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How to Measure Complexity
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approach described here is based on Tom McCabe s influential paper A Complexity Measure (1976).
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You probably have an intuitive feel for what makes a routine more or less complex. Researchers have tried to formalize their intuitive feelings and have come up with several ways of measuring complexity. Perhaps the most influential of the numeric techniques is Tom McCabe s, in which complexity is measured by counting the number of decision points in a routine. Table 19-2 describes a method for counting decision points.
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Table 19-2. Techniques for Counting the Decision Points in a Routine 1. 2. Start with 1 for the straight path through the routine. Add 1 for each of the following keywords, or their equivalents: if while repeat for and or
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19. General Control Issues
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Add 1 for each case in a case statement.
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if ( ( (status = Success) and done ) or ( not done and ( numLines >= maxLines ) ) ) then ...
In this fragment, you count 1 to start; 2 for the if; 3 for the and; 4 for the or; and 5 for the and. Thus, this fragment contains a total of five decision points.
What to Do with Your Complexity Measurement
After you have counted the decision points, you can use the number to analyze your routine s complexity. If the score is
0 5 6 10 10+ The routine is probably fine. Start to think about ways to simplify the routine. Break part of the routine into a second routine and call it from the first routine.
Moving part of a routine into another routine doesn t reduce the overall complexity of the program; it just moves the decision points around. But it reduces the amount of complexity you have to deal with at any one time. Since the important goal is to minimize the number of items you have to juggle mentally, reducing the complexity of a given routine is worthwhile. The maximum of 10 decision points isn t an absolute limit. Use the number of decision points as a warning flag that indicates a routine might need to be redesigned. Don t use it as an inflexible rule. A case statement with many cases could be more than 10 elements long, and, depending on the purpose of the case statement, it might be foolish to break it up.
Other Kinds of Complexity
The McCabe measure of complexity isn t the only sound measure, but it s the measure most discussed in computing literature, and it s especially helpful when you re thinking about control flow. Other measures include the amount of data used, the number of nesting levels in control constructs, the number of lines of code, the number of lines between successive references to variables ( span ), the number of lines that a variable is in use ( live time ), and the amount of input and output. Some researchers have developed composite metrics based on combinations of these simpler ones.
2 FURTHER READING For an
3 excellent discussion of
complexity metrics, see Software Engineering 5 Metrics and Models (Conte, 6 Dunsmore, and Shen 1986).
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CHECKLIST: Control-Structure Issues
Do expressions use True and False rather than 1 and 0 Are boolean values compared to True and False implicitly
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19. General Control Issues
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Are numeric values compared to their test values explicitly Have expressions been simplified by the addition of new boolean variables and the use of boolean functions and decision tables Are boolean expressions stated positively Do pairs of braces balance Are braces used everywhere they re needed for clarity Are logical expressions fully parenthesized Have tests been written in number-line order Do Java tests uses a.equals(b) style instead of a == b when appropriate Are null statements obvious Have nested statements been simplified by retesting part of the conditional, converting to if-then-else or case statements, moving nested code into its own routine, converting to a more object-oriented design, or improved in some other way If a routine has a decision count of more than 10, is there a good reason for not redesigning it
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