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ACM, 20, 10 (Oct. 1977), 762-772. Wirth. Algorithms and Data Structures. 1 Introduction The primary purpose of this chapter is to provide an extensive set of examples illustrating the use of the data structures introduced in the preceding chapter and to show how the choice of structure for the underlying data profoundly influences the algorithms that perform a given task. Sorting is also a good example to show that such a task may be performed according to many different algorithms, each one having certain advantages and disadvantages that have to be weighed against each other in the light of the particular application.

T(s n-1)> We shall briefly investigate the necessary operations for transforming representations of natural numbers for input and output. The basis is that a number x represented by the sequence of decimal digits d = has the value x = Si: i = 0 .. Wirth. Algorithms and Data Structures. Oberon version 33 x = dn-1 × 10n-1 + dn-2 × 10n-2 + … + d1 × 10 + d0 x = ( … (dn-1 × 10 + dn-2) × 10 + … + d1) × 10 + d0 Assume now that the sequence d is to be read and transformed, and the resulting numeric value to be assigned to x.

There are not many techniques that do not occur somewhere in connection with sorting algorithms. In particular, sorting is an ideal subject to demonstrate a great diversity of algorithms, all having the same purpose, many of them being optimal in some sense, and most of them having advantages over others. It is therefore an ideal subject to demonstrate the necessity of performance analysis of algorithms. The example of sorting is moreover well suited for showing how a very significant gain in performance may be obtained by the development of sophisticated algorithms when obvious methods are readily available.

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