Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm hoping that someone can shed some light on this running time.

I have a "tree", for lack of a better description, that has a length $l$ and depth $d$. I want to maximize the tree size, which we'll call $N$. The tree size is $$N=l^d$$

I also want to minimize the running time $t$, which is $$t=l \cdot d^2$$

I'd like to determine the fastest running time for a given $N$. That is, I'd like to find a formula for $t$ in terms of $N$. What is this formula?

MY IDEAS

I thought that we may be able to use calculus to somehow maximize the ratio $N/t$. After that, we can divide by $t$ to get the formula. But I don't know how to do this with an equation like this.

Possibly someone knows of something similar that has already been analyzed.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.