The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+3 votes

asked in Algorithms by Boss (6k points) | 71 views
Answer should be D.

2 Answers

+3 votes
Best answer

mit quiz pdf link. here is the required part:

answered by Veteran (57.5k points)
selected by
+3 votes
$f(n) = \Theta(g(n))$ and $g(n) = \Theta(h(n))$ implies $f(n) = \Theta(h(n))$ (by transitivity).

Now $f(n) = \Theta(h(n))$ implies $h(n) = \Theta(f(n))$ (symmetry property). So statement I is true.

Similarly in statement II, by transitivity, we get $f(n) = O(h(n))$ this implies $h(n) = \Omega(f(n))$, by transpose symmetry.

Statement III is false.  consider  $f(n) = n^2$ and $g(n)=4n^2$

Statement III would be true, if the conclusion was $f(n) = \Theta(g(n))$ or $g(n) = \Theta(f(n))$.

You can refer to these properties in CLRS.
answered by Loyal (4k points)

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

29,138 questions
36,959 answers
34,803 users