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18. Table-Driven Methods
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and increase the possibility of errors in the table if only because the table would contain redundant data.
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Transform the key to make it work directly A second way to make Age work as a direct key is to apply a function to Age so that it works well. In this case, the function would have to change all ages 0 through 17 to one key, say 17, and all ages above 66 to another key, say 66. This particular range is well behaved enough that you could just use min() and max() functions to make the transformation. For example, you could use the expression
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max( min( 66, Age ), 17 )
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to create a table key that ranges from 17 to 66. Creating the transformation function requires that you recognize a pattern in the data you want to use as a key, and that s not always as simple as using the min() and max() routines. Suppose that in this example the rates were for five-year age bands instead of one-year bands. Unless you wanted to duplicate all your data five times, you d have to come up with a function that divided Age by 5 properly and used the min() and max() routines.
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Isolate the key-transformation in its own routine Anytime you have to fudge data to make it work as a table key, put the operation that changes the data to a key into its own routine. A routine eliminates the possibility of using different transformations in different places. It makes modifications easier when the transformation changes. A good name for the routine, like KeyFromAge(), also clarifies and documents the purpose of the mathematical machinations.
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18.3 Indexed Access Tables
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Sometimes a simple mathematical transformation isn t powerful enough to make the jump from data like Age to a table key. Some such cases are suited to the use of an indexed access scheme. When you use indexes, you use the primary data to look up a key in an index table and then you use the value from the index table to look up the main data you re interested in. Suppose you run a warehouse and have an inventory of about 100 items. Suppose further that each item has a four-digit part number that ranges from 0000 through 9999. In this case, if you want to use the part number to key directly into a table that describes some aspect of each item, you set up an index
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18. Table-Driven Methods
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array with 10,000 entries (from 0 through 9999). The array is empty except for the 100 entries that correspond to part numbers of the 100 items in your warehouse. As Figure 18-4 shows, those entries point to an item-description table that has far fewer than 10,000 entries.
Array of Indexes into Lookup Table (mostly empty) Lookup Table (mostly full)
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Figure 18-4 Rather than being accessed directly, an indexed access table is accessed via an intermediate index.
Indexed access schemes offer two main advantages. First, if each of the entries in the main lookup table is large, it takes a lot less space to create an index array with a lot of wasted space than it does to create a main lookup table with a lot of wasted space. For example, suppose that the main table takes 100 bytes per entry and that the index array takes 2 bytes per entry. Suppose that the main table has 100 entries and that the data used to access it has 10,000 possible values. In such a case, the choice is between having an index with 10,000 entries or a main data member with 10,000 entries. If you use an index, your total memory use is 30,000 bytes. If you forgo the index structure and waste space in the main table, your total memory use is 1,000,000 bytes. The second advantage, even if you don t save space by using an index, is that it s sometimes cheaper to manipulate entries in an index than entries in a main table. For example, if you have a table with employee names, hiring dates, and salaries, you can create one index that accesses the table by employee name, another that accesses the table by hiring date, and a third that accesses the table by salary.
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