White Box Basics

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White Box Basics Part 3

• Complexity 1

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COVERAGE Simple Structure
What did we learn so far ? We found out a lot
about Statement Coverage Anweisungsüberdeckung B
ranch Coverage Zweigüberdeckung Path
Coverage Pfadüberdeckung We are not
so sure about Branch Conditions
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COVERAGE Simple Structure
We had a close look at some simple structures. I
called them Mickey Mouse structures
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COVERAGE Simple Structure
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COVERAGE Simple Structure
proc1
proc2
proc3
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COVERAGE Simple Structure
NOT SO SIMPLE ANY MORE
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COMPLEXITY

• We have to find a
• Measure for the
• Complexity of our
• Test Objects

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COMPLEXITY
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COMPLEXITY
THIS IS AN
EDGE
KANTE
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COMPLEXITY
THIS IS A
NODE
KNOTEN
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COMPLEXITY
EDGES
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COMPLEXITY
EDGES
NODES
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COMPLEXITY
EDGES
NODES
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COMPLEXITY
EDGES
NODES
EDGE ?
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COMPLEXITY
EDGES
NODES
NODE ?
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COMPLEXITY
NODE
EDGES
NODES
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COMPLEXITY
NODE
EDGES
NODES
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COMPLEXITY
NODE
EDGES
NODES
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COMPLEXITY
EDGES
NODES
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COMPLEXITY
This looks too simple
Lets make it look like it was made by a GENIUS
!
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COMPLEXITY
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COMPLEXITY
Lets tidy this up !
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COMPLEXITY
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COMPLEXITY
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COMPLEXITY
We have got four NODES
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COMPLEXITY
e1
e2
e4
e3
We have got four EDGES
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COMPLEXITY
e1
e2
e4
e3
n 4 e 4 e n 0
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COMPLEXITY
n 6 e 6 e n 0
Lets add Terminators
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COMPLEXITY

• We have added two nodes
• We have added two edges
• We did not add complexity

n 6 e 6 e n 0
n 4 e 4 e n 0
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COMPLEXITY
n 6 e 6 e n 0
Control Flow Graph
Kontrollfluss-Graph
Now lets give it a nice Name
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COMPLEXITY
n 6 e 7 e n 1
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COMPLEXITY
n 7 e 8 e n 1
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COMPLEXITY
n 11 e 13 e n 2
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COMPLEXITY

• The Difference Edges - Nodes
• gives us a clue about Complexity

n 11 e 13 e n 2
n 4 e 4 e n 0
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COMPLEXITY
n 6 e 5 e n -1
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COMPLEXITY
Do you think this structure has
NEGATIVE Complexity ?
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COMPLEXITY
I think it rather has ZERO Complexity
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COMPLEXITY

• The Difference Edges - Nodes
• gives us a clue about Complexity

e n 1
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COMPLEXITY
Professor McCabe says it has a Complexity of ONE
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COMPLEXITY

• I do not want to argue about that

e n 2
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COMPLEXITY

• Cyclomatic Complexity
• Zyklomatische Zahl

e n 2
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COMPLEXITY
This measure is often used for Risk Analysis
Cyclomatic Complexity Risk Evaluation
1-10 a simple program, without much risk
11-20 more complex, moderate risk
21-50 complex, high risk program
greater than 50 untestable program (very high risk)
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COMPLEXITY
CC 1 We will need 1 Case for Statement Coverage
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COMPLEXITY
CC 1 C0 1 We will need 1 Case
for Branch Coverage
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COMPLEXITY
CC 1 C0 1 C1 1 We will need 1 Case
for Path Coverage
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COMPLEXITY
CC 1 C0 1 C1 1 C2 1
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COMPLEXITY
n 6 e 6 e n 0 CC 2
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COMPLEXITY
CC 2 C0 1 C1 2 C2 2
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COMPLEXITY
CC 3 C0 1 C1 2 C2 4
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COMPLEXITY
n 11 e 13 e n 2
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COMPLEXITY
CC 4 C0 ? C1 ? C2 ?
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COMPLEXITY
CC 4 C0 ? C1 ? C2 ?
3 Test Cases for Statement Coverage
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COMPLEXITY
CC 4 C0 3 C1 ? C2 ?
3 Test Cases for Branch Coverage
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COMPLEXITY
CC 4 C0 3 C1 3 C2 ?
6 Test Cases for Path Coverage
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COMPLEXITY
CC 4 C0 3 C1 3 C2 6
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COMPLEXITY
n 8 e 10 e n 2
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COMPLEXITY
CC 4 C0 ? C1 ? C2 ?
n 8 e 10 e n 2
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COMPLEXITY
CC 4 C0 ? C1 ? C2 ?
1 Test Case for Statement Coverage
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COMPLEXITY
CC 4 C0 1 C1 ? C2 ?
3 Test Cases for Branch Coverage
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COMPLEXITY
CC 4 C0 1 C1 3 C2 ?
6 Test Cases for Path Coverage
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COMPLEXITY
CC 4 C0 1 C1 3 C2 6
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COMPLEXITY
CC 3 C0 1 C1 2 C2 4
CC 2 C0 1 C1 2 C2 2
CC 1 C0 1 C1 1 C2 1
CC 4 C0 1 C1 3 C2 6
CC 4 C0 3 C1 3 C2 6
CC 4 C0 3 C1 3 C2 6
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COMPLEXITY

• Obviously,
• higher Cyclomatic Complexity
• means more Test Cases

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COMPLEXITY

• Obviously,
• higher Cyclomatic Complexity
• means more Test Cases
• Especially, C2 grows fast

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COMPLEXITY HOMEWORK

• start
• if C1 true
• then do P1
• if C2 true
• then do P3
• else do P4
• endif
• else do P2, P5
• endif
• if C3 true
• then do P6
• else
• if C4 true
• then do P7
• else do P8, P9
• endif
• do P10, P11
• endif
• end

• Draw a flowchart of
• this procedure (with the
• yes-branches to the left
• and the no-branches to
• the right)

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COMPLEXITY HOMEWORK

• Convert the flowchart to
• a diagram like that
• Control Flow Graph
• 3. Calculate the Complexity
• 4. Calculate C0
• 5. Calculate C1
• 6. Calculate C2

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Dr. Wolfgang J. Schneider - Start
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