Problem 1 Rank the following functions by order of growth; that is, find an arrangement g, g2, . .. g2o of the functions satisfying g,=0( g2),g2 =0 (g3), . . , g19 = 0 (g20). Partition your list into equivalence classes such that functions f (n) and g(n) are in the same class if and only if f (n) = O(g(n)). Lgn n2 n! (lgn)! 22 4'gn (3/2)" n3 (lgn)² 2gn 22 Ig(n!) Inln(n) (n + 1)! п. 2n n" nlgn 1 n

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