1. Chapter 6 Path Testing 322 235 Software TestingBy
Wararat Songpan(Rungworawut),PH.D.
Department of Computer Science,
Faculty of Science, Khon Kaen University

2. Path Testing
Path testing is a Structural Testing method 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 1 1 2 2 3 3 6 4 6 4 7 8 5 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 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 6 7 8 9 10
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7. Flow Graphs consist of 2
A decision is a program point at which the control can diverge.
(e.g., if and case statements) 3 4 5 6 7 N Y Y 8 N
Switch case 9
While Loop
Until Loop 10

8. Flow Graphs consist of 2
A junction is a program point where the control flow can merge.
(e.g., end if , end loop, goto label) 3 4 5 6 7
Goto 8
Connector 9 10

9. Flow Graphs consist of 2
A process block is a sequence of program statements uninterrupted by either decisions of junction.
(i.e. straight-line code) 3 4 5
Sequence 6 7 8 9 10
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10. Flow Graph Example(2) 1 2 3 4 5 6 7 8 9 10 11 scanf(“%d %d”,&x, &y);
If (y<0)
pow = -y;
else
4. pow = y;
Z = 1.0
While (pow != 0) {
z = z*x;
pow = pow -1; }
If (y <0)
z = 1.0 /z;
printf(“%f”,z); 3 4 5 6 7 8 9 10 11

11. What is Path?
A path through a program is a sequence of statements that starts at an entry, junctions, or decision and ends.
A path may go through several junctions, processes, 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 3 4 5 6 7 8 9 10 For example: Path1 = 2-3-4-5-6-8-9-1012

13. What is Path? 2 3 4 5 6 7 8 9 10 For example: Path2 = 2-3-4-5-7-8-9-1013

14. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i 8 j 9

15. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i 8 j 9

16. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i
Statement Testing < Branch Testing < Path Testing 8 j 9

17. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i
Statement Testing < Branch Testing < Path Testing 8 j 9

18. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i
Statement Testing < Branch Testing < Path Testing 8 j 9

19. Path Testing Strategies
Statement Testing
100% statement / node coverage
Branch Testing
100% branch/ link coverage
Path Testing
100% path coverage 1 a 2 b T F c 3 4 d e 5 T F f g 6 7 h i
Statement Testing < Branch Testing < Path Testing 8 j 9

20. A Coverage Table Paths Decisions Process-Link 2 5 a b c d e f g h i j
(a-b-d-f-h-j) T 
(a-c-e-g-i-j) F
(a-b-d-g-i-j)
(a-c-e-f-h-j) 1 a 2 b c T F 3 4 d e 5 f T F g 6 7 h i 8 j 9 20
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21. Exmple Flow Graph Flow Graph 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
13. If IsTriangle
then if (a=b) AND (b=c)
then Output (“equilateral”)
else if (a != b) AND (a != b) AND (b != c)
then Output ( “Scalene”)
else Output (“Isosceles”)
endif
endif
else Output (“not a triangle”)
22. endif
23. end Triangle2 4 5 6 7 8 9
Flow Graph 10 11 12 13 21 14 15 16 17 18 20 19 22 23

22. Basis Path Testing Select Path is shortest or simple path For example:4 5 6 7 8
Select Path is shortest or simple path
For example: 9 10 11 12 13 21 14 15 16 17 18 20 19 22 23 22
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23. Test Case for Path Coverage  
Path
Decision
Test case
Expected Results 9 13 14 16 a b c  T F
100
200
Not A triangle 
Equilateral  50 60
Scalene 
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 25
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26. Condensation of Code to Table then to Flow Graph
Path/node
name
DD-path
Case
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
13. If IsTriangle
then if (a=b) AND (b=c)
then Output (“equilateral”)
else if (a NE b) AND (a NE b) AND (b NE c)
then Output ( “Scalene”)
else Output (“Isosceles”)
endif
endif
else Output (“not a triangle”)
22. endif
23. end Triangle2
Skip 1- 3
(or w/4)
first
5 – A B C D E F H I J K L M N G O
last
Def of
DD-paths on

