First Course, Springer 1996] or [Donald E. Knuth, The Art of Computer Programming: Sorting and Searching, Addison-Wesley, 1998].