Question: 4. (25 marks) A certain algorithm has running time T(n) on input of size n given by T (n) = n Lign+ 2n-211g n+1 (a)

4. (25 marks) A certain algorithm has running time T(n) on

4. (25 marks) A certain algorithm has running time T(n) on input of size n given by T (n) = n Lign+ 2n-211g n+1 (a) Prove that T (n) is (n log n). (b) Prove that T(n) -nlgn is O(n) (c) Explain why the limit rule could not be used for (b) Hint: Let L(n) := lgn-ugn] and think about the properties of the function L. For example, how large can it be, and what values does it take when n = 1, 2

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