141-meyer-07spex01 - S(Orkn‘x 20:3 Math 141 I Exam 1...

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Unformatted text preview: S (Orkn‘x 20:3?- Math 141 I Exam 1 Version 2 Name: ' Lecture: (circle one) I or 2 1. "We admit that this ballot measure is popular. But we also urge you to note that there are so many bond issues on this ballot that the whole thing is getting ridiculous." What type of fallacy? Give a reason. 2. 'Tfyou're not first you ’re last." What type of fallacy? Give a reason. 3. What is the degree of vertex A in the graph below? 4. Every graph that has an Euler circuit is connected. A) True B) False Page 1 5. Which of the graphs below have Euler" circuits? A) I only B) 11 only _ C) Both I and II D) Neither I nor II 6. After a major natural disaster, such as a flood, hurricane er tornado, many tasks need to be completed as efficiently as possible. For which situation below would finding an Euler circuit or an efficient eule'rization of a graph be the appropriate mathematical technique to apply? A) Relief food supplies must be delivered to eight emergency shelters located at different sites in a large city. B) The Department of Public Works must inspect traffic lights at intersections in the city to determine which are still working. C) An insurance claims adjuster must visit 10' homes in various neighborhoods to write reports. D) The Department of Public Works must inspect all streets in the city to remove dangerous debris. - 7 7. Cousider the paths represented by the numbered sequence of edges on the graphs below. Which path represents an Euler circuit? A) I only B) II only C) Both I and II D) Neither I nor H Page 2 8. Which of the graphs shown below gives the best eulerization of the given graph. (In the graphs below, added edges are denoted with zig—zag lines.) 1% ha [LE (1% 9. In order to eulerize the graph below, give the fewest number of edges that need to be added or duplicated? A) 1 B) '2 C) 3 D) 4 Page 3 10.- Whjch of the following describes a Hamiltonian circuit for the graph below? 11. A A A C B A) ABCDEFGA B) ACBAEGFDEA C) ACBFGDEA D) ABCDGEF For the graphlbelow, what is the cost of the Hamiltonian circuit obtained by using the 7 sorted-edges algorithm? Page 4 12. For the graph below, what is the cost of the Hamiltonian circuit obtained by using the nearest-neighbor algorithm, starting at A? A) 215 B) 220 C) 235 D) 295 13. A hemisticaigorithm wiIl always produce optimal results. A) True B) False 14. Use Kruskal's algorithm for minimum-cost spanning trees on the graph below. The cost of the tree found is: 8 A. 4 A) 23 B) 20 C) 16 D) 5 Page 5 15. 16. 17. 18. Kruskal's algorithm for finding minimum—cost spanning trees always gives optimal results. ' A) True B) False A connected graph G has 32 vertices. How many edges does a spanning tree of G have? A) 30 B) 31 C) 32 D) 33 If the order-requirement digraph for a collection of tasks is shown below, then What is the minimum completion time for the collection of tasks? T1 T2 E A) 64 minutes B) 43 minutes C) 36 minutes D) 28 minutes Suppose that a crew can currently complete in a minimum amount of time the job whose order-requirement digraph is shown below. If Task T2 is shortened from 9 minutes to 6 minutes, then What is the maximum amount by which the completion time of the entire job can be shortened? ' T T2 T3 6) ————> @ mm? 6) T4 T5 T6 A) It cannot be reduced. B) 1 minute C) 2 minutes D) 3 minutes Page 6 19. 20. 21. 22. Suppose a pizza delivery person needs to take pizzas to 10 houses in different neighborhoods and then return to pick up the next set to be delivered. The technique most likely to be useful in solving this problem is - A) finding an Euler circuit on a graph. B) applying the nearest—neighbor algorithm for the traveling salesman problem. C) applying Kruskal's algorithm for finding a minimum—cost spanning tree for a graph- D) None of these techniques is likely to apply. A local cafeteria offers a choice of 5 meats, 6 vegetables, and 3 salads. A complete dinner includes 1 meat, 1 vegetable, and 1 salad- How many different dinners can be created? A) 14 B) 45 C) 90 D) 120 Given the order—requirement digraph below (with time given in minutes) and the priority list Ti, T2, T 3, T4, T5, T5, T7, apply the list—processing algorithm to construct a schedule using two processors. How much time does the resulting schedule require? 6-) @_______;@ ~—'———e® :®/ \Ts® A) 16———% minutes B) 17 minutes C) 18 minutes D) 21 minutes "E Use the decreasing—time—list algorithm to schedule these tasks on two machines: 3 minutes, 5 minutes, 8 minutes, 4 minutes, 6 minutes, 2 minutes How much time does the resulting schedule require? A) 14 minutes B) 15 minutes C) 16 minutes D) 18 minutes Page 7 23 .' What is the minimum time required to complete eight independent tasks on two processors when the sum of all the times of the eight tasks is 72 minutes? A) 4 minutes B) 9 minutes C) 16 minutes D) 36 minutes 24. Choose the packing that results from the use of the first fit (FF) bin-packing algorithm to pack the following weights into bins that can hold no more than 8 lbs. 6 lbs, 2 lbs, 4 lbs, 3 lbs, 5 lbs, 3 lbs, 2 lbs, 4 lbs “Ill "IHI I “a "IE IE" 25. Choose the packing that results from the use of the next fit (N F) bin-packing algorithm to pack the following weights into bins that can hold no more than 8 lbs. 6 lbs, 2 lbs, 4 lbs, 3 lbs, 5 lbs, 3 lbs, 2 lbs, 4 lbs El It" "a la Ill Ell _ Page 8 26. Which of the following is a correct vertex coloring of the given graph? (Capital letters indicate which color the vertex is colored.) LIN v R ILW a w. w 1r w a v v' A) Ionly ' B) 11 only C) v Bothland 11 D) Neitherln‘or II 27. Find the chromatic number of the graph below: ‘1’! A! Page 9 ...
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