Proving Space Requirements for van Emde Boas Tree Recurrence Relation [duplicate]

I know the space requirements for a van Emde Boas tree is $Θ(u)$, and that the recurrence relation for this looks like:

$$S(u) = (\sqrt u + 1) S(\sqrt u) + Θ(\sqrt u)$$

I'm curious and can't seem to find it anywhere but, how would one go about proving this recurrence relation is true? I.e., how do you prove $S(u) = Θ(u)$ ?

marked as duplicate by D.W.♦Mar 1 '17 at 2:41

• Please refer to the methods shown there for an approach to solve this, try to solve your problem again by using those methods, and then if you are still stuck, edit your question to show what you've tried, what progress you've made, and where you got stuck. Your question can be considered for re-opening at that time. Also, what do you mean by "proving this recurrence relation is true"? Do you mean proving that the solution to this recurrence is $S(u) = \Theta(u)$? Please edit your question further when you can address this feedback. Thank you! – D.W. Mar 1 '17 at 7:01