data structures - Minimum number of levels in an n-ary tree?

Question

I understand intuitively why in a binary tree there are a minimum of floor(log₂(n)) + 1 levels. I was wondering if there is an equivalently straightforward algorithm for the minimum number of levels in an n-ary tree. Say a full/complete ternary tree for example: my intuition tells me this would involve log₃(n) somehow but I cannot figure it out.

question from:https://stackoverflow.com/questions/65927775/minimum-number-of-levels-in-an-n-ary-tree

Answer 1

You can find the formula for an m-ary tree by first checking what the maximum number of nodes is that you can store in a tree with degree m:

levels	n
1	1
2	1+m
3	1+m+m2
4	1+m+m2+m3
...	...
k	1+m+m2+...+mk?1