Question

Maximum height of a 11 vertex binary tree is?

Answer 1

Answer:

YOUR ANSWER

Step-by-step explanation:

1. In a binary tree, a node can have maximum two children. If there are n nodes in binary tree, maximum height of the binary tree is n-1 and minimum height is floor(log2n).

Answer 2

We need to recall the following rules about the height of a binary tree.

• The maximum height of a fully binary tree with $n$ numbers of vertices is $log_2(n+1)$.
• The maximum height of a non-fully binary tree with $n$ numbers of vertices is $(n-1)$.

Given:

Number of vertex of a binary tree $=12$

From the above rules, we get

For non-fully binary tree:

Maximum height $=11-1$

Maximum height $=10$

Hence, the maximum height of a non-fully binary tree is $10$.

For a fully binary tree:

Maximum height $=log_2(11+1)$

Maximum height $=log_2(12)$

Maximum height $=3.58$

Hence, the maximum height of a fully binary tree is approximate $3$.