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18. Table-Driven Methods
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A final advantage of an index-access scheme is the general table-lookup advantage of maintainability. Data encoded in tables is easier to maintain than data embedded in code. To maximize the flexibility, put the index-access code in its own routine and call the routine when you need to get a table key from a part number. When it s time to change the table, you might decide to switch the index-accessing scheme or to switch to another table-lookup scheme altogether. The access scheme will be easier to change if you don t spread index accesses throughout your program.
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18.4 Stair-Step Access Tables
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Yet another kind of table access is the stair-step method. This access method isn t as direct as an index structure, but it doesn t waste as much data space. The general idea of stair-step structures, illustrated in Figure 18-5, is that entries in a table are valid for ranges of data rather than for distinct data points.
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Figure 18-5 The stair-step approach categorizes each entry by determining the level at which it hits a staircase. The step it hits determines its category.
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For example, if you re writing a grading program, the B entry range might be from 75 percent to 90 percent. Here s a range of grades you might have to program someday:
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90.0% < 90.0% < 75.0% < 65.0% < 50.0% A B C D F
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This is an ugly range for a table lookup because you can t use a simple datatransformation function to key into the letters A through F. An index scheme
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would be awkward because the numbers are floating point. You might consider converting the floating-point numbers to integers, and in this case that would be a valid design option, but for the sake of illustration, this example will stick with floating point. To use the stair-step method, you put the upper end of each range into a table and then write a loop to check a score against the upper end of each range. When you find the point at which the score first exceeds the top of a range, you know what the grade is. With the stair-step technique, you have to be careful to handle the endpoints of the ranges properly. Here s the code in Visual Basic that assigns grades to a group of students based on this example:
Visual Basic Example of a Stair-Step Table Lookup
' set up data for grading table Dim rangeLimit() As Double = { 50.0, 65.0, 75.0, 90.0, 100.0 } Dim grade() As String = ... ' assign a grade to a student based on the student's score gradeLevel = 0 studentGrade = "A" While ( ( studentGrade = "A" ) and ( gradeLevel < maxGradeLevel ) ) If ( studentScore < rangeLimit( gradeLevel ) ) Then studentGrade = grade( gradeLevel ) End If gradeLevel = gradeLevel + 1 Wend { "F", "D", "C", "B", "A" } maxGradeLevel = grade.Length 1
Although this is a simple example, you can easily generalize it to handle multiple students, multiple grading schemes (for example, different grades for different point levels on different assignments), and changes in the grading scheme. The advantage of this approach over other table-driven methods is that it works well with irregular data. The grading example is simple in that, although grades are assigned at irregular intervals, the numbers are round, ending with 5s and 0s. The stair-step approach is equally well suited to data that doesn t end neatly with 5s and 0s. You can use the stair-step approach in statistics work for probability distributions with numbers like this:
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0.627764 0.776883 0.893211 0.957665 0.976544 0.987889
$514.77 $747.82 $1,042.65 $5,887.55 $12,836.98 $27,234.12
... Ugly numbers like these defy any attempt to come up with a function to neatly transform them into table keys. The stair-step approach is the answer.
This approach also enjoys the general advantages of table-driven approaches. It is flexible and modifiable. If the grading ranges in the grading example were to change, the program could easily be adapted by modifying the entries in the RangeLimit array. You could easily generalize the grade-assignment part of the program so that it would accept a table of grades and corresponding cut-off scores. The grade-assignment part of the program wouldn t have to use scores expressed as percentages; it could use raw points rather than percentages, and the program wouldn t have to change much. Here are a few subtleties to consider as you use the stair-step technique:
Watch the endpoints Make sure you ve covered the case at the top end of each stair-step range. Run the stair-step search so that it finds items that map to any range other than the uppermost range, and then have the rest fall into the uppermost range. Sometimes this requires creating an artificial value for the top of the uppermost range.
Be careful too about mistaking < for <=. Make sure that the loop terminates properly with values that fall into the top ranges and that the range boundaries are handled correctly.
Consider using a binary search rather then a sequential search In the grading example, the loop that assigns the grade searches sequentially through the list of grading limits. If you had a larger list, the cost of the sequential search might become prohibitive. If it does, you can replace it with a quasi-binary search. It s a quasi binary search because the point of most binary searches is to find a value. In this case, you don t expect to find the value; you expect to find the right category for the value. The binary-search algorithm must correctly determine where the value should go. Remember also to treat the endpoint as a special case.
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