zcw10-Graded_Assignment_Sep_2025_CT_Qualifier (1)

Graded Assignment - (Sep 2025 - CT - Qualifier)

The due date for submitting this assignment has passed. Due on 2025-12-03, 23:59 IST. You may submit any number of times before the due date. The final submission will be considered for grading.

Last Submitted: You have last submitted on: 2025-12-03, 13:00 IST

Note: ++++++++++++++++++++++++++++++++++

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Question 1

If matrixPh[i] [j] = 1, then

• i scored at most 10 and at least 20 more marks in Physics than j
• i scored at least 10 and at most 20 more marks in Physics than j
• j scored at least 10 and at most 20 more marks in Physics than i
• j scored at most 10 and at least 20 more marks in Physics than i

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• i scored at least 10 and at most 20 more marks in Physics than j

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Question 2

Choose the correct statement based on above pseudocode.

• For all i, j with i $\ne$ j, matrixPh[i][j] + matrixPh[j][i] = 1
• For all i, j with i $\ne$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 0
• For all i, j with i $\ne$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 1
• For all i, j with i $\ne$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 1
• For all i, j with i $\ne$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 0

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• For all i, j with i $\ne$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 0

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Question 3

Consider the dictionary D, and the matrices matrixPh, matrixCh and matrixMa computed in the previous question. The following pseudocode generate the adjacency matrix matrixHelp.

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n = length(keys(D))

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matrixHelp = createMatrix(n, n)

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    foreach i in rows(matrixHelp){

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        foreach j in columns(matrixHelp){

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            matrixHelp[i][j] = matrixCh[i][j] + matrixPh[i][j] + matrixMa[i][j]

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        }

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}

Let i and j be indices of two students. Choose the correct statement(s) from the given options. It is a Multiple Select Question (MSQ)

• 0 ⇐ matrixHelp[i][j] ⇐ 3
• matrixHelp[i][j] + matrixHelp[j][i] ⇐ 3
• matrixHelp[i][j] $\ne$ matrixHelp[j][i]
• if matrixHelp[i][j] = 0, then matrixHelp[j][i] = 3
• if matrixHelp[i][j] = 3, then matrixHelp[j][i] = 0

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• 0 ⇐ matrixHelp[i][j] ⇐ 3
• matrixHelp[i][j] + matrixHelp[j][i] ⇐ 3
• if matrixHelp[i][j] = 3, then matrixHelp[j][i] = 0

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Question 4

At the end of the following pseudocode, A captures the number of distinct pairs of students who can help each other in at least one subject, and B captures the number of distinct pairs of students where one can help the other in all subjects. Choose the correct code fragment to complete the pseudocode.

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A = 0, B = 0

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foreach i in rows(matrixHelp){

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    foreach j in columns(matrixHelp){

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        ***********************

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         *** Fill the code ***

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        ***********************

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    }

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}

9

​

• xxxxxxxxxx 1 if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){ 2 A = A + 1 3 } 4 if(matrixHelp[i][j] == 3){ 5 B = B + 1 6 }
• xxxxxxxxxx 1 if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){ 2 A = A + 1 3 } 4 if(matrixHelp[i][j] > 2){ 5 B = B + 1 6 }
• xxxxxxxxxx 1 if(i < j){ 2 if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){ 3 A = A + 1 4 } 5 if(matrixHelp[i][j] > 2){ 6 B = B + 1 7 } 8 }
• xxxxxxxxxx 1 if(i < j){ 2 if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){ 3 A = A + 1 4 } 5 } 6 if(matrixHelp[i][j] > 2){ 7 B = B + 1 8 }

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• if(i < j){ if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){ A = A + 1 } } if(matrixHelp[i][j] > 2){ B = B + 1 }

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Question 5

The following pseudocode generates a graph G from books. Each node corresponds to an author. There is an edge between two different authors i and j if they have co-authored a book, and the edge is labeled with the number of books they have co-authored. Choose the correct code fragment to complete the following pseudocode.

