By Derek Coleman (auth.)

ISBN-10: 0333219430

ISBN-13: 9780333219430

ISBN-10: 1349159816

ISBN-13: 9781349159819

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**Example text**

Such that solving firstP 1 , thenP2 and so on will be a solution to the original P. This approach is then applied to each of the subproblems P 1 , P 2 , P 3 , • .. , producing a set of sub-subproblems whose solutions taken together are a solution to P 1 • We continue this process until the problems are sufficiently small to be capable of solution directly. It is the continual outside-in analysis of the problem which develops the solution to the problem. 1. In that each level of the tree ignores the details of the level below it, we may refer to levels of abstraction when discussing a solution produced by stepwise refinement.

An is referred to as the vector a, in programming such a structure is known as an array and would be declared in Algol as array a [ 1 : n] . Elements of an array are all of the same type and may be individually selected by the use of subscripts. The idea of an array extends easily to sets of variables with two subscripts so providing an analogue of the matrix. For example, the set of variables a= {a;jli = 1, 2, ... , m andj = 1, 2, ... , n} declared in Algol by array a [ 1 : m, 1 : n] , is a two-dimensional array.

3 A darts board consists of the numbered regions 1 to 20; each dart may score one of these numbers and may be doubled or trebled. There are also the inner and outer hull's eye regions which score 25 and 50 respectively. Design a program which, for a given input positive integer value, will output 'yes' or 'no' depending on whether or not it can be scored with a maximum of three darts. If it can, the program should output the individual scores of the minimum number of darts required. 4 Design a program that given a positive integer will output in words the value of the integer (the output for 315 should be three hundred and fifteen).

### A Structured Programming Approach to Data by Derek Coleman (auth.)

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