Master theorem

Rank the following functions from lowest asymptotic order to highest. List any two or more that are of the same order on the same line.

Solving algorithm Given the following two functions: f(n) = 6n3 + 4n2 + 2 g(n) = 5n2 + 9 Use L’Hopital’s rule and limits to prove or disprove each of the following: f (g) g (f) Rank the following functions from lowest asymptotic order to highest. List any two or more that are of the […]

Develop an algorithm that finds all the candidate hotels in O(nlgn) time using divide-and-conquer, listed in increasing distance to the beach.

Questions: [8 marks] Prove the following two identities using the limit method. Recall that lgn = log2 n. (i) [4 marks] n/lgn = o(n/lglgn). (ii) [4 marks] √nlgn = o(n/lgn). Give sufficient details in your solutions. For example, to show lim = 0, give the steps of applying l’Hopital’s Rule. [12 marks] For each of […]

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