Capella MAT2051 2019 October Unit 6 Quiz Latest

Question # 00745091 Posted By: rey_writer Updated on: 11/28/2019 10:58 AM Due on: 11/28/2019
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MAT2051 Discrete Mathematics

Unit 6 Quiz

•             Question 1          How many times does the computer print the string "Hello"?

i = 2

while (i < 4) {

print ("Hello")

i = i + 1}:                                              

Answers:             a. 1.

                b. 2.

                c. 3.

                d. 4.

•             Question 2          Which of the following is O(n)?                                 

Answers:             a. 3n + 1.

                b. n * log(n).

                c. n * n + n.

                d. None of the above.

•             Question 3          If each of the following describes the run time of an algorithm, which of the following could have the longest run time?                                   

Answers:             a. O(nlog(n)).

                b. O(n!).

                c. O(n/2).

                d. O(n * n).

•             Question 4          What does the following algorithm return?

f(n){

if (n< 2)

return 1

else

return f(n - 1) * n:                                           

Answers:             a. n!

                b. The maximum divisor of n.

                c. (n - 1)!

                d. n 2.                   

•             Question 5          Given that S_n denotes the number of n-bit strings that do not contain the pattern 00, what are the initial conditions?                                    

Answers:             a. S_1 = 2, S_2 =3.

                b. S_1 = 1, S_2 =2.

                c. S_1 = 0, S_2 =2.

                d. None of the above.

•             Question 6          Given that S_n denotes the number of n-bit strings that do not contain the pattern 00, what is the recurrence relation?                                      

Answers:             a. S_n = S_{n - 1} + S_{n - 2}.

                b. S_n = S_{n - 1} + 1.

                c. S_n = S_{n - 1} + 2.

                d. None of the above.

•             Question 7          Given that S_n denotes the number of n-bit strings that do not contain the pattern 00, what is S_4?                                               

Answers:             a. 5.

                b. 30.

                c. 8.

                d. None of these.

•             Question 8          Assume that the number of multiplication terms during the entire calculation within the line "return f(n - 1) * n" is denoted by b_n. Given the following algorithm, what is the initial condition of b_n?

f(n){

if (n< 2)

return 1

else

return f(n - 1) * n:                                           

Answers:             a. b_1 = 0.

                b. b_2 = 0.

                c. b_2 = 2.

                d. b_1 = 1.

                                               

•             Question 9          Assume that the number of multiplications in line return "f(n - 1) * n" is denoted by b_n. Given the following algorithm, what is the recurrence relation of b_n?

f(n){

if (n< 2)

return 1

else

return f(n - 1) * n:                                           

Answers:             a. b_n =b_{n - 1} + 1.

                b. b_n = n.

                c. b_n = b_{n - 1} + 2.

                d. b_n = n * b_{n - 1}.

•             Question 10        In terms of n, what is the closest-fit worst-case time complexity of the following algorithm?

f(n){

if (n< 2)

return 1

else

return f(n - 1) * n:                                           

Answers:             a. O(n).

                b. O(log(n)).

                c. O(n!).

                d. None of the above.

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