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SOFTWARE DESIGN AND DEVELOPMENT Successful computer software is produced in a sequence of stages that are typically managed by separate teams of developers. These stages are illustrated in Figure 1.1. The first stage is a recognition of the problem to be solved. In a corporate setting, this determination could come from market research. The second stage, which might be omitted as a formal process, is a study of whether the project is feasible. For example, do the development tools exist to produce the software In the third stage, a document is typically produced that specifies precisely what the software should do. This requirements document should have enough detail to be used as a standard when the completed software is tested. In the fourth stage, a thorough analysis is done before any effort or resources are spent designing and implementing the project. This could include a survey of comparable software already available and a cost-benefit analysis of the value of spending the anticipated resources. Once a decision has been made to proceed, the software design team works from the requirements document to design the software. This includes the specification of all the software components and their interrelationships. It may also require the specification of specialized algorithms that would be implemented in the software. The implementation consists of programmers coding the Figure 1.1 Software life cycle design to produce the software. The testing team attempts to ensure that the resulting software satisfies the requirements document. Failure at this point may require a redesign or even some fine-tuning of the requirements. Those eventualities are represented by the two feedback loops shown in Figure 1.1.

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The sequential search runs in linear time, which means that the time is proportional to the number of elements. So an array with twice as many elements would take twice as long to process: 20 ms. The binary search runs in logarithmic time, so squaring the size of the problem should only double its running time. So an array with 10002 elements would take twice as long to process: 10 ms. The interpolation search runs in hyperlogarithmic time, so squaring the size of the problem should have no appreciable effect on its running time. So an array with 1,000,000 elements would also take about 2 ms to process.

The convolution of two finite-length sequences will be finite in length. 1s it true that the convolution of a finite-length sequence with an infinite-length sequence will be infinite in length

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It is not necessarily true that the convolution of an infinite-length sequence with a finite-length sequence will be infinite in length. It may be either. Clearly, if x ( n ) = 6 ( n ) and h ( n ) = (OS)"u(n), the convolution will be an infinite-length sequence. However, it is possible for the finite-length sequence to remove the infinite-length tail of an infinite-length sequence. For example, note that

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Testing occurs at several levels. Individual classes and methods have to be tested separately, and then their success at working together must be verified. Finally, the product as a whole is tested against the requirements document. One final aspect of software development that is not shown in the figure is the maintenance process. After the software has been delivered, its developers remain obliged to maintain it with corrected versions, service packages, and even major revisions. Any major revision itself would follow the same life cycle steps. OBJECT-ORIENTED DESIGN One common approach to software design is a top-down design strategy that gradually breaks the problem down into smaller parts. This is also called step-wise refinement. It focuses on the functional aspects of the problem and the implementation of algorithms. This procedure-oriented design is common in scientific programming. In contrast, object-oriented design focuses on the data components of the software, organizing the design around their representatives. For example, an air traffic control system might be designed in terms of airplanes, airports, pilots, controllers, and other objects. The Java programming language is particularly well-suited for implementing object-oriented designs. All executable code in Java is organized into classes that represent objects. For this reason, Java is regarded as an object-oriented programming language. An object is a software unit that is produced according to a unique class specification. It is called an instance of its class, and the process of creating it is called instantiating the class. For example, this code instantiates the java.util.Date class:

public class TestBinarySearch { private static final int SIZE = 10000; private static final int START = 0; private static final int RANGE = 10000; private static Random random = new Random(); private static int count = 0; public static void main(String[] args) { int[] a = new int[SIZE]; load(a, START, RANGE); Arrays.sort(a); search(a, random.nextInt(10000)); System.out.println(count + " iterations"); } public static void load(int[] a, int start, int range) { for (int i = 0; i < a.length; i++) { a[i] = start + random.nextInt(range); // random 5-digit numbers } } public static int search(int[] a, int x) { int lo = 0; int hi = a.length; while (lo < hi) { ++count; int i = (lo + hi)/2; if (a[i] == x) { return i; } else if (a[i] < x) { lo = i+1; } else { hi = i; } } return -1; } }

Therefore, the convolution of x ( n ) = 6 ( n ) - f S ( n - I) with h ( n ) = (OS)"u(n) will be finite in length: