Ace Test Series: Programming & DS - Binary Tree

Question

A binary tree has 127 nodes. Which of the following is an invalid height for this tree ?

$a). 16 $

$b). 6$

$c). 21$

$d). 43$

Comments

@vijaycs,the best ans in link conflicts with what you have said,,,

http://stackoverflow.com/questions/4065439/height-of-a-tree-with-only-one-node

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http://stackoverflow.com/questions/33259398/confusion-between-the-notion-of-height-and-depth-of-a-node-in-binary-tree?noredirect=1&lq=1

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@prabhanjan, its okay. but I said you considering gate exam because when ever I see a question related to height, it always consider no of edge in the longest path from root to any leaf node unless it is said exclusively that root node has zero height.
you can see prev year question also,

https://gateoverflow.in/2163/gate2012_47

if you see any more question where its an amibigity between 0 and 1 in gate paper then please let me know..  

Answer 1

Option A ==> Height = 16 , max number of nodes possible is  2^16 - 1;

Option B ==> Height = 6 , max number of nodes possible is  2^6 - 1;

Option C ==> Height = 21 ,max number of nodes possible is  2^21 - 1;

Option D ==> Height = 43 , max number of nodes possible is  2^43 - 1;

Numer of nodes here is 127 which is not possible with Option B.

Comments

According to you no. of nodes in a binary tree of height h is $2^h$$ -1$

Means for a binary tree of height 0, nodes = 0.

Source : Wikipedia

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It depends on height for single node.