Question

A full 5-ary tree has 37 internal nodes. how many nodes does it have in total?

Answer 1

A full 5-ary tree with 37 internal nodes has 381 nodes in total.

How to solve

In a full 5-ary tree, each internal node has 5 children. Let's denote the number of levels in the tree as h.

At each level, the number of nodes is given by the formula
`5^h.`

If we have 37 internal nodes, then the total number of nodes in the tree can be expressed as:

Total nodes =
`(5^(h+1) - 1) / 4`

We know that there are 37 internal nodes, so we can set up an equation:

37 =
`(5^(h+1) - 1) / 4`

Solving for h, we get:

h = 4

Now that we know the height of the tree, we can calculate the total number of nodes:

Total nodes =
`(5^(4+1) - 1) / 4 = 381`

Therefore, a full 5-ary tree with 37 internal nodes has 381 nodes in total.