Question

7. You have 5 algorithms, Al took O(n) steps, A2 took ©n log n) steps, and A3 took 2(n) steps, A4 took O(ny) steps, A5 took on?) steps. You had been given the exact running time of each algorithm, but unfortunately you lost the record. In your messy desk you found the following formulas: (e) 7n! (f) 23 logan (g) 22 log2 n For each algorithm write down all the possible formulas that could be associated with it.

Answer 1

(e) Th! for larger values of n, 7h! is very large Such that THI »n² or n3 or nlogn) which means there is only one option left and in for nzl which means 7n! = 2n)

Satog b= log ba? 3 logan s - 2 = n3 fa) = 0 (gen)) means F(x) scogers for all na do now no can3 for all nzl m3 = 0 (nº for 5 s glais means F(a) > c. gla) & nino since we know nzn, nZ1

2 logon 11 2 10 12 En2 for all now n²in : m? - een and for all n i n² = n3 and nz Lan2 for all nzl which means n² = 0 (02)