Foundation Graded Assignments – Students Community

Statistics Week 12 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:44:44 +0000

Statistics Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:39:08 +0000

Statistics week 11 graded assignment Complete Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments

A match predictor claims that he can predict the result of a match correctly 77% of the time. It is agreed that his claim will be accepted if he correctly predicts the results of at least 4 of 8 matches. What is the probability that his claim gets rejected?

\sum_{i = 1}^{3}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 0}^{3}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 0}^{4}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

\sum_{i = 1}^{4}^{8} C_{i} \times (0.77)^{i} \times (0.23)^{8 - i}

1 point

X \sim B in o mia l (n, p)

, then which of the following statement/s is/are always true? (

n > 0

and

0 < p < 1

)

E (X) \leq Va r (X)

E (X) < Va r (X)

E (X) \geq Va r (X)

E (X) > Va r (X)

Va r (X) \leq S . D (X)

Va r (X) \geq S . D (X)

Two friends (say ‘

A

‘ and ‘

B

‘) could not decide whether to play a racing game or a boxing game on Xbox. They decide to play a card-game first. If ‘

A

‘ wins at least 3 rounds out of the 5 rounds of the card game played, then the boxing game will be played. The chances of ‘

A

‘ winning in any round of the card game is 2:5. Find the probability that the boxing game will be played on Xbox? (Enter the answer correct to 2 decimal places)
Hint: If the chances of happening of an event is x:y then, the probability equals

x + y x

1 point

Let

X

~ Binomial(6,p). If the probabilities of 4 and 5 successes are approximately 0.311 and, 0.1866 respectively, then find the parameter ‘p’ of the distribution.(Enter the answer correct to 2 decimal places)

1 point

If the expected number of sixes hit by a batsman on

n

balls is 6.39 and the variance for the same is 1.8531, then what is the probability of him hitting at least one six on any randomly selected

n

balls? Assume that the probability of him hitting a six on any ball is constant. (Enter the answer correct to 4 decimal places)

1 point

The probability of a student clearing a competitive exam is

4 1

. If he gives the exam 6 times, then what is the probability of him clearing the exam at least twice?(Enter the answer correct to 2 decimal places)

1 point

Choose the correct condition/s about binomial distribution.

The probability of success

p

keeps varying for each trial.

The number of trials

n

is finite.

The trials are dependent on each other.

The trials are independent of each other.

Rithika wants to test whether the coin she has is a fair coin or not. To test this, she conducted an experiment of tossing the coin 5 times. Binomial random variable

X

is defined as the total number of heads(

i

) after 5 tosses. The probability distribution of the binomial random variable is given in Table 11.1.G.

Table 11.1.G: Binomial Distribution
$X = i$	$P (X = i)$
0	0.00032
1	0.0064
2	0.0512
3	0.2048
4	0.4096
5	0.32768

What is the approximate probability of getting a head in tossing the given coin? (Enter the answer correct to one decimal place)

1 point

At a school function, It is noticed that 9% of the students are not wearing polished shoes and 12% of students are not wearing school ties. It is announced that the students who have committed any of the infractions will be punished, and that these two infractions are independent of one another. If a teacher selects 5 students at random, then find the probability that exactly three of the students will be punished for any of the infractions?

^{5} C_{3} (0.1992)^{3} (0.8008)^{2}

^{5} C_{3} (0.0108)^{3} (0.9892)^{2}

^{5} C_{3} (0.09)^{3} (0.91)^{2} +^{5} C_{3} (0.12)^{3} (0.88)^{2}

^{5} C_{3} (0.21)^{3} (0.79)^{2}

1 point

There are 7 black and 20 blue pens in a box. A pen is chosen at random, and its colour is noted. If the process repeats independently, 13 times with replacement, then calculate the expected number of black pens chosen?

27 91

27 260

20 169

20 91

Number of calls received at an office follows a Poisson distribution with an average of 1 call per minute. Find the probability that no call will be received in two minutes at the office. (Enter the answer correct to 2 decimal accuracy.)

