Data Structures | Balanced Binary Search Trees | Question 5

Consider the following AVL tree.

         60
      /     \  
    20      100
           /   \
         80    120     

Which of the following is updated AVL tree after insertion of 70

A
        70
      /    \  
    60      100
   /       /    \
 20       80    120 

B
        100
      /    \  
    60      120
   /  \     /  
 20   70   80   


C
        80
      /    \  
    60      100
   /  \       \
 20   70      120

D
        80
      /    \  
    60      100
   /       /   \
 20      70    120  

(A) A
(B) B
(C) C
(D) D


Answer: (C)

Explanation: Refer following for steps used in AVL insertion.

AVL Tree | Set 1 (Insertion)

After insertion of 70, tree becomes following
         60
      /     \  
    20      100
           /   \
         80    120     
        /
       70

We start from 50 and travel up. We keep travelling up till we find an unbalanced node. In above case, we reach the node 60 and see 60 got unbalanced after insertion and this is Right Left Case. So we need to apply two rotations

         60                               60                            80
      /     \       Right Rotate(100)  /      \     Left Rotate(60)   /    \
    20      100    -----------------> 20        80 ---------------> 60      100 
           /   \                              /   \                /  \        \
         80    120                          70     100            20   70       120  
        /                                            \    
      70                                             120 

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