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UGC NET Computer Science Nov 2020 (Paper II)

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?

Solution

For a complete n-ary tree:

$L=(n-1)I+1$

Given:

$L=41,\ I=10$

So,

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

$40=10(n-1)$

$n-1=4$

$n=5$

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