Control Flow Graph

by | Dec 15, 2023 | Computer science

 

Below is a bubble sort program that sorts the elements in an array.

static void bubbleSort(int[] arr) {

int n = arr.length;

int temp = 0;

for (int i = 0; i < n; i++) {

for (int j = 1; j < (n – i); j++) {

if (arr[j – 1] > arr[j]) {

temp = arr[j – 1];

arr[j – 1] = arr[j];

arr[j] = temp;

}

}

}

}

1. Based on the program above, please draw a control flow graph for it. Hint: Annotating some statements or conditions on nodes/edges will be very helpful.
2. In your control flow graph, what are the test requirements for edge coverage?
3. List test path(s) that achieves the edge coverage.
4. Provide test cases for each test path you list in the previous question. If it is not possible to find the test input for certain test path, describe the reason.
Hint: Not providing expected outputs will get 2 points deduction. Not matching test paths with their corresponding input/output will get 3 points deduction.
5. In your control flow graph, what are the test requirements for edge-pair coverage?
6. List test paths that achieve the edge-pair coverage.
7. Provide test cases for each test path you list in the previous question. If it is not possible to find the test input for certain test path, describe the reason.

 

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

Sample Answer

Sample Answer

 

Control Flow Graph:

┌─► (int i = 0)
│
│ ┌─► (int j = 1)
│ │
│ │ ┌─► (arr[j – 1] &gt; arr[j])
│ │ │
◄───┼───┤
│ │ ┌─► temp = arr[j – 1]
│ │ │
└───┼───┼───► arr[j – 1] = arr[j]
│ │
└───┼───► arr[j] = temp
│
◄──► (j &lt; (n – i))
│
◄──► (i &lt; n)

Test Requirements for Edge Coverage:

Every edge in the control flow graph should be covered at least once.

Test Path(s) for Edge Coverage:

Path 1: (i = 0, j = 1, arr[j – 1] &gt; arr[j], temp = arr[j – 1], arr[j – 1] = arr[j], arr[j] = temp, j &lt; (n – i), i &lt; n)

Test Cases for Edge Coverage:

Test Case 1: arr = [4, 2, 1, 3]
Test Case 2: arr = [5, 1, 3, 2, 4]

Test Requirements for Edge-Pair Coverage:

Every pair of edges that share a common node should be covered at least once.

Test Paths for Edge-Pair Coverage:

Path 1: (i = 0, j = 1, arr[j – 1] &gt; arr[j], temp = arr[j – 1], arr[j – 1] = arr[j], arr[j] = temp, j &lt; (n – i), i &lt; n)
Path 2: (i = 0, j = 1, arr[j – 1] &lt;= arr[j], j &lt; (n – i), i &lt; n)
Path 3: (i = 0, j &lt; (n – i), i &lt; n)
Path 4: (i = 0, j &gt;= (n – i), i &lt; n)
Path 5: (i &gt;= n)

Test Cases for Edge-Pair Coverage:

Test Case 1: arr = [4, 2, 1, 3]
Test Case 2: arr = [5, 1, 3, 2, 4]
Test Case 3: arr = [2, 4, 6]
Test Case 4: arr = [1]
Test Case 5: arr = [] (empty array)

Note: It is not possible to find a test input that covers the path where i &gt;= n because it would mean that the outer loop has already terminated and the function has completed its execution.

 

 

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