Can someone help me understand this question? I may have it on my tomorrow exam but I can’t find similar question on internet or in my lectures.
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Can someone help me understand this question? I may have it on my tomorrow exam but I can’t find similar question on internet or in my lectures.
First you need to express each function as a
Theta(something).For instance, for the first one:
Theta((1-n)(n^3-17)) = Theta(n^4 + ...) = Theta(n^4).For the second one:
Theta(30+log(n^9)) = Theta(30 + 9logn) = Theta(logn).These are sorted as
g1, g2, becausen^4 = Omega(logn).And so on.
For the sorting: saying that
g1 = Omega(g2)means thatg1grows at least as fast asg2, that is we are defining a lower bound. So, sort them from the worst (slowest, with fastest growth), to the best (NB: it is strange that the exercise want “the first to be to most preferable”, but the definition of Omega leaves no doubt).Btw: if you want to be more formal, here is the definition of the Omega notation:
f = Omega(g) iff exist c and n0 > 0 such that forall n >= n0 we have 0 <= c*g(n) <= f(n)(in words: f grows at least as fast as g).