GATE CSE 1988 | Question: 7ii

Question

Mark the balance factor of each node on the tree given in the below figure and state whether it is height-balanced.

Answer 1

Balancing factor $ = $ the height of left subtree $-$ the height of right subtree

Balancing factors of all the nodes are marked in the figure. 

Since there is no node that has a balancing factor greater than $1,$ we can say that the tree is balanced.

Comments

@Akash Papnai

On the node 12 in the tree the balance factor would be 0 and not 1. please correct it.!!!

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please correct it..the balance factor of 12 is 0 not 1.

Answer 2

Balance Factor $=$ height $($left Sub Tree$)−$ height $($right Sub Tree$)$

for height balance tree, balance factor of every node  should be from $ -1  \ to \ 1 \ \  i.e. (-1,0,1)$

So, given tree is height balanced tree.