Chapter 6 Path Testing
:A White box techniques
322 235 Software Testing
By
Asst.Prof.Dr.Wararat Songpan(Rungworawut)
Department of Computer Science,
Faculty of Science, Khon Kaen University
1
Level of Testing
(Waterfall model)
User Acceptance Testing
Black Box
(BVT, EC, DT)
Requirements &
Specification
Design test scripts/test
cases
System
Testing
Execute
Preliminary
Design
Design
Integration
Testing
Execute
White Box
(Path Testing)
&
Black box
Detailed
Coding
Design
Coding
Unit Testing
Execute test
scripts/test
cases
Path Testing
• Path testing is a Structural Testing method (White box)
that involves using the source code of a program to
attempt to find every possible executable path.
• The idea is that are able to test each individual path
from source code is as many way as possible in order to
maximize the coverage of each test case.
• Therefore, we use knowledge of the source code to
define the test cases and to examine outputs.
• Test cases derived to exercise the basis set are
guaranteed to execute every statement in the program
at least one time during testing
3
Flow Graph
• Given a program written in an imperative
programming language, its program graph is a
directed graph in which nodes are statement
fragments, and edges represent flow of control
• It may be called “Control Flow Graph”
4
Flow chart & Flow Graph
Flow Chart
Flow Graph
0
0
1
1
2
2
3
3
4
6
7
8
6
5
4
7
8
5
9
9
11
10
11
10
5
Flow Graph Notation
Notation
Description
A circle in a graph represents a
node, which stands for a sequence of
one or more procedural statements
A node containing a simple
conditional expression is referred to
as a predicate node which has two
edges leading out from it (True and
False)
An edge, or a link, is a an arrow
representing flow of control in a
specific direction
- An edge must start and
terminate at a node
- An edge does not intersect or
cross over another edge
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6
Flow Graph Example(1)
2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Program ‘Simple Subtraction’
Input(x,y)
Output (x)
Output(y)
If x> y then Do
x-y = z
Else y-x = z
EndIf
Output(z)
Output “End Program”
3
4
5
7
6
8
9
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7
Flow Graphs consist of
2
• A decision node is a program
point at which the control can
diverge.
• (e.g., if and case statements)
3
4
5
N
Y
Y
7
6
8
N
9
Switch case
While Loop
Until Loop
10
8
Flow Graphs consist of
2
• A junction node is a program
point where the control flow
can merge.
• (e.g., end if , end loop, goto
label)
3
4
5
7
6
Goto
Connector
8
9
10
9
Flow Graphs consist of
2
• A sequence node is a
sequence of program
statements uninterrupted by
either decisions of junction.
• (i.e. straight-line code)
Sequence
3
4
5
7
6
8
9
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10
10
Flow Graph Example(2)
1
1. scanf(“%d %d”,&x, &y);
2. If (y<0)
3.
pow = -y;
else
4. pow = y;
5. Z = 1.0
6. While (pow != 0) {
7.
z = z*x;
8.
pow = pow -1; }
9. If (y <0)
10. z = 1.0 /z;
11. printf(“%f”,z);
2
4
3
5
6
7
8
9
11
10
11
What is Path?
• A path through a program is a sequence of
statements that starts at an entry, junctions,
sequence, or decision and ends.
• A path may go through several junctions,
sequences, or decisions, on or more times.
• Paths consist of segments that has smallest segment
is a link between 2 nodes.
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12
What is Path?
2
• For example:
Path1 = 2-3-4-5-6-8-9-10
3
4
5
7
6
8
9
10
13
What is Path?
2
• For example:
Path2 = 2-3-4-5-7-8-9-10
3
4
5
7
6
8
9
10
14
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
o 100% branch/ link coverage
o 100% path coverage
i
8
j
9
15
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
o 100% branch/ link coverage
o 100% path coverage
i
8
j
9
16
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
i
8
o 100% branch/ link coverage
o 100% path coverage
Statement Testing < Branch Testing < Path Testing
j
9
17
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
i
8
o 100% branch/ link coverage
o 100% path coverage
Statement Testing < Branch Testing < Path Testing
j
9
18
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
i
8
o 100% branch/ link coverage
o 100% path coverage
Statement Testing < Branch Testing < Path Testing
j
9
19
Path Testing Strategies
• Statement Testing
1
•
a
• Branch Testing
2
b
T
100% statement / node coverage
F c
3
• Path Testing
4
d
e
5
f T
Fg
6
7
h
i
8
o 100% branch/ link coverage
o 100% path coverage
Statement Testing < Branch Testing < Path Testing
j
9
20
A Coverage Table
Decisions
1
a
2
b
c
T
F
3
4
d
e
5
f T
F g
6
7
h
i
8
j
9
21 322 235
Process-Link
Paths
2
5
a
1-2-3-5-6-89
(a-b-d-f-h-j)
T
T
 