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matrix = createMatrix(n, n)

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foreach i in keys(books){

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    foreach j in books[i]{

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        foreach k in books[i]{

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           ***********************

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            *** Fill the code ***

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           ***********************        

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        }

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    }

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}

• xxxxxxxxxx 1 matrix[j][k] = matrix[j][k] + 1
• xxxxxxxxxx 1 if(j != k){ 2 matrix[j][k] = matrix[j][k] + 1 3 }
• xxxxxxxxxx 1 if(j != k){ 2 matrix[j][k] = matrix[j][k] + 1 3 matrix[k][j] = matrix[k][j] + 1 4 }
• xxxxxxxxxx 1 matrix[j][k] = matrix[j][k] + 1 2 matrix[k][j] = matrix[k][j] + 1

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• if(j != k){ matrix[j][k] = matrix[j][k] + 1 }

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Question 6

The following pseudocode creates adjacency matrix matrix2 of another graph H from books. For two different authors i and j, what does the value matrix2[i][j] represent at the end of the execution?

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matrix2 = createMatrix(n, n)

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foreach j in rows(matrix2){

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    foreach k in columns(matrix2){

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        matrix2[j][k] = []

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    }

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}

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foreach i in keys(books){

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    foreach j in book[i]{

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        foreach k in books[i]{

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            foreach h in books[i]{

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                if(j != k and j != h and k != h and not member(matrix2[j][k], h)){

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                    matrix2[j][k] = matrix2[j][k] ++ [h]

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                    matrix2[k][j] = matrix2[k][j] ++ [h]

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                }

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            }

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        }

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    }

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}

• List of authors who have co-authored a book with both i and j
• List of authors who have co-authored a book with either i or j
• List of authors who have co-authored at least two book with both i and j
• List of authors who have co-authored at least two book with either i or j

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• List of authors who have co-authored a book with both i and j

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Question 7

Which of the following combinations of entries in matrix and matrix2 is possible for two different authors i and j? It is Multiple Select Question (MSQ).

• matrix[i] [j] = 0 and matrix2[i] [j] = [ ]
• matrix[i][j] = 0 and matrix2[i][j] $\ne$ [ ]
• matrix[i][j] > 0 and matrix2[i][j] = [ ]
• matrix[i][j] > 0 and matrix2[i][j] $\ne$ [ ]

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• matrix[i] [j] = 0 and matrix2[i] [j] = [ ]
• matrix[i][j] > 0 and matrix2[i][j] = [ ]
• matrix[i][j] > 0 and matrix2[i][j] $\ne$ [ ]

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Question 8

Consider the matrices matrix and matrix2 constructed in the previous questions.

findAuthor(matrix) finds an author who has the maximum number of co-authors. Choose the correct implementation of the procedure findAuthor. It is a Multiple Select Question.

• xxxxxxxxxx 1 Procedure findAuthor(M) 2 Max = 0 3 A = 0 4 foreach i in rows(M){ 5 Sum = 0 6 foreach j in columns(M){ 7 if(M[i][j] > 0){ 8 Sum = Sum + 1 9 } 10 } 11 if(Sum > Max){ 12 Max = Sum 13 A = i 14 } 15 } 16 return(A) 17 End findAuthor
• xxxxxxxxxx 1 Procedure findAuthor(M) 2 Max = 0 3 A = 0 4 foreach i in rows(M){ 5 Sum = 0 6 foreach j in columns(M){ 7 if(M[i][j] > 0){ 8 Sum = Sum + M[i][j] 9 } 10 } 11 if(Sum > Max){ 12 Max = Sum 13 A = i 14 } 15 } 16 return(A) 17 End findAuthor
• xxxxxxxxxx 1 Procedure findAuthor(M) 2 Max = 0 3 A = 0 4 foreach i in columns(M){ 5 Sum = 0 6 foreach j in rows(M){ 7 if(M[j][i] > 0){ 8 Sum = Sum + 1 9 } 10 } 11 if(Sum > Max){ 12 Max = Sum 13 A = i 14 } 15 } 16 return(A) 17 End findAuthor
• xxxxxxxxxx 1 Procedure findAuthor(M) 2 Max = 0 3 A = 0 4 foreach i in columns(M){ 5 Sum = 0 6 foreach j in rows(M){ 7 if(M[j][i] > 0){ 8 Sum = Sum + M[j][i] 9 } 10 } 11 if(Sum > Max){ 12 Max = Sum 13 A = i 14 } 15 } 16 return(A) 17 End findAuthor

