Question: Answer f and g from this exercise. Recall the definition: f(n) = O(g(n)) if there exist constants c> 0 and no >0 such that, for

Answer f and g from this exercise.

Recall the definition: f(n) = O(g(n)) if there exist constants c> 0 and no >0 such that, for all n > no, f(n) 0 and no > 0 such that, for all n > no, f(n) c.9(n). f(n) = (g(n)) if f(n)=0(9(n)) and f(n) = (g(n)). Equivalently, f(n) = (g(n)) if g(n) = O(n)sec Task 2.4(i) (a) Someone tells you that an algorithm A has running time O(n log n) and an algorithm B has running time O(na). Do you know which algorithm is faster? Simplify the following running times. Explain the simplifications. (b) (91n + 4n' + 3 log n + 12n"). +1/2. 1.001" +40.7100). (d) (5 log(57)). (e) (5.25n). (c) (100010001000 (f) You are given the following running time functions (in O-notation). Order them by order of growth! ! (log rey2 Vn 272 loger 221 11-20 log(n?) glown (g) In the lecture, we have seen running times depending on two parameters. For instance O(kn). Propose a formal definition for f(nt. ..., ) = 0(m...., n.:)), See Task 4 for more related questions. 1

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