1-2-4-5-7-89
(a-c-e-g-i-j)
F
F

1-2-3-5-7-89
(a-b-d-g-i-j)
T
F
 
1-2-4-5-6-89
(a-c-e-f-h-j)
F
T

การทดสอบซอฟต์แวร์
b
c
d
e


f




g
 
h

i
j


 

 


21
Example Flow Graph
1. Program Triangle
2. Dim a, b,c As Integer
3. Dim IsTriangle As Boolean
4
4. Output ( “enter a,b, and c integers”)
5. Input (a,b,c)
6. Output (“side 1 is”, a)
7. Output (“side 2 is”, b)
8. Output (”side 3 is”, c)
9. If (a<b+c) AND (b<a+c) And (c<b+a)
10. then IsTriangle = True
11. else IsTriangle = False
12. endif
5
6
T
เป็ น
สามเหลีย่ ม
7
9
8
F
10
ไม่เป็ น
สามเหลีย่ ม
11
12
F
Flow Graph
13. If IsTriangle
14. then if (a=b) AND (b=c)
15.
then Output (“equilateral”)
16.
else if (a != b) AND (a != b) AND (b != c)
17.
then Output ( “Scalene”)
18.
else Output (“Isosceles”)
19.
endif
20.
endif
21. else Output (“not a triangle”)
22. endif
23. end Triangle2
ไม่เป็ น
สามเหลีย่ ม
21
13
T
T
14
F
15
16
T
17
สามเหลีย่ ม
ด้านเท่า
20
F
18
19
22
23
สามเหลีย่ ม
ด้านไม่เท่า
สามเหลีย่ ม
หน้าจัว่
22
Basis Path Testing
4
• Select Path is shortest
or simple path
• For example:
5
6
7
8
9
10
11
12
13
4-5-6-7-8-9-11-12-13-21-22-23
21
14
15
16
17
20
18
19
22
23
23
Test Case for Path Coverage
 4-5-6-7-8-9-11-12-13-21-22-23
 4-5-6-7-8-9-10-12-13-14-15-20-22-23
 4-5-6-7-8-9-10-12-13-14-16-17-19-20-22-23
 4-5-6-7-8-9-10-12-13-14-16-18-19-20-22-23
Path
Decision
9
13
14

