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## Elementary Sorting Methods

For our first excursion into the area of sorting algorithms, we shall study several elementary methods that are appropriate either for small files or for files that have a special structure. There are several reasons for studying these simple sorting algorithms in detail. First, they provide context in which we can learn terminology and basic mechanisms for sorting algorithms, and thus allow us to develop an adequate background for studying the more sophisticated algorithms. Second, these simple methods are actually more effective than the more powerful general-purpose methods in many apps of sorting. Third, several of the simple methods extend to better general-purpose methods or are useful in improving the efficiency of more sophisticated methods.

Our purpose in this chapter is not just to introduce the elementary methods but also to develop a framework within which we can study sorting in later chapters. We shall look at a variety of situations that may be important in applying sorting algorithms, examine different kinds of input files, and look at other ways of comparing sorting methods and learning their properties.

We begin by looking at a simple driver program for testing sorting methods, which provides a context for us to consider the conventions that we shall follow. We also consider the basic properties of sorting methods that are important for us to know when we are evaluating the utility of algorithms for particular apps. Next, we delve into the subject of developing data type interfaces and implementations, along the lines that we have discussed in Chapters 3 and 4, for extending our algorithms to sort the kinds of data files that arise in practice. Then, we look closely at implementations of three elementary methods: selection sort, insertion sort, and bubble sort. Following that, we examine the performance characteristics of these algorithms in detail. Next, we look at shellsort, which is perhaps not properly characterized as elementary, but is easy to implement and is closely related to insertion sort. After a digression into the mathematical properties of shellsort, we consider linked-list sorting. The chapter concludes with a discussion of a specialized method that is appropriate when the key values are known to be restricted to a small range.

In numerous sorting apps, a simple algorithm may be the method of choice. First, we often use a sorting program only once, or just a few times. Once we have "solved" a sort problem for a set of data, we may not need the sort program again in the app manipulating those data. If an elementary sort is no slower than some other part of processing the data—for example, reading them in or printing them out—then there may be no point in looking for a faster way. If the number of items to be sorted is not too large (say, less than a few hundred elements), we might just choose to implement and run a simple method, rather than bothering with the interface to a system sort or with implementing and debugging a complicated method. Second, elementary methods are always suitable for small files (say, less than a few dozen elements)—sophisticated algorithms generally incur overhead that makes them slower than elementary ones for small files. This issue is not worth considering unless we wish to sort a huge number of small files, but apps with such a requirement are not unusual. Other types of files that are relatively easy to sort are ones that are already almost sorted (or already are sorted!) or ones that contain large numbers of duplicate keys. We shall see that several of the simple methods are particularly efficient when sorting such well-structured files.

As a rule, the elementary methods that we discuss here take time proportional to N2 to sort N randomly arranged items. If N is small, this running time may be perfectly adequate. As just mentioned, the methods are likely to be even faster than more sophisticated methods for tiny files and in other special situations. But the methods that we discuss in this chapter are not suitable for large, randomly arranged files, because the running time will become excessive even on the fastest computers. A notable exception is shellsort (see ), which takes many fewer than N2 steps for large N and is arguably the sorting method of choice for midsize files and for a few other special apps.

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