Question

1. (10 pts) For each of the following pairs of functions, indicate whether f = 0(g), f = Ω(g), or both (in which case f-6(1). You do not need to explain your answer. f(n) (n) a) n (b) n-1n+1 (c) 1000n 0.01n2 (d) 10n2 n (lg n)2 21 е) n (f) 3" (g) 4" rl. 72 i-0 2. (12 pts) Sort the following functions by increasing order of growth. For every pair of consecutive functions f(n) and g(n) in the sorted list, prove that f(n)-o (g(n)) nnlgn Hint: recall the limit rule for o(): ) oo g(n) f(m) - o(g(n)

Answer 1

SOLUTION:

g(n) loonS C o.olm2 2. 2. 2

lo 10 < 2디

(q(n) to))

(n)こ 2 (n)7, C.qn)

L- o 2 2 2 01

1 にu 2 O Log.Lq2. (n) = n + 1 tn

ram this hstan in^l that

NOTE:

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