F
F

T
T
T

T
T
F

T
T
T
Test case
16
Expected
Results
a
b
c
100
100
200
Not A
triangle
100
100
100
Equilateral
T
100
50
60
Scalene
F
100
100
50
Isosceles
24
DD-Paths
• It stand for Decision-to-Decision path in
a directed graph.
• A path are consists of the initial and
nodes and interior node has indegree = 1
and outdegree = 1
indegree =1
outdegree =1
25
DD-Paths
Characteristic of DD-Path has 5 cases:
•
•
•
•
•
Case 1: Single node with indeg =0
Case 2: Single node with outdeg = 0
Case 3: Single node with indeg >= 2 or outdeg >=2
Case 4: Single node with indeg = 1 and outdeg =1
Case 5: Maximum chain of length >=1
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Condensation of Code to Table then to Flow Graph
code statement
1. Program Triangle
2. Dim a, b,c As Integer
3. Dim IsTriangle As Boolean
4. Output ( “enter a,b, and c integers”)
5. Input (a,b,c)
6. Output (“side 1 is”, a)
7. Output (“side 2 is”, b)
8. Output (”side 3 is”, c)
9. If (a<b+c) AND (b<a+c) And (c<b+a)
10. then IsTriangle = True
11. else IsTriangle = False
12. endif
Def of
DD-paths on
13. If IsTriangle
14. then if (a=b) AND (b=c)
15.
then Output (“equilateral”)
16.
else if (a NE b) AND (a NE b) AND (b NE c)
17.
then Output ( “Scalene”)
18.
else Output (“Isosceles”)
19.
endif
20.
endif
21. else Output (“not a triangle”)
22. endif
23. end Triangle2
Path/node
name
DD-path
Case
Skip 1- 3
(or w/4)
4
5–8
first
A
1
5
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
B
C
D
E
F
H
I
J
K
L
M
N
G
O
last
3
4
4
3
3
3
4
3
4
4
3
3
4
3
2
DD-Path
First
4
5
6
7
8
A
9
B
10
11
C
D
12
E
13
21
F
14
G
15
H
16
I
17
J
18
K
20
L
19
N
M
22
O
23
Last
28
Path Analysis
• What is path analysis?
o Analyzes the number of paths that exist in the
system
o Facilitates the decision process of how many
paths to include in the test
29
Path Analysis: Cyclomatic complexity
measure (CFC)
A
CFC can be calculated by
B
V(G) = e-n+2
e : the number of edges
n : the number of nodes
Example: = 10-7+2 = 5
D
T
F
E
T
C
F
F
G
30
Path Analysis: Cyclomatic complexity
measure (CFC)
• If flow graph has link between
sink node(G) to source node(A) which is
called a strongly connected graph.
A
V(G) = e-n+1
e : the number of edges
n : the number of nodes
Example: 11-7+1 = 5
B
D
F
T
E
T
C
F
F
G
31
How to select path
• Independent Path
• McCabe’s Baseline
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32
Independent Path
• Independent program paths an
independent path is any path
through the program that introduces
at least one new set of processing
link, statements or a new condition.
• No count on traverse edge between
sink node-G to source node-A
o
o
o
o
o
P1: A-B-C-G
P2: A-B-C-B-C-G
P3: A-B-E-F-G
P4: A-D-E-F-G
P5: A-D-F-G
A
B
D
T
F
E
T
C
F
F
G
33
Independent Path
Problem of Independent path
o
o
o
o
o
o
o
P1: A-B-C-G
P2: A-B-C-B-C-G
P3: A-B-E-F-G
P4: A-D-E-F-G
P5: A-D-F-G
Ex1: A-B-C-B-E-F-G
Ex2: A-B-C-B-C-B-C-G
A
B
D
T
F
E
T
C
F
F
G
34
Independent Path
• example2
V(G) = e-n+2
= 11-9+2 =4
A
B
C
D
I
G
E
P1: A-I
P2: A-B-C-D-F-H-A-I
P3: A-B-C-E-F-H-A-I
P4: A-B-G-H-A-I
Is the path
A-B-G-H-A-B-C-D-F-H-A-I
and independent path?
F
H
35
McCabe’s Baseline
To determine a set of basis paths,
1. Pick a "baseline" path that corresponds to normal execution.
(The baseline should have as many decisions as possible.)
2. To get succeeding basis paths, retrace the baseline until you
reach a decision node. "Flip" the decision (take another
alternative) and continue as much of the baseline as possible.
3. Repeat this until all decisions have been flipped. When you
reach V(G) basis paths, you're done.
4. If there aren't enough decisions in the first baseline path, find
