2. a) For each of the following defined asymptotic notations, evaluate the constant c and no character. i. 100n + 5 € O(

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2 A For Each Of The Following Defined Asymptotic Notations Evaluate The Constant C And No Character I 100n 5 O 1 (303.38 KiB) Viewed 33 times

2. a) For each of the following defined asymptotic notations, evaluate the constant c and no character. i. 100n + 5 € O(n²) [3 marks] ii. η3 Ε Ω(n3) [3 marks] iii. n(n-1) € 0(n²) [3 marks] b) State the limit definition of comparing the order growth and use it to evaluate the following expression [1 Mark] [2 marks] i. log₂ n and √√n ii. n(n-1) and n² [3 marks] c) Given n disks of different sizes that can slide onto any of three pegs as illustrated in the figure below, and supposing that all the disks are initially on the first peg in order of size (thus: the largest on and the smallest on top); move all the disks intuiti to the third peg, using the second one as an auxiliary, if necessary. Note that you can only move one disk at a time, and it is forbidden to place a larger disk on top of a smaller one. What will be the cost in performing this task? [10 Marks] 3 2 d) Evaluate the cost of the function DA(n) = DA () +1 with DA(1)=1 [5 Marks]