I'm studying AVL Trees in my programming class and we got this exercise dealing with right, left, left-right and right-left rotations as a way to check if we understand the theoretical concept of AVL Trees. We're given the numbers $100,50,25,10,37,32,200$. Creating an AVL Tree until $37$ wasn't that difficult but then I got stuck at balancing out the tree when I insert $32$. The following is my method:

enter image description here

Now I know that there is a conflict at $52$ but since it has 3 nodes (LRL), I don't understand how I should rotate. I think, I should get $37$ as the root node $25$ as it's left child and $52$ as it's right child but I dunno.


I think, I should get 37 as the root node 25 as it's left child and 52 as it's right child but I dunno.

You plan is correct.

What you need to do is a left-right rotation as shown in the third column of the table below. That is, a left rotation at node 25 followed by a right rotation at 52. It is symmetric to the right-left rotation as shown in the fourth column and as explained in Wikipedia.

tree rebalancing picture at wikimedia


Balanced AVL tree

1st step : Left-Left rotation. 2nd & 3rd step :Left-Right Rotation. 4th step: Right-Right Rotation. 5th is Final AVL tree.


  • $\begingroup$ Can you explain how did you know in which directions to perform the rotations? $\endgroup$ – Yuval Filmus Mar 8 at 21:15
  • $\begingroup$ @Yuval Filmus , a link is added for better explanation. $\endgroup$ – NIKHIL Mar 9 at 9:15
  • $\begingroup$ OK but what happens if that link breaks? We're trying to be a collection of answers: Google already does the "links to answers" thing far better than we ever could. $\endgroup$ – David Richerby Mar 9 at 11:07
  • $\begingroup$ In that case that child will be added to same level where it was before rotation. $\endgroup$ – NIKHIL Mar 9 at 11:21

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