1 point

A quiz team is to be chosen randomly from 6 boys and 4 girls. The team has 3 slots which are to be filled randomly. If

X

denotes the number of boys in the quiz team, then using the given information, answer questions (12) and (13).

Calculate

P (X = 2)

. (Enter the answer correct to 2 decimal places)

1 point

Calculate the value of

E (X)

. (Enter the answer correct to 2 decimal places)

English Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:37:25 +0000

Maths Week 11 Graded Assignments IIT Madras

Khushi Dii — Tue, 15 Aug 2023 14:31:19 +0000

CT Week 11 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:24:56 +0000

Computational Thinking week 11 graded assignment Complete Questions Are Discussed In This Blog. Access From Below Link

1.reverse is a recursive procedure to reverse a list. Select the correct code fragment to complete the pseudocode given below. It is a Multiple Select Question (MSQ).

 
 
 
 
Procedure reverse(L)
    if(length(L) <= 1){
        return(L)
    }
     *********************
      * Fill the code *
     *********************
End reverse
 

return([last(L)] ++ reverse(init(L)))

return([first(L)] ++ reverse(rest(L)))

return([last(L)] ++ reverse(init(rest(L))) ++ [first(L)])

return([first(L)] ++ reverse(init(rest(L))) ++ [last(L)])

return([last(L)] ++ reverse(rest(init(L))) ++ [first(L)])

Question:2-4:

An auto-grading system for an online course is designed in the following way:

∙

A student’s submission is recorded as a dictionary with the following keys

\circ

The “roll” key maps to the student’s roll number.

\circ

The “time” key maps to the time of submission

\circ

The “score” key maps to the student’s score for that submission

∙

Each student can make multiple submissions before the deadline.

∙

Every time a student makes a submission, the dictionary corresponding to it is appended to the end of a list called scores.

An example:

 
scores =   [{“roll”: 12, “time”: 10:20, “score”: 80 },
            {“roll”: 20, “time”: 11:23, “score”: 70 },
            {“roll”: 12, “time”: 20:40, “score”: 90 },
            {“roll”: 12, “time”: 23:50, “score”: 95 },
            {“roll”: 20, “time”: 23:53, “score”: 65 }]

Study the following pseudocode:

 
Procedure isPresent(L, roll)
    foreach D in L{
        if(D[“roll”] == roll){
            return(True)
        }
    }
    return(False)
End isPresent

 
 
 
 
 
Procedure getSubs(L)
    firstSub = {}, restSub = []
    if(length(L) <= 1){
        return(L)
    }
    firstSub = first(L)
    restSub = rest(L)
    if(isPresent(restSub, firstSub[“roll”])){
        return(getSubs(restSub))
    }
    else {
        return([firstSub] ++ getSubs(restSub))
    }
End getSubs
 

Answer questions 2 to 4 after executing the pseudocode given below:

 
submisssions = []
  
scores = [ {“roll”: 12, “time”: 10:20, “score”: 80 },
           {“roll”: 20, “time”: 11:23, “score”: 70 },
           {“roll”: 12, “time”: 20:40, “score”: 90 },
           {“roll”: 12, “time”: 23:50, “score”: 95 },
           {“roll”: 20, “time”: 23:53, “score”: 65 } ]
    
submisssions = getSubs(scores)

4 points

2. What is the value of submissions?

[ {“roll”: 12, “time”: 10:20, “score”: 80 },

{“roll”: 20, “time”: 11:23, “score”: 70 } ]

[ {“roll”: 20, “time”: 11:23, “score”: 70 },

{“roll”: 12, “time”: 10:20, “score”: 80 } ]

[ {“roll”: 12, “time”: 23:50, “score”: 95 },

{“roll”: 20, “time”: 23:53, “score”: 65 } ]

[ {“roll”: 20, “time”: 23:53, “score”: 65 },

{“roll”: 12, “time”: 23:50, “score”: 95 } ]

4 points

3.What does the variable submissions represent?

