Sorting algorithms

In the remainder of today’s readings, we’ll study sorting algorithms, i.e., algorithms which take in an arbitrary list (possibly sorted, but probably not) and yield a sorted list that is a permutation of the original list.

You might wonder about the second condition—what do we mean by a permutation of the original list, and why do we care? If we left off the second condition about permutations, the following would be a valid sort:

It’s a very efficient sort—we do no comparisons at all! Nobody would seriously offer trivial_sort as a sorting algorithm, but without the second condition it would be ‘correct’. More realistically, a sort implementation might accidentally drop (or add) duplicate elements—and that would be incorrect, too.

Different sorts take different approaches, with interesting properties beyond our scope in this course (e.g., stability—do duplicate items retain their relative ordering in the list?). More importantly, some sorting algortithms are in-place while others produce new lists. Neither is the “right one”—it depends on circumstance which approach is best. Python’s list.sort is in-place.