Question 1 (Compulsory, 20 marks). a) Place the following functions into their proper asymptotic order: f:(n) = nlog.n; f;(n) = n(log,n)?: f(n) = 2 + 2 + .. + 2: f.(n) = log2 ( 2 + 21 + .. +2"). [4 marks] b) Work out the time complexity of the function: Function f(n){if (n>0{ x=x+1; f(n-1); f(n-1); f(n-1)}} [4 marks] c) Solve the linear recurrence relation: T. = 51,-1-61,2 [4 marks] d) A graph G= is given where V = {A, B, C, D, E, F, G, and E = {(A, G, 70), (A,B,100), (B, F, 20), (B, C, 60), (C, D, 40), (C, F, 40), (D,E, 200), (E, F, 80), (E, G, 100), (F, G, 100) Determine the convex hull of the graph G. [4 marks] e) Discuss why applying the selection sort algorithm to sort some input numeric set is a decision problem in class P. What would you classify it as given: tractable" and "efficient" as options. [4 marks)