Question

I am implementing AVL Trees in C++ on my own code but this problem is more about understanding AVL trees rather than the code itself. I am sorry if it doesn’t fit here but I have crawled through the Internet and I have still not found a solution to my problem.

My code works as expected with relatively small inputs (~25-30 digits) so I suppose it should work for more. I am using an array in which I hold the nodes I have visited during Insertion and then using a while loop I am raising the heights of each node when needed, I know that this procedure has to end when I find a node whose heights are equal (their subtraction result is 0 that is).

The problem is when it comes to balancing. While I can find the Balance Factor of each node and balance the tree correctly I am not sure if I should stop adjusting the heights after balancing and just end the Insertion loop or keep going until the condition is meant, and I just can’t figure it out now. I know that during deletion of a node and re-balancing the tree I should keep checking but I am not sure about Insertion and balancing.

Anyone can provide any insight to this and perhaps some documentation?

Answer 1

Just for reference of future readers there is no need to edit the heights of the nodes above the node you balanced if you have implemented the binary tree like my example:

           10
        (1)/ \(2)
         8   16
          (1)/ \(0)
            11 

(Numbers in parenthesis are the height of each sub tree)

Supposing than on the tree above we insert a node with data=15 Then the resulting subtree is as following:

           10
        (1)/ \(2)
         8   16
          (1)/ \(0)
            11
        (0)/  \(1)
              15

Notice how previous heights of sub trees are not yet edited. After a successful insertion we run back through the insertion path, in this case its (11, 16, 10). After running back through this path we edit the heights when needed. That means the left height of the sub tree of 16 will be 2 while it’s right height of sub tree is 0 resulting in an imbalanced AVL tree. After balancing the tree with a double rotation the sub tree is:

             15
         (1)/  \(1)
           11  16

So the subtree height is maximum 1, as it was before, therefore heights above the root of this subtree haven’t altered and the function changing the heights must return now.