Sorting is the process of arranging a list of items in a particular order. For example, if you had a list of names, you might want to sort them alphabetically. Or if you had a list of numbers, you might want to put them in order from smallest to largest. Sorting is a common task, and it’s one that we can do in many different ways.
Many computer scientists consider sorting to be the most fundamental problem in the study of algorithms. There are several reasons: Sometimes an application inherently needs to sort information. For example, in order to prepare customer statements, banks need to sort checks by check number. Algorithms often use sorting as a key subroutine. For example, a program that renders graphical objects which are layered on top of each other might have to sort the objects according to an “above” relation so that it can draw these objects from bottom to top. We shall see numerous algorithms in this text that use sorting as a subroutine. We can draw from among a wide variety of sorting algorithms, and they em- ploy a rich set of techniques. In fact, many important techniques used through- out algorithm design appear in the body of sorting algorithms that have been developed over the years. In this way, sorting is also a problem of historical interest. We can prove a nontrivial lower bound for sorting (as we shall do in Chapter 8). Our best upper bounds match the lower bound asymptotically, and so we know that our sorting algorithms are asymptotically optimal. Moreover, we can use the lower bound for sorting to prove lower bounds for certain other problems. Many engineering issues come to the fore when implementing sorting algo- rithms. The fastest sorting program for a particular situation may depend on many factors, such as prior knowledge about the keys and satellite data, the memory hierarchy (caches and virtual memory) of the host computer, and the software environment. Many of these issues are best dealt with at the algorith- mic level, rather than by “tweaking” the code.