The list of all the submissions made by the students sorted in the ascending order of time.

The list of all the submissions made by the students sorted in the descending order of time.

The list of the last submissions made by the students sorted in the ascending order of time.

The list of the last submissions made by the students sorted in the descending order of time.

The list of the first submissions made by the students sorted in the ascending order of time.

The list of the first submissions made by the students sorted in the descending order of time.

4 points

4.Assume that reverse is a procedure that reverses a list. Which of the following statements returns the list of the first submissions made by the students sorted in the ascending order of time?

getSubs(scores)

reverse(getSubs(scores))

getSubs(reverse(scores)))

reverse(getSubs(reverse(scores)))

4 points

5.outcomes is a list of strings that contains the information about the outcome of cricket matches played by India in a tournament. Assume that each element in the list is either “win” or “loss”. For example, if five matches have been played, then outcomes could look like this:

[“won”, “lost”, “lost”, “won”, “won”]

We call a list of outcomes a blank slate if the number of wins is equal to the number of losses. blankSlate is a procedure that accepts outcomes as input and returns True if it is a blank slate and False otherwise. Select the correct code fragment to complete the following pseudocode. It is a Multiple Select Question (MSQ).

 
 
 
 
Procedure blankSlate(outcomes)
    if(numeric(outcomes) == 0){
        return(True)
    }
    else{
        return(False)
    }
End blankSlate
  
*********************
* Fill the code *
*********************
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(last(L) == “won”){
        return(numeric(init(L)) + 1)
    }
    else{
        return(numeric(init(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return (0)
    }
    if(last(L) == “won”){
        return(numeric(rest(L)) + 1)
    }
    else{
        return(numeric(rest(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(first(L) == “won”){
        return(numeric(rest(L)) + 1)
    }
    else{
        return(numeric(rest(L)) − 1)
    }
End numeric
 

 
 
 
 
 
Procedure numeric(L)
    if(length(L) == 0){
        return(0)
    }
    if(first(L) == “won”){
        return(numeric(init(L)) + 1)
    }
    else{
        return(numeric(init(L)) − 1)
    }
End numeric
 

QUESTION-6-7

2n chess players are participating in a tournament. Each player is given a unique participant ID that is represented as a string. The player IDs are stored in a non-empty list players in the descending order of their rating, i.e., the first element in the list has the ID of the player with the highest rating.

The matches are scheduled as follows: The $i^{t h}$ match is between the $i^{t h}$ player from the top and the $i^{t h}$ player from the bottom of the rating list. We wish to create a list called matches which stores the sequences of matches, starting with the first match and ending with the last match. Each match is represented as a list of two players, the first element of which is the ID of the player with the higher rating, while the second element is the ID of the player with lower rating. Assume that no two players have the same rating.

Answer questions 6 and 7 based on this information.

4 points

matchThem is a recursive procedure that accepts players as argument and returns matches. Select the correct implementation of the procedure. It is a Multiple Select Question (MSQ).

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 2){
        return([players])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 2){
        return(players)
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 0){
        return([])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

 
 
 
 
 
Procedure matchThem(players)
    firstLast = [], middle = []
    if(length(players) == 0){
        return([players])
    }
    else{
        firstLast = [first(players), last(players)]
        middle = init(rest(players))
        return([firstLast] ++ matchThem(middle))
    }
End matchThem
 

3 points

7.matchThem is a non-recursive procedure that accepts players as argument and returns matches. Select the correct implementation of the procedure.

