Algorithm Design

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Chapter 2 Basics of Algorithm Analysis
~ gl(a) = 2 ~°4i~
" g2(n) = 2 n
i g4(n) ---- n4/3
g3(n) = n(log n) 3
gs(n) = nlog n
g6(n) = 2 2n
i gT(n) = 2 n2
Assume you have functions f and g such that f(n) is O(g(n)). For each of
the following statements, decide whether you think it is true or false and
give a proof or counterexample.
(a) log 2 f(n)’is O(log 2g(n))-
(b) 2 f(n) is O(2g(~)).
(C) /(n) 2 iS O(g(n)2).
Consider the following basic problem. You’re given an array A consisting
A[n]. You’d like to output a two-dimensional
n-by-n array B in which B[i,j] (for i