Data Structures | Binary Trees | Question 10

A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?

**(A)** 6

**(B)** 3

**(C)** 4

**(D)** 5

**Answer:** **(D)** **Explanation:** For an n-ary tree where each node has n children or no children, following relation holds

L = (n-1)*I + 1

Where L is the number of leaf nodes and I is the number of internal nodes.

Let us find out the value of n for the given data.

L = 41 , I = 10 41 = 10*(n-1) + 1 (n-1) = 4 n = 5