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In: Computer Science

Instructions: Answer the following questions. Submit your answers to questions 1-5 as a Rich Text Format...

Instructions:

Answer the following questions. Submit your answers to questions 1-5 as a Rich Text Format file (.rtf), Word document (.doc), or ASCII text file (.txt). For problem 6 submit an excel sheet containing your chart.

1. (12 points) State the order of magnitude for each of the following mathematical functions. (Hint: Find the dominant term and drop its coefficient)

  1. 5n2 + 105 nlogn
  2. 5n3 – 7n + 30
  3. (n2 / logn)+ 40000n + 1000
  4. (5n2 + 8n + 3n) / 7
  5. 5n + 6n!
  6. Log(logn) + logn

2. (12 points) Assume you have two algorithms, A and B, both of which perform the same function, although their implementations differ. Assume that algorithm A has a running time of O(N3 + 2N2 +6N +10) and algorithm B has a running time of O(6N2 + 3N +10 ). Also assume that the value of N is restricted to the set of Natural numbers i.e., {1, 2, 3, ...}. Answer the follow­ing questions:

  1. For what values of N Algorithm A is more efficient than algorithm B?

  1. For what values of N Algorithm B is more efficient than algorithm A?

  1. For what values of N might both algorithms be expected to operate with the same efficiency?

3. (8 points)Put the following growth-rate functions in order from the most efficient to the least efficient:

  1. 5000N!                     c. 106 N2
  2. 5N                          d. N3/logN
  3. 100NlogN

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venereology answered 2 hours ago
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