Order Notation 

Hello, could you guys tell me if i did this correctly based on the question since I am confused whether best run time means it grows the slowest or not?

Q) Rank the functions in Table 2 from best to worst runtime. Specifically, you should rank f (n) before g(n) if, and only if, f (n) = o(g(n)). There may be some ties (functions that grow at the same rate); you should indicates this with ”=”.

Best to Worst

(j) = (h)


(k) = (i) = (f) = (c)

(e) = (d)



Q) Rank in increasing order of growth rate

The second line is my solution


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Erdos Erdos
  • There is two parts one question at the bottom too! and Is this in best to worst run time? meaning (j) and (h) are the best run time and (a) is the worst run time? Also I am a bit confused about the constant, doesn't a constant have a slower run time than suppose a log function and therefore has a better run time

    • Erdos Erdos

      Yes, it is best to worst run time (smallest run time to the largest run time). About the constant function, note that log (n) goes to infinity as n gets large which is much larges than a constant. So a constant run time is better than any log (n).

  • Erdos Erdos

    I will add my solution to the second part in a few minutes.

    • Thank you, I appreciate your help!

    • Erdos Erdos

      You're most welcome :)

  • Oh okay I understand now! Thank you. I think you may have missed the other part that is below

The answer is accepted.
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