Question

How many leaves does a full \(3\)-ary tree with \({\bf{100}}\) vertices have?

Short answer

There are \({\bf{100}}\) leaves.

Step-by-step solution

Finding \({\bf{I}}\)

An 3-ary tree with n vertices have:

\({\bf{l = }}\frac{{{\bf{(m - 1)n + 1}}}}{{\bf{m}}}\)leaves

Finding \({\bf{m,n}}\)

From the given information, we have \(m = 3, n = 100\) so the tree has:

\(l = \frac{{2 \times 100 + 1}}{3} = \frac{{201}}{3} = 67\).