UGC NET CSE | October 2020 | Part 2 | Question: 23

Question

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. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Let N be the total number of nodes.

N= n*I + 1, Also N= I+ L = 41+10 = 51

51=n*10+1

n=5

Comments

CORRECT 👍

Answer 2

For strict n-ary trees the relationship between external(leaf) nodes and internal nodes is: $$L = (n-1)i + 1$$

Using this formula, L = $41$ , i = $10$

$$41 = (n-1)*10 + 1$$

$$n = 5$$

Answer 3

Answer-B

http://courses.cs.vt.edu/~cs3114/Fall09/wmcquain/Notes/T03a.BinaryTreeTheorems.pdf