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[last(players), first(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) >= 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(init(players))
    }
    return(matches)
End matchThem

 
Procedure matchThem(players)
    matches = [ ]
    while(length(players) > 0){
        matches = matches ++ [[first(players), last(players)]]
        players = rest(players)
    }
    return(matches)
End matchThem

Question 8-11

Consider the following graph with six nodes. A is a 6 × 6 matrix corresponding to this graph. Assume that it has already been computed:

In the following pseudocode:

graph is a matrix
parents is a dictionary
sequence is a list

 
 
 
 
 
Procedure DFS(graph, parents, sequence, i)
    sequence = sequence ++ [i]
    foreach j in columns(graph){
        if(graph[i][j] == 1 and not(isKey(parents, j))){
            parents[j] = i
            parents, sequence = DFS(graph, parents, sequence, j)
        }
    }
    return(parents, sequence)
End DFS
 

Answer questions 8 to 11 using the information given above. In all questions, S represents a list, P represents a dictionary, while A and B represent matrices.

4 points

8.What will be the value of S after executing the following pseudocode?

 
P = { }
S = [ ]
P[0] = -1
P, S = DFS(A, P, S, 0)

[0, 1, 2, 5, 3, 4]

[0, 1, 4]

[0, 1, 2, 3, 5, 4]

[0, 3, 1, 4, 5]

3 points

9.What will be the value of nodes after executing the following pseudocode?

 
P = { }
S = [ ], nodes = []
P[5] = -1
P, S = DFS(A, P, S, 5)
nodes = keys(P)

[5, 2, 1, 0, 3, 4]

[5, 2, 1, 4, 0, 3]

[5, 2, 3, 0, 1, 4]

Cannot be determined

3 points

10.Assume that sort is a procedure that accepts a list of integers as input and returns a sorted list in ascending order. If 0 ≤ start ≤ 5, which of the following statements are true at the end of execution of the following pseudocode? It is a Multiple Select Question (MSQ).

 
P = { }
S = [], nodes = []
P[start] = -1
P, S = DFS(A, P, S, start)
nodes = sort(keys(P))

nodes is equal to [0, 1, 2, 3, 4, 5]

S is equal to [0, 1, 2, 3, 4, 5]

The value of nodes is independent of start

The value of S is independent of start

The graph is connected.

The graph is not connected.

4 points

11.Execute the following pseudocode

 
 
 
 
P = { }
S = [ ]
P[3] = -1, parent = 0
P, S = DFS(A, P, S, 3)
B = createMatrix(6, 6)
foreach i in keys(P){
    if(i != 3){
        parent = P[i]
        B[parent][i] = 1
    }
}
 

Correct Answer

Statistics Week 10 Graded Assignments

Khushi Dii — Sat, 12 Aug 2023 04:22:00 +0000

Statistics Week 10 graded assignment Complete Solutions Key Given In This Page Check Below . We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments

There are

2^{6}

numbered cards in a deck among which

^{6} �_{�}

cards bear the number

�; � = 0, 1, 2, . . ., 6

. From the deck, 10 cards are drawn with replacement. What is the expectation of the sum of their numbers?(Enter the answer correct to 1 decimal accuracy)

1 point

An unbiased die is thrown 13 times. After each throw a ‘+’ is recorded for 2 or 5 and ‘-‘ is recorded for 1,3,4 or 6, the signs forming an ordered sequence. To each, except the first and last sign, a random variable

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Find the expected value of

�

\frac{183}{9}

\frac{139}{9}

\frac{22}{9}

\frac{66}{9}

1 point

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Which of the following statement(s) is/are true?

� (�) = 3 � (�) + 13

� (�) = 9 � (�)

� (�) = 9 � (�) + 13

� (�) = 9 � (�) + 13

1 point

Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability 0.66 and to the left with probability 0.34. Assume that the movements are independent of each other.
Hint: Consider the random variable

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the expected distance between the starting point and end point of Amandeep after 5 steps?

- 0.32

1.6

- 1.6

0.32

1 point

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the variance distance between the starting point and end point of Amandeep after 5 steps?