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• Procedure findAuthor(M) Max = 0 A = 0 foreach i in rows(M){ Sum = 0 foreach j in columns(M){ if(M[i][j] > 0){ Sum = Sum + 1 } } if(Sum > Max){ Max = Sum A = i } } return(A) End findAuthor
• Procedure findAuthor(M) Max = 0 A = 0 foreach i in columns(M){ Sum = 0 foreach j in rows(M){ if(M[j][i] > 0){ Sum = Sum + 1 } } if(Sum > Max){ Max = Sum A = i } } return(A) End findAuthor

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Question 9

Consider the adjacency matrix matrix constructed above. Assume that there exists a procedure removeDuplicate which receives a list as input and removes all duplicate elements in the list. When will findGoodSet(matrix) return True?

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Procedure findGoodSet(M)

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    foreach i in rows(M){

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        foreach j in columns(M){

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            foreach h in rows(M){

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                list1 = []

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                if(length(M[i][j]) == 1 and member(D[h], first(M[i][j]))){

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                    list1 = list1 ++ M[i][j]

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                }

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                if(length(M[i][h]) == 1 and member(D[j], first(M[i][h]))){

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                    list1 = list1 ++ M[i][h]

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                }

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                if(length(M[j][h]) == 1 and member(D[i], first(M[j][h]))){

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                    list1 = list1 ++ M[j][h]

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                }

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                list1 = removeDuplicate(list1)

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                if(length(list1) == 1){

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                    return(True)

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                }

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            }

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        }

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    }

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    return(False)

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End findGoodSet

• If there exists three customers who have visited all three shops.
• If there exist three customers such that every pair of customers among them have visited only one and the same shop in common.
• If there exists three customers who have visited exactly one shop.
• If there exists three customers where each pair among them have visited exactly one shop in common.

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• If there exist three customers such that every pair of customers among them have visited only one and the same shop in common.

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Question 10

For a pair of customers i and j, j is said to be shopping partner of i if i and j have visited at least two shops in common. findTopCustomer(matrix) finds a customer who has the maximum shopping partners. Choose the correct implementation of findTopCustomer.

• xxxxxxxxxx 1 Procedure findTopCustomer(M) 2 Max = 0, A = 0 3 foreach i in rows(M){ 4 C = 0 5 foreach j in columns(M) { 6 if(length(M[i][j]) == 2){ 7 C = C + 1 8 } 9 } 10 if(C > Max){ 11 Max = C 12 A = i 13 } 14 } 15 return(A) 16 End findTopCustomer
• xxxxxxxxxx 1 Procedure findTopCustomer(M) 2 Max = 0, A = 0 3 foreach i in rows(M){ 4 C = 0 5 foreach j in columns(M){ 6 if(length(M[i][j]) > 1){ 7 C = C + 1 8 } 9 } 10 if(C > Max){ 11 Max = C 12 A = i 13 } 14 } 15 return(A) 16 End findTopCustomer
• xxxxxxxxxx 1 Procedure findTopCustomer(M) 2 Max = 0, A = 0 3 foreach i in rows(M){ 4 C = 0 5 foreach j in columns(M) { 6 if(length(M[i][j]) == 2){ 7 C = C + 1 8 } 9 } 10 if(C > Max){ 11 Max = C 12 A = i 13 } 14 } 15 return(Max) 16 End findTopCustomer
• xxxxxxxxxx 1 Procedure findTopCustomer(M) 2 Max = 0, A = 0 3 foreach i in rows(M){ 4 C = 0 5 foreach j in columns(M){ 6 if(length(M[i][j]) > 1){ 7 C = C + 1 8 } 9 } 10 if(C > Max){ 11 Max = C 12 A = i 13 } 14 } 15 return(Max) 16 End findTopCustomer

Status: Yes, the answer is correct. Score: 5

Accepted Answers:

• Procedure findTopCustomer(M) Max = 0, A = 0 foreach i in rows(M){ C = 0 foreach j in columns(M){ if(length(M[i][j]) > 1){ C = C + 1 } } if(C > Max){ Max = C A = i } } return(A) End findTopCustomer

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