Search no from leaf nodes

Question

An n-ary tree has N sub-nodes for each node. If a tree has M non-leaf nodes, How to find no from leaf nodes?

Answer 1

First of all, if the root is a level 0, then the Knth level of the tree will have nodes N^K. You can start increasing the counter level at a level until you get the nodes M. This way you will find how many levels is this tree consisting of. And the number of leaf nodes is the number of nodes at the last level - this N^lastLevel.

Here is an example: N = 3, M = 4.

First level = 3^0 = 1
Second level = 3^1 = 3
1 + 3 = 4

So, we found that the tree has two levels (counting from 0). Answer: 3^2 = 9.

. , , M : 1 + 3 + 9 + 27 ... = M

, .

Answer 2

, .

0- - 1
1- - n
2- - n ^ 2
3- - n ^ 3
.... mth level - n ^ m

, m-1- 1 + n + n ^ 2 +.. + n ^ m-1.

1 + a + a ^ 2 + a ^ 3 +... + a ^ m, (1 - n ^ (m + 1))/(1-n), K.

, n ^ m, , , .. . , , n ^ m = K * (n-1) + 1.

. , 40, , 81, .