Program Complexity

1
Program Complexity

• Lecture 11
• 10/18/2000

2
Introduction to Complexity

• Complexity
• The number of mental objects that are required
  to be kept in mind simultaneously
• More objects require more concentration
• Control flow is the largest contributor to
  complexity (McCabe 1976)
• Control flow complexity leads to
• Low reliability
• Frequent errors

3
How to Measure Complexity

• McCabes complexity
• Metric calculated by counting the number of
  decision points in a routine

• Determining Number of Decision Points
• 1. Start with 1 for the straight path through
  the routine
• 2. Add 1 for each of the following keywords, or
  their equivalents if, while, repeat, for, and,
  or
• 3. Add 1 for each case in a case statement.

4
Code Fragment - Bubble Sort
Public static void bubbleSort2 (Sequence S)
Position prec, succ int n S.size() for
(int i 0 i lt n i) // i-th pass prec
S.first() for (int j1 j lt n - i j)
succ S.after(prec) if (valAtPos(prec)
gt valAtPos(succ)) S.swapElements(prec,
succ) prec succ
5
Complexity Heuristics

• Score
• 0 - 5 Routine is OK
• 6 - 10 Should consider if there are ways to
  simplify routine
• 10 Routine should be further decomposed
• Ways to Reduce Complexity
• Divide software into subsystems
• More independent subsystems, lower complexity
• Defined modules allows single focus
• Keep routines short
• Limit nesting of loops and control structures

6
Program Flow Graphs

• Way of visualizing complexity
• Number or paths through program

1
Simple Example
Statement 1 Statement 2 if X lt 10 then
Statement 3 Statement 4
2
T
3
if
F
4
7
Bubble Sort Example
declarations
int size
for
T (i lt n)
prec
F (j gt n)
F (i gt n)
for
T (j lt n)
T
succ
if precgtsucc
S.swap
precsucc
F
End Routine