We are given 44,000,000 elements. We want to store them in a B-Tree so that his height is 5 (no more than 5).

We are asked: “What is the minimal t we can choose?”

($ t$ is the minimal degree, in each vertex that is not the root we have at least $ t-1$ keys but no more than $ 2t-1$ )

We have a debate whether the minimal $ t$ for the minimal height is $ 10$ or $ 30$ :

Some calculated as so: $ 5 = \log_t(22,000,000)$

which gives us $ t \approx 29.4$ and so $ t = 30$

However then a some good questions were asked whether we know the inserting order or not, if we know then it may be $ t=10$ and if we do not it may be $ t=30$

The TA answered that while we show that we can insert all the elements under the constraints, it is valid, the height should not be more than $ 5$ . Given we know all the elements and now you create the tree, your task is to show how to build a B-Tree (the exact calculation for the minimal $ t$ )

We are stuck from here, we do not know which way is correct.

Thank you!