Posted: April 5th, 2023

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This assignment aligns with Module Objectives 7: 1-2, 8: 1-2, and 9: 1-2.

Note: this is a timed quiz. You may check the remaining time you have at any point while taking the quiz by pressing the keyboard combination SHIFT, ALT, and T… Again: SHIFT, ALT, and T…

Flag question: Question 1Question 110 pts

Select all the statements below which are TRUE:

Group of answer choicesBoolean Linear Programming is NP-hard.Let X = ALGO and Y = LEGO. Then {(1,1), (2,1), (3,3), (4,4)} is a possible alignment of X and Y.

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Change making problem with the system of coins {1, 4, 16, 64, 256} is solved optimally using Greedy.

Flag question: Question 2Question 25 pts

We are solving the Fractional Knapsack Problem using the Greedy algorithm learned in class. The number of objects is n = 5.

value viweight wi

object 1 128

object 21511

object 393

object 42015

object 5126

The knapsack weight is W = 35. Which object is the fourth selected object?

Group of answer choicesobject 4object 5

object 1

object 2

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object 3

Flag question: Question 3Question 35 pts

Consider the problem of Scheduling to Minimize Lateness. Consider the jobs J1(t1=5, d1=7), J2(t2=10, d2=15), and J3(t3=12, d3=22). What is the maximum lateness L for the schedule J2, J1, J3 ?

Group of answer choices101

2

5

Default

0

15

7

4

8

Flag question: Question 4Question 45 pts

Consider the topic of “Sequence Alignment in Linear Space via Divide-and-Conquer”. Refer to the PPT presentation, slide 12, the pseudocode “Divide-and-Conquer-Alignment(X,Y)”.

What is the running time for computing q in line 7, “let q be the index minimizing f(q,n/2) + g(q,n/2)” ?

Group of answer choicesO(n)O(mn)

O(2n)

O(mn)

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O(m)

Flag question: Question 5Question 55 pts

Solve the Independent Set problem for the tree below, using the dynamic programming algorithm learned in class. What is the cardinality of a maximum-size independent set?

Group of answer choices67

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5

9

14

12

8

Flag question: Question 6Question 610 pts

Lucky Puck Company has two warehouses for hockey helmets in Winnipeg and Saskatoon. There is an order of 250 hockey helmets from Vancouver and an order of 375 hockey helmets from Edmonton and Calgary. Edmonton and Calgary must receive together 375 helmets, and each of them must receive at least 50 helmets. Lucky Puck Company has 400 helmets in the warehouse in Winnipeg and 350 helmets in the warehouse in Saskatoon. From Winnipeg, it costs $6 to ship a helmet to Vancouver , $2 to ship it to Edmonton, and $4 to shp it to Calgary. From Saskatoon, it costs $5 to ship a helmet to Vancouver, $8 to ship it to Edmonton, and $3 to ship it to Calgary. How many helmets should the company ship from each warehouse to Vancouver, Edmonton, and Calgary to fill the order with the minimum cost?

(2 pt) Clearly define your variables.

(8 pts) Write the Linear Programming (LP) for solving this problem.

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Flag question: Question 7Question 710 pts

What is an optimal alignment for the sequences X=”FOREST” and Y=”EFFORTS”?

Assume that δ = 3 and consider the following matching/mismatching costs:

EFORST

E021154

F03231

O0514

R023

S05

T0

(7 pts) Fill out the table A.

(1 pt) What is the cost of an optimal alignment?

(2 pts) Write the optimal alignment of X and Y.

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Flag question: Question 8Question 810 pts

We discussed in class the Weighted Interval Scheduling problem using Dynamic Programming (see PPT presentation on Dynamic Programming). Let us assume that the n requests have start times s[1..n] and finish times f[1..n]. Assume that f[1] ≤ f[2] ≤ …. ≤ f[n].

Use pseudocode to write an algorithm which computes the values p(i) for each request i. The output of your algorithm is an array p[1..n] containing p(i) value for each request i. What is the RT of your algorithm, as a function of n?

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