Solve in Python:

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 such that, for all n > no, f(n) > c.9(n). . f(n) = (g(n)) if f(n)= O(g(n)) and f(n) = N(9(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(n). 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) (5.25). (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. ..., 1) = 0(m...., n.:)), See Task 4 for more related questions. 1