Question

1. What is the minimum number of vertices in a binary tree with height 5? What is the maximum number of vertices in a binary tree with height 5? See Chapter 4.4.

Answer 1

Answer:

Height = 5

Minimum number of vertices in a binary tree

whose height is h.

So, there must be  At least one node at each of first h levels.

Minimum number of vertices = h

So, Minimum number of vertices of height 5 is 5

The maximum number of nodes in a binary tree of height h = $2^{h+1}- 1$

Substitute h = 5

The maximum number of nodes in a binary tree of height 5 = $2^{5+1}- 1$

The maximum number of nodes in a binary tree of height 5 = 63

So, the maximum number of vertices in a binary tree with height 5 is 63