1. Order following functions based on their growth rate from slow to the fastest

loglogn, sqrt(n), (n+34)!, 2^log(n), 2ⁿ, 2¹⁰⁰⁰, log(n!), n³, nlogn, lognlogn, sqrt(logn)

2. Calculate the big O notations for following loops

for i =1 to n

for j = 1 to n²

{.}

for i =1 to n²

for j = 1 to i

{.}

for i =1 to n

for j = 1 to 100

{.}

for i =1 to n³

for j = 1 to n²

for k = 1 to n²

{.}

3. We have two algorithms solving the same problem. Algorithm As running time function is n²+3n+12, and algorithm Bs running time is 1000n+200000. Asymptotically, which algorithm is better? Is the asymptotically worse one totally useless? If not, when is it useful?

4. Given the following operation numbers, determine the closest big Oh notation for each of them

A.

B.

C.

D.

E.

F. , where a, b, c, d and k are constants