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2. Path Coverage:

In this we split the program into number of distinct paths. A

program can start from the beginning and take any of thepaths to its completion.

Path Coverage= (Total paths exercised/Total no. of paths

in a program)*100

Path Testing:

Path testing is the name given to a group of test

techniques based on judiciously selecting a set of testpaths through the program. If the set of paths is properly

chosen, then it means that we have achieved some

measure of test thoroughness.


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This type of testing involves:

1. generating a set of paths that will cover every branch in

the program.

2. finding a set of test cases that will execute every path in

the set of program paths.


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Flow Graph:The control flow of a program can be analyzed using a

graphical representation known as flow graph. The flow graphis a directed graph in which nodes are either entire statements

or fragments of a statement, and edges represent flow of

control.

Fig. : The basicconstruct of the flow graph


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DD Path GraphThe DD Path graph is known as decision to decision path

graph. Here, we concentrate only on decision nodes. Thenodes of flow graph, which are in a sequence are combined

into a single node.


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Fig. 18: Independent paths of prev

ious date prob

lem


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Structured testing is based on the pioneering work of Tom

McCabe. It uses an analysis of the topology of the control flow

graph to identify test cases.

o Derive the control flow graph from the software module.

The structured testing process consists of the following steps:

o Compute the graph's Cyclomatic Complexity (C).

o Select a set of C basis paths.

o Create a test case for each basis path.

o Execute these tests.


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Consider the following control flow graph:

An example control flow graph.


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McCabe defines the Cyclomatic Complexity (C) of a graph as

C = edges - nodes + 2P

Edges are the arrows, and nodes are the bubbles on the

graph, P are the connected components.

Here, edges=24, nodes=19, cyclomatic complex= 24-19+2=7

In some cases this computation can be simplified. If all

decisions in the graph are binary (they have exactly twoedges flowing out), and there are p binary decisions, then

C = p+1


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Two alternate methods are available for the complexity calculations.

1. Cyclomatic complexity V(G) of a flow graph G is equal to the number of

predicate (decision) nodes plus one.

V(G)= +1

Where is the number of predicate nodes contained in the flow graph G.

2. Cyclomatic complexity is equal to the number of regions of the flow

graph.


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Consider a flow graph given in Fig. and calculate the cyclomatic complexity by

all three methods.


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Solution

Cyclomatic complexity can be calculated by any of the three methods.

1. V(G) = e n + 2P

= 13 10 + 2 = 5

2. V(G) = + 1

= 4 + 1 = 5

3. V(G) = number of regions

= 5

Therefore, complexity value of a flow graph in Fig. 23 is 5.


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Cyclomatic Complexity is exactly the minimum number of

independent, nonlooping paths (called basis paths) that can,

in linear combination, generate all possible paths through the

module.

In terms of a flow graph, each basis path traverses at leastone edge that no other path does.

McCabe's structured testing technique calls for creating C test

cases, one for each basis path.

Important: Creating and executing C test cases, based on the

basis paths, guarantees both branch and statement coverage.


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A process for creating a set of basis paths is given by McCabe:

1. Pick a "baseline" path. This

path should be a

reasonably "typical" path of

execution rather than anexception processing path.

The best choice would be

the most important path

from the tester's view.

The chosen baseline basis path

ABDEGKMQS


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2. To choose the next path,

change the outcome of the first

decision along the baseline

path while keeping the

maximum number of otherdecisions the same as the

baseline path.

The second basis path ACDEGKMQS


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3. To generate the third path,

begin again with the

baseline but vary the

second decision rather than

the first.

The third basis path ABDFILORS


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4. To generate the fourth path,

begin again with the

baseline but vary the third

decision rather than the

second. Continue varyingeach decision, one by one,

until the bottom of the

graph is reached.

The fourth basis path ABDEHKMQS


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The fifth basis path ABDEGKNQS


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5. Now that all decisions

along the baseline path

have been flipped, we

proceed to the second

path, flipping its decisions,one by one. This pattern is

continued until the basis

path set is complete.

The sixth basis path ACDFJLORS


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The seventh basis path ACDFILPRS


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Thus, a set of basis paths for this graph are:

ABDEGKMQS

ACDEGKMQS

ABDFILORS

ABDEHKMQS

ABDEGKNQS

ACDFJLORS

ACDFILPRS


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Example 13

Consider the problem for the determination of the nature ofroots of a quadratic equation. Its input a triple of positive

integers (say a,b,c) and value may be from interval [0,100].

The program is given in fig. 19. The output may have one of

the following words:

[Not a quadratic equation; real roots; Imaginary roots; Equal

roots]

Draw the flow graph and DD path graph. Also find

independent paths from the DD Path graph.


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Fig. 19: Code of quadratic equation problem


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Fig. 19 (a): Program flow graph


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Fig. 19 (b): DD Path graph

ABCDEFGHIJNRS

ABGHIJNRS

ABCDFGHIJNRS

ABGHIKLNRS

ABGHIKMNRS

ABGOPRS

ABGOQRS


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The mapping table forDD path graph is:


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Independent paths are:

(i) ABGOQRS (ii) ABGOPRS(iii) ABCDFGOQRS (iv) ABCDEFGOPRS

(v) ABGHIJNRS (vi) ABGHIKLNRS

(vi) ABGHIKMNRS


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Example 14

Consider a program given in Fig.20 for the classification of a

triangle. Its input is a triple of positive integers (say a,b,c) from

the interval [1,100]. The output may be [Scalene, Isosceles,

Equilateral, Not a triangle].

Draw the flow graph & DD Path graph. Also find the

independent paths from the DD Path graph.


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Fig. 20 : Code of tr

iang

lecl

assific

ation prob

lem


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Solution : Flow graph of triangle problem is:

Fig. 20 (a): Program flow graph


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The mapping table forDD path graph is:


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Fig. 20 (b): DD Path graph

Independent paths are:i. ABFGNPQR

ii. ABFGNOQR

iii. ABCEGNPQR

iv. ABCDEGNOQR

v. ABFGHIMQR

vi. ABFGHJKMQR

vii. ABFGHJMQR

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