Exercises 15 in Visual Basic .NET

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Exercises 15
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Write algorithms (in numbered step-by-step format): 1 To add sales tax (at 175%) to the price of a single purchase (refer to the price as P) 2 To calculate the cost per person of a meal for 10 where the total price is 15000 plus sales tax (at 175%), including a gratuity of 15%
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141 Approaches to Task Decomposition
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Of course, breaking a task into a sequence of steps may not be as innocuous as it sounds Given a complex problem, it is not always a trivial job to deconstruct it into a sensible sequence of smaller problems To get around this, software designers tend
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to use well-tried recipes (which are themselves algorithms) for task decomposition The two most common approaches are known as top-down decomposition and bottom-up composition
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1411 Top-Down Task Decomposition
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Top-down task decomposition is done by examining an overall task and dividing it into a few (commonly somewhere between two and eight) smaller sub-tasks It is also known as stepwise-re nement and top-down design It is characterized by a move from a general statement of what an operation is to do towards detailed statements describing how information is to be processed To perform a top-down decomposition of a task:
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start with the overall task description and divide this into the rst level decomposition by breaking it into a number of steps; treat each step in the rst level decomposition as a whole task, and decompose as for the top level; continue this until each step is computationally trivial
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Using this approach, it is possible to make almost any complex task easier to do Since programming languages will allow us to perform only relatively simple operations, top-down decomposition is a necessary requirement if we are to do useful work with them During the top-down decomposition process, it is necessary to follow some simple guidelines to make sure that the task is well de ned Among these are:
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steer clear of programming language speci c details it is possible to bias a design towards a particular language simply because of working habits, but this is not a good design trait, since it limits the range of possible implementations postpone the working out of details until you have reached the lower levels of the task description formalize each level (keeping to well understood conventions of notation and design) verify each level (aim to demonstrate that the current level of design is correct, in that its parts are a true description of the task or sub-task they describe, before moving on to the next one)
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For example, you might consider the overall task of writing a formal letter as being: 1 2 3 4 write the recipient s address at the top-left of the paper write the sender s address at the top-right of the paper write the body of the letter write the closure of the letter (eg yours truly )
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Having created the rst level of decomposition, we can then consider each sub-task separately, and deal with them in a similar way:
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1 write the recipient s address at the top-left of the paper 11 write the recipient s name 12 write the recipient s street address 13 write the recipient s town 14 write the recipient s post code 2 write the sender s address at the top-right of the paper 21 write the sender s name 22 write the sender s street address 23 write the sender s town 24 write the sender s post code 3 write the body of the letter 31 write the introductory paragraph 32 write the main content of the letter 33 write the concluding paragraph 4 write the closure of the letter 41 if this is a business letter, write Yours faithfully 42 if this is a personal letter, write Yours sincerely 43 if this is a threatening letter, write Or else 44 write the sender s name Note that the notation has been consistent throughout a feature that will make this easier to understand when you return to it at a later date Note also that some of the parts of step 4 in the decomposition are conditional, in that one of a number of options will be taken depending on a certain condition (the type of letter being written) Software task decomposition continues along these lines until the sub- or sub-sub(or even sub-sub-sub-) tasks are trivial enough to convert directly into program statements For example, although we could proceed with much of the letter outlined above, we have not decomposed stage 3 suf ciently to allow us to write the whole letter To do this, we would probably have to concentrate on decomposing step 32 (to 321, 322 , then possibly 3211, 3212, etc) until the actual information required to be in the letter was complete Note that to do this would involve the introduction of semantic information (meaning) that is not clear from the initial speci cation We would have to return to the task of extracting requirements speci cations from the customer; no amount of computer programming could add this information In fact, our inability to complete the letter due to lack of information points to an inadequate requirements speci cation in the rst place Figure 15 shows pictorially how an overall task (level 1) can be broken down into successive sub-tasks by top-down decomposition
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