Please provide solution/methods so I can understand how this work.
Lets consider theta notation since it provide asymptotic upper
and lower bounds.
if f(n) = Theta(g(n)) then there exist c1, c2 and n0 such that
c1*g(n) <= f(n) <= c2*g(n) for all n>=n0
and c1, c2>0 , n0>=0
We know that logn and n terms are asymptotically smaller than n^2.
lets assume g(n) = n^2
So for all cases,
limit n-> infinity g(n)/f(n) = n^2/(con*n^2 + smaller terms than n^2)
limit n-> infinity g(n)/f(n) = 1/(con + (small terms) / n^2) = 1/con which is constant. That means they grow at similar rate
where con = 5, 3, 1/17 for worst, average and best case
Now let c1 = 1 and c2=10
c1*g(n) = n^2 / 18 <= f(n) in best, worst and average
case
c2*g(n) = 10*n^2 >= f(n) in best, worst and average case
and n0 = 100 or 1000 maybe (works for both)
(10n^2 > 5n^2 + 4n + 14 and similarly for other cases)
(n^2/18 < 5n^2 + 4n + 14 and similarly for other cases)
so we have f(n) = Theta(n^2) which provide tight bounds for f(n)
Option B) is correct
to disprove other options, we can see that bounds can provide
upper or lower limit correctly
like option K) Theta(n^2 logn) this can provide upper bound but not
lower
Please provide solution/methods so I can understand how this work. Given a algorithm with f(n) 5n2...
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