4.49

0.9

1.56

1

A box contains 10 white and 6 black balls. 2 balls are drawn at random without replacement. Find the expected value of the number of white balls drawn. (Enter the answer correct to 2 decimal places)

1 point

Rohit wants to open his door with

5

keys(out of which

1

will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from further selection, then Find the expected number of trials required to open the door.
Hint: Suppose Rohit gets the first success at

�^{� ℎ}

trial, i.e., he is unable to open the door in the first

(� - 1)

trials.
And, P(he gets first success at second trial)=

(1 - \frac{1}{5}) \times \frac{1}{4}

�

and

�

are independent random variables with means 14 and 20, and variances 2 and 6 respectively. Find the variance of

3 � + 6 �

1 point

Table Q10.1.G. represents the probability mass function of a random variable X

Table Q10.1.G: Probability Mass Function
$�$	-1	4	5
$� (� = �)$	$\frac{1}{6}$	$\frac{1}{3}$	$\frac{9}{18}$

Calculate the value of

� (2 � + 1)^{2}

. (Enter the answer correct to 2 decimal places)

1 point

Suppose that

�

is a random variable for which

� (�) = 15

and

� � � (�) = 22

. Find the positive values of

�

and

�

such that

� = � � - �

, has expectation

0

and variance

1

\frac{- 1}{\sqrt{22}}

\frac{- 15}{\sqrt{22}}

1

15

\frac{1}{22}

\frac{15}{\sqrt{22}}

\frac{1}{\sqrt{22}}

\frac{15}{\sqrt{22}}

CT Week 10 Graded Assignments IIT Madras

Khushi Dii — Sat, 12 Aug 2023 04:21:00 +0000

Computational Thinking week 10 graded assignment Complete Solutions Are Discussed In This Blog. We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments

1.The following pseudocode is executing using the “Scores” table. At the end of the execution, matrix represents the adjacency matrix of the graph generated from the “Scores” table.

 
 
 
 
D = {}
while(Table 1 has more rows){
    Read the first row X in Table 1
    D[X.SeqNo] = {"P": X.Physics, "C": X.Chemistry, "M": X.Mathematics}
    Move X to Table 2
}
matrixPh = getAdjMatrix(D, "P")
matrixCh = getAdjMatrix(D, "C")
matrixMa = getAdjMatrix(D, "M")
  
Procedure getAdjMatrix(D, Subject)
    n = length(keys(D))
    matrix = createMatrix(n, n)
    foreach i in rows(matrix){
        foreach j in columns(matrix){
            if(i != j){
                diff = D[i][Subject] - D[j][Subject]
                if(10 <= diff and diff <= 20){
                    matrix[i][j] = 1
                }
            }
        }
    }
    return(matrix)
End getAdjMatrix
 

5 points

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

5 points

2.Choose the correct statement based on above pseudocode.

For all i, j with i

≠

$\neq =$ j, matrixPh[i][j] + matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 0

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 1 then matrixPh[j][i] = 1

For all i, j with i

≠

$\neq =$ j, if matrixPh[i][j] = 0 then matrixPh[j][i] = 0

5 points

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.

 
n = length(keys(D))
matrixHelp = createMatrix(n, n)
    foreach i in rows(matrixHelp){
        foreach j in columns(matrixHelp){
            matrixHelp[i][j] = matrixCh[i][j] + matrixPh[i][j] + matrixMa[i][j]
        }
}

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]

≠

$\neq =$ matrixHelp[j][i]

if matrixHelp[i][j] = 0, then matrixHelp[j][i] = 3

if matrixHelp[i][j] = 3, then matrixHelp[j][i] = 0

5 points

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.

 
 
 
 
A = 0, B = 0
foreach i in rows(matrixHelp){
    foreach j in columns(matrixHelp){
        ***********************
         *** Fill the code ***
        ***********************
    }
}
 

 
if(matrixHelp[i][j] > 0 and matrixHelp[j][i] > 0){
    A = A + 1
}
if(matrixHelp[i][j] == 3){
    B = B + 1
}

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

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

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

Question (5-8)
The following table contains information regarding books in a library. Each entry in the table corresponds to a book and is authored by at least two authors. There is a pool of n authors, each author being assigned a unique index between 0 and n − 1. There are M books in total.

