Big OH Notation help

**p00ndawg** · Jun 16th 2009, 08:04 AM

Problem 1. Find a function g such that $N^2$ = Θ (g(n)).
Problem 2. Find a function g such that $2N^2$ = Θ (g(n)).

I need help with these two problems.
Ive never seen the theta sign before.

from what I understand theta means that, T(N) = Θ(h(N)) if and only if T(N) = O(h(N)) and T(N) = Ω(h(N))‏.

for the first would $2n^2$ work?

**Spec** · Jun 16th 2009, 01:14 PM

If $f(n)=\Theta(g(n))$ then $c_1g(n) \leq f(n) \leq c_2g(n)$ for some positive real constants $c_1$ and $c_2$ .

In other words, what we're looking for is the order of $f(n)$ .

What is the order of $C\cdot n^2$ where $C$ is some constant?

**p00ndawg** · Jun 16th 2009, 03:11 PM

Originally Posted by Spec

If $f(n)=\Theta(g(n))$ then $c_1g(n) \leq f(n) \leq c_2g(n)$ for some positive real constants $c_1$ and $c_2$ .

In other words, what we're looking for is the order of $f(n)$ .

What is the order of $C\cdot n^2$ where $C$ is some constant?

would it be just n^2 for both?

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