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A HashTable is a form of Dictionary, derived from the DictionaryBase class Dictionary collections store pairs of objects, usually referred to as Key and Value pairs In the same way that a real-world dictionary provides us with a way to associate pairs of items (a word and its de nition or translation), so a Dictionary collection allows us to associate pairs of objects Normally, the Key object is a value that would be looked up (like looking up a word in the Oxford English Dictionary) and the Value object is the object that is returned from the look-up In this way, we can build complex structures that allow us to collect pairs of objects, where one is used as a way of accessing the other Typically, the Key of an entry in a Dictionary collection is a string that uniquely identi es the Value object; for example we could use a person s social security number as the key to an object containing other data referring to the person, or a licence number as the key to an object containing a lot of data about a speci c car A HashTable gets its name from the way data is stored and retrieved in it A hashing function, or hash function, is a function that takes some data, jumbles it up and converts it into a number that is seemingly random This type of function, fairly useless on its own, is ideal for distributing a lot of key values evenly across a numeric range To see why this is useful, consider the job done by a local post of ce sorting of ce Mail is arranged into bins, where each bin contains mail for a particular area Since the actual areas (normally a postman s walk ) can be selected by the post of ce, they are organized so that each area (and bin) will be approximately the same size, and will therefore receive a similar amount of mail This is organizationally sensible Now consider a situation where we cannot predetermine how items would be distributed Organizing items into bins by the initial letter of someone s surname, for example, would be more haphazard We call the property or piece of data that we use to identify an item its key and although the aim is to have an even distribution of keys, this is unlikely for real-world data We would not divide the population of a country into 26 groups, where each group is of people with the same initial letter to their surname, and expect each group to be the same size If we used the initial letter of a surname, for example, we would have 26 bins, one for each letter A to Z see Figure 64) However, each bin would not be likely to have to accommodate a similar amount of mail In the UK, names beginning with certain letters are quite unlikely (X and Z for example) These two bins would be nearly.

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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 ack 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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