27. DD-Path First 4 5 6 7 8 A 9 B 10 11 C D 12 E 13 F 21 14 G H 15 16 I J17 18 K L 20 19 N M 22 O 23
Last

28. Path Analysis What is path analysis?
Analyzes the number of paths that exist in the system
Facilitates the decision process of how many paths to include in the test

29. Path Analysis: Cyclomatic complexity measure (CFC)
CFC can be calculated by V(G) = e-n+2 e : the number of edges n : the number of nodes Example: = = 5 A B D F T E F T C 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.
V(G) = e-n+1
e : the number of edges
n : the number of nodes
Example: = 5 A B D F T T E F C F G 30
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31. How to select path Independent Path McCabe’s Baseline
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32. Independent Path A B D E C F G
Independent program paths an independent path is any path through the program that introduces at least one new set of processing statements or a new condition.
Cyclomatic complexity is a software metric that provides a quantitative measure of the logical complexity if a program
No count on traverse edge between sink node-G to source node-A
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 F T E T F C F G

33. Independent Path Problem of Independent path A B D E C F G 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 F T E T F C F G

34. 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.

35. McCabe’s Baseline A B D E C F G P1: A-B-C-B-E-F-G P2: A-D-E-F-G
P3: A-D-F-G
P4: A-B-E-F-G
P5: A-B-C-G A B D F T E T F C F G

36. McCabe’s Path of Triangle Program
First
McCabe
Paths
Expected Results
Original
P1: First-A-B-C-E-F-H-J-K-M-N-O-Last
Scalene
Flip P1 at B
P2: First-A-B-D-E-F-H-J-K-M-N-O-Last
Infeasible path
Flip P1 at F
P3: First-A-B-C-E-F-G-O-Last
Flip P1 at H
P4: First-A-B-C-E-F-H-I-N-O-Last
Equilateral
Flip P1 at J
P5: First-A-B-C-E-F-H-J-L-M-N-O-Last
Isosceles A B C D E F G H I J K L N M O
Last

37. 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-O-Last
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-O-Last
Isosceles

38. From path analysis to test case designb c
Expected Results
From Path 1 3 4 5
Scalene P1 2
Not a Triangle P6
Equilateral P4
Isosceles P5

39. Steps of path testing Deriving Test Cases
Using the design or code, draw the corresponding flow graph.
Determine the cyclomatic complexity of the flow graph.
determine a set of path by basis/independent/McCabe’s paths.
Prepare test cases that will force execution of each path in the basis set.

40. Basis 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 * rushCharge; } 5. else if (amount >= 200) { 6.      shipcharge = amount * rushCharge; } 7.  else if (amount >= 100) { 8.      shipcharge = rushCharge; } 9.  else if (amount >= 50) { 10.      shipcharge = rushCharge; } 11. else if (amount >= 25) { 12.      shipcharge = rushCharge; }      else { 13.     shipcharge = rushCharge; }
14. total = amount + tax + shipcharge;
14. return total;
} //end calculate  

41. Basis Path Testing Example1
Here is a drawing of the flowgraph. 2 3 4 5 6 7 8 10 9 11 12 13 14

42. Basis Path Testing Example
Step 2: Determine the cyclomatic complexity of the flow graph.
V(G) = E - N + 2         =         =  7

43. Basis Path Testing Example
Step 3: Determine the basis set of independent paths.
Path 1:  Path 2:  Path 3:  Path 4:  Path 5:  Path 6:  Path 7: 

44. Basis Path Testing Example
step 4: Prepare test cases that force execution of each path in the basis set.
Path
Nextday
Amount
Expected Results P1
yes  10
30.48 P2 No
1500 P3
300
345.75 P4
150 P5
75  P6 30
39.425 P7
15.975