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Let $T$ be a binary search tree with $15$ nodes. The minimum and maximum possible heights of $T$ are:

Note: The height of a tree with a single node is $0$.

1. $4$ and $15$ respectively.
2. $3$ and $14$ respectively.
3. $4$ and $14$ respectively.
4. $3$ and $15$ respectively.
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The maximum height of a binary search tree will be when the tree is fully skewed Maximum height  $= n - 1 = 15 – 1 = 14$

The minimum height of a binary search tree will be when the tree is full. Minimum height  $= \log_2( n + 1 ) – 1 = \log_2( 15 + 1 ) – 1 = \log_2( 16 ) – 1 = 4 - 1 = 3$

Correct Answer: $B$

by Boss (10.7k points)
edited

Min height of a binary tree is given by $\log _{2}(n+1)-1=4-1=3$

max height of the binary tree is $n - 1$ (skewed binary tree$= 15 - 1 =14$

Ans:B) $3,14$

by Loyal (8k points)
edited by
B) 3,14 .

Worst case : skewed
by Active (2.1k points) please do correct me if I m wrong

by Active (1.9k points)
Height will be maximum when the BINARY SEARCH TREE is completely skewed

example for an ASCENDING order sequence of numbers say {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} hence maximum height will be

14

height will be minimum when tree is maximally packed that is every level is filled completely before moing to next level...

in that case

level 1->1 node

level 2-> 2 node

level 3-> 4 node

level 4-> 8 nodes

so in 4 level total nodes are 1+2+4+8=15

so min height is 3

option (B)
by Active (3.4k points)
it is 3 and 14 respectively
by Boss (18k points)
the height of the tree from simple drawing will be 3 and 14 respectively
by Boss (18k points)
Height of a binary search tree is minimum if it is a complete binary search tree..

Minimum height is lg(n+1)-1 as given n = 15 hence on solving We get lg(15+1) -1 which is equal to 3.

In the worst case the binary search tree will be skewed hence the max height will be 14.

Correct me if I am wrong.

I am new to this platform so please guide me further..
by (245 points)