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26 votes
26 votes

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:

  1. $2^h -1$

  2. $2^{h-1} -1$

  3. $2^{h+1} -1$

  4. $2^{h+1}$

4 Answers

Best answer
44 votes
44 votes
$2^{h+1} - 1$ just try this taking a small complete binary

never try to remember these formulae as remembering formulae is an overhead try to take examples in such cases.

Correct Answer: $C$
edited by
10 votes
10 votes

At maximum tree is given as above

So maximum height = 2 (15 - > 10 -> 8) or other all are same height

Put h = 2 in option and find number of nodes

A- 22 -1 = 3  wrong 

B- 21-1 = 1 wrong 

C- 23-1 = 7 correct

D- 23 = 8 wrong 

SO option C is correct option

4 votes
4 votes

height H=0 ( only root node ) , no of node N=1=20

H=1 , N=21

... so on 

total =20 +21+22+.......2H =2H+1-1

Ans is C

0 votes
0 votes

=2$^0$+2$^1$+2$^2$+...+2$^h$ this a  gp

=2$^h$$^+$$^1$-1

Answer:

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