The table is represented by a dictionary named books, with the keys as serial numbers and values as the corresponding list of authors. Assume that books has already been computed. For example, we have: books[0] = [0, 2, 3]. Consider the followig question.

5 points

4.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.

 
 
 
 
matrix = createMatrix(n, n)
foreach i in keys(books){
    foreach j in books[i]{
        foreach k in books[i]{
           ***********************
            *** Fill the code ***
           ***********************        
        }
    }
}
 

 
matrix[j][k] = matrix[j][k] + 1

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

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

 
matrix[j][k] = matrix[j][k] + 1
matrix[k][j] = matrix[k][j] + 1

5 points

5.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?

 
 
 
 
matrix2 = createMatrix(n, n)
foreach j in rows(matrix2){
    foreach k in columns(matrix2){
        matrix2[j][k] = []
    }
}
foreach i in keys(books){
    foreach j in book[i]{
        foreach k in books[i]{
            foreach h in books[i]{
                if(j != k and j != h and k != h and not member(matrix2[j][k], h)){
                    matrix2[j][k] = matrix2[j][k] ++ [h]
                    matrix2[k][j] = matrix2[k][j] ++ [h]
                }
            }
        }
    }
}
 

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

5 points

6.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]

≠

$\neq =$ [ ]

matrix[i][j] > 0 and matrix2[i][j] = [ ]

matrix[i][j] > 0 and matrix2[i][j]

≠

$\neq =$ [ ]

5 points

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.

 
 
 
 
 
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 rows(M){
        Sum = 0
        foreach j in columns(M){
            if(M[i][j] > 0){
                Sum = Sum + M[i][j]
            }
        }
        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
 

 
 
 
 
 
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 + M[j][i]
            }
        }
        if(Sum > Max){
            Max = Sum
            A = i
        }
    }
    return(A)
End findAuthor
 

Question (9-10)

The following pseudocode is executing using the “Shopping bills” dataset. Each customer is being assigned a unique index between 0 and n − 1. Dictionary D has already been computed with keys as index and values as list of distinct shops visited by the corresponding customer. Assume that there exists a procedure intersection which takes two lists as input and outputs another list which contains the common elements in the input lists.

 
 
 
 
n = length(keys(D))
matrix = createMatrix(n, n)
foreach i in rows(matrix){
    foreach j in columns(matrix){
        if(i != j){
            matrix[i][j] = intersection(D[i], D[j])
        }
        else{
            matrix[i][j] = []
        }
    }
}
 

5 points

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?

 
 
 
 
Procedure findGoodSet(M)
    foreach i in rows(M){
        foreach j in columns(M){
            foreach h in rows(M){
                list1 = []
                if(length(M[i][j]) == 1 and member(D[h], first(M[i][j]))){
                    list1 = list1 ++ M[i][j]
                }
                if(length(M[i][h]) == 1 and member(D[j], first(M[i][h]))){
                    list1 = list1 ++ M[i][h]
                }
                if(length(M[j][h]) == 1 and member(D[i], first(M[j][h]))){
                    list1 = list1 ++ M[j][h]
                }
                list1 = removeDuplicate(list1)
                if(length(list1) == 1){
                    return(True)
                }
            }
        }
    }
    return(False)
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.

5 points

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.

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M) {
            if(length(M[i][j]) == 2){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(A)
End findTopCustomer
 

 
 
 
 
 
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
 

 
 
 
 
 
Procedure findTopCustomer(M)
    Max = 0, A = 0
    foreach i in rows(M){
        C = 0
        foreach j in columns(M) {
            if(length(M[i][j]) == 2){
               C = C + 1
            }
        }
        if(C > Max){
           Max = C
           A = i
        }
    }
    return(Max)
End findTopCustomer
 

 
 
 
 
 
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(Max)
End findTopCustomer