Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?


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|cite|improve this question

Your Answer


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

Browse other questions tagged or ask your own question.