a second baseline and repeat steps 2 and 3.
36
McCabe’s Baseline
•
•
•
•
•
P1: A-B-C-B-E-F-G
P2: A-B-E-F-G
P3: A-B-C-G
P4: A-D-E-F-G
P5: A-D-F-G
A
B
D
T
F
E
T
C
F
F
G
37
McCabe’s Path of Triangle Program
First
McCabe
Paths
Expected Results
Original
P1: First-A-B-C-E-F-H-J-KM-N-O-Last
Scalene
P2: First-A-B-D-E-F-H-J-KM-N-O-Last
Infeasible path
Flip P1 at F
P3: First-A-B-C-E-F-G-OLast
Infeasible path
E
Flip P1 at H
P4: First-A-B-C-E-F-H-I-NO-Last
Equilateral
F
Flip P1 at J
P5: First-A-B-C-E-F-H-J-L-MN-O-Last
Isosceles
Flip P1 at B
A
ไม่เป็ น
สามเหลีย่ ม
B
เป็ น
สามเหลีย่ ม
ไม่เป็ น
สามเหลีย่ ม
C
D
If IsTriangle
G
H
I
J
K
สามเหลีย่ ม
ด้านเท่า
N
L
M
O
Last
สามเหลีย่ ม
ด้านไม่เท่า
สามเหลีย่ ม
หน้าจัว่
38
McCabe’s Path
• Weakness of McCabe’s Path may occur “infeasible
path” which means no found test case design to
match with the path.
McCabe
Paths
Expected
Results
P1
Original
P1: First-A-B-C-E-F-H-J-K-M-N-OLast
Scalene
P6(from P2 and
P3)
New
P6: First-A-B-D-E-F-G-O-Last
Not a
Triangle
P4
Flip P1 at H
P4: First-A-B-C-E-F-H-I-N-O-Last
Equilateral
P5
Flip P1 at J
P5: First-A-B-C-E-F-H-J-L-M-N-OLast
Isosceles
39
From path analysis to test case design
Test Case
From
Path
a
b
c
Expected Results
1
P1
P6
P4
P5
3
4
5
3
4
1
5
2
5
2
5
2
Scalene
2
3
4
Not a Triangle
Equilateral
Isosceles
40
Steps of path testing
• Deriving Test Cases
1. Using the design or code, draw the corresponding
flow graph.
2. Determine the cyclomatic complexity of the flow
graph.
3. determine a set of path by
basis/independent/McCabe’s paths.
4. Prepare test cases that will force execution of
each path in the basis set.
41
Path Testing Example
public double calculate(int amount)
{
1. double rushCharge = 0;
if (nextday.equals("yes") )
{
2.
rushCharge = 14.50; }
3 double tax = amount * .0725;
3 if (amount >= 1000) {
4.
shipcharge = amount * .06 + rushCharge; }
5. else if (amount >= 200) {
6.
shipcharge = amount * .08 + rushCharge; }
7. else if (amount >= 100) {
8.
shipcharge = 13.25 + rushCharge; }
9. else if (amount >= 50) {
10.
shipcharge = 9.95 + rushCharge; }
11. else if (amount >= 25) {
12.
shipcharge = 7.25 + rushCharge; }
else {
13. shipcharge = 5.25 + rushCharge; }
14. total = amount + tax + shipcharge;
15. return total;
} //end calculate
42
Path Testing Example
• Here is a drawing of the flowgraph.
1
3
2
4
5
6
7
8
9
10
11
12
13
14
43
Path Testing Example
• Step 2: Determine the cyclomatic complexity of the
flow graph.
• V(G) = E - N + 2
= 19 - 14 + 2
= 7
44
Path Testing Example
(McCabe’s Path )
• Step 3: Determine the basis set of paths using
McCabe’s Path
Path 1: 1 - 2 - 3 - 5 - 7 - 9 - 11 - 13 - 14
Path 2: 1 - 3 - 5 - 7 - 9 - 11 - 13 - 14
Path 3: 1 - 3 - 4 - 14
Path 4: 1 - 3 - 5 - 6 - 14
Path 5: 1 - 3 - 5 - 7 - 8 - 14
Path 6: 1 - 3 - 5 - 7 - 9 - 10 - 14
Path 7: 1 - 3 - 5 - 7 - 9 - 11 - 12 - 14
45
Path Testing Example
(McCabe’s Path)
• step 4: Prepare test cases that force execution of
each path with McCabe’s Path.
Path
Next day
Amount
Expected
Results
P1
yes
10
30.475
P2
No
10
15.975
P3
No
1500
1713.25
P4
No
300
345.75
P5
No
150
174.125
P6
No
75
90.3875
P7
No
30
39.425
46
Path Testing Example
(basis path) 1
• Determine the basis set of paths
using basis path
P1: 1-3-4-14
P2: 1-2-3-4-14
P3: 1-2-3-5-6-14
P4: 1-2-3-5-7-8-14
P5: 1-2-3-5-7-9-10-14
P6: 1-2-3-5-7-9-11-12-14
P7: 1-2-3-5-7-9-11-13-14
3
2
4
5
6
7
8
9
10
11
12
13
14
47
Path Testing Example
(Independent path)
• Determine the basis set of paths
using independent path
P1: 1-3-5-6-14
P2: 1-2-5-6-14
P2: 1-2-3-4-14
P3: 1-2-3-5-7-8-14
P4: 1-2-3-5-7-9-10-14
P5: 1-2-3-5-7-9-11-12-14
P7: 1-2-3-5-7-9-11-13-14
1
3
2
4
5
6
7
8
9
10
11
12
13
14
48