By Derek Coleman (auth.)

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**Extra resources for A Structured Programming Approach to Data**

**Example text**

For each account the bank wants a list showing the balance at the beginning of the period, the number of deposits and withdrawals made, and the final balance. Each accounts file record contains the account number and the account balance at the beginning of the period. The accounts file is sorted in ascending order of account number. Each transaction file record contains the account number, the transaction type (deposit or withdrawal) and the transaction amount. 8 A one-dimensional array of integers a : array [ 1 ..

2 ARRAYS AND FUNCTIONS Arrays are particularly important in programming because of their relationship to functions and mappings. Programming is essentially using computers to evaluate functions. A function F: D ~ R, tells us how the elements of one set, the domain D, may be transformed into the elements of another, the rangeR. 1 Diagrammatic representation of some functions Consider the function squareof, it is normally specified by an algorithm; however, if its domain is made finite (for example, if we restrict it to positive integers less than 100) we could equally well specify square of by a linear table of range values, the value of squareof(i) occurring in the position corresponding to a;.

To find the underlying structure of the program we initially discard as much detail as possible without destroying the essence of the problem. Clearly we can ignore the details and processing of individual record structures. Another simplification is to assume that the transaction file contains at most one record per stock code. Finally, the ordering of the records is an unnecessary detail at this first level of abstraction. Conceptually at this level the program has, as inputs and outputs, sets of stock codes, and may be reformulated in the following terms.