Question

How many vertices does a full \(5\)-ary tree with \(100\) internal

vertices have?

Short answer

There is\(501\)vertices.

Step-by-step solution

Finding \({\bf{m}}\) and \({\bf{i}}\)

A full m-ary tree with i internal vertices have \({\bf{n = m i + 1}}\) vertices.

From the given information, we have \({\bf{m = 5, i = 100}}\)

Finding \({\bf{n}}\)

So, \(n = 5 \times 100 + 1 = 501\)

Therefore, a full 5-ary tree with 100 internal vertices have 501 vertices.