Question

suppose that a full 4-ary tree has 100 leaves. howmany internal vertices does it have?

please explain in detail.

i dont want to know about no. of vertices i just need to find internal vertices . can you also explain how is 4 ary tree look alike.?

thanks,

Answer 1

for n-ary tree we have
if it is 1-ary tree and i is the internal node then no. of leaves is 1.
if it is 2-ary tree and i is the internal node then no. of leaves is i+1.
if it is 3-ary tree and i is the internal node then no. of leaves is 2i+ 1.
if it is 4-ary tree and i is the internal node then no. of leaves is 3i+ 1.
if n-ary tree and i is the internal node then no. of leaves are (n-1)i + 1
so L=(n-1)i+1
we have
n=4
L=100 we have to calculate i
100=(4-1)i+1
99=3i
i=33 so total no. of internal vertices will be 33.

a 4 ary tree will look like this

A+ A- A+ B+A B-