CS3261 - 35 + 30 = 65 > D Not enough space, skip...

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CS326 Algorithms Fall 07 Homework 2- Part 2 1-e 26 3 22 8 9 21 34 47
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2-a i) No, greedy algorithms does not always produce the best solution. ii) Counter Example: Assume D=20 Assume program sizes as follows: 10, 6, 9, 4 Using the same greedy algorithm, it will select the programs from smallest to largest as follows: 4, 6, 9, 10 It will operate as follows to fill the memory space: 4 + 6 = 10 10 + 9 = 19 The algorithm will not be able to add the last ‘10’ because the only memory size available is 1 out of 20. (20-19=1) A better solution can be as follows: 4+6 = 10 10 + 10 = 20 The algorithm leaves out ‘9’ since choosing ‘10’ would produce a more optimal solution. 2-b i) No, greedy algorithms does not always produce the best solution. ii) Counter Example: Assume D=50 Assume program sizes as follows: 10, 20, 25, 30, 35
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Using the same greedy algorithm, it will select the programs from largest to smallest as follows: 35, 30, 25, 20, 10 It will operate as follows to fill the memory space:
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Unformatted text preview: 35 + 30 = 65 > D Not enough space, skip 30 35 + 25 = 60 > D Not enough space, skip 25 35 + 20 = 55 > D Not enough space, skip 20 35 + 10 = 45 < D Accepted! The algorithm will consume 45 out of 50 units of memory. However, it is not the best solution to the problem. A better solution can be as follows: 30 + 20 = 50 (50 = = D) 3-a No. A short path in an original tree from one point to another will be also the shortest in the MST. 3-b Explanation:-If each edge has one and only one weight, then there will only be one MST.-If the edge of point A is larger than any edges connected to A, then it cannot be in the MST.-If the edge of point A is smaller than all other edges, then it will definitely be in the MST. In the following graph, the shortest path from A to F is: A, B , C, D, E, F If we take the MST of the graph, the path is also the same:...
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CS3261 - 35 + 30 = 65 > D Not enough space, skip...

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