Question

Which of the following cannot be the number of vertices present in a full binary tree?
1.15
2.7
3.3
4.12
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Answer 1

Answer:

the answer will be 12

because

2^n - 1 is the formula to calculate this,

so

2^n - 1 = 12

2^n = 12+1

2^n = 13

as we cannot conver 13 in 2's power

and n has to be natural number

so the answer is 4th option i.e. 12

Answer 2

In a full binary tree the number of vertices cannot be (4) 12

Step-by-step explanation:

Given:

• A full binary tree

To be found: The vertices which cannot be in a full binary tree.

Formula used: No. of vertices = $2^{n}-1$

Solution:

As we know the number of vertices can be calculated by the formula,  $2^{n}-1$.

So, let the number of vertices is 12.

$2^{n}-1=12\\ 2^{n}=12+1\\ 2^{n}=13$

And 13 cannot be simplified in terms of the power of 2.
So, 12 cannot be the number of vertices in a full binary tree.

Explanation for incorrect options:

(1). 15
let the number of vertices is 15.

$2^{n}-1=15\\ 2^{n}=15+1\\ 2^{n}=16\\ 2^{n}=2^4\\ \therefore n=4$
(2). 7

$2^{n}-1=7\\ 2^{n}=7+1\\ 2^{n}=8\\ 2^{n}=2^3\\ \therefore n=3$
(3). 3
$2^{n}-1=3\\ 2^{n}=3+1\\ 2^{n}=4\\ 2^{n}=2^2\\ \therefore n=2$